Cambridge IGCSE Mathematics 0580 — 2025 Oct/Nov Paper 1 · Variant 3
0580/13/O/N/25 · 27 questions · 80 marks · 90 min
The question paper and its mark scheme, free to read here and free to download. This is Cambridge’s own paper, exactly as it was sat.
Question paper16 pages
Mark scheme9 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · A B (a) Measure the length of line AB in centimetres
1 A B (a) Measure the length of line AB in centimetres. ............................................ cm [1] (b) Draw a line that is parallel to line AB. [1]
Mark scheme: Question Answer Marks Partial Marks 1(a) 5.6 1 1(b) Ruled line parallel to AB 1
Q2 · Write the number 83 042 in words
2 (a) Write the number 83 042 in words. ..................................................................................................................................................... [1] (b) Write down the value of the 7 in the number 346 709. ................................................. [1] (c) Write 8453 correct to (i) the nearest hundred ................................................. [1] (ii) the nearest ten. ................................................. [1]
Mark scheme: 2(a) Eighty-three thousand [and] forty-two 1 2(b) 700 1 2(c)(i) 8500 1 2(c)(ii) 8450 1
Q3 · A (a) Measure angle a
3 a (a) Measure angle a. ................................................. [1] (b) Write down the mathematical name of this type of angle. ................................................. [1]
Mark scheme: 3(a) 123 1 3(b) Obtuse 1
Q4 · Ben records the favourite sport of each of 20 students
4 Ben records the favourite sport of each of 20 students. Football Cricket Hockey Rugby Football Tennis Rugby Football Football Rugby Tennis Football Rugby Football Cricket Football Rugby Football Cricket Cricket Complete the frequency table. You may use the tally column to help you. Sport Tally Frequency Cricket Football Hockey Rugby Tennis [2]
Mark scheme: 4 4 2 B1 for 3 correct frequencies 8 If 0 scored SC1 for all correct tallies if 1 frequency column blank 5 or for all correct frequencies but in tally 2 column
Q5 · The diagram shows quadrilateral ABCD on a 1 cm 2 grid
5 The diagram shows quadrilateral ABCD on a 1 cm 2 grid. y 4 3 B C 2 1 – 4 – 3 – 2 – 1 0 1 2 3 4 x – 1 – 2 A D – 3 – 4 (a) Write down the coordinates of point B. (...................... , ......................) [1] (b) Write down the mathematical name of quadrilateral ABCD. ................................................. [1] (c) Find the area of quadrilateral ABCD. ......................................... cm2 [1] (d) On the grid, plot the point E at ( –3 , 2) . [1]
Mark scheme: 5(a) (–1, 2) 1 5(b) trapezium 1 5(c) 16 1 5(d) Point plotted at (–3,2) 1
Q6 · Anna thinks of a number, she multiplies it by 2 and then finds the square root
6 Anna thinks of a number, she multiplies it by 2 and then finds the square root. The answer is 12. What number did Anna think of? ................................................. [2]
Mark scheme: 6 72 2 M1 for 122 [÷ 2]
Q7 · A journey starts at 10 55 and ends at 16 10
7 A journey starts at 10 55 and ends at 16 10. Find how long the journey takes. Give your answer in hours and minutes. ......................... h ............ min [1]
Mark scheme: 7 5[hours] 15[minutes] cao 1
Q8 · These are the masses, in kg, of each of 11 bags
8 These are the masses, in kg, of each of 11 bags. 23 16 8 10 27 19 4 17 13 4 14 (a) Complete the stem-and-leaf diagram to show this information. 0 1 2 Key: 2 | 7 represents 27 kg [2] (b) Find the median. ............................................ kg [1]
Mark scheme: 8(a) 2 B1 for a correct diagram with one error 0 4 4 8 or omission or for a fully correct 1 0 3 4 6 7 9 unordered stem-and-leaf diagram 2 3 7 8(b) 14 1
Q9 · Find the value of (a) 25 ................................................
