Cambridge IGCSE Mathematics 0580 — 2025 Feb/March Paper 1 · Variant 2
0580/12/F/M/25 · 26 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 paper20 pages
Mark scheme10 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Write the number twenty thousand in figures
1 Write the number twenty thousand in figures. ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1 20 000 1
Q2 · Write 0.07 (a) as a percentage ............................................
2 Write 0.07 (a) as a percentage ............................................. % [1] (b) as a fraction ................................................. [1] (c) in standard form. ................................................. [1]
Mark scheme: 2(a) 7 1 2(b) 7 1 100 2(c) 7 10− 2 1
Q3 · Write down all the factors of 18
3 Write down all the factors of 18. ............................................................. [2]
Mark scheme: 3 1 2 3 6 9 18 2 B1 for 4 correct and no extras or for 6 correct and one incorrect
Q4 · Find the value of (a) 103 ................................................
4 Find the value of (a) 103 ................................................. [1] (b) 3 27 ................................................. [1] (c) 70. ................................................. [1]
Mark scheme: 4(a) 1000 1 4(b) 3 1 4(c) 1 1
Q5 · On the diagram, draw all the lines of symmetry
5 (a) On the diagram, draw all the lines of symmetry. [2] (b) Shade one square so that the diagram has rotational symmetry of order 2. [1]
Mark scheme: 5(a) 2 correct lines of symmetry drawn 2 B1 for one line correct and no extras or for 2 lines correct and one extra 5(b) 1 square correctly shaded 1
Q6 · Find the value of the reciprocal of 0.25
6 Find the value of the reciprocal of 0.25 . ................................................... [2]
Mark scheme: 6 4 2 1 M1 for oe 0.25
Q7 · Work out - 6 # - 3 + 7 # 2
7 Work out - 6 # - 3 + 7 # 2 . ................................................. [2]
Mark scheme: 7 32 2 B1 for 18 or 14
Q8 · Write these numbers in order, starting with the smallest
8 Write these numbers in order, starting with the smallest. 34% r 1 3 3 3 10 ......................1......................1......................1......................1...................... [2] smallest
Mark scheme: 8 3 1 2 B1 for 4 in the correct order 34% 3 π or M1 for decimal equivalents to compare 10 3 numbers 0.34, 3.1..,0.33, [3], 0.3
Q9 · A film starts at 19 35
9 A film starts at 19 35. The film lasts for 70 minutes. Work out the time the film finishes. ................................................. [1]
Mark scheme: 9 2045 1
Q10 · A shape is drawn on a 1 cm 2 grid
10 A shape is drawn on a 1 cm 2 grid. (a) Find the area of the shape. ......................................... cm2 [1] (b) On the grid, shade 50% of the shape. [1]
Mark scheme: 10(a) 20 1 10(b) 10 squares shaded 1
Q11 · 19.5 # 20 .4 = 397
11 19.5 # 20 .4 = 397. 8 Work out. (a) 1.95 # 2 .04 ................................................. [1] (b) 3978 ' 204 ................................................. [1]
Mark scheme: 11(a) 3.978 1 11(b) 19.5 1
Q12 · Kat has a method for finding the difference between two square numbers, a 2 - b 2
12 (a) Kat has a method for finding the difference between two square numbers, a 2 - b 2 . Her method is (the sum of a and b) # (the difference between a and b) . She shows her method for 17 2 - 13 2 . 17 2 - 13 2 = ( 17 + 13) # ( 17 - 13) = 30 # 4 = 120 Work out 29 2 - 21 2 using Kat’s method. ................................................. [2] (b) In this part, all lengths are in centimetres. 17 NOT TO SCALE 17 13 13 100 The diagram shows a prism. Work out the volume of the prism. ......................................... cm3 [2]
Mark scheme: 12(a) ( 29 + 21) ( 29 − 21) M1 = 50 8 400 A1 12(b) 12000 2 2 2 M1 for 17 − 13 [ ×100] oe ( )
Q13 · Convert 8 litres into cm3
13 Convert 8 litres into cm3. ......................................... cm3 [1]
Mark scheme: 13 8000 1
Q14 · C NOT TO SCALE 4 cm D 6 cm A 6 cm B The diagram shows a triangular prism
