Introduction to algebra — Paper 3 · IGCSE Mathematics 0580

7 (a) Rajeesh thought of a number. For He multiplied this number by 2. Examiner's He then added 10. Use The answer was 42. (i) What was the number Rajeesh first thought of? Answer(a)(i) [1] (ii) Simon thought of a number x. He multiplied this number by 3 and then added 8. Write down an expression in x for his answer. Answer(a)(ii) [2] (b) Simplify − 8a + 7b − a − 2b. Answer(b) [2] (c) Factorise fully 6a − 9a2 . Answer(c) [2] (d) Make t the subject of the formula v = u + at. Answer(d) t= [2] (e) Solve the simultaneous equations 8x + 2y = 13, 3x + y = 4. Answer(e) x = , y = [4]

13 marks

Mark scheme: 7 a) i) 16 1 ii) 3x + 8 o.e. 2 M1 for 3x. allow n instead of x. deduct 1 for ‘= x’ or ‘= 0’ or = any number, but allow a different letter b) -9a 1 +5b 1 c) 3a(2 – 3a) 2 M1 for any correct partial factorisation d) v - u 2 M1 for v – u seen o.e. a e) (x=) 2.5 2 M1 for correct multiplication of LHS of one or both equations to equalise coefficients or for a recognisable attempt to eliminate one variable (y=) -3.5 2 M1 for correct substitution of their other value or M2 correct matrix method 13

This question in 0580/31 Oct/Nov 2004

2 (a) Complete the table for the equation y = − x2 + x + 2. For Examiner's Use x −3 −2 −1 0 1 2 3 4 y −10 0 2 2 0 [3] (b) On the grid below draw the graph of y = − x2 + x + 2. y 3 2 1 x 3 2 1 0 1 2 3 4 1 2 3 4 5 6 7 8 9 10 [4] (c) On the grid, draw the line of symmetry of your graph. [1] (d) Use your graph to find the maximum value of y. Answer(d) y = [1] (e) Draw the line y = 1 on the grid. [1] (f) Write down the two values of x for which − x2 + x + 2 = 1. Answer(f) x = or x = [2]

12 marks

Mark scheme: 2 (a) –4 –4 –10 3 1 for each correct entry (b) 1 P3ft P2 for 6 or 7 correct. ft 8 correctly plotted points, within square. P1 for 4 or 5 correct. ft 2 Allow small errors in the points Smooth curve through 8 points C1 provided shape is maintained. (c) x = 0.5 drawn. 1 must be from (0.5, –9) to curve at least (d) 2.2 to 2.4 1ft (e) y = 1 drawn. 1 must touch curve as min. length (f) (x =) –0.7 to –0.5 1 (x =) 1.5 to 1.7 1 12

This question in 0580/31 Oct/Nov 2006

9 In the pattern below each diagram shows a letter E formed by joining dots. For Examiner's Diagram 1 Diagram 2 Diagram 3 Diagram 4 Use (a) Draw the next letter E in the pattern. [1] (b) Complete the table showing the number of dots in each letter E. Diagram 1 2 3 4 5 Dots 8 15 [3] (c) How many dots make up the letter E in (i) Diagram 10, Answer(c)(i) [2] (ii) Diagram n? Answer(c)(ii) [2] (d) The letter E in Diagram n has 113 dots. Write down an equation in n and use it to find the value of n. Answer(d) n = [3]

11 marks

Mark scheme: 9 (a) Letter E correctly drawn B1 (b) 22, 29, 36 B3 B1 for each correct number. (c) (i) 71 B2 B1 for 7 × 10 + 1 or 8 + 9 × 7 seen. (ii) 7n + 1 or 8 + (n – 1) × 7 oe B2 SC1 for 7n + k seen. (k is an integer) oe (d) Their (c)(ii) = 113 B1ft ft any expression involving n. Full method of solution of their M1ft ft only a linear equation. equation. (113 – k)/ ‘7’ 16 A1cao www B2 [11]

This question in 0580/31 May/June 2007

8 (a) The width of a rectangle is x centimetres. For Examiner's The length of the rectangle is 3 centimetres more than the width. Use Write down an expression, in terms of x, for (i) the length of the rectangle, Answer(a)(i) cm [1] (ii) the area of the rectangle. Answer(a)(ii) cm2 [1] (iii) The area of the rectangle is 7 square centimetres. Show that x2 + 3x − 7 = 0. Answer (a)(iii) [1] (b) (i) Complete the tables of values for the equation y = x2 + 3x − 7. x −5 −4 −3 −2 −1 0 1 2 y 3 −7 −9 −7 3 [3] (ii) On the grid below, draw the graph of y = x2 + 3x − 7 for −5 Y x Y 2. For y Examiner's Use 4 2 x –5 –4 –3 –2 –1 0 1 2 A –2 –4 –6 –8 –10 [4] (c) (i) Use your graph to find the solutions to the equation x2 + 3x − 7 = 0. Answer(c)(i) x = or x = [2] (ii) Find the length of the rectangle in part (a). Answer(c)(ii) cm [1] (d) The point A(1, −1) is marked on the grid. (i) Draw a straight line through A with a gradient of 2. [1] (ii) Write down the equation of this line in the form y = mx + c. Answer(d)(ii) y = [2]

16 marks

Mark scheme: 8 (a) (i) x + 3 B1 (ii) x (x + 3) or x² +3x B1 ft from their (a)(i) (iii) x² +3x = 7 x² +3x - 7 = 0 E1 both lines seen (b) (i) -3, -9, -3 B3 B1, B1, B1 (ii) 8 points correctly plotted P3 ft P2ft or 6 or 7, P1ft for 4 or 5 (+/- 1/2 small square) smooth curve C1 (must go below y = -9) IGCSE – May/June 2008 0580/0581 03 (c) (i) 1.5 to 1.6 B1 ft -4.5 to -4.6 B1 ft ft is their intersections with the x-axis (ii) 4.5 to 4.6 B1 ft ft is their positive (c)(i) + 3 (d) (i) correct line L1 long enough to cross y axis (+/- 1/2 small square) (ii) (y =) 2x - 3 B1,B1ft B1 for 2 (as coefficient of x) B1 ft for their intersection with the y-axis [16]

This question in 0580/31 May/June 2008

9 In this question, all construction arcs must be shown clearly. For Examiner's Jalal buys an area of land on which to build a school. Use The land, ABCDE, is in the shape of a polygon with 5 sides. (a) Write down the mathematical name of this polygon. Answer(a) [1] (b) Jalal starts to make an accurate plan of the land, as shown below. He uses a scale of 1 centimetre to represent 10 metres. D A m 45 m B C 70 m (i) The actual lengths of AB and BC are written on the plan. Write the actual length of CD on the plan. [1] (ii) Use compasses to find the point E such that AE = 64 m and DE = 58 m. Draw the lines AE and DE. [2] (c) The land is to be divided into distinct regions. For Examiner's Construct, using a straight edge and compasses only, Use (i) the perpendicular bisector of BC, [2] (ii) the bisector of angle ABC. [2] (d) The music department building will be nearer to B than to C and nearer to BC than to BA. Write a letter M on the plan where the music department could be. [1] (e) The school gate, PQ, will be 8 metres wide. It will lie along AB so that AP = QB. Mark P and Q accurately on the plan. [2]

