Types of number — Paper 3 · IGCSE Mathematics 0580

3 For A Examiner's Use NOT TO SCALE 2 cm B 10 cm 6 cm 40o C E D On the above diagram, AB = 2 cm, BD = 6 cm, AE = 10 cm, angle BCD = 40° and angle BDE = 90°. (a) Write down the length of AD. Answer(a) AD = cm [1] (b) Calculate the length of DE. Answer(b) DE = cm [2] (c) Calculate the size of angle AED. Answer(c) angle AED = [2] (d) Calculate the length of CD. Answer(d) CD = cm [3] (e) Find the length of CE. Answer(e) CE = cm [1]

9 marks

Mark scheme: 3 In this question alternative methods must be complete a) 8 1 b) 6 2 M1 for 100 − 64 o.e. must show square root c) art 53.1 2 M1 for sin and 8/10 seen o.e. d) art 7.15 3 M1 for tan 40 and 6 seen +M1 for 6/tan 40 o.e. e) 13.15 or 13.2 1√ f.t. for their b) + d) to 3 s.f. or better 9

This question in 0580/31 Oct/Nov 2004

1 (a) For Examiner's 2 Use 2 3 3.14 35 10 24 37 45 88 3 From the list of numbers above choose one that is (i) an irrational number, Answer(a) (i) [1] (ii) the cube root of 27, Answer(a) (ii) [1] (iii) a multiple of 9, Answer(a) (iii) [1] (iv) a prime number, Answer(a) (iv) [1] (v) a factor of 44, Answer(a) (v) [1] (vi) the product of 6 and 4. Answer(a) (vi) [1] (b) The diagram below shows a sequence of patterns made with small triangular tiles. Pattern 1 2 3 4 number (i) Draw the next pattern in the sequence. [1] (ii) Complete the table below. Pattern number 1 2 3 4 5 6 Number of tiles 1 4 9 [2] (iii) How many tiles will be in the 100th pattern? Answer(b) (iii) [1] (iv) How many tiles will be in the nth pattern? Answer(b) (iv) [1] (v) What is the special name given to the numbers in the second row of the table? Answer(b) (v) [1]

12 marks

Mark scheme: 1 (a) (i) √35 1 (ii) 3 1 (iii) 45 1 (iv) 2 or 3 or 37 1 accept any combination (v) 2 1 (vi) 24 1 (b) (i) Correct arrangement of triangles drawn. 1 accept if only 1 internal line missing (ii) 16 25 36 2 1 mark for 2 correct (iii) 10000 or 1 x 104 1 Not 1002 (iv) n2 or n × n 1 accept t = n2 etc. do not accept x2 (v) Square (numbers) 1 accept squares, squared 12

This question in 0580/31 Oct/Nov 2006

2 5 (a) –4 –16 0.12 7 144 7 2 For 3 Examiner's Use From this list of numbers, write down (i) the smallest number, Answer(a)(i) [1] (ii) a natural number, Answer(a)(ii) [1] (iii) a square number, Answer(a)(iii) [1] (iv) an irrational number. Answer(a)(iv) [1] (b) Write down 40 as a product of prime numbers. (1 is not a prime number.) Answer(b) 40 = [2] (c) Three pairs of prime numbers have a sum of 40. One pair is 3 and 37. Find the other two pairs. Answer(c) and and [2]

8 marks

Mark scheme: 5 (a) (i) –16 B1 cao (ii) 7 or 144 or both B1 (iii) 144 B1 cao (iv) √7 B1 cao (b) 2 x 2 x 2 x 5 B2 B1 for 8x5, 2x20, 4x10, 2x4x5, or list 2, 2, 2, 5 (c) 11, 29 B1 cao 17, 23 B1 cao [8] IGCSE – October/November 2007 0580 and 0581 3

This question in 0580/31 Oct/Nov 2007

1 (a) (i) 1, 2 and 36 are factors of 36. Examiner's Use Write down all the other factors of 36. Answer(a)(i) [2] (ii) 1 and 2 are common factors of 36 and 90. Write down two more common factors of 36 and 90. Answer(a)(ii) [2] (b) Write down all the square numbers between 20 and 50. Answer(b) [3] (c) p and q are prime numbers. p3 × q = 56 Find p and q. Answer(c) p = q = [2]

9 marks

Mark scheme: Qu. Answers Mark Part Marks 1 (a) (i) 3, 4, 6, 9, 12, 18 2 W1 for 4 or 5 correct and no errors or 6 correct and 1 error. (ii) Any two of 3, 6, 9,18 2 W1 for 1 correct and no errors or 2 correct and one extra, incorrect given. (b) 25, 36, 49 3 −1 each error or omission SC2 for all of 52, 62, 72. SC1 for all of 5, 6, 7 (c) p = 2, q = 7 2 W1 for either correct.

This question in 0580/32 May/June 2010

2 (a) Write down Examiner's Use (i) five numbers which are multiples of 7, Answer(a)(i) , , , , [2] (ii) two common multiples of 4 and 7. Answer(a)(ii) and [2] (b) 10 12 13 16 17 23 25 39 From the list above, write down (i) a square number that is also an odd number, Answer(b)(i) [1] (ii) a prime number that is one more than a square number. Answer(b)(ii) [1] (c) n is an integer and n3 is between 60 and 70. Find the value of n. Answer(c) n = [1] (d) k and m are prime numbers. k2 + m = 23 Find k and m. Answer(d) k = m = [2]

9 marks

Mark scheme: 2 (a) (i) Any 5 multiples of 7 2 –1 each error or omission (ii) Two multiples of 28 2 W1, W1 (b) (i) 25 1 cao (ii) 17 1 cao (c) 4 1 cao (d) (k =) 2, (m =) 19 2 W1, W1 IGCSE – May/June 2010 0580 33 3 (a) 3, 5, −1 3 1 each f f i f i

This question in 0580/33 May/June 2010

1 (a) Write down For Examiner's (i) a multiple of 7 between 80 and 90, Use Answer(a)(i) [1] (ii) a prime number between 30 and 40, Answer(a)(ii) [1] (iii) a square number between 120 and 130, Answer(a)(iii) [1] (iv) a cube number between 100 and 200. Answer(a)(iv) [1] (b) Write the following numbers in order, starting with the smallest. 5 0.31 55% 9 Answer(b) I I [2]

6 marks

Mark scheme: Qu. Answers Mark Part Marks 1 (a) (i) 84 cao 1 (ii) 31 or 37 cao 1 (iii) 121 cao 1 (iv) 125 cao 1 5 (b) 55 % < < .031 oe for each term 2 M1 for all numbers written as decimals or for all 9 numbers written as percentages

This question in 0580/31 Oct/Nov 2010

2 (a) (i) f × g = 90 For Examiner's f and g are both integers greater than 1. Use Write down one possible pair of values of f and g. Answer(a)(i) f = and g = [1] (ii) Find all the prime factors of 90. Answer(a)(ii) [3] (b) Six number cards are shown below. 0 4 9 5 1 8 One or more of the cards are chosen to make different numbers. For example 5 9 makes the number 59. Choosing a card or cards, write down (i) a 2-digit odd number less than 40, Answer(b)(i) [1] (ii) the largest 3-digit even number, Answer(b)(ii) [1] (iii) a 2-digit square number greater than 50, Answer(b)(iii) [1] (iv) a cube number, Answer(b)(iv) [1] (v) a 2-digit multiple of 13, Answer(b)(v) [1] (vi) the cube root of 64, Answer(b)(vi) [1] (vii) a prime number between 100 and 120. Answer(b)(vii) [1]

11 marks

Mark scheme: 2 (a) (i) 2 and 45 or 3 and 30 or 5 and 18 1 or 6 and 15 or 9 and 10 (ii) 2, 3, and 5 (ignore 1 if included) 3 B1 for each correct prime factor –1 for 1 or more non prime factors of 90 given in addition And –1 once if any non factors of 90 are given (b) (i) 15 or 19 1 (ii) 984 1 (iii) 81 1 (iv) 8 or 1 1 (v) 91 1 (vi) 4 1 (vii) 109 1 IGCSE – October/November 2010 0580 32

This question in 0580/32 Oct/Nov 2010

5 (a) The table below shows how many sides different polygons have. For Examiner's Complete the table. Use Name of polygon Number of sides 3 Quadrilateral 4 5 Hexagon 6 Heptagon 7 8 Nonagon 9 [3] (b) Two sides, AB and BC, of a regular nonagon are shown in the diagram below. C NOT TO SCALE x° A B (i) Work out the value of x, the exterior angle. Answer(b)(i) x = [2] (ii) Find the value of angle ABC, the interior angle of a regular nonagon. Answer(b)(ii) Angle ABC = [1]

6 marks

Mark scheme: 5 (a) Triangle, Pentagon, Octagon 1,1,1 In correct position in the table (b) (i) (x =) 40 2 M1 for 360 ÷ 9 or complete long method (ii) 140 1ft ft 180 − (b)(i)

This question in 0580/32 May/June 2011

1 (a) Write twenty five million in figures. For Examiner's Answer(a) [1] Use (b) Write the following in order of size, starting with the smallest. 2 65% 0.6 3 Answer(b) I I [1] (c) In a sale a coat costing $250 is reduced to $200. Find the percentage decrease in the cost. Answer(c) % [3] (d) Basketball NOT TO SCALE 90° 150° Football Tennis 120 students are asked to choose their favourite sport. The results are shown in the pie chart. Calculate the number of students who chose (i) basketball, Answer(d)(i) [1] (ii) football. Answer(d)(ii) [2]

8 marks

Mark scheme: Qu. Answers Mark Part Marks 1 (a) 25 000 000 cao 1 2 (b) 0.6 < 65% < 1 3 their 50 (c) 20% 3 B1 for 50 seen M1 for × 100 250 or B1 for 0.8 or 80 seen M1 for 1 – their 0.8 or 100 – their 80 (d) (i) 30 1 (ii) 40 2 M1 for 360 – (90 + 150) implied by 120 seen

This question in 0580/31 Oct/Nov 2011

3 36 29 41 45 15 10 13 Examiner's Use Use the numbers in the list above to answer all the following questions. (a) Write down (i) two even numbers, Answer(a)(i) , [1] (ii) two prime numbers, Answer(a)(ii) , [2] (iii) a square number, Answer(a)(iii) [1] (iv) two factors of 90 . Answer(a)(iv) , [2] (b) (i) Calculate the mean of the seven numbers. Answer(b)(i) [2] (ii) Find the median. Answer(b)(ii) [2] (iii) Find the range. Answer(b)(iii) [1] (c) A number from the list is chosen at random. For Examiner's Find the probability that the number is Use (i) even, Answer(c)(i) [1] (ii) a multiple of 5. Answer(c)(ii) [1]

13 marks

Mark scheme: 3 (a) (i) 36, 10 1 (ii) 29, 41, 13 any two 2 B1 for each (iii) 36 1 (iv) 45, 15, 10 any two 2 B1 for each (b) (i) 27 2 B1 for 36 + 29 + … + 13 seen implied by 189 (ii) 29 2 M1 for attempting to order the numbers (iii) 35 cao 1 2 (c) (i) oe 1 7 3 (ii) oe 1ft Their denominator from (c)(i) 7 IGCSE – October/November 2011 0580 31

This question in 0580/31 Oct/Nov 2011

4 In this question all the measurements are in centimetres. For Examiner's Use 11 – x NOT TO 2x + 3 SCALE 3x The diagram shows a triangle with sides of length 2x + 3, 11 – x and 3x. (a) Explain why x must be less than 11. Answer(a) [1] (b) Write down an expression, in terms of x, for the perimeter of the triangle. Give your answer in its simplest possible form. Answer(b) [2] (c) The perimeter of the triangle is 32 cm. (i) Write down an equation in terms of x and solve it. Answer(c)(i) x = [3] (ii) Work out the length of the shortest side of the triangle. Answer(c)(ii) cm [2]

8 marks

Mark scheme: 4 (a) If x is more than 11 then 11 – x 1 would be negative oe (b) 14 + 4x cao 2 M1 for 2x + 3 + 11 – x + 3x accept 2(2x + 7) (c) (i) 4.5 cao 3 B1ft for “their (b)” = 32 M1ft for collecting their like terms correctly to give simplified expression of form ax = b b OR M1ft x = a (ii) 6.5 2ft M1ft for clear attempt at substituting their (c)(i) into 2 or more sides of triangle IGCSE – May/June 2012 0580 31 5 (a) Correct diagram: 4 rows & 6 1 columns

This question in 0580/31 May/June 2012

2 (a) Find all the factors of 28 . For Examiner's Use Answer(a) [2] (b) Write down a multiple of 8 that is greater than 20 . Answer(b) [1] (c) Work out 183 . Answer(c) [1] (d) p and q are prime numbers. p3 × q2 = 200 Find the values of p and q. Answer(d) p = q = [2] (e) A town has two bus companies. Buses from Western Travel stop at the Town Hall every 8 minutes. Buses from Eastern Travel stop at the Town Hall every 14 minutes. (i) Write down the lowest common multiple of 8 and 14 . Answer(e)(i) [2] (ii) A bus from each company stops at the Town Hall at 08 00. When is the next time that a bus from each company stop together at the Town Hall? Answer(e)(ii) [1] (iii) The cost of an adult ticket on Western Travel is $a and the cost of a child’s ticket is $c. One day 84 adult tickets and 36 child tickets are sold. Write an expression, in terms of a and c, for the total cost of these tickets. Answer(e)(iii) $ [2]

11 marks

Mark scheme: 2 (a) 1, 2, 4, 7, 14, 28 2 1 for four or five correct or 1 × 28 and 2 × 14 and 4 × 7 (b) 24 1 (c) 5832 1 (d) (p =) 2 1 (q =) 5 1 (e) (i) 56 2 M1 for a method to achieve this such as prime factors, 8 = 23 and 14 = 2 × 7 or another multiple of 56, or two trials (ii) 08 56 1ft accept 8 56 (am) (iii) 84a + 36c final answer 2 B1 for either 84a or 36c IGCSE – May/June 2012 0580 33

This question in 0580/33 May/June 2012

9 The diagram shows a regular hexagon inside a circle, centre O and radius 8 cm. For Each vertex of the hexagon is on the circumference of the circle. Examiner's A and B are two vertices of the hexagon and M is the midpoint of AB. Use NOT TO SCALE O 8 cm A M B (a) Calculate (i) angle AOB, Answer(a)(i) Angle AOB = [1] (ii) angle AOM. Answer(a)(ii) Angle AOM = [1] (b) Write down the length AB. Answer(b) AB = cm [1] (c) Show that the length of OM = 6.93 cm, correct to 3 significant figures. Answer(c) [2] (d) Calculate the area of triangle AOB. For Examiner's Use Answer(d) cm2 [2] (e) Calculate the shaded area. Answer(e) cm2 [4] Question 10 is printed on the next page.

