Cambridge IGCSE Mathematics 0580 — 2025 Oct/Nov Paper 1 · Variant 2
0580/12/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 scheme10 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Write down the value of the 3 in the number 23 679
1 Write down the value of the 3 in the number 23 679. ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1 3000 1
Q2 · Tom buys 2 books costing $8.20 each
2 Tom buys 2 books costing $8.20 each. Work out how much change he receives from $20. $ ................................................. [2]
Mark scheme: 2 3.6[0] 2 M1 for 20 − 2 × 8.20 or B1 for 16.4[0]
Q3 · Write 17 469 correct to the nearest ten
3 (a) Write 17 469 correct to the nearest ten. ................................................. [1] (b) Write 5.073 correct to 1 decimal place. ................................................. [1]
Mark scheme: 3(a) 17 470 cao 1 3(b) 5.1 cao 1
Q4 · Write down the value of 144
4 (a) Write down the value of 144. ................................................. [1] (b) Work out the value of 53. ................................................. [1]
Mark scheme: 4(a) 12 1 4(b) 125 cao 1
Q5 · The diagram is made from equilateral triangles
5 The diagram is made from equilateral triangles. (a) On the diagram, draw all the lines of symmetry. [2] (b) Write down the order of rotational symmetry. ................................................. [1]
Mark scheme: 5(a) 3 correct lines 2 B1 for two correct lines and no extras or 3 correct lines and one extra 5(b) 3 1
Q6 · 6 (a) Write as a decimal
3 6 (a) Write as a decimal. 4 ................................................. [1] 9 (b) Write as a percentage. 100 ..............................................% [1] (c) Write 143% as a decimal. ................................................. [1]
Mark scheme: 6(a) 0.75 1 6(b) 9 1 6(c) 1.43 cao 1
Q7 · A bag contains 8 discs numbered 1 to 8
7 A bag contains 8 discs numbered 1 to 8. A disc is picked at random from the bag. 0 1 On the probability scale, draw an arrow ( ) to show the probability that the number is (a) an even number, label the arrow A [1] (b) 9, label the arrow B [1] (c) less than 3, label the arrow C. [1]
Mark scheme: 7(a) Arrow labelled A on 0.5 1 7(b) Arrow labelled B on 0 1 7(c) Arrow labelled C on 0.25 1
Q8 · A number, n, is a factor of 144 and a multiple of 9
8 A number, n, is a factor of 144 and a multiple of 9. Find all the values for n. .............................................................................. [3]
Mark scheme: 8 9, 18, 36, 72, 144 3 B2 for 3 correct and no extras or 5 correct and 1 extra as the answer or B1 for two correct and no extras or M1 factors of 144 up to 72 or multiples of 9 up to 72
Q9 · The temperature at midday on Monday is –3 °C
9 The temperature at midday on Monday is –3 °C. The temperature at 10 pm on Monday is –15 °C. (a) Calculate the difference between these two temperatures. ............................................. °C [1] (b) The temperature at midday on Tuesday is 23 °C higher than the temperature at 10 pm on Monday. Calculate the temperature at midday on Tuesday. ............................................. °C [1]
Mark scheme: 9(a) 12 1 9(b) 8 1
Q10 · A bag contains red balls and green balls
10 A bag contains red balls and green balls. They are in the ratio red balls : green balls = 2 : 3. A ball is picked at random. Find the probability that it is a red ball. ................................................. [1]
Mark scheme: 10 2 1 oe 5
Q11 · The stem-and-leaf diagram shows the number of customers entering a shop each day for 20…
11 The stem-and-leaf diagram shows the number of customers entering a shop each day for 20 days. 3 0 1 5 9 4 1 4 6 8 9 5 1 3 4 4 4 7 8 6 3 6 6 7 2 Key : 3 0 represents 30 customers (a) Find the range. ................................................. [1] (b) Find the mode. ................................................. [1] (c) Work out the percentage of these 20 days when more than 55 customers enter the shop. ..............................................% [2] (d) (i) Find the median. ................................................. [1] (ii) On the next day 48 customers enter the shop. Will the median increase or decrease? Give a reason for your answer. .................... because ................................................................................................................. ............................................................................................................................................. [1]
