Cambridge IGCSE Mathematics 0580 — 2024 Oct/Nov Paper 2 · Variant 1
0580/21/O/N/24 · 23 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 concert starts at 19 50 and finishes 2 hours 42 minutes later
1 A concert starts at 19 50 and finishes 2 hours 42 minutes later. Work out the time the concert finishes. ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1 22 32 or 10 32 pm 1
Q2 · 2 Find the reciprocal of 1 4
1 2 Find the reciprocal of 1 4. ................................................. [1]
Mark scheme: 2 4 1 or 0.8 5
Q3 · Use one of the symbols 1, 2 or = to make each statement true
3 Use one of the symbols 1, 2 or = to make each statement true. 2 ....................... 0.2861 7 99 ....................... 11% 900 13 ....................... 40 [2]
Mark scheme: 3 < 2 B1 for two correct = =
Q4 · Safia has a piece of fabric of length 5.6 m
4 Safia has a piece of fabric of length 5.6 m. She cuts the fabric into two parts, with lengths in the ratio 3 : 4. Calculate the length of the longer part. .............................................. m [2]
Mark scheme: 4 3.2 2 5.6 M1 for k where k = 1, 3 or 4 3 + 4
Question 5
5 Work out. 6 (a) 3 e o - 4 f p [1] 4 - 7 (b) e o + e o -1 5 f p [1]
Mark scheme: 5(a) 18 1 −12 5(b) −3 1 4
Q6 · The diagram shows a right-angled triangle ABC and a quadrilateral AEDC
6 The diagram shows a right-angled triangle ABC and a quadrilateral AEDC. C y° 17° NOT TO SCALE D z° 122° x° 34° A B E Find the value of (a) x x = ................................................ [1] (b) y y = ................................................ [1] (c) z. z = ................................................ [1]
Mark scheme: 6(a) 58 1 6(b) 39 1 6(c) 251 1
Question 7
7 Factorise. 28x - 35 ................................................. [1]
Mark scheme: 7 7(4x – 5) final answer 1
Q8 · Edith invests $3000 in a savings account
8 Edith invests $3000 in a savings account. The account pays simple interest at a rate of 2.6% per year. Calculate the total interest earned at the end of 3 years. $ ................................................. [2]
Mark scheme: 8 234 2 3000 2.6 3 M1 for 100
Q9 · NOT TO SCALE `x + 132j ° x° The diagram shows part of a regular polygon
9 NOT TO SCALE `x + 132j ° x° The diagram shows part of a regular polygon. The interior angle of the polygon is 132° larger than the exterior angle. Calculate the number of sides of this polygon. ................................................. [3]
Mark scheme: 9 15 3 B2 for [x =] 24 OR M1 for x + x + 132 = 180 oe soi 360 M1 for oe provided this gives an their x integer answer
Q10 · Jacinda plays a game with her friend
10 Jacinda plays a game with her friend. She can win, lose or draw the game. The probability that she wins the game is 0.28 . (a) Jacinda is twice as likely to draw the game as to lose the game. Work out the probability that she loses the game. ................................................. [2] (b) Jacinda plays the game 150 times. Find the expected number of times that she wins. ................................................. [1]
Mark scheme: 10(a) 0.24 oe 2 M1 for 1 – 0.28 oe 10(b) 42 1
Q11 · 4 11 Without using a calculator, work out 5 - 3
1 4 11 Without using a calculator, work out 5 - 3 . 3 7 You must show all your working and give your answer as a mixed number in its simplest form. ................................................. [3]
Mark scheme: 11 B1 Correct step for dealing with mixed numbers 16 25 1 4 or − 16 k 25 k Allow or 3 7 23 7 3k 7 k M1 Correct method to find common denominator 112 75 12 7 and 72 and e.g. 5 and 312 21 21 21 21 21 21 16 A1 121 cao
Q12 · Solve the simultaneous equations
12 Solve the simultaneous equations. You must show all your working. 5x + 6y = 9 3x - 2y = - 17 x = ....................................................... y = ....................................................... [3]
Mark scheme: 12 Correctly eliminating one variable M1 x = –3 A1 If A0 scored SC1 for 2 values satisfying one of the original equations. y = 4 A1
Q13 · A sequence has nth term 3n 2 - 1
13 (a) A sequence has nth term 3n 2 - 1. Find the second term in this sequence. ................................................. [1] (b) The table shows the first five terms of sequences A and B. 1st term 2nd term 3rd term 4th term 5th term nth term Sequence A –6 –2 2 6 10 Sequence B 3 17 55 129 251 Complete the table to show the nth term of each sequence. [4]
Mark scheme: 13(a) 11 1 13(b) 4n –10 oe final answer 4 B2 for 4n – 10 oe final answer or B1 for 4n + j or kn − 10 (k ≠ 0) or 4n – 10 seen then spoilt and 2n3 + 1 oe final answer B2 for 2n3 + 1 oe final answer or B1 for any cubic expression in n or 3rd difference = 12 or for correct answer seen then spoilt