11 marks

Mark scheme: 9 (a) Pentagon B1 (b) (i) 61 to 63 B1 (ii) AE = 6.3 to 6.5 cm and DE = 5.7 to 5.9 cm B1 correct arcs seen B1 accept concave polygon SC1 if lengths reversed and with arcs (c) (i) perpen.bisector of BC B1 +/- 1mm and +/- 1 degree accuracy correct arcs seen B1 (ii) bisector of angle ABC B1 +/- 1 degree accuracy correct arcs seen B1 (d) "M" correctly marked B1 dep. on at least first B1 in each part of (c) (e) 2 marks 0.8 (+/-0.1) apart B1 1.85 (+/-0.1) from A and B B1 [11]

This question in 0580/31 May/June 2008

7 (a) Complete the table of values for the equation y = x2 + x − 3. For Examiner's Use x −4 −3 −2 −1 0 1 2 3 y 9 −1 −3 −1 9 [3] (b) On the grid, draw the graph of y = x2 + x − 3. y 10 9 8 7 6 5 4 3 2 1 x –4 –3 –2 –1 0 1 2 3 –1 –2 –3 –4 [4] (c) Write down the coordinates of the lowest point of the curve. Answer(c) ( , ) [2] (d) (i) Draw the line of symmetry of the graph. [1] (ii) Write down the equation of the line of symmetry. Answer(d)(ii) [1]

11 marks

Mark scheme: y 7 (a) 3, −3, 3 W3 W1 for each correct value (b) 8 correctly plotted points W3ft W2 for 6 or 7 points, W1 for 4 or 5 points Smooth curve W1 Half square accuracy must go below line y = −3 (c) ( −0.5, −3.25) W2ft W1 for one coordinate correct Ft their graph but −1 < x < 0 and y < −3 Allow calculated if exact values (W2 or W1) (d) (i) Line x = −0.5 drawn W1cao Half square accuracy (ii) x = −0.5 oe W1ft Ft any vertical line only

This question in 0580/31 Oct/Nov 2008

4 (a) Garcia and Elena are each given x dollars. For Examiner's (i) Elena spends 4 dollars. Use Write down an expression in terms of x for the number of dollars she has now. Answer(a)(i) $ [1] (ii) Garcia doubles his money by working and then is given another 5 dollars. Write down an expression in terms of x for the number of dollars he has now. Answer(a)(ii) $ [1] (iii) Garcia now has three times as much money as Elena. Write down an equation in x to show this. Answer(a)(iii) [1] (iv) Solve the equation to find the value of x. Answer(a)(iv) x = [3] (b) Solve the simultaneous equations 3x – 2y = 3, x + 4y = 8. Answer(b) x = y = [3]

9 marks

Mark scheme: 4 (a) (i) x − 4 1 (ii) 2x + 5 1 Allow x + x + 5 (iii) ‘2x + 5’ = 3 × ‘(x − 4)’ oe 1ft Only ft linear expressions in x. (iv) (x =) 17 www 3cao M1 ‘3x − 12’ M1 indep px = q Reducing their equation to a single term in x and a single constant. (b) (x =) 2, (y =) 1.5 3 M1 for complete correct method A1 for 1 correct answer ww both correct W3 ww one correct W0 Multiply and add/subtract. 2 terms correct. Eliminate x: subtract + 2 terms right Eliminate y: add + 2 terms right. Substitution M1 for 3(8 − 4y) − 2y = 3 or 3 x − 3 8 − x ) = 3 or x + 4( ) = 8 or 3x − 2( 2 4 3 − 2 y 3 + 2 y ( ) + 4y = 8 or ( ) = 8 − 4y or 3 3 3 x ± 3 8 ± x ( ) = ( ) or better. 2 4

This question in 0580/31 May/June 2009

3 For 6 (a) Complete the table of values for the function y = , x ≠ 0. Examiner's x Use x −3 −2.5 −2 −1.5 −1 −0.5 −0.3 0.3 0.5 1 1.5 2 2.5 3 y −1 −1.2 −2 −3 −6 3 2 1.5 1 [3] 3 (b) On the grid below, draw the graph of y = for −3 Y x Y −0.3 and 0.3 Y x Y 3. x y 10 9 8 7 6 5 4 3 2 1 x –3 –2 –1 0 1 2 3 –1 –2 –3 –4 –5 –6 –7 –8 –9 [5] –10 3 For (c) Use your graph to solve the equation = 7. Examiner's x Use Answer(c) x = [1] 2 x (d) Complete the table of values for y = − 1 . 3 x −3 0 3 y [2] 2 x (e) On the grid, draw the straight line y = − 1 for −3 Y x Y 3. [2] 3 2 x (f) Write down the co-ordinates of the points where the line y = − 1 intersects 3 3 the graph of y = . x Answer(f) ( , ) and ( , ) [2]

15 marks

Mark scheme: 6 (a) –1.5 –10 10 6 1.2 3 B2 for 3 or 4 correct, B1 for 2 correct (b) 14 points plotted accurately P3ft P2ft for 11, 12 or 13 points, P1ft for 8, 9 or 10 2 smooth correct curves C1 No part across y-axis B1 Indep (c) 0.4 to 0.5 1 (d) −3 −1 1 2 B1 for 2 correct (e) Ruled line from (−3, −3) to (3, 1) 2 SC1 for freehand or short ruled line – must meet curve twice or P1 for their 3 points plotted (f) (−1.5, −2) and (3, 1) 1, 1

This question in 0580/31 May/June 2010

7 Alex has d dollars to spend. For He buys a book which costs $9 less than 2 times d. Examiner's Use (a) Write down an algebraic expression, in terms of d, for the cost of the book. Answer(a) $ [2] (b) The actual cost of the book is $7.80. Find the value of d. Answer(b) d = [2] (c) How much does Alex have left after buying the book? Answer(c) $ [1]

5 marks

Mark scheme: 7 (a) 2d – 9 2 SC1 for 9 – 2d (b) 8.4(0) 2 M1 for their (a) = 7.8(0) (c) 0.6(0) 1ft ft their (b) – 7.80, only if positive

This question in 0580/33 Oct/Nov 2010

9 For Examiner's Use Diagram 1 Diagram 2 Diagram 3 Diagram 4 Diagram 5 The Diagrams above form a pattern. (a) Draw Diagram 5 in the space provided. [1] (b) The table shows the numbers of dots in some of the diagrams. Complete the table. Diagram 1 2 3 4 5 10 n Number of dots 3 5 [5] (c) What is the value of n when the number of dots is 737? Answer(c) [2] (d) Complete the table which shows the total number of dots in consecutive pairs of diagrams. For example, the total number of dots in Diagram 2 and Diagram 3 is 12. Diagrams 1 and 2 2 and 3 3 and 4 4 and 5 10 and 11 n and n + 1 Total number of 8 12 16 dots [3]

11 marks

Mark scheme: 9 (a) Diagram drawn 1 (b) 7, 9, 11 2 B1 for 2 correct 21 1 2n + 1 oe 2 SC1 for 2n + or – any integer (c) 368 2ft Must be integer for 2 marks M1 for their 2n + 1 = 737 ft if linear (d) 20, 44, 1, 1 4(n + 1) oe 1