11 marks

Mark scheme: 9 (a) (i) 60 1 (ii) 30 1ft ft their (i) ÷ 2 (b) 8 (cm) 1 x (c) cos 30 = or 82 = x2 + 42 M1ft ft their angle AOM or AB 8 6.928 … A1 (d) 27.7(2) cao 2 1 M1 × their (b) × 6.93 soi 2 (e) 34.7–34.9 4 M1 (circle) = π × 82 soi M1 (hexagon) = 6 × their (d) soi M1dep their circle – their hexagon

This question in 0580/33 May/June 2012

1 (a) (i) Write down two numbers that are multiples of 10. For Examiner's Use Answer(a)(i) and [1] (ii) Find the lowest common multiple of 10 and 15. Answer(a)(ii) [2] (b) 4 6 9 15 23 27 32 36 From the list above, write down (i) a factor of 18, Answer(b)(i) [1] (ii) a cube number, Answer(b)(ii) [1] (iii) a prime number. Answer(b)(iii) [1] (c) Give an example to show that each of these statements is not true. (i) All square numbers are even. Answer(c)(i) [1] (ii) When two prime numbers are added the answer is always even. Answer(c)(ii) [1] (d) Write the following in order of size, starting with the smallest. 25 80 4–2 169 Answer(d) I I I [2]

10 marks

Mark scheme: Qu. Answers Mark Part Marks 1 (a) (i) Any two multiples of 10 1 (ii) 30 2 B1 for any other common multiple of 10 and 15 ie 30k (b) (i) 6 or 9 or 6 and 9 cao 1 (ii) 27 cao 1 (iii) 23 cao 1 (c) (i) Example of odd square number 1 (ii) Example of odd sum of primes 1 (d) 4–2, 80, 169 , 25 2 B1 for only 1 out of order or for three seen correctly evaluated

This question in 0580/31 Oct/Nov 2012

6 For Examiner's Use Diagram 1 Diagram 2 Diagram 3 Diagram 4 A sequence of diagrams is made from black counters and white counters. The first four diagrams in the sequence are shown. (a) Complete the table. Diagram 1 2 3 4 5 Number of black counters 1 4 Number of white counters 1 4 [4] (b) Complete the statement. The numbers of black counters are all numbers. [1] (c) How many white counters are needed for (i) Diagram 8, Answer(c)(i) [1] (ii) Diagram n? Answer(c)(ii) [2] (d) Diagram p contains 58 white counters. For Examiner's Use (i) Find the value of p. Answer(d)(i) p = [2] (ii) Find the number of black counters in Diagram p. Answer(d)(ii) [1]

11 marks

Mark scheme: 6 (a) 9 16 25 2 B1 for 2 correct 7 10 13 2 B1 for 2 correct, or difference of 3 between diagrams 4 and 5 (b) square 1 (c) (i) 22 1 (ii) 3n – 2 oe final answer 2 B1 for 3n ± j seen Or kn – 2, where k ≠ 0 (d) (i) 20 2 ft M1 for ‘their (c)(ii)’ = 58 or better, seen (ii) 400 1ft ‘their (d)(i)’2 (must be evaluated) IGCSE – October/November 2012 0580 31

This question in 0580/31 Oct/Nov 2012

6 (a) (i) Write down all the factors of 22. For Examiner′s Use Answer(a)(i) … [2] (ii) Write down a multiple of 13 between 30 and 50. Answer(a)(ii) … [1] (b) 1 2 6 9 15 17 19 21 27 (i) Write down all the prime numbers in this list. Answer(b)(i) … [2] (ii) Write down a cube number from this list. Answer(b)(ii) … [1] (c) (i) Write 0.0035 in standard form. Answer(c)(i) … [1] (ii) Calculate (6.3 × 106) ÷ (1.5 × 102). Write your answer in standard form. Answer(c)(ii) … [2] _____________________________________________________________________________________

9 marks

Mark scheme: 6 (a) (i) 1, 2, 11, 22 2 B1 for just three of these or 3 correct with 1 extra or all four and up to 2 extras or 1 × 22 and 2 × 11 (ii) 39 1 (b) (i) 2,17,19 2 B1 for just two of these or all three and an extra one (ii) 1 or 27 1 (c) (i) 3.5 × 10–3 1 (ii) 4.2 × 104 2 M1 for 42 000 oe

This question in 0580/31 May/June 2013

10 (a) (i) Find the highest common factor (HCF) of 24 and 36. For Examiner′s Use Answer(a)(i) … [2] (ii) Factorise. 24x + 36y Answer(a)(ii) … [1] (b) Simplify. (i) w + 8k – 5w + 2k Answer(b)(i) … [2] (ii) (x4)5 Answer(b)(ii) … [1] (c) Here are the fi rst four terms of a sequence. 7 11 15 19 Find the nth term of this sequence. Answer(c) … [2] (d) Solve the simultaneous equations. 3x + y = 8 x + 5y = 5 Answer(d) x = … y = … [3]

11 marks

Mark scheme: 10 (a) (i) 12 2 B1 for any other common factor other than 1 (ii) 12(2x + 3y) cao 1 (b) (i) 10k – 4w 2 B1 for either 10k ± nw or qk – 4w p,q ≠ 0 (ii) x20 1 (c) 4n + 3 oe final answer 2 B1 for 4n + c or kn + 3 , k ≠ 0 (d) [x] = 2.5, [y] = 0.5 3 M1 for correct method to eliminate one variable. A1 for x or y correct.

This question in 0580/32 May/June 2013

2 (a) For Examiner′s 2 12 144 40 .625 110 11 4 80 0.25 Use From this list of numbers, write down (i) a two-digit odd number, Answer(a)(i) … [1] (ii) a square number, Answer(a)(ii) … [1] (iii) the value of 2–2, Answer(a)(iii) … [1] (iv) an irrational number, Answer(a)(iv) … [1] (v) the lowest common multiple of 8 and 10, Answer(a)(v) … [2] (vi) the cube root of 8. Answer(a)(vi) … [1] (b) (i) Find the smallest factor, apart from 1, of 2013. Answer(b)(i) … [1] (ii) Write 2013 as the product of its prime factors. Answer(b)(ii) … × … × … [2] _____________________________________________________________________________________

10 marks

Mark scheme: 2 (a) (i) 11 1 (ii) 144 or 4 or 0.25 1 (iii) 0.25 1 (iv) 12 1 (v) 40 cao 2 B1 for 80 or any common multiple of 40 (vi) 2 1 (b) (i) 3 1 (ii) 3 [×] 11 [×] 61 2 B1 for two of 3, 11 and 61 seen IGCSE – May/June 2013 0580 33

This question in 0580/33 May/June 2013

7 (a) For Examiner′s 8.4 cm B C Use NOT TO SCALE 5.5 cm h 70° A 12.5 cm D In the quadrilateral ABCD, BC is parallel to AD. AB = 5.5 cm, BC = 8.4 cm, AD = 12.5 cm and angle BAD = 70°. The height of the quadrilateral is h. (i) Write down the mathematical name of the quadrilateral ABCD. Answer(a)(i) … [1] (ii) Use trigonometry to show that h = 5.2 cm, correct to 1 decimal place. Answer(a)(ii) [2] (iii) Calculate the area of the quadrilateral ABCD. Answer(a)(iii) … cm2 [2] (iv) The quadrilateral forms the cross section of a prism with length 6.8 cm. For Examiner′s Use Calculate the volume of the prism. Give your answer correct to 2 signifi cant fi gures. Answer(a)(iv) … cm3 [2] (b) B 95° NOT TO SCALE w° x° C 64° A z° y° E D The diagram shows a pentagon, ABCDE. AB is parallel to DC. A straight line, parallel to ED, passes through the vertex C. (i) Find the values of w, x and y. Answer(b)(i) w = … x = … y = … [3] (ii) The sum of the angles of a pentagon is 540°. Find the value of z. Answer(b)(ii) z = … [2] _____________________________________________________________________________________

12 marks

Mark scheme: 7 (a) (i) Trapezium 1 (ii) h M1 = sin 70 or better 5.5 5.17 or 5.16(8...) seen A1 (iii) 54.3 or 54.34 or 54.(0...) 2 M1 for 0.5 (8.4 + 12.5) × 5.2 oe (iv) 370 2ft B1ft Their (a)(iii) × 6.8 not correctly rounded to 2sf (b) (i) 64 1 21 1ft ft 85 – their (b)(i) 116 1 (ii) 154 2ft M1 for 540 – (90 + 95 + 64 + their x + their y)

This question in 0580/33 May/June 2013

2 (a) (i) 1 and 120 are factors of 120. For Examiner′s Use Write down another factor of 120. Answer(a)(i) … [1] (ii) Find the highest common factor of 120 and 900. Answer(a)(ii) … [2] (b) 2 5 15 24 49 60 258 512 From the list, write down (i) a multiple of 30, Answer(b)(i) … [1] (ii) a square number, Answer(b)(ii) … [1] (iii) the cube root of 8. Answer(b)(iii) … [1] (c) Give an example to show that the following statements are not true. (i) An odd number multiplied by an even number gives an odd number. Answer(c)(i) … [1] (ii) The cube of a negative number is positive. Answer(c)(ii) … [1] (d) Use < , > , or = to complete the following statements. Each symbol may be used more than once. 3 (i) 0.5 … [1] 8 (ii) 1.5 … 105% [1] 11 (iii) 0.78 … [1] 14 _____________________________________________________________________________________

11 marks

Mark scheme: 2 (a) (i) 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 1 Award mark for any one from list. 40, 60. (ii) 60 2 B1 for any common factor on answer line, 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 (b) (i) 60 1 (ii) 49 1 (iii) 2 1 (c) (i) Any correct example 1 Calculation and correct answer must be seen IGCSE – October/November 2013 0580 31 (ii) Any correct example 1 Calculation and correct answer must be seen (d) (i) > 1 (ii) > 1 (iii) < 1

This question in 0580/31 Oct/Nov 2013

2 Ravi sells cars. For Examiner′s Use (a) He has a total of 144 cars for sale. (i) 64 of these cars are 3 or more years old. What fraction of the cars are less than 3 years old? Give your answer in its simplest form. Answer(a)(i) … [2] (ii) Some of the 144 cars use petrol, some use diesel and some are electric cars. The ratio of petrol to diesel to electric cars is 6 : 5 : 1 . Work out the number of these cars that use diesel. Answer(a)(ii) … [2] (b) Lola buys a car from Ravi. There are two ways she can pay for the car. Option 1: one payment of $5200 . 2 Option 2: a payment of of $5200 plus 24 monthly payments, each of $175 . 5 Work out how much more Lola pays using Option 2 than Option 1. Answer(b) $ … [3] (c) For one week, Ravi reduces all his car prices by 15%. The price of a car was $3450. Show that the reduced price of the car is $2932.50 . Answer(c) [2] (d) Ravi buys a car for $2500 . He sells it for $3300 . Calculate his percentage profi t. Answer(d) … % [3] _____________________________________________________________________________________

12 marks

Mark scheme: 5 80 2 (a) (i) 2 B1 for or better or 0.556 or 0.555… or 9 144 4 answer 9 (ii) 60 2 M1 for 144 ÷ (6+5+1) or 144÷12 (b) 1080 3 M1 for 2 ÷ 5 × 5200 soi by 2080 And M1 for their 2080 + 24×175 – 5200 or better (c) 0.85 × 3450 2 B1 for 0.85 or for 0.15 × 3450 Or 3450 – 0.15 × 3450 3300 − 2500 (d) 32 3 M2 for × 100 oe 2500 3300 or ( – 1 ) × 100 oe 2500 Or 3300 − 2500 3300 B1 for 800 or or or 2500 2500 1.32 or 132 or 0.32

This question in 0580/32 Oct/Nov 2013

8 (a) Complete the table. For Examiner′s Use Name of polygon Number of sides Quadrilateral 4 Heptagon 5 [2] (b) B C D NOT TO 23° SCALE 55° A E In the diagram, AB is parallel to EC and BCD is parallel to AE. Angle BAE = 55° and angle CED = 23°. (i) Complete the following statement. The mathematical name for quadrilateral ABDE is … . [1] (ii) Work out the size of angle ABC. Answer(b)(ii) Angle ABC = … [1] (iii) Work out the size of angle CDE. Answer(b)(iii) Angle CDE = … [2] (c) For Examiner′s B Use C NOT TO O 35° SCALE A 52° D Points A, B and C lie on a circle with centre O. DA is a tangent to the circle at A. Angle BAC = 35° and angle ADC = 52°. (i) Write down the size of angle ABC giving a reason for your answer. Answer(c)(i) Angle ABC = … because … … [2] (ii) Work out the size of angle BCA. Answer(c)(ii) Angle BCA = … [1] (iii) Work out the size of angle BCD. Answer(c)(iii) Angle BCD = … [3] _____________________________________________________________________________________

12 marks

Mark scheme: 8 (a) 7 1 Pentagon 1 (b) (i) trapezium 1 (ii) 125° 1 (iii) 32° 2 M1FT for 180 – 125 – 23 or better or 180 – their 125 – 23 or better (c) (i) 90° 1 angle [in a] semicircle [=90°] 1 (ii) 55° 1 (iii) 93° 3 M2 for 90 – 52 or 180 – 90 – 52 or 38 If M0 then B1 for angle CAD = 90° indicated

This question in 0580/32 Oct/Nov 2013

3 (a) Using only the integers from 1 to 50, fi nd For Examiner′s Use (i) a multiple of both 4 and 7, Answer(a)(i) … [1] (ii) a square number that is odd, Answer(a)(ii) … [1] (iii) an even prime number, Answer(a)(iii) … [1] (iv) a prime number which is one less than a multiple of 5. Answer(a)(iv) … [1] (b) Find the value of (i) ^ 5 h 2 , Answer(b)(i) … [1] (ii) 2–3 × 63. Answer(b)(ii) … [2] _____________________________________________________________________________________

7 marks

Mark scheme: 3 (a) (i) 28 1 (ii) 25 or 49 or 9 or 1 1 (iii) 2 1 (iv) 19 or 29 1 1 (b) (i) 5 1 B1 for or 216 seen 8 (ii) 27 2

This question in 0580/33 Oct/Nov 2013

4 (a) A regular polygon has 9 sides. For Examiner′s For this polygon, calculate Use (i) the size of one exterior angle, Answer(a)(i) … [2] (ii) the size of one interior angle. Answer(a)(ii) … [1] (b) C w° B 24° y° NOT TO SCALE D O E x° z° A F In the diagram, A, B, C and D are points on the circumference of a circle, centre O. AB is the diameter and EF is a tangent to the circle at A. AB is parallel to DC and angle ACD = 24°. Find (i) w, Answer(b)(i) w = … [1] (ii) x, Answer(b)(ii) x = … [1] (iii) y. Answer(b)(iii) y = … [1] (c) Complete the statement. z = … because … … [2] _____________________________________________________________________________________

8 marks

Mark scheme: 4 (a) (i) 40 2 M1 for 360 ÷ 9 (ii) 140 1FT 180 – their (a)(i) (b) (i) [w =] 90 1 (ii) [x =] 24 1 (iii) [y =] 66 1FT 180 – (their w + their x) (c) [z =] 66 1FT (90 – their x) or their y [Angle between] tangent [and] 1 diameter/radius [=] 90°

This question in 0580/33 Oct/Nov 2013

2 (a) From the integers 50 to 100, fi nd (i) a multiple of 43, Answer(a)(i) … [1] (ii) a factor of 165, Answer(a)(ii) … [1] (iii) an odd number that is also a square number, Answer(a)(iii) … [1] (iv) a number which is a square number and also a cube number. Answer(a)(iv) … [1] (b) (i) Find the square root of 5929. Answer(b)(i) … [1] (ii) Find the lowest common multiple of 24 and 30. Answer(b)(ii) … [2] (c) Elena goes on a journey to the North Pole. She leaves home at 7 am on 15 July and arrives at the North Pole at 10 pm on 27 July. How long, in days and hours, did her journey take? Answer(c) … days … hours [2] __________________________________________________________________________________________

9 marks

Mark scheme: 2 (a) (i) 86 1 (ii) 55 1 (iii) 81 1 (iv) 64 1 (b) (i) 77 1 (ii) 120 2 B1 for any other multiple of 120 (c) 12 [days] 15 [hours] 1,1 IGCSE – May/June 2014 0580 31

This question in 0580/31 May/June 2014

1 (a) Here is a list of numbers. 2 4 5 8 9 12 Write down all the numbers from this list which are (i) odd, Answer(a)(i) … [1] (ii) square, Answer(a)(ii) … [1] (iii) cube, Answer(a)(iii) … [1] (iv) prime. Answer(a)(iv) … [1] (b) Write one of these symbols >, < or = to make each statement true. 22 π … 7 2 … 2 ^ h2 1 … 2 1 + 1 (–1)2 … –1 [2] (c) Put one pair of brackets in each statement to make it true. (i) 16 + 8 ÷ 4 – 2 = 4 [1] (ii) 16 + 8 ÷ 4 – 2 = 20 [1] (d) (i) Write 84 as a product of its prime factors. Answer(d)(i) … [2] (ii) Find the highest common factor of 84 and 24. Answer(d)(ii) … [2] (iii) Find the lowest common multiple of 84 and 24. Answer(d)(iii) … [2] (e) Here are the fi rst four terms of a sequence. 3 7 11 15 (i) Write down the next term in this sequence. Answer(e)(i) … [1] (ii) Explain how you found your answer. Answer(e)(ii) … [1] (iii) Write down an expression for the n th term of this sequence. Answer(e)(iii) … [2] (iv) Explain why 125 is not in this sequence. Answer(e)(iv) … … [1] __________________________________________________________________________________________

19 marks

Mark scheme: Qu Answers Mark Part Answers 1 (a) (i) 5 and 9 cao 1 (ii) 4 and 9 cao 1 (iii) 8 cao 1 (iv) 2 and 5 cao 1 (b) < = < > 2 B1 for 3 correct (c) (i) (16 + 8) ÷ 4 ─ 2 = 4 1 (ii) 16 + 8 ÷ (4 ─ 2) = 20 1 (d) (i) 2 × 2 × 3 × 7 2 B1 for 2, 3, 7 or 2, 2, 3, 7, or 1 × 2 × 2 × 3 × 7 (ii) 12 2 B1 for 2, 3, 4 or 6 or 2 × 2 × 3 or 22 × 3 or 4 × 3 or 2 × 6 seen as ans (iii) 168 2 B1 for any other multiple of 168 or 2 × 2 × 2 × 3 × 7 oe (e) (i) 19 1 any other terms must be correct (ii) +4 oe 1 e.g. add 4 (iii) 4n – 1 oe final answer 2 B1 for 4n + k , qn – 1 q ≠ 0 (iv) accept any correct statement 1 IGCSE – May/June 2014 0580 32

