Cambridge IGCSE Mathematics 0580 — 2024 Feb/March Paper 2 · Variant 2
0580/22/F/M/24 · 26 questions · 70 marks · ≈79 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 paper12 pages
Mark scheme7 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · A night bus runs from 21 50 to 05 18 the next day
1 A night bus runs from 21 50 to 05 18 the next day. Work out the number of hours and minutes that the night bus runs. ................... h .................... min [1]
Mark scheme: Question Answer Marks Partial Marks 1 7h 28min 1
Q2 · Calculate 5.76 + 2.83
2 Calculate 5.76 + 2.83 . ................................................. [1]
Mark scheme: 2 24.352 1
Q3 · Simplify 4m + 7k - m + 3k
3 Simplify 4m + 7k - m + 3k . ................................................. [2]
Mark scheme: 3 3m + 10k final answer 2 B1 for 3m or 10k in final answer or for 3m + 10k seen and spoilt
Q4 · B cm NOT TO SCALE c cm d cm a cm Base The diagram shows the net of a cuboid with its base…
4 b cm NOT TO SCALE c cm d cm a cm Base The diagram shows the net of a cuboid with its base shaded. The length of the cuboid is 10 cm, its width is 4 cm and its height is 5 cm. Write down the values of each of a, b, c and d. a = ........................., b = ........................., c = ........................., d = ......................... [4]
Mark scheme: 4 a = 18 b = 10 c = 4 d = 9 4 B1 for each If 0 scored, SC1 for b or c = 4, 5 or 10
Q5 · There are 20 cars in a car park and 3 of the cars are blue
5 There are 20 cars in a car park and 3 of the cars are blue. (a) James wants to draw a pie chart to show this information. Find the angle of the sector for the blue cars in this pie chart. ................................................. [2] (b) One of the 20 cars is picked at random. Find the probability that this car is not blue. ................................................. [1]
Mark scheme: 5(a) 54 2 3 360 M1 for 360 oe or 3 oe 20 20 5(b) 17 1 oe 20
Q6 · Y 5 B 4 3 2 A 1 x −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 Write AB as a column vector
6 y 5 B 4 3 2 A 1 x −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 Write AB as a column vector. AB = [1] f p
Mark scheme: 6 −10 1 final answer 3
Q7 · As the temperature increases, the number of people who go swimming increases
7 As the temperature increases, the number of people who go swimming increases. Write down the type of correlation that this statement describes. ................................................. [1]
Mark scheme: 7 Positive 1
Q8 · The nth term of a sequence is n 2 - 3
8 (a) The nth term of a sequence is n 2 - 3 . Find the first three terms of this sequence. ............... , ............... , ............... [2] (b) These are the first five terms of a different sequence. 1 3 9 27 81 Find the nth term of this sequence. ................................................. [2]
Mark scheme: 8(a) −2 1 6 2 B1 for any 2 correct in correct position If 0 scored SC1 for −−3 2 1 8(b) 3n−1 2 B1 for 3an + k , a ≠ 0 or 3c for any integer c>1
Q9 · The line y = 2x - 5 intersects the line y = 3 at the point P
9 The line y = 2x - 5 intersects the line y = 3 at the point P. Find the coordinates of the point P. ( ......................., .......................) [2]
Mark scheme: 9 ( 4, 3 ) 2 B1 for each or M1 for 3 = 2x – 5 or better
Q10 · 5.3 cm S R NOT TO 4.4 cm 3.83.8 cmcm SCALE P Q 8.7 cm The diagram shows a trapezium PQRS
10 5.3 cm S R NOT TO 4.4 cm 3.83.8 cmcm SCALE P Q 8.7 cm The diagram shows a trapezium PQRS. Calculate the area of the trapezium. ......................................... cm2 [2]
Mark scheme: 10 26.6 2 1 M1 for ( 5.3 + 8.7 ) 3.8 oe 2
Q11 · 511 Without using a calculator, work out 1 -