This question in 0580/33 May/June 2011

11 For Examiner's Use Diagram 1 Diagram 2 Diagram 3 The diagrams show a sequence of shapes. (a) On the grid, draw Diagram 4. [1] (b) Complete the table showing the number of lines in each diagram. Diagram (n) Number of lines 1 6 2 11 3 4 5 [3] (c) Work out the number of lines in Diagram 8. Answer(c) [1] (d) Write down an expression, in terms of n, for the number of lines in Diagram n. Answer(d) [2] (e) Work out the number of lines in Diagram 100. Answer(e) [1] (f) The number of lines in Diagram p is 66. Find the value of p. Answer(f) p = [2]

10 marks

Mark scheme: 11 (a) Correct shape drawn 1 (b) 16, 21, 26 3 B1 for each SC1 “their 16” + 5 SC1 “their 21” + 5 (c) 41 1 (d) 5n + 1 2 B1 for 5n, B1 for +1 (e) 501 1ft Their (d) if linear (f) 13 2ft Their (d) if linear B1 for their (d) = 66

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

5 For Examiner's Use Diagram 1 Diagram 2 Diagram 3 Diagram 4 The number of crosses in each Diagram forms a sequence. (a) On the grid draw Diagram 4. [1] (b) Write down the number of crosses needed to draw Diagram 5. Answer(b) [1] (c) Diagram 1 has 1 row of 3 crosses. Diagram 2 has 2 rows of 4 crosses. (i) Complete this statement for Diagram n. Diagram n has n rows of crosses. [1] (ii) Write down, in terms of n, how many crosses are needed to draw Diagram n. Answer(c)(ii) [1] (iii) Find the number of crosses needed to draw Diagram 20. Answer(c)(iii) [1]

5 marks

Mark scheme: their (a)(i) (b) 5 1ft Ft is 34 (c) Said by 1.5 secs 3ft ' their (a)(ii)' M1ft (= 32.5) 4 ' their (a)(ii)' M1ft 34 – (34 – 32.5) 4 120 120 (d) (i) 67.4° 2 M1 ‘tan’= or ‘sin’= 50 their 130 50 or ‘cos’= their 130 (ii) 113° or 112.6° 1ft 180 – ‘their (d)(i)’

This question in 0580/31 May/June 2012

5 (a) A = 1 (a + b)h Examiner'sFor 2 Use Work out the value of A when a = 9.6, b = 12.4 and h = 7.5 . Answer(a) [2] (b) (i) Expand x(x2 – 3y). Answer(b)(i) [2] (ii) Expand and simplify 4(2w – 3) + 5(w – 2). Answer(b)(ii) [2] (c) A quadrilateral has sides x, 2x, y and 3y. (i) Write down and simplify a formula for the perimeter, p, of the quadrilateral. Answer(c)(i) p = [2] (ii) Make y the subject of the formula in part (c)(i). For Examiner's Use Answer(c)(ii) y = [2] (d) Joseph is 3 times as old as Amy. In 5 years time Joseph will be 2 times as old as Amy. (i) Amy is now n years old. Write down an equation in n connecting the ages of Joseph and Amy in 5 years time. Answer(d)(i) [2] (ii) Solve the equation to find n. Answer(d)(ii) n = [3]

15 marks

Mark scheme: 15 (a) 82.5 2 M1 for 2 (9.6 + 12.4) × 7.5 or better (b) (i) x3 − 3xy final ans 2 B1 for x 3 or −3xy seen (ii) 13w − 22 final ans 2 B1 for 13w or −22 or 8w − 12 or 5w − 10 seen (c) (i) (p =) 3x + 4y final ans 2 B1 for 3x or 4y seen or x + 2x + y + 3y seen p−3x 2ft p 3 x (ii) (y =) 4 oe B1ft for 4y = p − 3x or = + y 4 4 (d) (i) 2(n + 5) = 3n + 5 oe 2 B1 for 2(n + 5) or 2n + 10 or 3n + 5 seen or B1 for any different letter to n in 2(n + 5) = 3n + 5 oe (ii) (n =) 5 cao 3 M1 for clearing bracket M1 for an = b

This question in 0580/32 May/June 2012

10 The Patterns shown below form a sequence. For Examiner's Pattern 1 has 6 dots and 6 lines. Use Pattern 2 has 10 dots and 11 lines. Pattern 1 Pattern 2 Pattern 3 Pattern 4 (a) On the grid, draw Pattern 4. [1] (b) (i) Find the number of dots in Pattern 5. Answer(b)(i) [1] (ii) Explain how you worked out your answer in part (b)(i). Answer(b)(ii) [1] (c) Write down an expression, in terms of n, for the number of dots in Pattern n. Answer(c) [2] (d) The number of dots in Pattern n is 62 . Find n. Answer(d) n = [2]

7 marks

Mark scheme: 10 (a) correct pattern 1 (b) (i) 22 1 (ii) add 4 1 must have 4 with a direction, accept plus 4 (c) 4n + 2 or 4(n – 1) + 6 oe 2 B1 for 4n + j or kn + 2 (k ≠ 0) seen (d) 15 cao 2 M1 their (c) = 62 or multiple additions or subtractions

This question in 0580/33 May/June 2012

2 Three children have some marbles. For Examiner′s Shireen has m marbles. Use Nazaneen has three times as many marbles as Shireen. Karly has 4 more marbles than Shireen. (a) Write down an expression, in terms of m, for (i) the number of marbles Nazaneen has, Answer(a)(i) … [1] (ii) the number of marbles Karly has. Answer(a)(ii) … [1] (b) The three children have a total of 84 marbles between them. (i) Write down an equation in m. Answer(b)(i) … [1] (ii) Solve your equation. Answer(b)(ii) m = … [2] (c) Shireen weighs the 84 identical marbles. Their total weight is 4.2 kg. Calculate, in grams, the weight of one marble. Answer(c) … g [2] (d) The children now decide to share the 84 marbles in the ratio Shireen : Nazaneen : Karly = 2 : 7 : 3 . Calculate the number of marbles each receives. Answer(d) Shireen … Nazaneen … Karly … [3] _____________________________________________________________________________________

10 marks

Mark scheme: 2 (a) (i) 3m 1 (ii) m + 4 1 (b) (i) m + 3m + m + 4 = 84 oe isw 1ft ft m + (a)(i) + (a)(ii) = 84 if and only if (a)(i) and (a)(ii) are both in terms of m (ii) 16 2 M1ft for “5”m = “80” i.e. pm = q (could be seen in bi) May be implied by a correct answer (c) 50 2 M1 for 4.2/84 × 1000 or better SC1 for figs ‘5’ or 4200 seen (d) [Shireen =] 14 1 if M0 then M1 for 84/(2 + 7 + 3) or [Nazaneen =] 49 1 better [Karly =] 21 1 and / or SC1 3 correct answers in wrong order. IGCSE – May/June 2013 0580 32

This question in 0580/32 May/June 2013

8 (a) Simplify the following expressions. For Examiner′s Use (i) 3m – 5m + 6m Answer(a)(i) … [1] (ii) 5e – 4f – 3e – 6f Answer(a)(ii) … [2] (b) s = u + at (i) Calculate the value of s when u = 27, a = –2 and t = 15. Answer(b)(i) s = … [2] (ii) Make t the subject of the formula s = u + at. Answer(b)(ii) t = … [2] (c) Solve the simultaneous equations. 5x + 2y = 4 4x – y = 11 Answer(c) x = … y = … [3] _____________________________________________________________________________________