This question in 0580/32 May/June 2014

5 (a) Write in fi gures six million three thousand and seventy six. Answer(a) … [1] (b) (i) Work out the value of p when p = –0.6 ÷ 1.6 . Answer(b)(i) p = … [1] (ii) Work out the value of q when q = –0.6 – 1.6 . Answer(b)(ii) q = … [1] (iii) Use one of the symbols >, <, [, Y, = to complete this statement. p … q [1] (c) Mount Robson in Canada has a height of 3950 metres, correct to the nearest 10 metres. Complete the following statement about the height, h m, of Mount Robson. Answer(c) … Y h < … [2] 1 1 . (d) Calculate 2 ÷ 1 12 4 Give your answer as a decimal, correct to 4 signifi cant fi gures. Answer(d) … [2] (e) (i) Write down the value of 80. Answer(e)(i) … [1] (ii) Work out 5–3. Write your answer as a fraction. Answer(e)(ii) … [1] (iii) Simplify the expression. 8x5 × 3x4 Answer(e)(iii) … [2] __________________________________________________________________________________________

12 marks

Mark scheme: 5 (a) 6 003 076 1 (b) (i) –0.375 1 (ii) –2.2 1 (iii) > 1FT FT their answers to (i) and (ii) (c) 3945, 3955 1, 1 SC1 for both correct but reversed 2 (d) 1.667 cao 2 B1 for 1 3 or better (e) (i) 1 1 1 (ii) 1 125 (iii) 24x9 2 B1 for 24xk or kx9

This question in 0580/31 Oct/Nov 2014

9 Diagram 1 Diagram 2 Diagram 3 Diagram 4 Diagrams 1 to 4 show a sequence of shapes made up of lines and dots at the intersections of lines. (a) (i) Complete the table showing the number of dots in each diagram. Diagram 1 2 3 4 5 6 Dots 3 8 13 [3] (ii) Write down the rule for continuing the sequence of dots. Answer(a)(ii) … [1] (iii) Write down an expression, in terms of n, for the number of dots in Diagram n. Answer(a)(iii) … [2] (iv) Find the number of dots in Diagram 15. Answer(a)(iv) … [1] (b) The dots are joined by sloping lines and horizontal lines. (i) Diagram 1 has 2 sloping lines and Diagram 2 has 6 sloping lines. Find the number of sloping lines in Diagrams 3 and 4. Answer(b)(i) Diagram 3 … Diagram 4 … [2] (ii) Write down an expression, in terms of n, for the number of sloping lines in Diagram n. Answer(b)(ii) … [2]

11 marks

Mark scheme: 9 (a) (i) 18 23 28 1, 1, 1 Allow one mark for each addition of 5 to the previous answer (ii) Add 5 oe 1 (iii) 5n – 2 oe 2 B1 for 5n + j or kn – 2 k ≠ 0 (iv) 73 1FT FT their (a)(iii) if linear. (b) (i) 10 14 1, 1 Allow 1 mark for addition of 4 on their value for 3rd diagram. (ii) 4n – 2 oe 2 B1 for 4n + j or kn – 2 k ≠ 0

This question in 0580/31 Oct/Nov 2014

2 (a) Write down the mathematical name of a polygon with 8 sides. Answer(a) … [1] (b) Calculate the interior angle of a regular 8-sided polygon. Answer(b) … [3] (c) Diagram 1 Diagram 2 Diagram 3 The pattern of diagrams above forms a sequence. (i) Complete the table. Diagram 1 2 3 4 5 Number of dots 8 15 [2] (ii) Find an expression, in terms of n, for the number of dots in Diagram n. Answer(c)(ii) … [2] (iii) Find the number of dots in Diagram 10. Answer(c)(iii) … [1] (iv) Find the value of n for a diagram with 92 dots. Answer(c)(iv) … [2] __________________________________________________________________________________________

11 marks

Mark scheme: 2 (a) Octagon 1 (b) 135 3 M2 for 180 – (360 ÷ 8) or M2 for (8 − 2) × 180 8 or M1 for (360 ÷ 8) or M1 for (8 – 2) × 180 (c) (i) 22 29 36 2 B1 for two terms in correct places or 2 terms with a difference of 7. (ii) 7n + 1 oe 2 B1 for 7n + j or kn + 1 (k ≠ 0) (iii) 71 1FT FT for their (c)(ii) if linear (iv) 13 nfww 2 M1FT for their (c)(ii) = 92 or M1 for (92 – 1) ÷ 7 or 91 ÷ 7 or M1 for 7 × 13 + 1 = 92

This question in 0580/32 Oct/Nov 2014

9 (a) (i) Calculate the cube root of 68 921. Answer(a)(i) … [1] (ii) Write 68 921 in standard form. Answer(a)(ii) … [1] (iii) Write 68 921 correct to 2 significant figures. Answer(a)(iii) … [1] (b) 96 550 kg is reduced to 88 826 kg. Calculate the percentage reduction. Answer(b) … % [3] (c) (i) Work out 5–2. Answer(c)(i) … [1] 2 (ii) Simplify ^ 5 h . Answer(c)(ii) … [1] (iii) Explain why 6 is not a prime number. Answer(c)(iii) … … [1] (iv) Explain the term ‘irrational number’. Answer(c)(iv) … … [1]

10 marks

Mark scheme: 9 (a) (i) 41 1 (ii) 6.8921 × 104 1 (iii) 69 000 1 96550 − 88826 (b) 8% 3 M2 for × 100 oe 96550 88826 or M1 for 7724 seen or 96550 1 (c) (i) or 0.04 1 25 (ii) 5 1 (iii) Has more than 2 factors oe 1 (iv) A decimal that is not truncated and it 1 does not recur (or can’t be written as a fraction) oe

This question in 0580/32 Feb/March 2015

1 (a) Write down (i) two factors of 12, Answer(a)(i) … [1] (ii) the next prime number after 19, Answer(a)(ii) … [1] (iii) the cube root of 64, Answer(a)(iii) … [1] (iv) two million five hundred and seven in figures, Answer(a)(iv) … [1] (v) two multiples of 75, Answer(a)(v) … [1] (vi) the value of π correct to 5 significant figures. Answer(a)(vi) … [1] (b) Write as a percentage. (i) 1.63 Answer(b)(i) … % [1] 3 (ii) 40 Answer(b)(ii) … % [1] (c) (i) Write 63 521.769 correct to 1 decimal place. Answer(c)(i) … [1] (ii) Write 63 521.769 correct to the nearest hundred. Answer(c)(ii) … [1] (d) (i) Change 234 mm into metres. Answer(d)(i) … m [1] (ii) Change 876 m2 into square centimetres. Answer(d)(ii) … cm2 [1] __________________________________________________________________________________________

12 marks

Mark scheme: Question Answer Mark Part marks 1 (a) (i) At least two of 1, 2, 3, 4, 6, 12 1 No incorrect factors (ii) 23 1 (iii) 4 1 (iv) 2 000 507 1 (v) e.g. 75, 150 1 Accept any 75k, k > 0 (vi) 3.1416 1 (b) (i) 163 1 (ii) 7.5 1 (c) (i) 63521.8 1 (ii) 63500 cao 1 (d) (i) [0].234 1 (ii) 8 760 000 1

This question in 0580/31 May/June 2015

1 (a) 4 3 0 2 9 5 7 From the list above, write down (i) the factors of 24, Answer(a)(i) … [1] (ii) a prime factor of 24, Answer(a)(ii) … [1] (iii) the highest common factor (HCF) of 56 and 91, Answer(a)(iii) … [1] (iv) the square root of 49, Answer(a)(iv) … [1] (v) the cube root of 27. Answer(a)(v) … [1] (b) (i) Using four numbers from the list in part (a), form the largest 4-digit number. Answer(b)(i) … [1] (ii) Write your answer to part (b)(i) in words. Answer(b)(ii) … … [1] (c) Find (i) the common multiple of 5 and 8 between 100 and 150, Answer(c)(i) … [1] (ii) the square number between 350 and 390. Answer(c)(ii) … [1] __________________________________________________________________________________________

9 marks

Mark scheme: Qu Answer Mark Part answers 1 (a) (i) 2, 3, 4 1 (ii) 2 or 3 1 (iii) 7 1 (iv) 7 1 (v) 3 1 (b) (i) 9754 1 (ii) Nine thousand seven hundred [and] 1FT FT their (b)(i) provided it has at least four fifty four figures (c) (i) 120 1 (ii) 361 1

This question in 0580/32 May/June 2015

2 (a) Write down a number between 20 and 30 that is (i) a multiple of 6, Answer(a)(i) … [1] (ii) a square number, Answer(a)(ii) … [1] (iii) a cube number, Answer(a)(iii) … [1] (iv) a prime number. Answer(a)(iv) … [1] (b) Find (i) 3 4913 , Answer(b)(i) … [1] (ii) 35, Answer(b)(ii) … [1] (iii) 60, Answer(b)(iii) … [1] (iv) 2–4. Answer(b)(iv) … [1] (c) (i) Write 84 as a product of its prime factors. Answer(c)(i) … [2] (ii) Find the highest common factor (HCF) of 84 and 126. Answer(c)(ii) … [2] __________________________________________________________________________________________

12 marks

Mark scheme: 2 (a) (i) 24 or 30 1 (ii) 25 1 (iii) 27 1 (iv) 23 or 29 1 (b) (i) 17 1 (ii) 243 1 (iii) 1 1

This question in 0580/31 Oct/Nov 2015

1 (a) Write down in figures the number twenty one million. Answer(a) … [1] (b) Write down the four factors of 21. Answer(b) … , … , … , … [2] (c) Write 21% as a fraction. Answer(c) … [1] (d) Put brackets in this calculation to make it correct. 210 + 21 ÷ 2.1 + 21 = 10 [1] (e) Write down the first two prime numbers after 21. Answer(e) … and … [2] (f) Fill in the missing number. 21 210 = 210 ff [1] (g) Calculate 21 2 - 21 . Answer(g) … [1] (h) Work out ( 21 ) 2. Answer(h) … [1] (i) Write down the value of 210. Answer(i) … [1] (j) Write 0.0021 in standard form. Answer(j) … [1] (k) Write down the lowest common multiple (LCM) of 21 and 15. Answer(k) … [2]

14 marks

Mark scheme: Question Answer Mark Part marks 1 (a) 21 000 000 1 (b) 1, 3, 7, 21 2 M1 for 3 correct and one incorrect (or missing) or for 4 correct and one extra 21 (c) 1 100 (d) (210 + 21) ÷ (2.1+ 21) 1 (e) 23 1 If zero scored SC1 for any two other prime 29 1 numbers greater than 21 (f) 2100 1 (g) 436 or 436.4... 1 (h) 21 1 (i) 1 1 (j) 1.2 × 10 − 3 1 (k) 105 2 M1 for [1 ×] 3 × 5 × 7 or 105k or for [1], 3, 7 and [1], 3, 5 seen or for [1], 3, 5, 7 (maybe in a table) or for listing multiples of 15 and 21 to at least 105 with not more than one error

This question in 0580/32 Oct/Nov 2015

1 Joel spins a fair five-sided spinner numbered 2, 3, 4, 5 and 6. (a) Write down the probability that the spinner lands on (i) an odd number, … [1] (ii) a prime number, … [1] (iii) the number 7. … [1] (b) Here are the results of his first 20 spins. Number 2 3 4 5 6 Frequency 3 2 6 4 5 (i) Write down the mode. … [1] (ii) Calculate the mean. … [3] (iii) Joel wants to draw a pie chart to show the results in the table. (a) Show that the sector angle for the number 2 is 54°. [1] (b) Find the sector angle for the number 6. … [2] (c) Joel asks 30 students to guess the number that the spinner will next land on. The results are shown in this pie chart. 2 3 6 4 5 (i) The sector angle for the number 6 is 168°. How many students guessed the number 6? … [2] (ii) Find the percentage of the students who guessed a number less than 5. … % [3] (iii) Joel spins the spinner. 10% of the 30 students guessed correctly. Which number did the spinner land on? … [2]

17 marks

Mark scheme: Question Answer Mark Part marks 1 (a) (i) 2 oe 1 Allow 0.4 , 40% 5 (ii) 3 oe 1 Allow 0.6 , 60% 5 (iii) 0 1 (b) (i) 4 1 (ii) 4.3 3 M1 for 2×3 + 3×2 + 4×6 + 5×4 + 6×5 or 86 M1dep for their 86 ÷ 20 If M0M0 SC1 for 57.5 3 (iii) (a) × 360 1 20 5 360 (b) 90 2 M1 for oe or oe implied by 18 seen 20 20 168 360 (c) (i) 14 2 M1 for oe or oe implied by 12 seen 360 30 (ii) 43.3 3 B1 for [total angle=] 156° their angle M1 for [× 100] oe 360 If B0M0 SC1 for 53.3 10 (iii) 5 2 M1 for × 360 oe or 36 100

This question in 0580/31 May/June 2016

2 (a) 3 6 19 20 24 27 30 32 35 36 48 49 51 From this list of numbers write down (i) a factor of 15, … [1] (ii) a multiple of 18, … [1] (iii) an odd square number, … [1] (iv) a cube number. … [1] (b) Write as a percentage. (i) 0.43 … % [1] 1 (ii) 2 … % [1] 28 (c) Write in its lowest terms. 42 … [1] (d) (i) Write 45 as a product of its prime factors. … [2] (ii) Find the highest common factor (HCF) of 45 and 105. … [2]

11 marks

Mark scheme: 2 (a) (i) 3 1 (ii) 36 1 (iii) 49 1 (iv) 27 1 (b) (i) 43 1 (ii) 50 1

This question in 0580/31 May/June 2016

2 (a) Here are five number cards. 1 2 6 7 8 Place two cards side-by-side to show (i) a two-digit multiple of 7, [1] (ii) a two-digit square number, [1] (iii) a two-digit cube number, [1] (iv) a two-digit prime number. [1] (b) 2 5.85 4.12 r Write down all the numbers in this list that are irrational. … [1] (c) Put one pair of brackets into this calculation to make it correct. 7 × 5 – 2 + 3 = 42 [1] (d) Work out. (i) 3 .0729 … [1] (ii) 54 … [1] (iii) 4−2 … [1] (e) (i) Write 60 as a product of its prime factors. … [2] (ii) Find the lowest common multiple (LCM) of 36 and 60. … [2]

13 marks

Mark scheme: 2 (a) (i) 21 or 28 1 (ii) 16 or 81 1 (iii) 27 1 (iv) 17 or 61 or 67 or 71 1 (b) 2 and π 1 (c) 7 × (5 – 2 + 3) = 42 1

This question in 0580/32 May/June 2016

7 (a) 25° 98° NOT TO SCALE y° x° The diagram shows three straight lines crossing at a point. (i) Find the value of x. x = … [1] (ii) Work out the value of y. y = … [1] (b) C A 49° NOT TO SCALE 41° B A, B and C are points on the circumference of a circle. Explain why AB must be a diameter of the circle. … … [2] (c) Q 17.8 cm NOT TO SCALE 35° P R PQR is a right-angled triangle. Use trigonometry to calculate PR. PR = … cm [2] (d) K NOT TO 28.9 cm SCALE M L 21.5 cm KLM is a right-angled triangle. Calculate KL. KL = … cm [3]

9 marks

Mark scheme: 7 (a) (i) 25 1 (ii) 57 1 (b) [∠BCA =] 180 – 49 – 41 = 90° B1 B1 Angle [in a ] semicircle PR (c) 14.6 or 14.58… 2 M1 for cos35 = or better 17.8 (d) 19.3 or 19.31… 3 M2 for [KL =] 28.9 2 − 21.5 2 or better or M1 for 28.92 = KL2 + 21.52 or better

This question in 0580/32 May/June 2016

6 (a) For the integers from 40 to 70, write down (i) a multiple of 19, … [1] (ii) a common multiple of 6 and 8, … [1] (iii) the square root of 2500, … [1] (iv) a factor of 106, … [1] (v) an odd number where the tens digit is double the units digit, … [1] (vi) a number that is both a square number and a cube number, … [1] (vii) a number that has exactly 3 factors, … [1] (viii) three prime numbers. … , … , … [2] (b) Write 234 as a product of its prime factors. … [2] (c) Write the answer to 34 × 37 (i) in the form 3x, … [1] (ii) as an integer, … [1] (iii) in standard form. … [1] (d) (i) Write 3−2 as a fraction. … [1] (ii) Find the value of 3x0 when x = 5. … [1]