14 C NOT TO SCALE 4 cm D 6 cm A 6 cm B The diagram shows a triangular prism. ABC is an isosceles triangle with AC = BC. The perpendicular height of triangle ABC is 4 cm. AB = 6 cm and BD = 6 cm. (a) Complete this statement. The prism has ......................... faces and ......................... edges. [2] (b) Show that the length of BC is 5 cm. [2] (c) Complete the net of the prism on the 1 cm 2grid. The base has been drawn for you. [3]
Mark scheme: 14(a) 5 9 2 B1 for each 14(b) 2 2 2 2 2 3 + 4 [=5] M1 for 3 + 4 14(c) correct net drawn 3 B2 for 3 correct extra faces drawn in correct places or B1 for 1 correct extra face drawn in correct place
Q15 · D NOT TO SCALE y° A B C The diagram shows a triangle BCD and a straight line ABC
15 D NOT TO SCALE y° A B C The diagram shows a triangle BCD and a straight line ABC. DB=DC=BC. (a) Write down the mathematical name for triangle BCD. ................................................. [1] (b) Work out the value of y. Give two geometrical reasons for your answer. y = ....................... because 1. ........................................................................................................................................................ 2. ........................................................................................................................................................ [4]
Mark scheme: 15(a) equilateral 1 15(b) 120 2 B1 for DBC=60 Angles in an equilateral triangle are 1 equal Angles on a straight line add to 180 1
Q16 · Jill records the temperature and the number of people on a beach for each of ten days
16 Jill records the temperature and the number of people on a beach for each of ten days. The results are shown in the scatter diagram. Number of people Temperature (a) What type of correlation is shown in the scatter diagram? ................................................. [1] (b) Describe the relationship between the temperature and the number of people on the beach. ............................................................................................................................................................ ..................................................................................................................................................... [1]
Mark scheme: 16(a) positive 1 16(b) the higher the temperature the higher 1 the number of people oe
Q17 · Line L is shown on the grid
17 Line L is shown on the grid. y 7 L 6 5 4 3 2 1 0 x 1 2 3 4 5 6 7 8 (a) Find the equation of line L in the form y = mx + c . y = ................................................ [2] (b) Line L crosses the x-axis at P. Find the coordinates of P. (...................... , ......................) [2]
Mark scheme: 17(a) 2 1 y = 1 x + 3 final answer B1 for x + c 2 2 or B1 for mx + 3 where m ≠ 0 17(b) ( −6,0 ) 2 B1 for (−6, j) or (k, 0) 1 or M1 for 0 = their x + 3 or better 2
Q18 · Complete the table of values for y =
18 (a) Complete the table of values for y = . x x -6 -4 -3 -2 -1 1 2 3 4 6 y -3 -6 6 3 [3] 12 (b) On the grid, draw the graph of y = for - 6 G x G -1 and 1 G x G 6 . x y 12 10 8 6 4 2 x -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -2 -4 -6 -8 -10 -12 [4] (c) On the grid, draw the line y =- 9 . [1] 12 (d) Use your graph to solve =- 9 . x x = ................................................ [1]
Mark scheme: 18(a) −2 − 4 − 12 12 4 2 3 B2 for 4 correct or B1 for 1 correct 18(b) Correct curve 4 B3FT for 9 points correctly plotted or B2FT for 7 points correctly plotted or B1FT for 5 points correctly plotted 18(c) y = −9 correctly drawn, ruled 1 18(d) −1.4 to − 1.2 1 FT their curve and y = −9
Q19 · N is an odd number
19 (a) n is an odd number. Write down the values of n that satisfy 7 1 n G 15 . ................................................. [2] (b) x –1 0 1 2 3 4 5 6 7 8 9 Pip thinks -1 1 x 1 8 is the inequality represented on the number line. Complete the statement. Pip’s inequality is not correct because ....................................................................................... ..................................................................................................................................................... [1]