10 marks

Mark scheme: 8 (a) (i) 4m 1 (ii) 2e – 10f 2 B1 for ae – 10f or 2e ± bf (a,b ≠ 0) (b) (i) –3 2 M1 for 27 + (–2) × 15 or better (ii) s − u s u 2 M1 first step correct [t=] or − a a a SC1 for s – u ÷ a www (c) [x =] 2, [y =] –3 3 M1 for correct method to eliminate one variable. A1 for x or y correct IGCSE – May/June 2013 0580 33

This question in 0580/33 May/June 2013

3 (a) Sweets are sold in packets. For Examiner′s There are n sweets in each packet. Use (i) Maya has 4 packets of sweets and 21 extra sweets. Write an expression, in terms of n, for the number of sweets Maya has. Answer(a)(i) … [1] (ii) Tassos has 5n + 3 sweets. Roma has 3n + 27 sweets. Tassos and Roma each have the same number of sweets. Write down an equation, in terms of n, and solve it. Answer(a)(ii) n = … [3] (iii) Work out the number of sweets Tassos and Roma have altogether. Answer(a)(iii) … [1] (b) A different packet of sweets contains 6 red sweets, 10 yellow sweets and 4 green sweets. Simon takes one sweet from the packet at random. (i) Write down the colour of sweet Simon is most likely to take. Answer(b)(i) … [1] (ii) On the probability scale, draw an arrow to show the probability that Simon’s sweet is yellow. 0 1 [1] (iii) Write down the probability that Simon’s sweet is green. Answer(b)(iii) … [1] (iv) Write down the probability that Simon’s sweet is red or yellow. Answer (b)(iv) … [1] _____________________________________________________________________________________

9 marks

Mark scheme: 3 (a) (i) 4n + 21, final answer 1 (ii) 5n + 3 = 3n + 27 1 [n =] 12 2 M1 for 5n – 3n = 27 – 3 or better (iii) 126 1FT (b) (i) yellow 1 (ii) arrow pointing at 0.5 1 4 (iii) o.e. or 0.2 or 20% 1 20 16 (iv) o.e. or 0.8 or 80% 1FT SC1 for 4 out of 20 and 16 out of 20 20 IGCSE – October/November 2013 0580 32

This question in 0580/32 Oct/Nov 2013

6 (a) Complete the table of values for y = x2 + 2x – 3 . x –4 –3 –2 –1 0 1 2 3 4 y 0 –3 –4 –3 0 5 21 [2] (b) On the grid, draw the graph of y = x2 + 2x – 3 for –4 Ğ x Ğ 4 . y 25 20 15 10 5 x –4 –3 –2 –1 0 1 2 3 4 –5 [4] (c) On the grid, draw the line y = 10 . [1] (d) Use your graphs to solve the equation x2 + 2x – 3 = 10 for –4 Y x Y 4 . Answer(d) x = … [1] __________________________________________________________________________________________

8 marks

Mark scheme: 6 (a) 5 12 2 B1, B1 (b) 9 points plotted correctly 3FT B2FT for 7 or 8 points correctly plotted B1FT for 5 or 6 points correctly plotted correct smooth curve through all 1 9 correct points (c) correct ruled line 1 minimum length must touch y axis and curve (d) 2.7 to 2.8 1FT FT their curve and ruled line IGCSE – May/June 2014 0580 32

This question in 0580/32 May/June 2014

7 Today it is Simon’s birthday. (a) Simon is x years old. Katy is twice as old as Simon. Bob is 8 years younger than Simon. (i) Write expressions, in terms of x, for the ages of Katy and Bob. Answer(a)(i) Katy … Bob … [2] (ii) The sum of their three ages is 40 years. Write an equation in terms of x. Answer(a)(ii) … [1] (iii) Solve your equation for x. Answer(a)(iii) x = … [2] (b) Simon’s birthday cake weighs 600 grams. 1 He eats of the cake. 8 Katy eats 25% of the cake. Bob eats 0.3 of the cake. Find the weight of the cake that is left. Answer(b) … g [4] (c) Aunty Millie gives Simon $150 for his birthday. He invests the money in a bank at a rate of 6% per year compound interest. Calculate the total amount Simon will have after 3 years. Answer(c) $ … [3] (d) One of Simon’s presents is a bag of sweets. He decides to eat the sweets in a sequence. On day 1 he eats 1 sweet, on day 2 he eats 5 sweets, on day 3 he eats 9 sweets and so on. (i) Describe in words the rule for continuing the sequence 1, 5, 9, 13, 17 … . Answer(d)(i) … [1] (ii) Write down an expression for the number of sweets he eats on day n. Answer(d)(ii) … [2] __________________________________________________________________________________________

15 marks

Mark scheme: 7 (a) (i) 2x 1, 1 x – 8 (ii) x + 2x + x – 8 = 40 or better 1FT FT if algebraic (iii) 12 cao 2 M1 FT for ax = b and a and b not zero (b) 195 cao 4 B1 for 75 B1 for 150 B1 for 180 (c) 178.65 3 M2 for 150 × 1.063 oe or 178.7 or or 179 M1 for 150 × 1.06 × 1.06 (d) (i) Add 4 oe 1 (ii) 4n – 3 oe, final answer 2 M1 for 4n + k (k not -3), qn–3 (q not 0 or 4) seen

This question in 0580/33 May/June 2014

4 Three friends are going on holiday. They travel by plane. (a) Ahmed’s suitcase has mass m kilograms. (i) The mass of Sonia’s suitcase is 5 kg more than the mass of Ahmed’s suitcase. Write down an expression, in terms of m, for the mass of Sonia’s suitcase. Answer(a)(i) … kg [1] (ii) The mass of Hala’s suitcase is twice the mass of Ahmed’s suitcase. Write down an expression, in terms of m, for the mass of Hala’s suitcase. Answer(a)(ii) … kg [1] (iii) The total mass of the three suitcases is 47 kg. Write down an equation in terms of m. Answer(a)(iii) … [1] (iv) Solve your equation and find the mass of each suitcase. Answer(a)(iv) Ahmed’s suitcase … kg Sonia’s suitcase … kg Hala’s suitcase … kg [3] (b) Each friend carries one bag of hand luggage onto the plane. (i) The rule for the maximum size of each bag of hand luggage is length + width + height  115 cm. The measurements of Ahmed’s bag are shown in the table. Length Width Height 550 mm 395 mm 200 mm Can Ahmed carry this bag onto the plane? Explain your answer. Answer(b)(i) … because … … [2] (ii) The mass of Ahmed’s bag is 5 kg, correct to the nearest kilogram. Write down the upper bound of the mass of his bag. Answer(b)(ii) … kg [1] (c) The friends change money from dollars into euros (€) to spend on holiday. The exchange rate is $1 = €0.68 . (i) Sonia changes $150 into euros. Work out how many euros she receives. Answer(c)(i) € … [1] (ii) Hala pays €25.50 for a meal. Work out how much this is in dollars. Answer(c)(ii) $ … [2] __________________________________________________________________________________________