16 marks

Mark scheme: 6 (a) (i) 57 1 (ii) 48 1 (iii) 50 1 (iv) 53 1 (v) 63 1 (vi) 64 1 (vii) 49 1 (viii) Any three from 2 B1 for 2 correct and at most one error 41 43 47 53 59 61 67 (b) 2 × 32 × 13 or 2 × 3 × 3 × 13 2 B1 for 2, 3 and 13 only identified as factors or for a correct product eg 2 × 9 × 13 , 18 × 13 (c) (i) 311 1 (ii) 177 147 1 (iii) 1.77[147] × 105 1FT follow through their (c)(ii) (d) (i) 1 1 9 (ii) 3 1

This question in 0580/33 May/June 2016

3 (a) 6 144 63 11 288 72 8 From the list, write down (i) the multiple of 7, … [1] (ii) the cube of 2, … [1] (iii) the prime number, … [1] (iv) the lowest common multiple (LCM) of 16 and 18. … [1] (b) Without using a calculator explain why the square of 4.86 must be between 16 and 25. … [1] (c) Find the value of (i) 47, … [1] (ii) 120, … [1] (iii) 8.32 + 27. … [1] (d) Write 90 as the product of its prime factors. … [2]

10 marks

Mark scheme: 3 (a) (i) 63 1 (ii) 8 1 (iii) 11 1 (iv) 144 1 (b) 42 [=] 16 52 [=] 25 1 (c) (i) 16384 1 (ii) 1 1 (iii) 74.1 or 74.08 to 74.09 1 (d) 2 × 32 × 5 or 2 × 3 × 3 × 5 2 B1 for prime factors 2 , 3 , 5 (and no others) identified or B1 for any correct product e.g. 9 × 10, 5 × 18, 6 × 3 × 5, 1 × 3 × 30

This question in 0580/31 Oct/Nov 2016

9 (a) The area of Cuba, in square kilometres, is one hundred and five thousand eight hundred and six. Write this number in figures. … [1] (b) The population of an island is 103 000. Write this number in standard form. … [1] (c) The table shows some populations in 2014. Population Puerto Rico 3.68 × 106 St Maarten 4.61 × 104 Haiti 1.05 × 107 US Virgin Islands 1.07 × 105 (i) Write the population of St Maarten as an ordinary number. … [1] (ii) Complete the statement. The population of Haiti is approximately … times the population of the US Virgin Islands. [1] (iii) Find the difference between the population of Haiti and the population of Puerto Rico. Give your answer in standard form. … [2] (d) In 2013 the population of a town was 30 405. In 2014 the population was 30 851. Calculate the percentage increase in the population. … % [3]

9 marks

Mark scheme: 9 (a) 105 806 1 (b) 1.03 × 105 1 (c) (i) 46 100 1 (ii) 100 1 (iii) 6.82 × 106 2 B1 for figs 682  30 851  (d) 1.47 or 1.466 to 1.467 3 M2 for  − 1  [×100] oe soi by 0.0146….  30 405  or 0.0147  30 851 or  × 100 [–100] oe soi by 101.46….  30 405  or 101.47  30 851  or M1 for   soi by 1.0146……. or 1.0147  30 405  Alternative method 30 851 − 30 405 M2 for [× 100 ] oe soi by 0.0146…. 30 405 or 0.0147 or B1 for 30 851 – 30 405 soi by 446

This question in 0580/31 Oct/Nov 2016

6 (a) Write down a factor of 24 that is a square number. … [2] (b) Write down the cube number between 100 and 200. … [1] (c) Find (i) 12.25, … [1] (ii) 173, … [1] (iii) 4–2. … [1] 1 2 (d) s = 2 at Find the value of s when a = 0.7 and t = 4.2 . s = … [2] (e) Simplify. (i) a0 … [1] (ii) b 3 # b 2 … [1] c 4 (iii) 8 c … [1]

11 marks

Mark scheme: 6 (a) 4 or 1 2 B1 for 2 or 3 or 6 or 8 or 12 or 24 or 22 or 12 (b) 125 1 1 1 (c) (i) 3.5 or 32 (ii) 4913 1 1 1 (iii) 0.0625 or 16 1 2 (d) 6.174 2 M1 for × 0.7 × 4.2 soi by 6.17 2 (e) (i) 1 1 (ii) b5 1 1 1 (iii) c–4 or 4 c

This question in 0580/32 Oct/Nov 2016

5 (a) (i) Write down the two square numbers between 50 and 99. … and … [2] (ii) Find a common multiple of 30 and 45. … [1] (iii) Write down all the factors of 54 that are odd numbers. … [2] (iv) Find the highest common factor (HCF) of 64 and 80. … [2] (b) Without using your calculator, work out 1 56 ' 25 . Write down all the steps in your working and write your answer as a mixed number. … [4] (c) For each of these sequences, write down the next term and the rule for continuing the sequence. (i) 8, 11, 14, 17, … Next term is … The rule is … [2] (ii) 25, 17, 9, 1, … Next term is … The rule is … [2] (iii) 2, 4, 7, 11, … Next term is … The rule is … [2] (iv) 1, 8, 27, 64, … Next term is … The rule is … [2]

19 marks

Mark scheme: 5 (a) (i) 64 81 and no others 2 B1 for 1 correct and no others or 2 correct and 1 wrong (ii) 90k 1 accept any multiple of 90 (iii) 1, 3, 9, 27 only 2 B1 for three correct and no extras or four correct and one extra (iv) 16 2 B1 for 2, 4 or 8 as answer (b) 11 B1 oe 6 11 5 FT their11 × oe M1 6 6 2 55 oe 12 A1 7 4 B1 12 Dep on A1 (c) (i) 20 1 Add 3 oe 1 (ii) –7 1 Subtract 8 oe 1 (iii) 16 1 Differences increase by 1 oe 1 (iv) 125 1 Cube numbers 1

This question in 0580/33 Oct/Nov 2016

1 (a) Write down (i) a square number between 30 and 40, … [1] (ii) the number three million, three hundred and thirty in figures, … [1] (iii) the next cube number after 64, … [1] (iv) the five factors of 16, … , … , … , … , … [2] (v) a common multiple of 6 and 8, … [1] (vi) a prime number between 20 and 30. … [1] (b) Write 567.4892 correct to (i) the nearest ten, … [1] (ii) 2 decimal places. … [1] (c) Complete these calculations. (i) 4 + 6 ' 2 = … [1] (ii) (8 - 20) ' … = 4 [1] (iii) 6432 # … = 64.32 [1]

12 marks

Mark scheme: Question Answer Marks Part marks 1 (a) (i) 36 1 (ii) 3 000 330 cao 1 (iii) 125 1 (iv) 1, 2, 4, 8, 16 2 M1 for 3 or 4 correct factors and no extras or for 5 correct factors and one extra (v) Any multiple of 24 1 (vi) 23 or 29 1 (b) (i) 570 cao 1 (ii) 567.49 cao 1 (c) (i) 7 1 (ii) –3 1 (iii) [0].01 oe 1

This question in 0580/32 Feb/March 2017

4 (a) 4 10 11 18 20 27 28 32 36 40 56 From the list above, write down (i) a multiple of 12, … [1] (ii) a factor of 8, … [1] (iii) a prime number, … [1] (iv) a square number, … [1] (v) a cube number. … [1] (b) Find the lowest common multiple (LCM) of 32 and 80. … [2] (c) Find the value of (i) 68.89, … [1] (ii) 3 19683 . … [1]

9 marks

Mark scheme: 4(a)(i) 36 1 4(a)(ii) 4 1 4(a)(iii) 11 1 4(a)(iv) 36 or 4 or both 1 4(a)(v) 27 1 4(b) 160 cao 2 M1 for any common multiple 160 n or any product that equals 160 or two lists of correct multiples of each number or either number correctly reduced to its prime factors 4(c)(i) 8.3 1 4(c)(ii) 27 1

This question in 0580/32 May/June 2017

4 (a) Measure the reflex angle at A. A … [1] (b) b° NOT TO SCALE 68° Find the value of b. Give a reason for your answer. b = … because … [2] (c) e° NOT TO 36° SCALE d° c° Find the values of c, d and e. c = … d = … e = … [3] (d) A regular polygon has 24 sides. Work out the size of one of the interior angles of the polygon. … [3] (e) Town Y is 6.7 km from town X. The bearing of town Y from town X is 113°. On the scale drawing, draw a line from X and mark the position of Y. The scale is 1 centimetre represents 1 kilometre. North Scale: 1 cm to 1 km X [2] (f) Give the correct mathematical name for each of the shapes described below. (i) I am a quadrilateral. I have two pairs of parallel sides but no right angles. I have two lines of symmetry. … [1] (ii) I am a quadrilateral. I have one pair of opposite angles that are equal. I have one line of symmetry. … [1]

13 marks

Mark scheme: 4(a) 328 1 4(b) 68 1 corresponding 1 4(c) 72 1 108 1FT FT is 180 – their c 72 1FT FT is their c 4(d) 165 3 360 M2 for 180 – or (180 × ( 24 − 2 ) ÷ 24 ) or better 24 360 or M1 for or 180 × (24 – 2) or better 24 4(e) Correct distance XY 1 Correct bearing 1 4(e)(ii) Rhombus 1 4(e)(ii) Kite 1

This question in 0580/33 May/June 2017

8 The quadrilateral ABCD is a scale drawing of a farmer’s field. Side AD and side BC are parallel. Angle DAB and angle ABC are right angles. A D B C (a) Write down the mathematical name of the quadrilateral. … [1] (b) The side of the field, AB, is 28 m. (i) Complete this statement. The scale of the diagram is 1 centimetre represents … metres. [2] (ii) Work out the actual area of the field in m2. … m2 [3] (c) The field has two fences. Each fence extends across the field until it meets another side. • Fence 1 is the perpendicular bisector of CD. • Fence 2 is the bisector of angle ABC. Using a straight edge and compasses only, construct the two fences on the diagram. Show all your construction arcs. [4] (d) The region of the field that is 16 m or less from A is planted with wheat. (i) Using a ruler and compasses only, construct and shade the region planted with wheat. [3] (ii) Work out the actual area of the region that is planted with wheat. … m2 [2] Question 9 is printed on the next page.

15 marks

Mark scheme: 8(a) trapezium 1 8(b)(i) 4 2 B1 for 7 cm seen 8(b)(ii) 1120 nfww 3 B1 for 8 [cm] and 12 [cm] seen or 8 × their (b)(i) [m] or 12 × their (b)(i) [m] evaluated ( their 8 + their12 ) M1 for × their 7 or 2 ( their 32 + their 48 ) × 28 oe 2 8(c) correct perpendicular bisector 2 B1 for correct bisector drawn without arcs or wrong arcs drawn with 2 pairs of arcs and or correct short line with arcs extending across field to side or for two pairs of correct arcs BC correct angle bisector drawn 2 B1 for correct bisector drawn without arcs or wrong arcs with 2 pairs of arcs and or correct short line with arcs extending across field to side or for two pairs of correct arcs AD 8(d)(i) Accurately drawn and correct 3 B1 for 4 cm length seen or implied region shaded B1 one arc drawn centre A and touching AB and AD B1 correct shading Maximum B2 8(d)(ii) 201 nfww or 201.06 to 201.09 2 M1 for π × 162 or π × their radius 2 or better

This question in 0580/33 May/June 2017

6 (a) Find (i) all the factors of 18, … [2] (ii) a multiple of 30, … [1] (iii) 2134.44, … [1] (iv) 2.53, … [1] (v) (0.2) −1. … [1] (b) Write 72 as a product of its prime factors. … [2] (c) Find the lowest common multiple (LCM) of 16 and 30. … [2] (d) Clock A chimes every 6 hours. Clock B chimes every 9 hours. Both clocks chime at 2 am. At what time will the two clocks next chime together? … [3]

13 marks

Mark scheme: 6(a)(i) 1, 2, 3, 6, 9, 18 only 2 B1 for 4 or 5 correct factors and no extras or 6 correct with one extra 6(a)(ii) Any multiple of 30 1 6(a)(iii) 46.2 1 6(a)(iv) 15.625 1 6(a)(v) 5 1 6(b) 23 × 32 2 M1 for a complete factor tree or 2, 2, 2, 3, 3 clearly identified as factors 6(c) 240 2 M1 for [16=] 24 or 2 × 2 × 2 × 2(×1) or [30=] 2 × 3 × 5(×1) or lists of multiples of both at least up to 240, or any product that equals 240 or B1 for 240n 6(d) 20 00 or 8 pm 3 M1 for [LCM of 6 and 9 =] 18(00) or M1 for lists of multiples B1FT for “2 am” + their 18 correctly worked out soi OR B2 for [clock A = 2] 8, 14, 20… and [clock B = 2] 11, 20…. or B1 for [clock A = 2] 8, 14, 20…or [clock B = 2] 11, 20…

This question in 0580/31 Oct/Nov 2017

2 (a) Write the number 8045 in words. … [1] (b) Write down a number between 60 and 70 that is (i) a square number, … [1] (ii) a prime number, … [1] (iii) a common multiple of 4 and 17. … [1] (c) (i) Write 98 as a product of its prime factors. … [2] (ii) Find the highest common factor (HCF) of 98 and 182. … [2] (d) Find the value of (i) 64, … [1] (ii) 3 24 389 , … [1] (iii) 141, … [1] (iv) 5−3. … [1]

12 marks

Mark scheme: 2(a) Eight thousand [and] forty-five 1 2(b)(i) 64 1 2(b)(ii) 61 or 67 1 2(b)(iii) 68 1 2(c)(i) 2 × 72 or 2 × 7 × 7 2 M1 for 2, 7, 7 or 2, 72 or 1 × 2 × 7 × 7 or 1 × 2 × 72 2(c)(ii) 2 M1 for (182 = ) 2 × 7 × 13 or 2, 7, 13 14 or B1 for 2 or 7 or 2 × 7 as final answer 2(d)(i) 1296 1 2(d)(ii) 29 1 2(d)(iii) 14 1 2(d)(iv) 1 1 0.008 or 125

This question in 0580/32 Oct/Nov 2017

2 (a) Write down (i) the number twenty seven million, three hundred and sixty thousand and forty five in figures, … [1] (ii) the six factors of 20, … , … , … , … , … , … [2] 7 (iii) a fraction that is equivalent to , 9 … [1] (iv) a prime number between 30 and 40. … [1] (b) For each statement, insert one pair of brackets to make it correct. (i) 17 - 3 # 5 - 3 = 11 [1] (ii) 3 + 2 2 - 4 = 21 [1] (c) Find 3 4913 . … [1]

8 marks

Mark scheme: 2(a)(i) 27 360 045 1 2(a)(ii) 1, 2, 4, 5, 10, 20 2 B1 for 4 or 5 correct factors 2(a)(iii) 7 k 1 where k ≠ 1 9 k 2(a)(iv) 31 or 37 1 2(b)(i) 17 – 3 × (5 – 3) = 11 1 2(b)(ii) (3 + 2)2 – 4 = 21 1 2(c) 17 1

This question in 0580/31 May/June 2018

1 (a) Find the value of (i) the square root of 19 044, … [1] (ii) 27. … [1] (b) n is an integer and 120 < n < 140. Find the value of n when it is (i) a multiple of 45, n = … [1] (ii) a square number, n = … [1] (iii) a factor of 402, n = … [1] (iv) a cube number. n = … [1] 21 - 15 # 3 (c) Work out the value of . 18 ' 6 - 4 … [2] 19.2 # 8.64 (d) Estimate the value of by rounding each number in the calculation to 1 significant 31.6 ' 6.32 figure. Show all your working by filling in the calculation below. … # … = … [2] … ' …

10 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 138 1 1(a)(ii) 128 1 1(b)(i) 135 1 1(b)(ii) 121 1 1(b)(iii) 134 1 1(b)(iv) 125 1 1(c) 24 2 B1 for numerator of −24 or denominator of −1 or answer of –24 1(d) 20 × 9 M1 M1 for all correct roundings 30 ÷ 6 12 A1 If 0 scored SC1 for 3 correct roundings or 20.[0] and 9.0[0] and 30.[0] and 6.0[0]