Mark scheme: 11(a) 42 1 11(b) 54 1 11(c) 30 2 6 B1 for oe 20 11(d)(i) 52 1 11(d)(ii) Decrease AND acceptable reason e.g. 48 1 is below the median
Q12 · The diagram shows a parallelogram
12 The diagram shows a parallelogram. ( 3x + 10 ) ° NOT TO SCALE ( x - 30 ) ° (a) Use the information in the diagram to write an equation and solve it to find the value of x. x = ................................................ [4] (b) Find the value of the largest angle in this parallelogram. ................................................. [1]
Mark scheme: 12(a) 4x = 200 oe M3 M2 for x – 30 + 3x + 10 = 180 oe M1 for attempt to simplify to ax − b = c or ax = b + c OR If M0 scored M2 for correct simplification to ax = b + c FT from their linear equation or M1 for correct simplification to ax − b = c FT from their linear equation OR If M0 award SC2 for answer of 50 from no working or from no incorrect working 50 A1 12(b) 160 nfww 1 FT 3 × their 50 + 10
Q13 · 5 cm NOT TO 3 cm SCALE 4 cm 4 cm The diagram shows a right-angled triangular prism
13 5 cm NOT TO 3 cm SCALE 4 cm 4 cm The diagram shows a right-angled triangular prism. Complete the net of this prism on the 1 cm2 grid. One face has been drawn for you. [3]
Mark scheme: 13 Fully correct net 3 B2 for the two correct rectangles, in either order below the given face and two 3,4,5 triangles, one on each side or B1 for 1 correct rectangle in either place below the given face or for two 3, 4, 5 triangles, one each side
Q14 · The diagram shows a smaller triangle DEF which has vertices on the sides of a larger…
14 The diagram shows a smaller triangle DEF which has vertices on the sides of a larger triangle ABC. NOT TO A SCALE 100° E x° 25° D 50° 45° 35° 30° B C F Find the value of x. x = ................................................ [3]
Mark scheme: 14 10 3 B2 for any two correct angles identified from BDF = 85, FDE = 70 and DFE = 100 or B1 for any one of them OR B1 for AED = 55 and B1 for CEF = 115
Q15 · Three sisters share $n in the ratio 10 : 3 : 2
15 Three sisters share $n in the ratio 10 : 3 : 2. The smallest share is $120. Find the value of n. n = ................................................ [3]
Mark scheme: 15 900 3 120 M2 for (10 + 3 + 2 ) oe 2 120 or M1 for [k ] (k = 1, 3 or 10) 2
Q16 · 9857 # 10 -2 .35 # 102 1.54 # 10 1 6.5 # 10 -2 Write these numbers in order, starting…
16 .9857 # 10 -2 .35 # 102 1.54 # 10 1 6.5 # 10 -2 Write these numbers in order, starting with the smallest. ......................... < ......................... < ......................... < ......................... [2] smallest
Mark scheme: 16 6.5 × 10–2, 9.857 × 10-2, 1.54 × 101, 2 B1 for 3 in the correct order 3.5 × 102 or M1 for 0.09857, 350, 15.4, 0.065 oe
Q17 · 8 cm NOT TO SCALE 6 cm 14 cm Calculate the area of this trapezium
17 8 cm NOT TO SCALE 6 cm 14 cm Calculate the area of this trapezium. ........................................... cm2 [2]
Mark scheme: 17 66 2 8 + 14 M1 for 6 oe 2
Question 18
18 Work out. 5 1 2 ' 4 6 4 Write your answer as a fraction in its simplest form. ................................................. [3]
Mark scheme: 18 2 3 17 4 cao M2 for 3 6 17 their17 4 or M1 for 6 their17 17 4 or B1 for or17 or 6 4 17 Alternative : 34 51 M2 for 12 12 their 34 their 51 or M1 for 12 12
Q19 · The grid shows two flags, F and A
19 The grid shows two flags, F and A. y 7 6 5 F 4 3 2 1 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 x – 1 A – 2 – 3 – 4 – 5 – 6 – 7 (a) On the grid, draw the image of flag F after a reflection in the line x =- 1 . [2] (b) On the grid, draw the image of flag F after a rotation of 180° about (0, 0). [2] (c) Describe fully the single transformation that maps flag F onto flag A. ..................................................................................................................................................... ..................................................................................................................................................... [2]