9 Find the value of (a) 25 ................................................. [1] (b) 60. ................................................. [1]
Mark scheme: 9(a) 32 1 9(b) 1 1
Q10 · X° 40° NOT TO SCALE y° The diagram shows an isosceles triangle between a pair of parallel…
10 x° 40° NOT TO SCALE y° The diagram shows an isosceles triangle between a pair of parallel lines. (a) Find the value of x. x = ................................................ [2] (b) Find the value of y. Give a geometrical reason for your answer. y = ...................... because ....................................................................................................... ..................................................................................................................................................... [2]
Mark scheme: 10(a) 70 2 180 − 40 M1 for oe 2 10(b) 110 1 FT 180 – their (a) Angles on a straight line add to 180 oe 1 nfww
Q11 · Sam buys 3 apples at 40 cents each
11 (a) Sam buys 3 apples at 40 cents each. He also buys 5 peaches. The total cost is $3.45 . Find the cost of 1 peach. ........................................ cents [3] (b) Pears cost 55 cents each. Bananas cost 36 cents each. Write an expression, in cents, for the cost of x pears and y bananas. ................................................. [2]
Mark scheme: 11(a) 45 3 345 − ( 3 40 ) M2 for oe 5 or M1 for 345 – (3 × 40) or B1 for 120 11(b) 55x + 36y final answer 2 B1 for 55x or 36y in final answer or final answer seen and spoilt If 0 scored SC1 for 0.55x + 0.36y
Question 12
12 (a) Simplify. 3y - 4y + 2y ................................................. [1] (b) Solve. (i) x + 5 = 19 x = ................................................ [1] (ii) 6x - 5 = 7 x = ................................................ [2]
Mark scheme: 12(a) y 1 12(b)(i) 14 1 12(b)(ii) 2 2 5 7 M1 for 6x = 7 + 5 or x − = or better 6 6
Q13 · X – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 Write down the inequality represented on the number line
13 x – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 Write down the inequality represented on the number line. ................................................. [2]
Mark scheme: 13 –5 ⩽ x < 1 oe 2 B1 for –5 ⩽ x or x < 1
Q14 · Victoria invests $2000 at a rate of 5% per year simple interest
14 Victoria invests $2000 at a rate of 5% per year simple interest. Calculate the value of her investment after 4 years. $ ................................................ [3]
Mark scheme: 14 2400 nfww 3 B2 for 400 nfww 5 or M2 for 2000 × 4 + 2000 100 5 or M1 for 2000 [× 4] 100
Question 15
15 Complete each statement. (a) 0.0000047 m 2 = ....................... cm2. [1] (b) 8500 cm 3 = ....................... litres. [1]
Mark scheme: 15(a) 0.047 1 15(b) 8.5 1
Q16 · Kai, Jo and Liz share some money in the ratio Kai : Jo : Liz = 4 : 7 : 13
16 Kai, Jo and Liz share some money in the ratio Kai : Jo : Liz = 4 : 7 : 13. Jo receives $1400. Find the total amount of money they share. $ ................................................ [3]
Mark scheme: 16 4800 3 1400 M2 for ( 4 + 7 + 13 ) oe 7 1400 or M1 for [× k] ( k = 1, 4 or 13) 7
Q17 · K x # k 5 = k 20 Find the value of x
17 (a) k x # k 5 = k 20 Find the value of x. x = ................................................ [1] (b) Expand and simplify. ( x + 5)( x - 4) ................................................. [2] (c) Factorise. 21r 3 - 7r ................................................. [2]
Mark scheme: 17(a) 15 1 17(b) x2 + x – 20 final answer 2 B1 for x2 – 4x + 5x – 20 with at least 3 terms correct 17(c) 7r(3r2 – 1) final answer 2 B1 for 7(3r3 – r) or r(21r2 – 7) or for 7r(3r2 – 1) seen then spoilt
Q18 · The diameter of a circle is 16 cm
18 The diameter of a circle is 16 cm. Find the area of the circle. Leave your answer in terms of r. ......................................... cm2 [2]
Mark scheme: 18 64π 2 2 16 M1 for 2
Q19 · Find the number of sides of a regular polygon with interior angle 160°
19 Find the number of sides of a regular polygon with interior angle 160°. ................................................. [2]
Mark scheme: 19 18 2 360 M1 for 180 −160 180 ( n − 2 ) or for = 160 n
Q20 · The height, h cm, of a door is 180 cm, correct to the nearest centimetre
20 The height, h cm, of a door is 180 cm, correct to the nearest centimetre. Complete this statement about the value of h. ........................ G h 1 ........................ [2]
Mark scheme: 20 179.5 180.5 2 B1 for each If 0 scored SC1 for both correct but reversed
Q21 · These are the first four terms of a sequence