This question in 0580/32 May/June 2018

3 (a) A museum’s opening times are shown in this table. Day Opening times Monday to Thursday 09 00 to 17 00 Friday 08 30 to 18 00 Saturday 09 00 to 19 00 Sunday Closed Work out how many hours in a week the museum is open for. … hours [3] (b) The table shows the cost of tickets for the museum. Cost Adult $4.20 Senior (aged over 60) $2.80 Child (aged 5 to 15 ) $1.80 Child (aged under 5) Free The Reeve family visit the museum. Mrs Reeve is aged 36, her father is 67, her mother is 65, and her three children are 2, 7 and 12. Work out the total cost for these six people to visit the museum. $ … [3] (c) Mrs Reeve buys 6 ice creams. Each ice cream costs $1.30 . How much change does she receive from $10? $ … [2] (d) Last year, the museum had twenty seven thousand and fifty three visitors. Write this number in figures. … [1] (e) In 2015, there were 12 400 visitors to the museum. In 2016, there were 14 100 visitors to the museum. Calculate the percentage increase in the number of visitors from 2015 to 2016. … % [3] (f) The door to the museum has an 8-digit code to unlock it. • The next odd number after 35 gives digits 1 and 2. • The next prime number after 23 gives digits 3 and 4. • The square root of 225 gives digits 5 and 6. • The value of 26 gives digits 7 and 8. Use this information to complete the door code. Digits 1 and 2 have been completed for you. Digit 1 2 3 4 5 6 7 8 Code 3 7 [3]

15 marks

Mark scheme: 3(a) 51.5 3 M2 for 4 × 8 + 9.5 + 10 oe or B1 for two from 8 or 32, 9.5 and 10 3(b) 13.4[0] 3 M2 for 4.2[0] + 2 × 2.8[0] + 2 × 1.8[0] oe or M1 for two correct categories 3(c) 2.2[0] 2 M1 for 6 × 1.3[0] implied by 7.8[0] 3(d) 27 053 1 3(e) 13.7 or 13.70 to 13.71 3 14100 − 12400 M2 for [ × 100] or 12400 14100  14100  × 100 [–100] or  − 1  [× 100] 12400  12400  14100 or M1 for 14100 – 12400 or oe 12400 3(f) 2 9 1 5 6 4 3 B1 for each pair of 29, 15 and 64

This question in 0580/33 May/June 2018

2 (a) Write down all the factors of 18. … [2] (b) Write down a prime number between 40 and 50. … [1] 7. 85 . (c) Calculate 1.09 + 6.21 - 4.37 Give your answer correct to 1 decimal place. … [2] (d) Find the value of (i) .2 89, … [1] (ii) 143, … [1] (iii) 4–2. … [1] (e) (i) 126 = 2 # 32 # k Find the value of k. k = … [1] (ii) Write 90 as the product of its prime factors. … [2] (iii) Find the lowest common multiple (LCM) of 90 and 126. … [2]

13 marks

Mark scheme: 2(a) 1, 2, 3, 6, 9, 18 2 B1 for four or more correct and no extras or six correct and one extra 2(b) 41 or 43 or 47 1 2(c) 5.4 2 B1 for 5.35[6…] or 5.36 2(d)(i) 1.7 1 2(d)(ii) 2744 1 2(d)(iii) 1 1 0.0625 or 16 2(e)(i) 7 1 2(e)(ii) 2 × 32 × 5 or 2 × 3 × 3 × 5 2 M1 for a complete factor tree or 2, 3, 3, 5 clearly identified as factors or B1 for a correct product that equals 90 2(e)(iii) 630 2 B1 for 630k, where k ⩾ 2 or for list of multiples of 90 and 126 to at least 630

This question in 0580/31 Oct/Nov 2018

7 (a) Write in figures the number eight million and twenty three thousand. … [1] (b) Write these in order of size, starting with the smallest. 3 7 42% 0.45 7 17 … 1 … 1 … 1 … [2] smallest (c) 25 64 2.9 97 39 47 4.63 111 1.5 × 106 13 Write down a number from this list that is (i) prime, … [1] (ii) a multiple of 13, … [1] (iii) irrational. … [1] (d) The number, n, is given as 5300, correct to 2 significant figures. Complete this statement about the value of n. … G n 1 … [2] 3 2(e) Without using a calculator, work out 1 # 1 . 4 7 Show all your working and give your answer as a mixed number in its simplest form. … [3]

11 marks

Mark scheme: 7(a) 8 023 000 1 7(b) 7 3 2 B1 for converting to decimals or percentages 42% 0.45 e.g. [0].428 … or [0].429, [0].42, (.45), [0].41.. 17 7 7(c)(i) 47 1 7(c)(ii) 39 1 7(c)(iii) 97 1 7(d) 5250 5350 2 B1 for each If 0 scored SC1 for both correct but reversed 7(e) 7 9 B1 either fraction seen or 4 7 7 9 9 63 M1 or equivalent improper fractions × = or 4 7 4 28 7 k 9 m 9 n × = 4 k 7 m 4 n 2 14 cao A1

This question in 0580/32 Oct/Nov 2018

6 (a) Write the number 602 047 in words. … [1] (b) Find (i) a multiple of 14, … [1] (ii) 562, … [1] (iii) 3 103823 , … [1] (iv) 120. … [1] (c) Find the lowest common multiple (LCM) of 12 and 78. … [2] (d) Find the highest common factor (HCF) of 12 and 78. … [2] (e) Write 432 as a product of its prime factors. … [2]

11 marks

Mark scheme: 6(a) Six hundred (and) two thousand (and) 1 forty seven 6(b)(i) Any multiple of 14 1 6(b)(ii) 3136 1 6(b)(iii) 47 1 6(b)(iv) 1 1 6(c) 156 2 M1 for (12 =) 2, 2, 3 and (78 =) 2, 3, 13 or for 2, 2, 3, 13 or for list of multiples of 12 and 78 to at least 156 If 0 scored SC1 for 156k 6(d) 6 2 B1 for 2 or 3 as final answer 6(e) 24 × 33 or 2 × 2 × 2 × 2 × 3 × 3 × 3 2 M1 for a complete factor tree with at most one error or 2, 2, 2, 2, 3, 3, 3 clearly identified as factors or B1 for a correct product that equals 432

This question in 0580/33 Oct/Nov 2018

2 (a) Work out 48 ' 3 - 5 # 2 . … [1] (b) Insert one pair of brackets to make this statement correct. 3 + 2 # 12 - 4 = 19 [1] (c) Write the following in order, starting with the smallest. 3 11 0.749 76% 4 15 … 1 … 1 … 1 … [2] smallest (d) Find the value of (i) 265.69, … [1] (ii) 83. … [1] (e) Write down the smallest prime number. … [1] (f) Write down all the factors of 18. … [2] (g) Write down a common factor of 16 and 72 that is greater than 2. … [1] 28(h) Write as a fraction in its simplest form. 140 … [1] (i) Jeff and his friends win a prize. 5 Jeff’s share is $160 which is of the prize. 11 Work out the value of the prize. $ … [2]

13 marks

Mark scheme: 2(a) 6 1 2(b) 3 + 2 × (12 – 4) = 19 1 2(c) 15 11 [0].749 34 76[%] 2 B1 for 3 in the correct order or 0.75, (0.749) , 0.76, 0.73… or 75%, 74.9%, (76%), 73….% 2(d)(i) 16.3 1 2(d)(ii) 512 1 2(e) 2 1 2(f) 1 2 3 6 9 18 2 B1 for 4 or 5 correct factors only or 6 correct factors with one extra or 1 × 18, 2 × 9, 3 × 6 2(g) 4 or 8 1 2(h) 1 5 cao 1 2(i) 352 2 M1 for 160 ÷ 5 [ × 11]

This question in 0580/31 May/June 2019

1 (a) (i) Write 26% as a decimal. … [1] (ii) Write 0.48 as a fraction. … [1] (b) Write down 5 (i) a fraction that is equivalent to , 9 … [1] (ii) the 7th odd positive number, … [1] (iii) a decimal number that is larger than 0.0467 but smaller than 0.0468 . … [1] (c) Find the value of (i) 3 512 , … [1] 6 8 (ii) 6 , 2 … [1] (iii) 70. … [1] (d) Find the first even multiple of seven that is greater than 100. … [2] - 1 - 3 7 (e) 6 10 .897 # 10 64 5 From the list, write down the irrational number. … [1]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 0.26 cao 1 1(a)(ii) 48 1 or equivalent fraction 100 1(b)(i) 5k 1 where k ≠ 1 9k 1(b)(ii) 13 1 1(b)(iii) Any decimal between 0.0467 and 1 0.0468 1(c)(i) 8 1 1(c)(ii) 26 244 1 1(c)(iii) 1 1 1(d) 112 2 B1 for any multiple of 7 greater than 100 seen 1(e) 10 1

This question in 0580/32 May/June 2019

1 (a) Write this number in figures. One million three hundred and two thousand five hundred and ninety-six. … [1] (b) (i) Two numbers are added together to give the number in the box immediately above. 2 5 – 3 – 4 Complete the diagram. [2] (ii) Two numbers are multiplied together to give the number in the box immediately above. 5 – 3 – 4 Complete the diagram. [3] (c) Write these in order of size, starting with the smallest. 5 -1 18.4% .183 # 10 5-1 27 … 1 … 1 … 1 … [2] smallest (d) Work out 142 as a percentage of 304. … % [1] (e) (i) Find the highest common factor (HCF) of 28 and 98. … [2] (ii) Find the lowest common multiple (LCM) of 28 and 98. … [2] (f) The average distance from Earth to Mars is .225 # 108 km. A space ship travels from Earth to Mars at an average speed of .58 # 104 km/h. Find how long, in hours, the journey takes. … hours [2]

15 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 1 302 596 1 1(b)(i) −5 2 B1 for −7 −7 B1FT for 2 + their −7 1(b)(ii) −180 3 B1 for −15 −15 12 B1 for 12 and B1FT for their −15 × their 12 1(c) 5 2 M1 for 3 in correct order or for 1.83 × 10−1 18.4% 5−1 27 5 three of [ =]0.185 … , [18.4% =] 0.184, 27 [1.83 × 10−1 =] 0.183, [5−1=] 0.2 1(d) 46.7 or 46.71... 1 1(e)(i) 14 2 B1 for answer of 2 or 7 or 2 × 7 or 2 × 2 × 7 and 2 × 7 × 7 or list (28 =) 2, 2, 7 and (98 =)2, 7, 7 1(e)(ii) 196 2 B1 for 28, 56, 84, 112,… and 98, 196 or [1 ×]2 × 2 × 7 × 7 or 196k 1(f) 3880 or 3879[⋅…] 2 M1 for 2.25 × 108 ÷ 5.8 × 104 oe or 3.88(0...) × 103 or 3.879… × 103 or figs (388 or 3879…) as the answer

This question in 0580/33 May/June 2019

4 (a) Write the number four hundred and eighteen thousand and seventy two in figures. … [1] (b) Write down all the factors of 16. … [2] (c) Write down a prime number between 30 and 40. … [1] (d) Find the value of (i) 729, … [1] (ii) 183, … [1] (iii) 70. … [1] (e) Saskia has $600. 1 1 She spends of the $600 on a coat and gives of the $600 to her son. 5 3 What fraction of the $600 does she have left? Give your answer in its simplest form. … [3] (f) Find the lowest common multiple (LCM) of 15 and 27. … [2] (g) Write 432 as the product of its prime factors. … [2] (h) Ella invests $4000 for 3 years at a rate of 1.2% per year compound interest. Calculate the value of her investment at the end of the 3 years. $ … [3]

17 marks

Mark scheme: 4(a) 418 072 1 4(b) 1 2 4 8 16 2 B1 for 3 or 4 correct and no extra or all correct and one extra 4(c) 31 or 37 1 4(d)(i) 27 1 4(d)(ii) 5832 1 4(d)(iii) 1 1 4(e) 7 3 5 3 8k cao M2 for + or 15 15 15 15k 320 280 7 k or or or , k must be an 600 600 15k integer 1 1 or M1 for + 5 3 or 120 + 200 or 320 or 280 or 600 – 120 − 200 oe 47 If M0 scored, SC1 for answer of 100 467 4667 1000 10000 4(f) 135 2 M1 for listing at least 3 multiples of 15 and 27 or [15=]3 × 5 and [27=]3 × 3 × 3 or 3³ or B1 for 135k as final answer or B1 for 3 × 3 × 3 × 5 or 33 × 5 4(g) 24 × 33 or 2 × 2 × 2 × 2 × 3 × 3 × 3 2 M1 for a complete correct factor tree or 2,2,2,2,3,3,3 clearly identified as factors or B1 for a correct product that equals 432 4(h) 4145.7[3] or 4145.70 or 4150 or 4146 3  1.2  3 M2 for 4000 ×  1 +  oe  100   1.2  2 or M1 for 4000 ×  1 +  oe  100 

This question in 0580/31 Oct/Nov 2019

3 (a) Write down (i) all the factors of 18, … [2] (ii) a square number between 30 and 50, … [1] (iii) a prime number between 90 and 100. … [1] (b) Put one pair of brackets into each calculation to make it correct. (i) 24 ' 6 + 2 # 3 = 9 [1] (ii) 24 ' 6 + 2 # 3 = 2 [1] (c) Calculate. 4.85 # 6.14 8.91 + 3.89 Give your answer correct to 2 decimal places. … [2] (d) (i) Find the highest common factor (HCF) of 36 and 90. … [2] (ii) Find the lowest common multiple (LCM) of 36 and 90. … [2] (e) (i) Write .42 # 10 -3 as an ordinary number. … [1] (ii) Calculate (8. 1 # 10 5 ) + ( 7. 9 # 10 4 ) . Give your answer in standard form. … [2]

15 marks

Mark scheme: 3(a)(i) 1, 2, 3, 6, 9, 18 2 B1 for 4 or 5 correct and no extras or 6 correct and one extra 3(a)(ii) 36 or 49 1 3(a)(iii) 97 1 3(b)(i) 24 ÷ (6 + 2) × 3 1 3(b)(ii) 24 ÷ (6 + 2 × 3) 1 3(c) 2.33 nfww 2 B1 for 2.32[648…] If 0 scored, SC1 for rounding their answer given to 3dp or more correctly to 2dp 3(d)(i) 18 2 B1 for 2 or 3 or 6 or 9 or 2 × 3 × 3 as final answer or for [36 = ] 2 × 2 × 3 × 3 or 22 × 32 and [90 = ] 2 × 3 × 3 × 5 or 2 × 32 × 5 3(d)(ii) 180 2 B1 for answer 180k where k is a positive integer or 2 × 2 × 3 × 3 × 5 3(e)(i) [0].0042 1 3(e)(ii) 8.89 × 105 2 B1 for figs 889

This question in 0580/32 Oct/Nov 2019

11 (a) Write as a decimal. 4 … [1] 36 (b) Write as a fraction in its lowest terms. 124 … [1] 5 (c) Work out of 128. 8 … [1] (d) Write down all the factors of 24. … [2] (e) Find the highest common factor (HCF) of 24 and 108. … [2] (f) Write down an irrational number between 3 and 9. … [1] (g) Write down the value of 250. … [1] (h) $8400 is invested for 2 years at a rate of 3.5% per year compound interest. Work out the total amount of interest earned by the end of the 2 years. $ … [3] 1 4(i) Without using a calculator, work out 2 + . 3 5 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

15 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) [0].25 1 1(b) 9 1 cao 13 1(c) 80 1 1(d) 1, 2, 3, 4, 6, 8, 12, 24 2 B1 for 6 or 7 correct factors and no extras or 8 correct factors and at most one extra 1(e) 12 2 B1 for 2, 3, 4 or 6 as final answer or 2 × 2 × 3 or for 2 × 2 × 2 × 3 and 2 × 2 × 3 × 3 × 3 1(f) Accept any irrational number between 1 3 and 9 1(g) 1 1 1(h) 598.29 cao 3 2  3.5  M2 for 8400 × 1 + oe    100  OR  3.5  2 M1 for 8400 ×  1 +  oe  100  A1 for 8998.29 1(i) 5 12 35 B1 allow denominators with multiples of 15 or or 35k 5 k 15 15 15 e.g. , 15k 15 k 5 12 35 12 M1 allow other common denominators [ 2 ] [+] or [+] 15 15 15 15 [2]17 or 47 leading to 2 cao A1 with no errors or omissions seen 15 15 315

This question in 0580/33 Oct/Nov 2019

5 (a) Using the integers from 60 to 75 only, find (i) a multiple of 17, … [1] (ii) the prime numbers. … [2] (b) Find (i) the square root of 4489, … [1] (ii) 43, … [1] (iii) 3 274 625 , … [1] (iv) 2 -3 # 24 2 . … [1] (c) Write down the reciprocal of 7. … [1] (d) Write 3.72194 correct to 3 decimal places. … [1] (e) Find the lowest common multiple (LCM) of 8 and 14. … [2] (f) The average temperature at the North Pole is -23 °C in January and -11 °C in March. (i) Find the difference between these temperatures. … °C [1] (ii) The average temperature in July is 28 °C higher than the average temperature in March. Find the average temperature in July. … °C [1]