12 marks

Mark scheme: 4 (a) (i) m + 5 1 (ii) 2m 1 (iii) m + m + 5 + 2m = 47 isw 1FT FT m + their (a)(i) + their (a)(ii) = 47 isw or 4m + 5 = 47 isw (iv) 10.5 3 M1FT for correct first step to solve their (a)(iii) 15.5 A1FT for m = 10.5 21 (b) (i) Yes, [total = ] 114.5 [cm] 2 M1 for 55 + 39.5 + 20 oe or for 1145 mm (ii) 5.5 1 (c) (i) 102 1 (ii) 37.5[0] 2 M1 for 25.5[0] ÷ 0.68

This question in 0580/31 Oct/Nov 2015

9 A sequence of patterns is made from lines and dots. The first three patterns in the sequence are shown. Pattern 1 Pattern 2 Pattern 3 Pattern 4 (a) Draw Pattern 4 on the grid. [1] (b) Complete the table. Pattern 1 2 3 4 10 Number of dots 2 3 Number of lines 4 7 [4] (c) Find an expression, in terms of n, for (i) the number of dots in Pattern n, … [1] (ii) the number of lines in Pattern n. … [2] (d) One of these patterns has 76 lines. Work out how many dots are in this pattern. … [2]

10 marks

Mark scheme: 9 (a) 1 (b) 4 5 11 4 B1 for 11 10 13 31 B1 for 31 B2 for 4, 5, 10, 13 or B1 for two of 4, 5, 10, 13 (c) (i) n + 1 oe final answer 1 (ii) 3n + 1 oe final answer 2 B1 for 3n + k or cn + 1 c≠0 (d) 26 2 M1FT for their c(ii) = 76 or better or M1 implied by answer of 25

This question in 0580/32 Oct/Nov 2016

8 (a) Complete the table of values for y = x 2 - 2x . x - 3 - 2 - 1 0 1 2 3 4 y 3 - 1 3 [3] (b) On the grid, draw the graph of y = x 2 - 2x for - 3 G x G 4 . y 16 14 12 10 8 6 4 2 x 0 –3 –2 –1 1 2 3 4 –2 [4] (c) On the grid, draw the line y = 6 . [1] (d) Use your graph to solve the equation x 2 - 2x = 6 . Give your answers correct to 1 decimal place. x = … or x = … [2] Question 9 is printed on the next page.

10 marks

Mark scheme: 8 (a) 15 8 … 0 … 0 … 8 3 B1 for 8 and 8 in the correct place B1 for 0 and 0 in the correct place B1 for 15 in the correct place (b) Correct curve 4 B3FT for 7 or 8 correctly plotted points or B2FT for 5 or 6 correctly plotted points or B1FT for 3 or 4 correctly plotted points (c) Correct ruled line 1 (d) –1.8 or –1.7 or –1.6 2FT B1FT for one correct 3.6 or 3.7 or 3.8 or B1FT for both correct answers as co-ordinates or B1FT for both answers correct to more than 1dp

This question in 0580/33 Oct/Nov 2016

2 (a) Simplify. 5a + 6a - a … [1] (b) 3f – 4g NOT TO SCALE 5f + 2g Write an expression for the perimeter of the rectangle. Give your answer in its simplest form. … [3] (c) (i) Work out the value of 5x + 10 y when x = 7 and y = 9 . … [2] (ii) Work out the value of 4r 2 - pr when p = 3 and r = 5 . … [2] (d) Solve. 5 3x - 6 = 75 ^ h x = … [3] (e) Mr and Mrs Barker have three children, Molly, Dean and Raul. Age, in terms of x Molly’s age is x years x Dean is 5 years younger than Molly x - 5 Raul is 4 years older than Molly Mr Barker is 4 times older than Molly Mrs Barker is 6 years younger than Mr Barker (i) Complete the table with expressions in terms of x. [2] (ii) The total of the five ages is 125 years. Write down an equation in terms of x and show that it simplifies to 11x - 7 = 125 . [1] (iii) Solve the equation 11x - 7 = 125 to find Molly’s age. Molly’s age = … years [2]

16 marks

Mark scheme: 2(a) 10a final answer 1 2(b) 16f – 4g final answer 3 M2 for 2 × (5f + 2g) + 2×(3f − 4g) oe or or 4(4f – g) final answer B1 for 10f +4g or 6f −8g or 8f −2g or 16f + kg or kf – 4g 2(c)(i) 125 2 M1 for 5 × 7 + 9 × 10 or better 2(c)(ii) 85 2 M1 for 4 × 52 – 3 × 5 or better 2(d) 7 3 M1 for 15x – 30 [= 75] or 3x – 6 = 15 M1FT for correct second step 2(e)(i) x + 4 2 B1 for any two correct 4x 4x – 6 2(e)(ii) x + x–5 + x+4 + 4x + 4x–6 = 125 1 2(e)(iii) 12 2 7 125 M1 for 11x = 125 + 7 or x – = 11 11 or better

This question in 0580/32 May/June 2017

8 (a) Multiply out the brackets and simplify. 5 2x + 3 - 2 x + 4 ^ h ^ h … [2] (b) (i) An equilateral triangle has side length 2x. Write down an expression, in terms of x, for the perimeter of the triangle. Give your answer in its simplest form. … [1] (ii) A square has a perimeter of 20a. Write down an expression, in terms of a, for the length of one side of the square. Give your answer in its simplest form. … [1] (c) The diagram shows a rectangle. 3y + 1 NOT TO SCALE 2y + 5 Find an expression, in terms of y, for the perimeter of the rectangle. Give your answer in its simplest form. … [3] (d) One mint costs m cents. One toffee costs 6 cents more than one mint. The cost of 3 mints and 7 toffees is 182 cents. Write an equation, in terms of m, and solve it to find the cost of one mint. Cost of one mint = … cents [5]

12 marks

Mark scheme: 8(a) 8x + 7 final answer 2 B1 for 10x + 15 or –2x – 8 or 8x + j or kx + 7 as final answer 8(b)(i) 6x final answer 1 8(b)(ii) 5a final answer 1 8(c) 10y + 12 or 2(5y + 6) 3 M1 for 2(3y + 1) + 2(2y + 5) oe final answer B1 for 10y + j or ky + 12 (k≠0) 8(d) 7(m + 6) + 3m = 182 or 2 B1 for m + 6 7m + 42 + 3m = 182 or 7t + 3m = 182 14 3 M1 for 7m + 42 [+ 3m = 182] M1 for 7m + 3m = 182 − 42 or better OR M2 for [m=] (182 – (6 × 7)) / (7 + 3) or better or M1 for 182 – (6 × 7) or better

This question in 0580/31 Oct/Nov 2017

5 (a) A small box contains n biscuits. (i) A medium box contains 10 more biscuits than the small box. Write an expression, in terms of n, for the number of biscuits in the medium box. … [1] (ii) A large box contains twice as many biscuits as the medium box. Write an expression, in terms of n, for the number of biscuits in the large box. … [1] (iii) There are 52 biscuits in the large box. Write down an equation, in terms of n, and solve it. n = … [3] (iv) Olga buys a small box and a medium box of biscuits. How many biscuits does she have altogether? … [1] (b) In the large box, 13 of the 52 biscuits are chocolate. Leo takes a biscuit from the box at random. (i) Find the probability that Leo’s biscuit is chocolate. Give your answer as a fraction in its lowest terms. … [2] (ii) On the probability scale, draw an arrow to show the probability that Leo’s biscuit is not chocolate. 0 1 [1] (c) The mass of the large box of biscuits is 450 g. Work out the total mass of 6 large boxes of biscuits. Give your answer in kilograms. … kg [2] (d) The mass, m grams, of the small box of biscuits is 120 g, correct to the nearest 10 g. Complete the statement about the value of m. … G m 1 … [2]