1 511 Without using a calculator, work out 1 - . 4 6 You must show all your working and give your answer as a fraction in its simplest form. ................................................. [3]
Mark scheme: 11 5 1 1 B1 Correct method for dealing with mixed or + number 4 4 6 5k Allow 4 k 15 10 M1 Correct method to find common and denominator 12 12 10 e.g. 31 and 12 12 5 A1 cao 12
Q12 · Farid spins a three-sided spinner with sides labelled A, B and C
12 Farid spins a three-sided spinner with sides labelled A, B and C. The probability that the spinner lands on C is 0.35 . Farid spins the spinner 40 times. Calculate the number of times he expects the spinner to land on C. ................................................. [1]
Mark scheme: 12 14 1
Q13 · The bearing of B from A is 107°
13 The bearing of B from A is 107°. Calculate the bearing of A from B. ................................................. [2]
Mark scheme: 13 287 2 M1 for 360 – (180 – 107) oe or indicates correct angle on a diagram
Q14 · A train, 1750 metres long, is travelling at 55 km/h
14 A train, 1750 metres long, is travelling at 55 km/h. Calculate how long it will take for the whole train to completely cross a bridge that is 480 metres long. Give your answer in seconds, correct to the nearest second. ............................................... s [3]
Mark scheme: 14 146 cao 3 1750 + 480 M2 for 60 60 oe 55 1000 or M1 for distance = 1750 + 480 oe 55 1000 or oe soi 60 60 or correctly writing their whole number of seconds from a more accurate answer seen
Q15 · Y 4 3 2 1 B A – 10 – 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 x – 1 – 2 C – 3 – 4…
15 y 4 3 2 1 B A – 10 – 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 x – 1 – 2 C – 3 – 4 – 5 – 6 (a) Describe fully the single transformation that maps (i) triangle A onto triangle B ............................................................................................................................................. ............................................................................................................................................. [2] (ii) triangle A onto triangle C. ............................................................................................................................................. ............................................................................................................................................. [3] (b) Draw the image of triangle A after a rotation, 90° clockwise, about ( 1, 3) . [2]
Mark scheme: 15(a)(i) reflection 2 B1 for each x = −2 15(a)(ii) enlargement 3 B1 for each 1 [sf] 2 ( −3, −4 ) 15(b) Image at ( 0, 3 ) , ( −4, 3 ) , ( − 3, −1) 2 B1 for correct size and orientation, wrong centre
Q16 · X is an integer
16 x is an integer. %= {x : 1 G x G 10 } P = {x : x is an even number} Q = {x : x is a multiple of 5} P Q Complete the Venn diagram. [2]
Mark scheme: 16 2 B1 for two sections correct out of four P Q 2 4 10 5 6 8 1 3 7 9
Q17 · The height of each of 200 people is measured
17 The height of each of 200 people is measured. The table shows the results. Height (h cm) 100 1 h G 120 120 1 h G 1 30 130 1 h G 150 150 1 h G 190 Frequency 32 55 64 49 Calculate an estimate of the mean height. ............................................ cm [4]
Mark scheme: 17 138.425 4 M1 for mid-points soi (110, 125, 140, 170) M1 for use of fh with h in correct interval including both boundaries M1 for (dep on 2nd M1) for fh ¸ 200
Q18 · Find the highest common factor (HCF) of 28x 5 and 98x 3
18 Find the highest common factor (HCF) of 28x 5 and 98x 3. ................................................. [2]
Mark scheme: 18 14x 3 2 B1 for 14 kx or 7x 3 or 2x 3
Q19 · 15 Speed (m/s) NOT TO SCALE 0 20 140 190 Time (seconds) The speed–time graph shows…