Mark scheme: 19(a) Fully correct reflection, points (−4, 5) 2 B1 for a correct reflection in x = k or (−5, 5) (−4, 4) (−5, 4) (−4, 2) y = − 1 19(b) Fully correct rotation, points (−2, −2) 2 B1 for a correct rotation of 180° about (−2, −4) (−2, −5) (−3, −5) (−3, −4) the wrong centre 19(c) Translation 2 B1 for each 2 −6
Q20 · % = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {1, 3, 5, 7, 9} B = {1, 3, 6, 10} % A B (a) Use…
20 % = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {1, 3, 5, 7, 9} B = {1, 3, 6, 10} % A B (a) Use this information to complete the Venn diagram. [2] (b) List the elements of A + B . ................................................. [1] (c) Find n ( Bl) . ................................................. [1]
Mark scheme: 20(a) 2 B1 for at least 8 elements in the correct place 20(b) 1, 3 1 FT their (a) 20(c) 6 1 FT their (a)
Question 21
21 Simplify. 18 x 8 9x 2 ................................................. [2]
Mark scheme: 21 2x6 final answer 2 B1 for kx6 or 2xc as final answer or 2x6 seen and spoilt
Q22 · Work out the size of one interior angle of a regular hexagon
22 Work out the size of one interior angle of a regular hexagon. ................................................. [2]
Mark scheme: 22 120 2 M1 for 180 − (360 ÷ 6) oe or ( 6 − 2 ) 180 oe 6
Q23 · There are two charges for crossing a bridge
23 There are two charges for crossing a bridge. Cars $a Other vehicles $b On Monday 4 cars and 20 other vehicles pay a total of $130. On Tuesday 6 cars and 15 other vehicles pay a total of $105. Write down two equations and solve them to find the value of a and the value of b. a = ................................................ b = ................................................ [6]
Mark scheme: 23 4a + 20b = 130 oe 2 B1 for each 6a + 15b = 105 oe [a =] 2.5 4 M1FT for correctly equating one set of [b =] 6 coefficients M1FT for correct method to eliminate one variable A1 for a = 2.5 A1 for b = 6 If A0 scored, SC1 for two positive costs which satisfy one of the original conditions
Q24 · NOT TO SCALE A O 36° B C B is a point on the circle, centre O
24 NOT TO SCALE A O 36° B C B is a point on the circle, centre O. ABC is a tangent to the circle at B and angle OAB = 36°. Work out the size of angle AOB. Angle AOB = ................................................ [1]
Mark scheme: 24 54 1
Question 25
25 (a) Expand and simplify. ( x - 5)( x + 2) ................................................. [2] (b) Factorise. 5x 3 + 10 x ................................................. [2]
Mark scheme: 25(a) x2 – 3x – 10 final answer 2 B1 for x2 – 5x + 2x – 10 with at least 3 terms correct 25(b) 5x(x2 + 2) final answer 2 B1 for 5(x3 + 2x) or x(5x2 + 10) or 5x(x2 + 2) seen and spoilt
Q26 · The length, l metres, of a rope is 16.32 metres, correct to 2 decimal places
26 The length, l metres, of a rope is 16.32 metres, correct to 2 decimal places. Complete this statement about the value of l. ................... G l 1 ................... [2]
Mark scheme: 26 16.315 16.325 2 B1 for each If 0 scored, SC1 for both correct but reversed
Q27 · These are the first four terms of a sequence
27 (a) These are the first four terms of a sequence. 2 8 14 20 Find the nth term of this sequence. ................................................. [2] (b) The nth term of a different sequence is n 2 + 10 . Find the first three terms of this sequence. .............................. , .............................. , .............................. [2]
Mark scheme: 27(a) 6n – 4 oe final answer 2 B1 for 6n + c or kn – 4 (k ≠ 0) or 6n – 4 seen and spoilt 27(b) 11 14 19 2 B1 for two correct terms in the correct places
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.
3Angles2Area and perimeter2Fractions, decimals and percentages2Introduction to probability2Sets2Algebraic manipulation1Averages and range1Circle theorems1Equations1Limits of accuracy1Money1Ordering1Powers and roots1Ratio and proportion1Right-angled triangles1Sequences1Symmetry1The four operations1Transformations1What you needed in this session
Cambridge’s own grade thresholds for 2025 Oct/Nov, Paper 1 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.