21 These are the first four terms of a sequence. – 6 1 8 15 (a) Write down the next term. ................................................. [1] (b) Write down the term-to-term rule. ................................................. [1] (c) (i) Find the nth term. ................................................. [2] (ii) Is 688 a term in this sequence? Explain how you decide. .................... because ......................................................................................................... ............................................................................................................................................. [2]
Mark scheme: 21(a) 22 1 21(b) Add 7 1 21(c)(i) 7n – 13 oe final answer 2 B1 for 7n + j or kn – 13 k ≠ 0, or 7n – 13 seen then spoilt 21(c)(ii) 7n – 13 = 688 oe 1 FT their nth term an + b 7n = 701 if a > 1 and b ≠ 0 No, 701 is not divisible by 7 oe nfww 1
Q22 · The diagram shows triangles A and B
22 The diagram shows triangles A and B. y 10 9 8 7 B 6 5 4 3 2 A 1 0 1 2 3 4 5 6 7 8 9 10 x Describe fully the single transformation that maps triangle A onto triangle B. ............................................................................................................................................................. ............................................................................................................................................................. [3]
Mark scheme: 22 Enlargement 3 B1 for each Centre (0,0) [Scale factor] 3
Q23 · % A B Use set notation to describe the shaded region
23 (a) % A B Use set notation to describe the shaded region. ................................................. [1] (b) % = {people in a club} T = {people who play tennis} S = {people who go swimming} There are 60 people in the club. 36 people go swimming. % T S 30 10 (i) Complete the Venn diagram. [2] (ii) Find n ( Tl) . ................................................. [1]
Mark scheme: 23(a) A∩B 1 23(b)(i) 2 B1 for 14 in correct place T S B1 for 6 in correct place 14 6 30 If 0 scored SC1 for n(T) = 20 10 23(b)(ii) 40 1
Q24 · The scale on a map is 1 cm represents 12 km
24 (a) The scale on a map is 1 cm represents 12 km. Write this in the ratio 1 : n . 1 : ...................... [1] (b) The bearing of B from A is 070°. Find the bearing of A from B. ................................................. [2]
Mark scheme: 24(a) 1 200 000 1 24(b) 250 2 M1 for 70 + 180 or correct diagram indicating angle
Question 25
25 Work out. 3 2 # 1 4 3 Give your answer as a mixed number in its simplest form. ................................................. [3]
Mark scheme: 25 1 3 3 15 5 1 cao B2 for or or oe 4 112 12 4 5 or B1 for 3
Q26 · There are 2 sets of traffic lights on Li’s journey to work
26 There are 2 sets of traffic lights on Li’s journey to work. The probability he stops at the first set of traffic lights is 0.4 . The probability he stops at the second set of traffic lights is 0.7 . First set of traffic lights Second set of traffic lights Stops ................ Stops 0.4 ................ Does not stop Stops ................ ................ Does not stop ................ Does not stop (a) Complete the tree diagram. [2] (b) Work out the probability that Li does not stop at both sets of traffic lights. ................................................. [2] Question 27 is printed on the next page.
Mark scheme: 26(a) Correct tree diagram 2 B1 for 0.6 on the first branch or 0.7 and 0.3 correct on all second branches 26(b) 0.18 oe 2 FT their tree diagram for 2 marks M1 for their 0.6 × their 0.3
Q27 · Sam writes 851 000 in standard form as 85.1 # 104
27 Sam writes 851 000 in standard form as 85.1 # 104 . Explain why 85.1 # 104 is not a number in standard form. ............................................................................................................................................................. ............................................................................................................................................................. [1]
Mark scheme: 27 In standard form the value is written as 1 a × 10n where 1 ⩽ a < 10 and 85.1 is greater than 10 oe
What was in this paper
The subtopics covered by these 27 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
4Powers and roots2Units of measure2Algebraic manipulation1Circles, arcs and sectors1Classifying statistical data1Coordinates1Equations1Fractions, decimals and percentages1Inequalities1Introduction to probability1Limits of accuracy1Money1Percentages1Ratio and proportion1Sequences1Sets1Standard form1Statistical charts and diagrams1Time1Transformations1Types of number1What you needed in this session
Cambridge’s own grade thresholds for 2025 Oct/Nov, Paper 1 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.