19 15 Speed (m/s) NOT TO SCALE 0 20 140 190 Time (seconds) The speed–time graph shows information about a bus journey. Calculate the total distance travelled by the bus. ............................................. m [3]
Mark scheme: 19 2325 3 M2 for correct method for total area 1 e.g. 15 (190 + 120 ) 2 or M1 for correct method for one area e.g. 1 20 15 , (140 – 20) × 15 or 2 1 (190 − 140 ) 15 oe 2
Q20 · C NOT TO SCALE 5.6 cm 23° A B 4.9 cm Calculate the area of triangle ABC
20 C NOT TO SCALE 5.6 cm 23° A B 4.9 cm Calculate the area of triangle ABC. ......................................... cm2 [2]
Mark scheme: 20 5.36 or 5.360 to 5.361 2 1 M1 for 5.6 4.9 sin23 oe 2
Q21 · 5 3 = 3h Write down the value of h
21 (a) 5 3 = 3h Write down the value of h. h = ................................................ [1] 3 (b) Simplify 4x 3 . ` j ................................................. [2]
Mark scheme: 21(a) 1 1 oe 5 21(b) 64x9 2 B1 for 64 kx or kx 9 as final answer or correct answer spoiled
Q22 · Y is inversely proportional to the square of ( x + 3)
22 y is inversely proportional to the square of ( x + 3) . When x = 5 , y = 0.375 . Find y in terms of x. y = ................................................ [2]
Mark scheme: 22 24 2 oe final answer y = 2 k ( x + 3) M1 for y = ( x + 3) 2
Q23 · On the axes, sketch the graph of y = cos x , for 0° G x G 360°
23 (a) On the axes, sketch the graph of y = cos x , for 0° G x G 360° . y 1 0 x 180° 360° – 1 [2] (b) Solve the equation cosx = 0 .294 for 0° G x G 360° . x = .................. or x = .................. [2]
Mark scheme: 23(a) 2 M1 for correct cosine curve shape through (0, 1) Correct sketch to go through (0, 1), close to (360, 1) and reasonably close to (180, –1) 23(b) 72.9 and 287.1 2 B1 for one correct If 0 scored, SC1 for two angles with a sum of 360
Q24 · X 2 - 16 x + a can be written in the form ( x + b) 2
24 x 2 - 16 x + a can be written in the form ( x + b) 2 . Find the value of a and the value of b. a = ................................................ b = ................................................ [2] Questions 25 and 26 are printed on the next page.
Mark scheme: 24 [a =] 64 2 B1 for each [b =] −8 or for both (x – 8)2 and x2 – 16x + 64
Q25 · A bag contains 2 green buttons, 5 red buttons and 6 blue buttons
25 A bag contains 2 green buttons, 5 red buttons and 6 blue buttons. Two buttons are taken at random from the bag without replacement. Calculate the probability that the two buttons are different colours. ................................................. [4]
Mark scheme: 25 2 4 2 11 5 8 6 7 oe nfww M3 for + + oe 3 13 12 13 12 13 12 2 1 5 4 6 5 or 1 − + + oe 13 12 13 12 13 12 or M2 for sum of three or more correct product pairs and no incorrect pairs 2 1 5 4 6 5 or for + + and no 13 12 13 12 13 12 other pairs j k or M1 for 13 12 104 If 0 scored SC1 for answer oe 169
Q26 · A is the point (6, 1) and B is the point (2, 7)
26 A is the point (6, 1) and B is the point (2, 7). Find the equation of the perpendicular bisector of AB. Give your answer in the form y = mx + c . y = ................................................. [5]
Mark scheme: 26 2 4 5 B1 for midpoint ( 4, 4 ) soi y = x + final answer 3 3 7 −1 M1 for [gradient AB =] oe 2 − 6 −1 M1 for [m =] their gradient of AB M1 for substituting their midpoint into y = ( their m ) x + c dep on at least M1 earned
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.
3Rates3Area and perimeter2Equations of linear graphs2Introduction to probability2Averages and measures of spread1Fractions, decimals and percentages1Graphs of functions1Indices II1Powers and roots1Probability of combined events1Ratio and proportion1Scatter diagrams1Sequences1Sets1Surface area and volume1Time1Transformations1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2024 Feb/March, Paper 2 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.