13 marks

Mark scheme: 5(a)(i) n + 10 1 5(a)(ii) 2(n + 10) oe isw 1FT 5(a)(iii) their (ii) = 52 M1 16 final answer B2 M1 for 2n = 52 – 20 or n = 26 – 10 or better 5(a)(iv) 42 1FT FT 2 × their (iii) + 10 5(b)(i) 1 2 13 cao B1 for oe soi 4 52 5(b)(ii) 3 1 Correct arrow at 4 5(c) 2.7[00] 2 B1 for answer figs 27 or for 0.45 seen 5(d) 115 2 B1 for one correct or both values 125 correct but reversed

This question in 0580/33 Oct/Nov 2017

9 (a) Factorise. y2 + 8y … [1] (b) Expand the brackets and simplify. 3(2x – 1) – 4(x – 5) … [2] (c) Make p the subject of the formula k = 5m + 7p. p = … [2] (d) Solve the simultaneous equations. You must show all your working. 3x + 2y = 6 2x – 3y = 17 x = … y = … [4]

9 marks

Mark scheme: 9(a) y(y + 8) final answer 1 9(b) 2x + 17 final answer 2 B1 for 6x – 3 or –4x + 20 or 2x + j or kx + 17 as final answer 9(c) k − 5 m 2 k 5m oe final answer M1 for 7p = k – 5m or = + p 7 7 7 9(d) Correctly equating one set of coefficients M1 Correct method to eliminate one variable M1 Dependent on the coefficients being the same for one of the variables. Correct consistent use of addition or subtraction using their equations. x = 4 A1 y = –3 A1 If zero scored, SC1 if no working shown, but 2 correct answers given or SC1 for 2 values satisfying one of the original equations.

This question in 0580/33 Oct/Nov 2017

4 (a) Solve these equations. (i) 3x = 18 x = … [1] (ii) 8x - 15 = 6x + 2 x = … [2] (b) Factorise. 5x - 15 … [1] (c) Simplify. 2x - 6y + 3x + 2y … [2] (d) Find the value of 5u - 2v when u = 11 and v =- 3 . … [2] (e) Make p the subject of this formula. H = 7p - 3 p = … [2] (f) (i) Find the value of k when x 10 ' x k = x 3 . k = … [1] (ii) Find the value of n when y 10 # y n = 1. n = … [1]

12 marks

Mark scheme: 4(a)(i) 6 1 4(a)(ii) 8.5 2 M1 for 8x – 6x = 2 + 15 or better 4(b) 5(x – 3) final answer 1 4(c) 5x – 4y final answer 2 B1 for 5x + ky or kx – 4y (k could be 0) 4(d) 61 2 B1 for 55 or 6 or M1 for 5 × 11 – 2 × –3 4(e) H + 3 2 M1 for correct first step p = oe final answer 7 4(f)(i) 7 1 4(f)(ii) –10 1

This question in 0580/33 May/June 2018

5 Mrs Verma has a restaurant. In the restaurant each table has 8 chairs. Sometimes she puts tables together. The diagrams show how the tables are put together and the position of each chair (X). X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 1 table 2 tables 3 tables 4 tables The pattern of tables and chairs forms a sequence. (a) Draw the diagram for 4 tables. [1] (b) Complete the table. Number of 1 2 3 4 5 6 tables (t) Number of 8 10 12 chairs (c) [2] (c) Find a formula for the number of chairs, c, in terms of the number of tables, t. c = … [2] (d) 18 tables are put together in this way. Work out the number of chairs needed. … [2] (e) Work out the number of tables, put together in this way, when 80 chairs are needed. … [2]

9 marks

Mark scheme: 5(a) 4 tables and 14 chairs correctly drawn 1 5(b) 14, 16, 18 2 B1 for 2 correct or k, k + 2, k + 4 5(c) 2t + 6 oe final answer 2 B1 for 2t + j or kt + 6 , k ≠ 0 5(d) 42 cao 2 M1 for 18 correctly substituted into their (c) , provided a linear expression 5(e) 37 cao 2 M1 for their (c) = 80

This question in 0580/32 Feb/March 2019

6 (a) Complete the table of values for y = x 2 - 5x + 3 . x −1 0 1 2 3 4 5 6 y −1 −3 −3 −1 3 [2] (b) On the grid, draw the graph of y = x 2 - 5x + 3 for - 1 G x G 6 . y 10 9 8 7 6 5 4 3 2 1 x – 1 0 1 2 3 4 5 6 – 1 – 2 – 3 – 4 [4] (c) Use your graph to solve the equation x 2 - 5x + 3 = 0 . x = … or x = … [2]

8 marks

Mark scheme: 6(a) 9, 3, 9 2 B1 for two correct 6(b) Correct curve 4 B3FT for 7 or 8 correctly plotted points or B2FT for 5 or 6 correctly plotted points or B1FT for 3 or 4 correctly plotted points 6(c) 0.6 to 0.8, 4.2 to 4.4 2 FT their curve B1 for each

This question in 0580/32 Oct/Nov 2019

9 (a) c = 5 a - 2b (i) Find the value of c when a = 8 and b = −3. … [2] (ii) Make a the subject of the formula c = 5 a - 2 b . a = … [2] (b) Factorise 3x + 12 . … [1] (c) Expand x (2 y + x) . … [2] (d) Cara has n pencils. Alice has twice as many pencils as Cara. Leon has three more pencils than Alice. The three children have a total of 58 pencils. Use this information to write down an equation and solve it to find the value of n. n = … [4]

11 marks

Mark scheme: 9(a)(i) 46 2 M1 for 5 × 8 – 2 × –3 or better 9(a)(ii) c + 2b c 2b 2 c 2b oe or + oe M1 for c + 2b = 5a oe or = a − oe 5 5 5 5 5 final answer 9(b) 3(x + 4) final answer 1 9(c) 2xy + x2 final answer 2 B1 for 2xy or x2 or for 2xy + x2 not as final answer 9(d) n + 2n + 2n + 3 = 58 4 M2 for any correct equation which would or 5n + 3 = 58 lead to 5n + 3 = 58 leading to [n = ] 11 or B1 for 2n or 2n + 3 seen M1 for 5n = 55 or for rearranging their linear equation to an = b B1 for [n =]11

This question in 0580/32 Oct/Nov 2019

5 (a) T = 3a 2 b Find the value of T when a = 4 and b = 5. T = … [2] (b) (i) Multiply out the brackets. x ( 3 - 5 x) … [2] (ii) Factorise fully. 5x - 20x 2 … [2] (c) NOT TO SCALE 3a + b 4a - 5b a + 2b Find an expression for the perimeter of this triangle. Give your answer in its simplest form. … [3]

9 marks

Mark scheme: 5(a) 240 2 M1 for 3 × 42 × 5 oe 5(b)(i) 3x – 5x2 final answer 2 B1 for 3x or – 5x2 5(b)(ii) 5x(1 – 4x) final answer 2 B1 for 5(x – 4x2) or x(5 – 20x) 5(c) 8a – 2b 3 M1 for 3a + b + 4a – 5b + a + 2b B1 for 8a or – 2b