13 marks

Mark scheme: 5(a)(i) 68 1 5(a)(ii) 61, 67, 71, 73 2 B1 for 3 correct and none incorrect or 4 correct and one incorrect 5(b)(i) 67 1 5(b)(ii) 64 1 5(b)(iii) 65 1 5(b)(iv) 72 1 5(c) 1 1 7 5(d) 3.722 1 5(e) 56 2 B1 for 56k or lists of multiples of 8 and 14 (at least 3 of each) 5(f)(i) 12 1 5(f)(ii) 17 1

This question in 0580/31 May/June 2020

11 (a) (i) Write down a fraction equivalent to . 15 … [1] 1 2 (ii) Find a fraction that is greater than but less than . 15 15 … [1] (b) (i) Write 15% as a decimal. … [1] (ii) Shade 15% of this grid. [1] (c) Write down all the factors of 15. … [2] (d) Find the value of 15. Give your answer correct to 3 decimal places. … [2] (e) (i) Write down the reciprocal of 15. … [1] (ii) Write down the value of 150. … [1] (iii) Write 0.015 in standard form. … [1]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) k 1 cao 15k 1(a)(ii) a 1 a 2 1 , where < < b 15 b 15 1(b)(i) 0.15 cao 1 1(b)(ii) 6 squares shaded 1 1(c) 1, 3, 5, 15 2 B1 for 3 correct and no extras or 4 correct and one extra 1(d) 3.873 cao 2 B1 for 3.87 or 3.872... 1(e)(i) 1 1 15 1(e)(ii) 1 1 1(e)(iii) 1.5 × 10−2 cao 1

This question in 0580/33 May/June 2020

4 349 West side East side 347 348 346 NOT TO 7 SCALE 5 6 3 4 1 2 A road has 349 houses on it numbered from 1 to 349. The diagram shows some of these houses. The houses on the West side of the road have odd numbers. The houses on the East side have even numbers. (a) Put a ring around the numbers in this list that are on the West side. 25 87 126 178 252 329 [1] (b) On the East side, how many houses are there between the house numbered 168 and the house numbered 184? … [1] (c) How many houses on the road have a house number that is a multiple of 39? … [2] (d) Tomaz delivers a leaflet to every house on the West side of the road. He starts at house number 1 and then delivers to each house in order. (i) Find an expression, in terms of n, for the house number of the nth house he delivers to. … [2] (ii) Work out the house number of the 40th house he delivers to. … [1] (iii) Work out how many houses are on the West side of the road. … [2] (e) Alicia delivers a leaflet to every house on the East side of the road. She starts at house number 348 and then delivers to each house in order. (i) Find an expression, in terms of n, for the house number of the nth house she delivers to. … [2] (ii) What is the largest value of n that can be used in your expression? Give a reason for your answer. The largest value of n is … because … … [2]

13 marks

Mark scheme: 4(a) 25, 87, 329 circled 1 4(b) 7 1 4(c) 8 2 349 M1 for 39 or B1 for at least four of 39, 78, 117, 156, 195, 234, 273, 312 4(d)(i) 2n – 1 oe 2 B1 for 2n + c or kn – 1, k ≠ 0 4(d)(ii) 79 1 FT their (d)(i) if linear 4(d)(iii) 175 2 M1 for their ( 2 n − 1) = 349 348 350 or + 1 or 2 2 4(e)(i) 350 – 2n oe 2 B1 for −2n + c or kn + 350, k ≠ 0 4(e)(ii) 174 2 B1 for each n ⩾ 175 gives house numbers that are If 0 scored, SC1 for 175 zero/negative

This question in 0580/33 May/June 2020

3 (a) 8 15 18 33 39 41 51 57 60 81 From this list, write down (i) a factor of 54, … [1] (ii) a multiple of 19, … [1] (iii) a prime number. … [1] (b) Write down the reciprocal of 64. … [1] (c) (i) Write .481 # 10 - 3 as an ordinary number. … [1] (ii) Write 75 000 in standard form. … [1] .63 # 10 2 (iii) Calculate - 3 . 7 # 10 Write your answer in standard form. … [2] (d) (i)  = {2, 4, 8, 16, 32, 64} A = {square numbers} B = {cube numbers} Use this information to complete the Venn diagram. A B [2] (ii) On this Venn diagram, shade the region P , Q . P Q [1]

11 marks

Mark scheme: 3(a)(i) 18 1 3(a)(ii) 57 1 3(a)(iii) 41 1 3(b) 1 1 64 3(c)(i) [0].00481 cao 1 3(c)(ii) 7.5 × 104 1 3(c)(iii) 9 × 104 2 B1 for figs 9 3(d)(i) 2 B1 for 4 or 5 numbers in the correct place 3(d)(ii) 1

This question in 0580/31 Oct/Nov 2020

5 (a) Write one hundred and twenty thousand and twenty in figures. … [1] (b) Find the value of 3481. … [1] (c) (i) Write down the fraction of the rectangle that is shaded. … [1] (ii) Find the percentage of the rectangle that is not shaded. … % [1] (d) Write these numbers in order, starting with the smallest. 5 7 27% 0.268 17 29 … 1 … 1 … 1 … [2] smallest (e) Write 0.3728 correct to 1 decimal place. … [1] (f) Write down the value of 190. … [1] (g) The height, h metres, of a tower is 128 m, correct to the nearest metre. Complete the statement about the value of h. … G h 1 … [2] (h) Find the highest common factor (HCF) of 126 and 180. … [2] (i) Write down an irrational number with a value between 6 and 7. … [1]

13 marks

Mark scheme: 5(a) 120 020 1 5(b) 59 1 5(c)(i) 5 1 8 5(c)(ii) 37.5 1 5(d) 7 5 2 B1 for 3 in the correct order 0.268 27% or M1 for .27 .29… [.268] .24… 29 17 5(e) 0.4 1 5(f) 1 1 5(g) 127.5 128.5 2 B1 for each or SC1 for both correct but reversed 5(h) 18 2 B1 for an answer of 2 or 3 or 6 or 9 or 2 × 3 × 3 or 2 × 32 as final answer or for [126 =] 2 × 3 × 3 × 7 or 2 × 32 × 7 and [180 =] 2 × 2 × 3 × 3 × 5 or 22 × 32 × 5 or for complete correct list of factors for 126 and 180 5(i) Any irrational number between 6 and 7 1

This question in 0580/31 Oct/Nov 2020

6 (a) Write 60 025 in words. … [1] (b) Write 849.481 correct to 1 decimal place. … [1] (c) Write down (i) all the factors of 21, … [2] (ii) a prime number between 40 and 50. … [1] 2 (d) Write as a decimal. 5 … [1] (e) Find the value of (i) 3 2744 , … [1] (ii) 70. … [1] (f) Gino invests $6000 for 5 years at a rate of 1.2% per year compound interest. Calculate the value of his investment at the end of the 5 years. Give your answer correct to the nearest dollar. $ … [3]

11 marks

Mark scheme: 6(a) Sixty thousand [and] twenty five 1 6(b) 849.5 cao 1 6(c)(i) 1, 3, 7, 21 2 B1 for 3 factors and no extras or 4 correct and 1 extra 6(c)(ii) 41, 43 or 47 1 6(d) 0.4 cao 1 6(e)(i) 14 1 6(e)(ii) 1 1 6(f) 6369 cao 3  1.2  5 M1 for 6000 ×  1 +  or better  100  A1 for 6368.7 … , or 6368 or 6370 If A0 scored, SC1 for correctly rounding their decimal answer

This question in 0580/32 Oct/Nov 2020

1 (a) A cruise ship travels 2067 km. (i) Write 2067 in words. … [1] (ii) Write 2067 correct to the nearest hundred. … [1] (b) When full, the cruise ship carries 880 guests and 360 crew. Write the ratio guests : crew in its simplest form. … : … [1] (c) There are 480 cabins on the ship. On one cruise, 456 of these cabins were used. Find the percentage of cabins that were used. … % [1] (d) Last year the cost of a cruise was $4600. This year the cost of the same cruise is $4784. Work out the percentage increase in the cost. … % [2] (e) The cost of building the ship was $153 000 000. Write 153 000 000 in standard form. … [1] (f) There are 480 cabins on the ship. There are four types of cabin: Ocean-view, Balcony, Interior and Suite. Hannah starts to draw a pie chart to show the numbers of each type of cabin. Ocean-view 144° Balcony (i) Show that there are 120 Ocean-view cabins on the ship. [1] (ii) The table shows information about each type of cabin. Type of cabin Number of cabins Sector angle in a pie chart Ocean-view 120 90° Balcony 192 144° Interior 68 Suite 100 (a) Complete the table. [2] (b) Complete the pie chart. [1]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) Two thousand [and] sixty-seven 1 1(a)(ii) 2100 1 1(b) 22 : 9 1 1(c) 95 1 1(d) 4 nfww 2 4784 − 4600 M1 for [× 100] 4600  4784  or  − 1  [× 100]  4600  4784 or × 100 [– 100] oe 4600 1(e) 1.53 × 108 1 1(f)(i) 90 1 × 480 [= 120] oe 360 1(f)(ii)(a) 51 2 68 100 M1 for either × 360 or × 360 oe 75 480 480 or better 1(f)(ii)(b) Correct pie chart 1 FT dep on their 51° and their 75° adding to 126°

This question in 0580/33 Oct/Nov 2020

2 (a) Using numbers from 55 to 85, write down (i) a multiple of 23, … [1] (ii) a factor of 120, … [1] (iii) a common multiple of 8 and 12, … [1] (iv) a number that is both square and odd, … [1] (v) a number that has exactly 2 factors. … [1] (b) Write 220 as the product of its prime factors. … [2]

7 marks

Mark scheme: 2(a)(i) 69 1 2(a)(ii) 60 1 2(a)(iii) 72 1 2(a)(iv) 81 1 2(a)(v) 59 or 61 or 67 or 71 or 73 or 79 or 83 1 2(b) 22 × 5 × 11 or 2 × 2 × 5 × 11 2 B1 for 2, 2, 5, 11 or M1 for correct factor tree/diagram/list/ table

This question in 0580/33 Oct/Nov 2020

5 (a) Find. (i) 320.41 … [1] (ii) 6.4 2 + 1. 2 3 … [1] (iii) the reciprocal of 2 … [1] (iv) 90 … [1] 3 (v) of $42 7 $ … [1] (vi) 12% of $62 $ … [1] (b) Insert one pair of brackets in each statement to make it correct. (i) 20 - 5 ' 5 - 3 = 0 [1] (ii) 20 - 5 ' 5 - 3 = 17.5 [1] (c) Write one of the symbols 1 , 2 or = in each statement to make it correct. 7 … 0.07 10 1 … 20% 5 3 … 0.38 8 [2] (d) (i) Write 90 as the product of its prime factors. … [2] (ii) Find the lowest common multiple (LCM) of 35 and 90. … [1] (iii) Find the highest common factor (HCF) of 35 and 90. … [1]

14 marks

Mark scheme: 5(a)(i) 17.9 1 5(a)(ii) 42.688 cao 1 5(a)(iii) 1 2 or 0.5 1 5(a)(iv) 1 1 5(a)(v) 18 1 5(a)(vi) 7.44 1 5(b)(i) (20 – 5) ÷ 5 – 3 = 0 1 5(b)(ii) 20 – 5 ÷ (5 – 3) = 17.5 1 5(c) 7 2 B1 for 2 correct > 0.07 10 1 = 20% 5 3 < 0.38 8 5(d)(i) 2 × 3 × 3 × 5 or 2 × 32 × 5 2 B1 for 2, 3, 3, 5 or M1 for correct factor tree / diagram / table 5(d)(ii) 630 1 5(d)(iii) 5 1

This question in 0580/33 May/June 2021

1 (a) 14 17 25 27 30 36 48 From the list, write down (i) the square root of 289, … [1] (ii) a factor of 81, … [1] (iii) a common multiple of 3 and 5. … [1] (b) A, B and C are three consecutive whole numbers. • A is a prime number. • B is a cube number. • C is a square number. • A + B + C is less than 40. Find A, B and C. A = … B = … C = … [2] (c) Put one pair of brackets into each of these calculations to make them correct. (i) 4 # 3 + 7 ' 2 = 20 [1] (ii) 51 - 12 ' 3 + 6 = 19 [1] (d) Write down (i) the reciprocal of 8, … [1] (ii) the value of 140. … [1] (e) Calculate. (i) 54 … [1] (ii) 3 6859 … [1] 1 (iii) 16 - 2 … [1]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 17 1 1(a)(ii) 27 1 1(a)(iii) 30 1 1(b) 7, 8, 9 2 M1 for any 2 conditions in final answer from: A prime or B cube or C square or consecutive A + B + C < 40 1(c)(i) 4 × (3 + 7) ÷ 2 = 20 1 1(c)(ii) (51 – 12) ÷ 3 + 6 = 19 1 1(d)(i) 1 1 or 0.125 8 1(d)(ii) 1 1 1(e)(i) 625 1 1(e)(ii) 19 1 1(e)(iii) 1 1 or 0.25 4

This question in 0580/31 Oct/Nov 2021

2 (a) In one year, a theatre sells four hundred and ninety-six thousand and fifty tickets. Write this number in figures. … [1] (b) The theatre is used for performances of operas, plays, concerts and musicals. The pie chart shows information about the number of each type of performance. Operas 27° Musicals Plays Concerts (i) Complete these statements. The type of performance shown the most is … . The sector angle for this type of performance is … degrees. [2] (ii) Write down the percentage of performances that are plays. … % [1] (iii) The theatre is used for 320 performances in the year. Calculate the number of opera performances. … [2] (iv) The number of concert performances is in the ratio classical music : popular music = 7 : 5. There are 56 classical music concerts. Find the number of popular music concerts. … [2] (c) The table shows the prices of a child ticket and a senior ticket for a play. Adult Child Senior $ … $15.50 $35 Alex buys tickets for 2 adults, 3 children and 1 senior. He pays a total of $159.50 . Complete the table. [2] (d) Last week the cost of a ticket for a musical was $65. This week the same ticket costs $55.90 . Find the percentage reduction in the cost of this ticket. … % [2]

12 marks

Mark scheme: 2(a) 496 050 1 2(b)(i) Musicals 2 B1 for each 135 2(b)(ii) 25 1 2(b)(iii) 24 2 27 320 M1 for [× 320 ] oe or [× 27 ] oe 360 360 2(b)(iv) 40 2 56 M1 for [×k ] oe where k = 5 or 12 7 2(c) 39 2 M1 for 159.50 −×3 15.5 − 35 or better 2(d) 14 2 65 − 55.9 [ 0 ] M1 for [× 100] oe 65  55.9 [ 0 ]  or  1 −  [× 100 ] oe  65  55.9 [ 0 ] or [100 –] × 100 oe 65

This question in 0580/31 Oct/Nov 2021

2 (a) 8 17 26 35 49 51 72 From this list of numbers, write down (i) a multiple of 24, … [1] (ii) a square number, … [1] (iii) a cube number, … [1] (iv) a prime number. … [1] (b) Write 420 as a product of its prime factors. … [2] (c) Find the lowest common multiple (LCM) of 30 and 84. … [2] (d) By writing each number correct to 1 significant figure, show that an estimate for this calculation is 40. 9.875 + 18.305 + 27 . 837 3.418 [2]

10 marks

Mark scheme: 2(a)(i) 72 1 2(a)(ii) 49 1 2(a)(iii) 8 1 2(a)(iv) 17 1 2(b) 22 × 3 × 5 × 7 2 B1 for 2, 2, 3, 5, 7 or M1 for correct factor tree/diagram/list/ table 2(c) 420 2 B1 for 420k as final answer or M1 for [30=] 2 × 3 × 5 and [84 =] 22 × 3 × 7 or for list of multiples of 30 and 84 with at least 3 of each or 2 correct factor trees or tables or 2 × 2 × 3 × 5 × 7 oe 2(d) 10 + 20 M1 + 30 3 30 A1 If 0 scored, SC1 for 3 correctly rounded + 30 [= 40] numbers or for all 4 correct but with any 3 trailing zeros

This question in 0580/32 Oct/Nov 2021

7 (a) Write the number six hundred and three thousand eight hundred and twenty-one in figures. … [1] (b) Pens cost 47 cents each. Aroha buys 8 pens. How much change does she receive from $5? $ … [2] (c) Find the value of (i) 81, … [1] (ii) 63, … [1] (iii) 30. … [1] (d) Write 130 as a product of its prime factors. … [2] (e) A tower has two bells, A and B. Bell A rings every 12 minutes. Bell B rings every 14 minutes. Both bells ring at 09 30. Find the next time both bells ring together. … [3]