Mark scheme: 19(a) 9 11 13 15 final answer 2 B1 for 3 correct and no errors or for 4 correct and one extra 19(b) Pip needed to use two ⩽ signs oe 1
Q20 · The height, h metres, of a building is 635 m, correct to the nearest metre
20 The height, h metres, of a building is 635 m, correct to the nearest metre. Complete this statement about the value of h. ............................ G h 1 ............................ [2]
Mark scheme: 20 634.5 635.5 2 B1 for each If 0 scored SC1 for both correct but answers reversed
Q21 · X = 1 w 2 p 3 (a) Find the value of X when w = 5 and p = 6
21 X = 1 w 2 p 3 (a) Find the value of X when w = 5 and p = 6. X = ĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭ [2] (b) Make p the subject of the formula. p = ĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭĭ [2]
Mark scheme: 21(a) 50 2 1 2 M1 for 5 6 or better 3 21(b) 3 X −2 2 M1 for 3 X = w 2 p p = or p = 3 Xw w 2 X 1 2 1 or = p or Xw−= p 2 final answer w 3 3
Q22 · Work out 1 7 - 4
22 Work out 1 7 - 4 . 15 5 Give your answer as a fraction in its simplest form. ................................................. [3]
Mark scheme: 22 2 3 10 cao B2 for final answer or equivalent fraction 3 15 OR 22 7 1 B1 for or + 15 15 5 3 4 3 1 M1 for oe or oe 3 5 3 5
Q23 · Mai buys two batteries
23 Mai buys two batteries. The probability that a battery is faulty is 1 . 10 First battery Second battery ............ Faulty Faulty 1 10 Not faulty ............ ............ Faulty ............ Not faulty Not faulty ............ (a) Complete the tree diagram. [2] (b) Find the probability that Mai buys two faulty batteries. ................................................. [2] (c) A shop sells 3000 batteries in one month. Work out the expected number of faulty batteries the shop sells. ................................................. [1]
Mark scheme: 23(a) 9 1 9 1 9 2 1 1 B1 for and in correct places in 2nd 10 10 10 10 10 10 10 battery 9 or correctly placed for the first battery 10 23(b) 1 2 1 1 oe M1 for their 100 10 10 23(c) 300 1
Q24 · A circle has radius 7 cm
24 A circle has radius 7 cm. A square has side x cm. The circumference of the circle is the same length as the perimeter of the square. Find the value of x. Give your answer in terms of r. x = ................................................ [3]
Mark scheme: 24 7π 3 M2 for 2π×7=4x oe or 3.5π 2 or M1 for 2π 7 or14π or 4x
Q25 · Q B NOT TO 7 cm SCALE A 5 cm C P 10 cm R Triangle ABC is mathematically similar to…
25 Q B NOT TO 7 cm SCALE A 5 cm C P 10 cm R Triangle ABC is mathematically similar to triangle PQR. Show that QR = 14 cm. [1]
Mark scheme: 25 10 1 7 = 14 oe 5
Q26 · Solve the simultaneous equations
26 Solve the simultaneous equations. 4t - 3w = 11 6t + 2w =- 3 t = ................................................ w = ................................................ [4]
Mark scheme: 26 t = 0.5 4 w = − 3 M1 for correctly equating one set of coefficients M1 for correct method to eliminate one variable OR M1 for making t or w the subject of one equation M1 for substitution of t or w from their rearranged equation A1 for t = 0.5 A1 for w = −3 If A0 scored SC1 for 2 values satisfying one of the original equations
What was in this paper
The subtopics covered by these 26 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
3Algebraic manipulation2Area and perimeter2Ordering2The four operations2Angles1Compound shapes and parts of shapes1Equations1Equations of linear graphs1Fractions, decimals and percentages1Graphs of functions1Introduction to probability1Limits of accuracy1Percentages1Powers and roots1Scatter diagrams1Similarity1Symmetry1Time1Units of measure1What you needed in this session
Cambridge’s own grade thresholds for 2025 Feb/March, Paper 1 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.