This question in 0580/32 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) Write down the mathematical name for this (i) quadrilateral, … [1] (ii) solid. … [1] (b) The area of a square is 64 cm2. Work out the length of one side of the square. … cm [1] (c) The length, l, of a rectangle is 3 cm longer than the width, w. The perimeter of the rectangle is 26 cm. Calculate the length, l, and the width, w. l = … cm w = … cm [3] (d) A cuboid measures 6 cm by 3 cm by 1 cm. (i) On the 1 cm2 grid, draw an accurate net of this cuboid. One face has been drawn for you. [3] (ii) Calculate the surface area of the cuboid. … cm2 [2]

11 marks

Mark scheme: 3(a)(i) Trapezium 1 3(a)(ii) Cylinder 1 3(b) 8 1 3(c) 8 3 M2 for 4w = 20 oe 5 or M1 for w + w + 3 + w + w + 3 = 26 oe If 0 scored, SC2 for correct answers reversed or SC1 for 2 answers where l + w = 13 3(d)(i) Correct net 3 B2 for 4 more correct faces in correct position or B1 for 2 or 3 more correct faces in correct position 3(d)(ii) 54 2 M1 for [2 ×] (6 × 3 + 6 × 1 + 3 × 1) oe

This question in 0580/32 Oct/Nov 2020

3 (a) Complete the table of values for y = 1 + 5 x - x 2 . x - 1 0 1 2 3 4 5 y 1 5 7 1 [2] (b) On the grid, draw the graph of y = 1 + 5x - x 2 for - 1 G x G 5 . y 8 6 4 2 0 x – 1 1 2 3 4 5 – 2 – 4 – 6 [4] (c) (i) On the grid, draw the line y = 3 . [1] (ii) Use your line to solve the equation 1 + 5x - x 2 = 3 . x = … or x = … [2]

9 marks

Mark scheme: 3(a) –5, 7, 5 2 B1 for 2 correct 3(b) Correct curve 4 B3FT for 6 or 7 points correctly plotted or B2FT for 4 or 5 points correctly plotted or B1FT for 2 or 3 points correctly plotted 3(c)(i) Ruled line y = 3 1 3(c)(ii) 0.3 to 0.6 4.4 to 4.7 2 FT their y = k and their (b) B1 for one correct or B1 for both correct answers as coordinates

This question in 0580/33 Oct/Nov 2020

9 A sequence of patterns is made using black counters and white counters. Pattern 1 Pattern 2 Pattern 3 Pattern 4 (a) Draw Pattern 4. [1] (b) Complete the table. Pattern 1 2 3 4 5 Number of black counters 4 6 8 Number of white counters 1 4 9 [2] (c) Write an expression, in terms of n, for (i) the number of black counters in Pattern n, … [2] (ii) the number of white counters in Pattern n. … [1] (d) Elena has 30 black counters and 140 white counters. Can she make Pattern 12 using her counters? Explain your answer. … because … … [2]

8 marks

Mark scheme: 9(a) 1 9(b) 10 12 2 B1 for 2 or 3 correct 16 25 9(c)(i) 2n + 2 oe final answer 2 B1 for 2n + c or kn + 2, (k ≠ 0) as final answer or for 2n + 2 seen then spoilt 9(c)(ii) n2 1 9(d) No 2 M1 for 12 substituted into their 2n + 2 or with a correct supporting reason their n2 or 26 [black] or 144 [white] or 140 = 11.8... [white]

This question in 0580/33 Oct/Nov 2020

5 (a) Simplify. 5a - 3b + 7a + 2b … [2] (b) Find the value of 8x - 3y when x = 5 and y =- 2 . … [2] (c) Solve. 6x - 3 = 2x + 8 x = … [2] (d) P = t6 - 11 Make t the subject of this formula. t = … [2] (e) Solve the simultaneous equations. You must show all your working. 3x - 4y = 30 2x + 5y =- 3 x = … y = … [4]

12 marks

Mark scheme: 5(a) 12a – b final answer 2 B1 for 12a or – b in final answer or for correct answer spoilt 5(b) 46 2 M1 for 8 × 5 – 3 × −2 or B1 for 40 or [+] 6 5(c) 2.75 or 2 34 2 M1 for 6x – 2x = 3 + 8 or better 5(d) P + 11 2 P 11 [t =] oe final answer M1 for P + 11 = 6t or = t − 6 6 6 5(e) Correctly equating one set of coefficients M1 Correct method to eliminate one variable M1 Dependent on the coefficients being the same for one of the variables Correct consistent use of addition or subtraction using their equations [x =] 6 A1 [y =] −3 A1 If 0 scored, SC1 for two values that satisfy one of the original equations SC1 if no working shown, but 2 correct answers given

This question in 0580/32 Oct/Nov 2021

1 Roberto and his family fly from London to Los Angeles on a holiday. (a) The flight takes 11 hours 15 minutes. (i) The flight leaves London at 15 40 local time. The local time in Los Angeles is 8 hours behind the local time in London. Work out the local time in Los Angeles that the plane arrives. … [2] (ii) The plane flies a total of 8760 km. Calculate the average speed of the plane. … km/h [3] (b) Roberto hires a car. (i) The cost of hiring a car is $56 per day, plus a fixed cost of $436. Write down a formula for the cost, C dollars, of hiring a car for d days. … [2] (ii) Roberto is given a car at random. There are four colours of car. Colour Red Silver Black White Probability 0.17 0.24 0.3 Complete the table. [2] (c) The family visit a national park which has an area of 4986 km2. (i) Write 4986 correct to the nearest hundred. … [1] (ii) Write 4986 in standard form. … [1] (d) A ticket for the park costs $17.50 plus 8% tax. Calculate the amount of tax paid. $ … [1] (e) The scale drawing shows the positions of two viewing points, A and B, in the park. The scale is 1 centimetre represents 5 kilometres. North North B A Scale : 1 cm to 5 km (i) Work out the actual distance between point A and point B. … km [2] (ii) Point C is 20 km from point A on a bearing of 072°. On the scale drawing mark the position of point C. [2]

16 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 18 55 2 B1 for 07 40 or 02 55 or 3[h] 15 [min] or M1 for departure time + 11h 15 min −8h evaluated as a time with one interval correctly added 1(a)(ii) 779 or 778.6 to 778.7 3 8760 M2 for 8760 ÷ 11.25 oe × 60 675 or B1 for 11.25 or M1 for 8760 ÷ their time 1(b)((i) C = 56d + 436 cao 2 B1 for C = 56d + 436 seen and spoilt or 56d + 436 as final answer 1(b)(ii) 0.29 2 M1 for 1 – (0.17 + 0.24 + 0.3) oe or better 1(c)(i) 5000 1 1(c)(ii) 4.986 × 103 1 1(d) 1.4[0] 1 1(e)(i) 35 2 B1 for 7 1(e)(ii) Correct length and bearing 2 B1 for length 4 cm from A B1 for bearing 072° from A