11 marks

Mark scheme: 7(a) 603 821 1 7(b) 1.24 2 M1 for 5 – (0.47 × 8) oe 7(c)(i) 9 1 7(c)(ii) 216 1 7(c)(iii) 1 1 7(d) 2 × 5 × 13 2 B1 for 2, 5, 13 or M1 for correct factor tree/diagram/list/ table 7(e) 1054 3 B2 for 84 or 1 hr 24 mins or M1 for 84k or 2 × 2 × 3 × 7 or [12 =] 2 × 2 × 3 and [14 =] 2 × 7 or 2 correct factor trees / tables of both 12 and 14 OR M2 for listing times/multiples of both 12 and 14 to at least 1054 or 84 or M1 for listing at least 3 of each or one full list

This question in 0580/33 Oct/Nov 2021

1 (a) Write the number six and a half million in figures. … [1] (b) Write 6538 correct to the nearest ten. … [1] (c) Work out 6 # 5 + 12 ' 3 . … [1] (d) 9 16 18 29 57 64 87 96 From this list of numbers, write down (i) a factor of 48, … [1] (ii) a cube number, … [1] (iii) a prime number. … [1] (e) Find the value of .0001225 . … [1] (f) Find the reciprocal of 8. … [1] (g) Find the value of 80. … [1] (h) (i) Write 180 as a product of its prime factors. … [2] (ii) Find the lowest common multiple (LCM) of 160 and 180. … [2] (i) The mass of an aircraft, m tonnes, is 473 tonnes, correct to the nearest tonne. Complete this statement about the value of m. … G m 1 … [2]

15 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 6 500 000 1 1(b) 6540 1 1(c) 34 1 1(d)(i) 16 1 1(d)(ii) 64 1 1(d)(iii) 29 1 1(e) 0.035 1 1(f) 1 1 8 or 0.125 1(g) 1 1 1(h)(i) 2  2  3  3  5 2 B1 for 2, 2, 3, 3, 5 or M1 for correct factor tree or table 1(h)(ii) 1440 2 B1 for 1440k as final answer or M1 for [160 =] 2  2  2  2  2  5 and [180 =] 2  2  3  3  5 or a list of multiples of 160 and 180 with at least the first three correct or two correct factor trees or tables or 2, 2, 2, 2, 2, 5, 3, 3 or 2  2  2  2  2  5  3  3 oe 1(i) 472.5 473.5 2 B1 for each If zero scored, SC1 for both correct but reversed

This question in 0580/31 May/June 2022

5 (a) Work out the number of days in seven weeks. … days [1] (b) The summit of Mount Everest is 8848 metres above sea level. Ayding Lake is 154 metres below sea level. Work out the difference in height between these places. … m [1] (c) Find two integers that have a sum of - 12 and a product of 32. … and … [1] 3 (d) Write as 8 (i) a decimal, … [1] (ii) a percentage. … % [1] (e) Write down the reciprocal of 1. 9 … [1] (f) Find the value of (i) 45, … [1] (ii) 3 512 . … [1] (g) (i) Write 587 000 in standard form. … [1] (ii) Calculate 4.9 # 10 - 3 + 8.1 # 10 - 4 . Give your answer in standard form. … [1] (h) The height, h metres, of a fence post is 2.43 m, correct to the nearest centimetre. Complete the statement about the value of h. … G h 1 … [2]

12 marks

Mark scheme: 5(a) 49 1 5(b) 9002 1 5(c) −8 and −4 1 5(d)(i) [0].375 1 5(d)(ii) 37.5 1 5(e) 9 1 5(f)(i) 1024 1 5(f)(ii) 8 1 5(g)(i) 5.87 × 105 cao 1 5(g)(ii) 5.71 × 10−3 cao 1 5(h) 2.425 2.435 2 B1 for each If zero scored, SC1 for 242.5 ⩽ h < 243.5 or for both correct but reversed

This question in 0580/33 May/June 2022

4 (a) Find (i) a multiple of 3 between 70 and 80, … [1] (ii) a factor of 63 between 5 and 10, … [1] (iii) a cube number between 60 and 90, … [1] (iv) the reciprocal of 7. … [1] 2 (b) Work out of 84. 7 … [1] (c) Find the value of (i) 3 3375 , … [1] (ii) 120. … [1] (d) Rana hires a car. The cost is $74 per day plus a delivery cost of $17.50 . Rana pays a total of $461.50 . Calculate the number of days that Rana hires the car. … days [2] (e) A train to town A leaves a station every 25 minutes. A train to town B leaves the same station every 45 minutes. Both trains leave at 08 00. Find the next time both trains leave together. … [3]

12 marks

Mark scheme: 4(a)(i) 72 or 75 or 78 1 4(a)(ii) 7 or 9 1 4(a)(iii) 64 1 4(a)(iv) 1 1 or 0.143 or 0.142[8..] 7 4(b) 24 1 4(c)(i) 15 1 4(c)(ii) 1 1 4(d) 6 nfww 2 ( 461.5 –17.5 ) M1 for oe 74 4(e) 11 45 3 B2 for 225 or 3 hr 45 mins or M1 for 225k or 3  3  5  5 or [25 =] 5  5 and [45 =] 3  3  5 or two correct factor trees/tables of both 25 and 45 OR M2 for listing times/multiples of both 25 and 45 to at least 11 45 or 225 or M1 for listing at least 3 consecutive times/multiples of each correctly or one full list

This question in 0580/31 Oct/Nov 2022

1 (a) 2 18 27 29 39 49 80 92 From this list of numbers, write down (i) a multiple of 8, … [1] (ii) a factor of 46, … [1] (iii) a square number, … [1] (iv) a cube number, … [1] (v) a prime number. … [1] (b) Write 0.003 857 correct to (i) 3 decimal places, … [1] (ii) 3 significant figures. … [1] (c) Anna invests $16 000 at a rate of 3.8% per year compound interest. Calculate the value of her investment at the end of 5 years. $ … [2] (d) (i) Write 48 as the product of its prime factors. … [2] (ii) Find the lowest common multiple (LCM) of 48 and 126. … [2] (e) The mass of a truck, m tonnes, is 28.5 tonnes, correct to 1 decimal place. Complete this statement about the value of m. … G m 1 … [2]

15 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 80 1 1(a)(ii) 2 1 1(a)(iii) 49 1 1(a)(iv) 27 1 1(a)(v) 2 or 29 1 1(b)(i) 0.004 cao 1 1(b)(ii) 0.00386 cao 1 1(c) 19 300 or 19 280 2 3.8 5 M1 for 16 000 × (1 + ) oe or 19 279.98 to 19 279.99 100 1(d)(i) 2 × 2 × 2 × 2 × 3 or 24 × 3 2 B1 for 2, 2, 2, 2, 3 or M1 for a correct factor tree / diagram / list / table 1(d)(ii) 1008 2 B1 for 1008k as final answer or M1 for 2 × 2 × 2 × 2 × 3 × 3 × 7 oe or 2, 2, 2, 2, 3, 3, 7 or for [126=] 2×3×3×7 or 2, 3, 3, 7 or [126=] 6×21 and [48=] 6×8 or 6, 21 and 6, 8 or correct factor tree / diagram / list / table for 126 or a list of consecutive multiples of both 48 and 126 with at least 3 of each 1(e) 28.45 28.55 2 B1 for each If 0 scored, SC1 for both correct but reversed

This question in 0580/32 Oct/Nov 2022

9 (a) Write down the reciprocal of 1. 3 … [1] (b) Write down the value of 30. … [1] 3 4 (c) Find a fraction between and . 25 25 … [1] (d) Find the difference in temperature between −5 °C and 9 °C. … °C [1] (e) Write in standard form. (i) 5 600 000 … [1] (ii) 0.000 072 … [1] (f) Calculate ( 5.2 # 10 6 ) # (3 .8 # 10 -2 ) . Give your answer in standard form. … [1]

7 marks

Mark scheme: 9(a) 3 1 9(b) 1 1 9(c) Correct fraction e.g. 507 1 9(d) 14 1 9(e)(i) 5.6 × 106 1 9(e)(ii) 7.2 × 10-5 1 9(f) 1.976 × 105 1

This question in 0580/32 Oct/Nov 2022

1 (a) List all the factors of 68. … [2] (b) Put one pair of brackets into each calculation to make it correct. (i) 7 + 3 # 5 - 1 = 19 [1] (ii) 12 + 16 ' 2 + 5 = 19 [1] (c) Find (i) the reciprocal of 2, 7 … [1] (ii) the value of 100. … [1] (d) Calculate. (i) 3 2 + 3 4 … [1] (ii) 3 # 12 … [1] (iii) 5 -3 … [1] (e) Write these numbers in order of size, starting with the smallest. 22 10 .3142 .182 r 7 … 1 … 1 … 1 … 1 … [2] smallest (f) By writing each number in the calculation correct to 1 significant figure, work out an estimate for the value of 136 + 47.2 . 62.9 ' 18.1 You must show all your working. … [2] (g) Write .473 # 106 as an ordinary number. … [1] (h) Write down a prime number between 30 and 40. … [1]

15 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 1, 2, 4, 17, 34, 68 2 B1 for 4 or 5 correct and no extras or 6 correct and one extra 1(b)(i) 7 + 3  (5 – 1) = 19 1 1(b)(ii) (12 + 16) ÷ 2 + 5 = 19 1 1(c)(i) 7 1 1 or 3.5 or 3 2 2 1(c)(ii) 1 1 1(d)(i) 90 1 1(d)(ii) 6 1 1(d)(iii) 1 1 or 0.008 125 1(e) 22 2 B1 for 4 in correct order π, 3.142, , 10 , 1.82 7 or M1 for [ 10 =] 3.16…, [1.82=] 3.24, 22 [π =] 3.141…, [ =] 3.1428 to 3.1429 or 7 3.143 1(f) 100 + 50 M1 60  20 50 cao nfww A1 If 0 scored, SC1 for 3 correct roundings or for all correct but with any trailing zeros 1(g) 4 730 000 1 1(h) 31 or 37 1

This question in 0580/33 Oct/Nov 2022

3 (a) The population of Alaska is 735 720. (i) Write this number in words. … … [1] (ii) The land area of Alaska is 1 477 300 square kilometres. Work out the average number of people per square kilometre. … [1] (iii) In Alaska, the city with the highest population is Anchorage with 291 830 people. What percentage of the population of Alaska live in Anchorage? … % [1] (b) The length, L km, of a race is 1569 km, correct to the nearest kilometre. Complete this statement about the value of L. … G L 1 … [2] (c) The table gives some information about two mountains. The temperatures are taken at the top of each mountain on the same day. Maximum Minimum Height in metres temperature temperature Highest mountain Denali 6190 -9 °C -20 °C in Alaska Highest mountain Everest 8849 … °C -38 °C in the world (i) Find the difference between the height of Denali and the height of Everest. … m [1] (ii) Find the difference between the maximum temperature and the minimum temperature at the top of Denali. … °C [1] (iii) The maximum temperature at the top of Everest was 27 °C colder than the maximum temperature at the top of Denali. Complete the table. [1]

8 marks

Mark scheme: 3(a)(i) Seven hundred [and] thirty-five thousand, 1 seven hundred [and] twenty 3(a)(ii) 0.498 or 0.4980… 1 3(a)(iii) 39.7 or 39.66 to 39.67 1 3(b) 1568.5, 1569.5 2 B1 for each If 0 scored, SC1 for both values correct but reversed 3(c)(i) 2659 1 3(c)(ii) 11 1 3(c)(iii) –36 1

This question in 0580/33 Oct/Nov 2022

4 (a) Write 6479 correct to the nearest 100. … [1] (b) Write down the multiple of 13 that is between 100 and 110. … [1] (c) Find the reciprocal of 0.6 . … [1] (d) Work out. 3 + 4 # 2 … [1] (e) Write down an irrational number with a value between 15 and 20. … [1] (f) By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 423.8 - 78.4 . 23.5 You must show all your working. … [2]

7 marks

Mark scheme: 4(a) 6500 1 4(b) 104 1 4(c) 2 1 13 oe 4(d) 11 1 4(e) Any irrational number between 15 and 20 1 4(f) 400 − 80 M1 20 16 nfww A1 If 0 scored, SC1 for 2 correct roundings or all correct but with trailing zeros

This question in 0580/32 Feb/March 2023

1 (a) Write the number forty thousand and thirty-three in figures. … [1] (b) Find the value of 3 729 . … [1] 7 (c) Find the reciprocal of . 9 Give your answer as a decimal, correct to 3 decimal places. … [2] (d) Find the value of 6 5 ' 3 4 . … [2] (e) Work out ( - 9 ) # ( - 7 ) ' ( - 3) . … [1] (f) Work out. (i) 11 + 9 # 5 - 4 … [1] (ii) ( 11 + 9) # 5 - 4 … [1] 5(g) - 0 .67 123 49 3 .142 9 From this list, write down an irrational number. … [1] (h) (i) Find the lowest common multiple (LCM) of 24 and 104. … [2] (ii) Find the highest common factor (HCF) of 24 and 104. … [2]

14 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 40 033 1 1(b) 9 1 1(c) 1.286 cao 2 B1 for 97 or 1.29 or 1.285 or 1.285…… 1(d) 96 2 B1 for 7776 or 81 1(e) −21 1 1(f)(i) 52 1 1(f)(ii) 96 1 1(g) √123 1 1(h)(i) 312 2 B1 for 312k as final answer or M1 for [24 =] 2 × 2 × 2 × 3 or 23 × 3 and [104 =] 2 × 2 × 2 × 13 or 23 × 13 or 2 correct factor trees or tables or a list of multiples of both 24 and 104 with at least 3 of each or 2 × 2 × 2 × 3 × 13 oe 1(h)(ii) 8 2 B1 for 2 or 4 or 2 × 2 × 2 or 23 as final answer, or for a complete list of factors of 24 and 104

This question in 0580/31 May/June 2023

1 (a) Write the number three hundred thousand and three in figures. … [1] (b) Write 15 896 correct to (i) the nearest thousand … [1] (ii) the nearest ten. … [1] (c) By writing each number in the calculation correct to 1 significant figure, work out an estimate for the value of 28.9 # 5.49 . 0.472 + 0.97 You must show all your working. … [2] (d) Find the value of (i) 1849 … [1] (ii) 5 0 - 5 -1 … [1] 5 sin 30 - 8 (iii) . 11 … [1] (e) A cyclist travels at a constant speed of 8.5 metres per second. (i) Work out how long the cyclist takes to travel a distance of 5.27 kilometres. Give your answer in minutes and seconds. … min … s [4] (ii) The cyclist increases speed from 8.5 m/s to 10.2 m/s. Work out the percentage increase in speed. … % [2]

14 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 300 003 1 1(b)(i) 16 000 1 1(b)(ii) 15 900 1 1(c) 30  5 M1 0.5  1 100 A1 If 0 scored, SC1 for three correct from 30, 5, [0].5 and 1 or if all correct but with trailing zeros 1(d)(i) 43 1 1(d)(ii) 0.8 1 1(d)(iii) −0.5 1 1(e)(i) 10 (min) 20 (s) 4 B3 for 620 or 10.3… or 0.172… OR B1 for 5270 or 0.0085 or 510 or 30600 or 0.51 or 30.6 M1 for figs 527÷ figs 85 (imp by figs 62) or figs 527 ÷ figs 510 (imp by figs 103…) or figs 527 ÷ figs 306 (imp by figs172 … ) B1 for their time seen (assume time is in seconds unless units stated) and converted correctly to minutes and seconds (seconds must be correct to 3sf or better) 1(e)(ii) 20 2 10.2 8.5 M1 for [×100] oe 8.5 or (10.2  100 ) [–100 ] oe 8.5 or (10.2 )1 [×100] oe 8.5

This question in 0580/32 May/June 2023

8 (a) T = 5P + 3Q Find the value of T when P = 6 and Q = 8 . T = … [2] (b) Simplify. 3a - 7b + 2a + 4b … [2] (c) Multiply out. 5 ( 2x - 3y) … [1] (d) Solve. 5x - 1 = 3x + 19 x = … [2] (e) Make t the subject of the formula p = t5 - 3 . t = … [2] (f) Entry to a castle costs $x for an adult and $y for a child. Entry for 2 adults and 3 children costs $15.00 . Entry for 3 adults and 5 children costs $23.50 . Write down a pair of simultaneous equations to show this information and solve them to find the value of x and the value of y. You must show all your working. x = … y = … [6]

15 marks

Mark scheme: 8(a) 54 2 M1 for 5×6 + 3×8 or 30 or 24 8(b) 5a – 3b final answer 2 B1 for 5a or – 3b in final answer or for correct answer seen and spoilt 8(c) 10x – 15y final answer 1 8(d) 10 2 M1 for 5x – 3x = 19 + 1 or better 8(e) p  3 2 M1 for p + 3 = 5t or 5p t 53 oe [t=] oe final answer 5 8(f) 2x + 3y = 15 and 3x + 5y = 23.5 B2 B1 for each correctly equating one set of M1 FT coefficients correct method to eliminate one M1 FT variable Dependent on the coefficients being the same for one of the variables Correct consistent use of addition or subtraction using their equations [x =] 4.5 A1 [y =] 2 A1 If M0 scored, SC1 for 2 values satisfying one of correct equations or their equations

This question in 0580/32 May/June 2023

7 (a) D NOT TO SCALE C x° 108° y° 46° B A The diagram shows a triangle ABC and a straight line BCD. (i) Angle ACB = 108° . Write down the mathematical name for this type of angle. … [1] (ii) Work out the value of x. x = … [1] (iii) Work out the value of y. y = … [1] (b) Show that the mean of the angles in any triangle is 60°. [1] (c) NOT TO h cm SCALE 35° 8 cm The diagram shows a right-angled triangle. Calculate the value of h. h = … [3] (d) R C NOT TO SCALE 2.4 cm 7.92 cm A 1.36 cm B P 6.12 cm Q Triangle ABC is similar to triangle PQR. (i) Calculate PR. PR = … cm [2] (ii) Calculate BC. BC = … cm [2] (e) 24 cm NOT TO SCALE 26 cm The diagram shows a right-angled triangle. Calculate the perimeter of this triangle. … cm [4] Question 8 is printed on the next page.