This question in 0580/33 Oct/Nov 2021

7 (a) Simplify. 5g - 3h - 7g + 6h … [2] (b) j = 4k + 7m Find the value of j when k =- 5 and m = 6 . j = … [2] (c) Factorise completely. 14x 3 + 49x … [2] (d) Solve. 8 ( 3t - 9) = 108 t = … [3] (e) (i) 9 24 ' 9 w = 9 5 Find the value of w. w = … [1] (ii) 4x 2 = 256 Find the value of x. x = … [1] (f) Ranjit’s age is x years. Suzi’s age is 3 times Ranjit’s age. Juan’s age is 4 years more than Suzi’s age. The total of their ages is 46 years. Use this information to write down an equation and solve it to find the value of x. x = … [4]

15 marks

Mark scheme: 7(a) –2g +3h final answer 2 B1 for –2g or 3h in final answer or –2g+ 3h seen then spoilt 7(b) 22 2 M1 for 4  –5 + 7  6 or B1 for –20 or [+]42 7(c) 7x(2x2 + 7) final answer 2 B1 for 7(2x3 +7x) or x(14x2 + 49) or correct answer seen then spoilt 7(d) 7.5 3 M1 for a first correct step 24t – 72 = 108 or 3t –9 =13.5 M1FT for a second correct step e.g. 24t =180 or 3t =22.5 7(e)(i) 19 1 7(e)(ii) 8 1 7(f) x + 3x + 3x + 4 = 46 4 M2 for a correct equation which would or 7x + 4 = 46 lead to 7x + 4 = 46 leading to x = 6 or B1 for 3x or 3x + 4 seen M1 for 7x = 42 or for rearranging their equation to ax = b B1 for [x =] 6

This question in 0580/31 Oct/Nov 2022

5 The grid shows the first three diagrams in a sequence. Each diagram is made using sticks. Diagram 1 Diagram 2 Diagram 3 (a) On the grid, draw Diagram 4. Diagram 4 [1] (b) Complete the table. Diagram number 1 2 3 4 5 Number of sticks 5 9 13 [2] (c) (i) Find an expression, in terms of n, for the number of sticks in Diagram n. … [2] (ii) One of the diagrams has 73 sticks. Work out its Diagram number. Diagram … [2] (d) (i) Show that the total number of sticks needed to make the first 3 diagrams is 27. [1] (ii) The total number of sticks needed to make the first k diagrams is 2k 2 + 3k . Show that this expression gives the correct total number of sticks needed to make the first 3 diagrams. [2] (iii) Tobias wants to make the first 10 diagrams. He has already made the first 3 diagrams. He has 240 sticks left to make the remaining 7 diagrams. Work out how many sticks he has left when all 10 diagrams are made. … [4]

14 marks

Mark scheme: 5(a) Correct diagram drawn 1 5(b) 17, 21 2 B1 for each If B0 scored, SC1 for k , k  4 5(c)(i) 4 n  1 oe final answer 2 B1 for 4 n  k or an  1 , a  0 as final answers or for 4 n  1 oe seen and spoilt 5(c)(ii) 18 nfww 2 M1 for 4 n 1 73 or better or M1 for their(c)(i) = 73 5(d)(i) 5  9  13   27  1 5(d)(ii) 2  32 3 3 2 M1 for 2  32 3 3 leading to 27 as final answer 5(d)(iii) 37 4 M3 for 240  2  10 2 3 10  27 oe     or M2 for 2  10 2 3 10  27 oe or M1 for 2  10 2 3 10 oe

This question in 0580/33 May/June 2023

4 (a) Complete the table of values for y = x 2 - 4x - 2 . x -2 -1 0 1 2 3 4 5 y 3 -2 -5 -5 -2 3 [2] (b) On the grid, draw the graph of y = x 2 - 4x - 2 for - 2 G x G 5 . y 10 9 8 7 6 5 4 3 2 1 x -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 -6 [4] (c) Use your graph to solve the equation x 2 - 4x - 2 = 0 . x = … or x = … [2]

8 marks

Mark scheme: 4(a) 10 –6 2 B1 for each 4(b) Correct curve 4 B3FT for 7 or 8 points correctly plotted or B2FT for 5 or 6 points correctly plotted or B1FT for 3 or 4 points correctly plotted 4(c) –0.6 to –0.3, 4.3 to 4.6 2 FT their curve B1 for each

This question in 0580/32 Oct/Nov 2023

8 (a) y 8 7 L 6 5 4 3 2 1 0 x 0 1 2 3 4 5 6 7 8 (i) Find the equation of line L in the form y = mx + c . y = … [2] (ii) (a) Complete the table of values for y = 8 - 2x . x 0 2 4 y 4 [2] (b) On the grid, draw the graph of y = 8 - 2x for 0 G x G 4 . [1] (iii) Find the coordinates of the point where line L intersects the graph of y = 8 - 2x . ( … , … ) [1] (b) (i) Complete the table of values for y = x 2 - 4x - 4 . x -2 -1 0 1 2 3 4 5 6 y 8 -4 -8 -4 8 [2] (ii) On the grid, draw the graph of y = x 2 - 4x - 4 for - 2 G x G 6 . y 8 7 6 5 4 3 2 1 -2 -1 0 1 2 3 4 5 6 x -1 -2 -3 -4 -5 -6 -7 -8 [4] (iii) Write down the equation of the line of symmetry of the graph. … [1] (iv) Use your graph to solve the equation x 2 - 4x - 4 = 0 . x = … or x = … [2]

15 marks

Mark scheme: 8(a)(i) [y =] 12 x + 2 final answer 2 1 B1 for x + c or y = m x + 2 2 where m is their gradient and m ≠ 0 8(a)(ii)(a) 8 [4] 0 2 B1 for each 8(a)(ii)(b) Correct graph 1 8(a)(iii) 2.4 3.2 1 FT their graph 8(b)(i) 1 −7 −7 1 2 B1 for 2 or 3 correct 8(b)(ii) Correct curve 4 B3FT for 8 or 9 points plotted correctly OR B2FT for 6 or 7 points plotted correctly OR B1FT for 4 or 5 points plotted correctly 8(b)(iii) x = 2 oe 1 8(b)(iv) −0.7 to −0.9 2 FT their graph B1 for each 4.7 to 4.9

This question in 0580/32 Oct/Nov 2024

5 (a) A farmer plants t trees each day. Write an expression for the number of trees he plants in d days. … [1] (b) A train has p passengers. x passengers get off the train and y passengers get on the train. Write an expression for the number of passengers on the train now. … [1]

2 marks

Mark scheme: 5(a) dt oe final answer 1 5(b) p − x + y oe final answer 1

This question in 0580/32 Feb/March 2025

8 (a) T = 3 ( 5P - 8) + 4 Find the value of T when P = 12 . T = … [2] (b) W = t4 + 8 Find the value of t when W = 369 . t = … [2]

4 marks

Mark scheme: 8(a) 160 2 M1 for 3(5×12 – 8) + 4 oe or better 8(b) 90.25 2 M1 for 369 – 8 = 4t oe or better 369 8 or = t + oe or better 4 4 W − 8 or [= t] oe or better 4

This question in 0580/31 May/June 2025

11 Y = 3t 2 + 2m Find the value of Y when t = 6 and m = -3. Y = … [2]

2 marks

Mark scheme: 11 102 2 B1 for 108 or – 6 or M1 for 3 × 62 + 2 × − 3 oe

This question in 0580/32 Oct/Nov 2025