15 marks

Mark scheme: 7(a)(i) Obtuse 1 7(a)(ii) 72 1 7(a)(iii) 26 1 7(b) 180 1 3 7(c) 9.77 or 9.766… 3 8 8 M2 for  h   oe or oe cos35 sin55 8 or M1 for cos35  oe or h 8 sin55  oe h 7(d)(i) 10.8 2 1.36 2.4 M1 for  oe or better 6.12 PR 7(d)(ii) 1.76 2 6.12 7.92 M1 for  oe or better 1.36 BC 7(e) 60 4 M2 for 26 2  24 2 oe or better or M1 for 26 2  x 2  24 2 AND M1 for their10  24  26

This question in 0580/33 May/June 2023

1 (a) Write the number six and a half million in figures. … [1] (b) Write 37 508 correct to the nearest thousand. … [1] (c) 6 9 100 28 31 1000 32 36 From this list of numbers, write down (i) a factor of 18 … [1] (ii) a multiple of 12 … [1] (iii) a square number … [1] (iv) a prime number … [1] (v) an irrational number. … [1] (d) Put one pair of brackets in each statement to make it correct. (i) 24 - 4 # 3 + 2 = 62 [1] (ii) 24 - 4 # 3 + 2 = 4 [1] 3 (e) Write as a decimal. 4 … [1] 3(f) Work out of 126. 7 … [1] (g) Write down the value of the reciprocal of 0.5 . … [1] 2 1(h) Without using a calculator, work out 5 - 2 . 3 5 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

15 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 6 500 000 1 1(b) 38 000 1 1(c)(i) 6 or 9 1 1(c)(ii) 36 1 1(c)(iii) 9 or 36 1 1(c)(iv) 31 1 1(c)(v) 1000 1 1(d)(i) (24 − 4)  3 + 2 = 62 1 1(d)(ii) 24 − 4  (3 + 2) = 4 1 1(e) 0.75 1 1(f) 54 1 1(g) 2 1 1(h) 17 11 B1 Correct step for dealing with mixed or 17 k 11k 3 5 numbers, allow e.g. or 3k 5 k 85 33 M1 FT Correct method to find a common and denominator 15 15 3 157 cao A1 Alternative methods 2 1 10 3 7 3 − B1, and M1, 3 15 cao 3 5 15 15 A1 510 and 3 M1, 3 157 cao B1 A1 15 215 10 3 7 and M1, 3 15 cao B1A1 15 15

This question in 0580/31 Oct/Nov 2023

3 (a) Write the number fourteen thousand and ninety-seven in figures. … [1] (b) Write down a common multiple of 17 and 5. … [1] (c) Write 0.25 as a percentage. … % [1] (d) Find the value of (i) 75 … [1] (ii) 80. … [1] 5 (e) Ranjit buys some plants and sells of them. 11 He sells 190 plants. Work out how many plants he buys. … [2] (f) Factorise completely. 15x 3 y - 3x … [2] (g) Make n the subject of the formula V = 3n + t . n = … [2] (h) 7 15 ' 7 x = 7 9 Find the value of x. x = … [1]

12 marks

Mark scheme: 3(a) 14 097 1 3(b) Any correct multiple i.e. 85k 1 3(c) 25 1 3(d)(i) 16 807 1 3(d)(ii) 1 1 3(e) 418 2 M1 for 190 ÷ 5 soi by 38 3(f) 3x(5x2y – 1) final answer 2 B1 for 3(5x3y – x) or for x(15x2y – 3) or correct answer spoilt 3(g) V − t 2 V t oe final answer M1 for V – t =3n or = n + 3 3 3 3(h) 6 1

This question in 0580/32 Oct/Nov 2023

1 (a) 6 7 10 12 18 32 49 63 From this list of numbers, write down (i) a factor of 21 … [1] (ii) a square number … [1] (iii) a prime number. … [1] (b) Find the value of (i) the cube root of 1728 … [1] (ii) 25 … [1] (iii) 50 … [1] 2 (iv) 36 1. … [1] (c) Put one pair of brackets into this calculation to make it correct. 3 # 2 - 6 - 2 ' 2 = 4 [1] (d) Find the lowest common multiple (LCM) of 30 and 68. … [2]

10 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 7 1 1(a)(ii) 49 1 1(a)(iii) 7 1 1(b)(i) 12 1 1(b)(ii) 32 1 1(b)(iii) 1 1 1(b)(iv) 6 1 1(c) 3 × 2 – (6 – 2) ÷ 2 = 4 1 1(d) 1020 2 B1 for 1020k as final answer or M1 for [30 =] 2 × 3 × 5 and [68 =] 2 × 2 × 17 or for [30 =] 2 × 15 and [68 =] 2 × 34 or 2 correct factor trees or correct tables or correct Venn diagram or a list of multiples of both 30 and 68 with at least their first 3 correct or 2 × 2 × 3 × 5 × 17 oe

This question in 0580/32 May/June 2024

4 (a) Write down the value of the 8 in the number 39 829. … [1] (b) Write down all the factors of 18. … [2] (c) Show that 57 is not a prime number. [1] (d) x = 64 Find the value of x. x = … [1] (e) Find the first multiple of 40 that is greater than 620. … [1] (f) Find the reciprocal of 2. 3 … [1] 1(g) Find a fraction between and 1. 5 4 … [1] (h) Write down an irrational number with a value between 9 and 10. … [1] (i) Find the highest common factor (HCF) of 72 and 180. … [2]

11 marks

Mark scheme: 4(a) 800 1 4(b) 1 2 3 6 9 18 2 B1 for 4 or 5 correct no extras or 6 correct and 1 extra or for 1×18 and 2×9 and 3×6 4(c) [57 =] 3× 19 oe 1 4(d) 4096 1 4(e) 640 1 4(f) 1 12 or 1.5 1 4(g) Any correct fraction 1 4(h) Any correct irrational number 1 4(i) 36 2 B1 for any of 2, 3, 4, 6, 9, 12, 18 as answer or M1 for 2×2×3×3 oe as answer or [72 = ] 2×2×2 ×3×3 and [180 = ] 2×2 ×5× 3×3 or a complete list of factors of 72 and 180 or 2 correct factor trees or tables or Venn diagram

This question in 0580/33 May/June 2024

1 (a) Write the number six million and thirty in figures. … [1] (b) Write 7.896 correct to 2 decimal places. … [1] (c) 8 24 25 36 39 41 48 From this list of numbers, write down (i) a multiple of 16 … [1] (ii) a factor of 24 … [1] (iii) a cube number … [1] (iv) a prime number. … [1] (d) Put one pair of brackets into this calculation to make it correct. 10 - 12 ' 4 + 2 = 8 [1] (e) By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 596 # 0.047 . 8.65 You must show all your working. … [2] (f) Calculate ( 8 # 10 6 ) # ( 3 # 10 -2) . Give your answer in standard form. … [2] (g) 216 = 2 3 # 3 3 Write 2160 as a product of its prime factors. … [1]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 6 000 030 1 1(b) 7.90 cao 1 1(c)(i) 48 1 1(c)(ii) 8 or 24 1 1(c)(iii) 8 1 1(c)(iv) 41 1 1(d) 10 – 12 ÷ (4 + 2) 1 1(e) 600  0.05 M1 9 10 A1 If 0 scored SC1 for 2 correct roundings or for all correct but with any trailing zeros 1(f) 2.4 × 105 2 B1 for correct value but not in standard form 1(g) 24 × 33 × 5 1

This question in 0580/31 Oct/Nov 2024

2 (a) 3.142 87 14 41 56 117 121 From this list, write down (i) an odd number … [1] (ii) a factor of 28 … [1] (iii) a square number … [1] (iv) a prime number … [1] (v) a multiple of 9. … [1] (b) Write down the value of 50. … [1] (c) Write 60 as a product of its prime factors. … [2] (d) Calculate the value of 3 157 464 . … [1] (e) By rounding each number in the calculation correct to 1 significant figure, find an estimate for the value of 67.8 # 2.38 . 4.803 + 29.87 You must show all your working. … [2] (f) (i) .978 # 108 2 .04 # 10 9 Which of these two numbers is larger? Give a reason for your answer. … is larger because … [1] (ii) Calculate 1.732 # 10 3 ' 5 .73 # 10 -1 . Give your answer in standard form. … [2] (g) Two cars go round a track. One car completes each lap of the track in 96 seconds. The other car completes each lap in 120 seconds. Both cars start a lap together at 08 37. Find the next time when both cars start a lap together. … [3]

17 marks

Mark scheme: 2(a)(i) 41 or 117 or 121 1 2(a)(ii) 14 1 2(a)(iii) 121 1 2(a)(iv) 41 1 2(a)(v) 117 1 2(b) 1 1 2(c) 2 × 2 × 3 × 5 or 2 2 × 3 × 5 2 B1 for 2, 2, 3, 5 OR M1 for correct factor tree/table/list 2(d) 54 1 2(e) 70  2 M1 5 + 30 4 A1 If 0 scored SC1 for three correct from 70, 2, 5 and 30 or all correct but with trailing zeros 2(f)(i) 2.04 × 109 and it has the larger power of 1 10 oe 2(f)(ii) 3.02[2...] × 103 or 3.023 × 103 2 B1 for 3020 or 3023 or 3022[. ...] or or correct value but not in correct form 3.02[2...] × 101 or 3.023 × 101 or 30.2 or 30.23 or 30.2[2 ...] or correct value but not in correct form or for their value seen and correctly converted to standard form to at least 3 sf 2(g) 08 45 3 B2 for 480 or 8 mins or M1 for 480k or 2×2×2×2×2×3×5 or [96=] 25 × 3 and [120=] 23 × 3 ×5 or two correct factor trees/tables of both 96 and 120 OR M2 for listing the times/multiples of both 96 and 120 up to 480 or 08 45 or M1 for listing at least the next 2 of each or one full list

This question in 0580/32 Oct/Nov 2024

2 (a) Write the number 845 024 in words. … [1] (b) Write these numbers in order, starting with the smallest. 7 15 39% 0.388 18 40 … 1 … 1 … 1 … [2] smallest (c) Find the value of (i) 45 … [1] (ii) 60 … [1] (iii) 16 # 49 . … [1] (d) Solve. 6x + 5 = 29 x = … [2] (e) By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 2.7 # 42.4 . 8.6 - 4.3 You must show all your working. … [2] (f) 3 5 # 3 x = 3 20 Find the value of x. x = … [1] (g) Simplify ( x4 ) 3. … [1] (h) A boat to town A leaves a port every 16 minutes. A boat to town B leaves the same port every 34 minutes. Both boats leave the port at 07 30. Work out the next time both boats leave the port together. … [3]

15 marks

Mark scheme: 2(a) Eight hundred and forty five thousand 1 and twenty four 2(b) 15 7 2 0.388 39% 40 18 B1 for 3 in the correct order Or M1 for 0.389 or 0.3888 or 0.3889 and 0.39 and 0.375 2(c)(i) 1024 1 2(c)(ii) 1 1 2(c)(iii) 28 1 2(d) 4 2 5 29 M1 for 6x = 29 – 5 or x + = oe 6 6 2(e) 3  40 M1 9 – 4 24 A1 If 0 scored SC1 for 3 correct from 3, 40, 9 and 4 or for all correct but with trailing zeros 2(f) 15 1 2(g) x12 1 2(h) 12 02 3 B2 for 272 or 4 h 32 mins or M1 for 272k or 2  2  2  2  17 oe or [16 = ] 2  2  2  2 and [34 = ] 2  17 or 2 correct factor trees/tables of both 16 and 34 OR M2 for listing times/multiples of both 16 and 34 to at least 1202 or 272 or M1 for listing at least the next 2 of each or 1 full list

This question in 0580/33 Oct/Nov 2024

4 30 31 32 33 34 35 36 37 38 39 From this list, write down the number that is (a) a multiple of 13 … [1] (b) a factor of 140 … [1] (c) the largest prime number … [1] (d) divisible by an even cube number … [1] (e) 20% of 190. … [1]

5 marks

Mark scheme: 4(a) 39 1 4(b) 35 1 4(c) 37 1 4(d) 32 1 4(e) 38 1

This question in 0580/32 Feb/March 2025

19 (a) Write 2025 as the product of its prime factors. … [2] (b) Write 2025 as a product of two square numbers that are both greater than one. … [1]

3 marks

Mark scheme: 19(a) 4 2 2 B1 for 3,3,3,3,5,5 3  5 or M1 for correct factor tree/diagram/list/table 19(b) 25×81 or 225×9 1

This question in 0580/32 Feb/March 2025

1 2 6 16 18 24 26 27 33 From this list, write down the number that is (a) a multiple of 12 … [1] (b) a square number … [1] (c) a cube number. … [1]

3 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 24 1 1(b) 16 1 1(c) 27 1

This question in 0580/33 May/June 2025

20 (a) Work out the size of one interior angle of a regular 8-sided polygon. … [2] (b) D NOT TO C SCALE x° B 71° O E A A, B and C lie on the circumference of the circle, centre O. AB is a diameter. DBE is a tangent to the circle at B. Find the value of x. Give a geometrical reason for your answer. … because … … [2]

4 marks

Mark scheme: 20(a) 135 2 ( 8 − 2 )180 M1 for 180 – 360 ÷ 8 or oe 8 20(b) 19 2 B1 for each Angle between tangent and radius = 90

This question in 0580/31 Oct/Nov 2025

2 Write down all the factors of 32. … [2]

2 marks

Mark scheme: 2 1 2 4 8 16 32 2 B1 for 4 correct and no errors or 6 correct and one extra

This question in 0580/32 Oct/Nov 2025

6 0 1 8 27 39 51 59 81 From the list of numbers, write down (a) a square number … [1] (b) the value of 390 … [1] (c) a prime number. … [1]

3 marks

Mark scheme: 6(a) 1 or 81 accept 0 1 6(b) 1 1 6(c) 59 1

This question in 0580/32 Oct/Nov 2025

8 Complete these statements. 65 000 centimetres = … metres 3.25 litres = … millilitres [2]

2 marks

Mark scheme: 8 650 2 B1 for each 3250

This question in 0580/32 Oct/Nov 2025

1 Write down all the factors of 26. … [2]

2 marks

Mark scheme: Question Answer Marks Partial Marks 1 1 2 13 26 2 B1 for 3 correct and no extra or 4 correct and 1 extra

This question in 0580/33 Oct/Nov 2025

6 (a) Write down the reciprocal of 8. … [1] (b) Work out 193. … [1]

2 marks

Mark scheme: 6(a) 1 1 or 0.125 8 6(b) 6859 1

This question in 0580/33 Oct/Nov 2025

25 Find the lowest common multiple (LCM) of 20 and 36. … [2]

2 marks

Mark scheme: 25 180 2 B1 for 180k as final answer or M1 for [20 =] 2 × 2 × 5 and [36 =] 2 × 2 × 3 × 3 or 2 correct factor trees or tables or lists or a list of multiples of both 20 and 36 with at least 3 of each or 2 × 2 × 3 × 3 × 5 oe

This question in 0580/33 Oct/Nov 2025