Q14 · Two solid steel statues are mathematically similar
14 Two solid steel statues are mathematically similar. The smaller statue has height 12 cm and the larger statue has height 15 cm. The larger statue has a mass 2.5 kg. The density of steel is 8 g/cm3. Calculate the volume of the smaller statue. [Density = mass ÷ volume.] .......................................... cm3 [4]
Mark scheme: 14 160 4 2500 12 3 M3 for V = 3 oe 8 15 figs 25 12 3 or for answer figs 16 from × 8 15 3 or B2 for 1.28 [kg] OR M1 for 2500 ÷ 8 oe or 312.5 seen 12 3 15 3 M1 for or oe 15 12
Q15 · Students in class P take a test
15 Students in class P take a test. These statistics show information about their marks. • lower quartile = 38 • median = 53 • interquartile range = 28 • range = 81 • highest mark = 96 (a) Draw a box-and-whisker plot to represent this information. 0 20 40 60 80 100 Test marks [3] (b) Students in class Q take the same test. For class Q, the median is 49 and the interquartile range is 35. Make two comments comparing the distribution of marks for class P with that of class Q. 1. ........................................................................................................................................................ ........................................................................................................................................................ 2. ........................................................................................................................................................ ........................................................................................................................................................ [2]
Mark scheme: 15(a) Correct box-and-whisker plot 3 B1 for UQ = 66 or Lowest = 15 soi L = 15 M1 for at least 3 values correct within box and LQ = 38 whisker plot Median = 53 UQ = 66 H = 96 15(b) Class Q scored fewer marks on 2 B1 for each average [as median is lower] oe Class Q have a larger spread of marks [as IQR is higher] oe
Q16 · R cm NOT TO 6 cm SCALE 18 cm The diagram shows a sphere of radius 6 cm and a cylinder of…
16 R cm NOT TO 6 cm SCALE 18 cm The diagram shows a sphere of radius 6 cm and a cylinder of height 18 cm and radius R cm. The volume of the sphere is equal to the volume of the cylinder. Calculate the curved surface area of the cylinder. Give your answer in terms of r. 4 3 [The volume, V, of a sphere with radius r is V = r r ] 3 .......................................... cm2 [4]
Mark scheme: 16 144 cao 4 4 3 6 3 M2 for [ R2 =] oe 18 4 3 2 or M1 for 6 = R 18 oe 3 M1 for 2 theirR 18 oe
Question 17
17 Solve. 3x 2 - 7x - 16 = 0 You must show all your working and give your answers correct to 2 decimal places. x = .................... or x = .................... [4]
Mark scheme: 17 −− 7 ( − 7 ) 2 − 4 ( 3 )( −16 ) B2 B1 for ( − 7 ) 2 − 4 ( 3) ( −16 ) ) or better oe 2 3 p + q p − q and if in the form or then r r B1 for p = – (–7) and r = 2(3) 3.75 and –1.42 B2 B1 for each or SC1 for answers 3.8 or 3.754… and –1.4 or –1.42… or –1.421 or 3.75 and –1.42 seen in working or –3.75 and 1.42 as final answers
Q18 · G ( x) = 4x + 3 (a) Find x when g ( x) = 1
18 g ( x) = 4x + 3 (a) Find x when g ( x) = 1. ................................................. [1] -1 1 (b) Find g e o . 16 ................................................. [2]
Mark scheme: 18(a) –3 1 18(b) –5 2 1 M1 for or 4–2 4 2
Q19 · % = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} P = {odd numbers} Q = {multiples of 3} R = {square…
19 % = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} P = {odd numbers} Q = {multiples of 3} R = {square numbers} (a) Find P + Q + R . { ............................................... } [1] (b) (i) Find Q , R . { ............................................... } [1] (ii) Find n `P + ( Q , R ) lj. ................................................. [1]
Mark scheme: 19(a) 9 1 19(b)(i) 1, 3, 4, 6, 9 1 19(b)(ii) 2 1 FT 5 – numbers of odds in (b)(i)
Q20 · S NOT TO 4 cm SCALE 18 cm T 28° P Q R 9 cm The diagram shows two right-angled triangles…
20 S NOT TO 4 cm SCALE 18 cm T 28° P Q R 9 cm The diagram shows two right-angled triangles PQS and RQT. PQR and QTS are straight lines. Calculate angle QTR. Angle QTR = ................................................ [5]
Mark scheme: 20 63.7 or 63.68 to 63.69 5 9 M4 for tan [QTR] = oe 18sin28 − 4 OR M3 for 18sin28 – 4 or M2 for 18sin28 QS or M1 for = sin28 oe 18 and 9 M1 for tan [QTR] = oe theirQT
Q21 · Solve the equation 3 tanx + 5 = 1 for 0° G x G 360°
21 Solve the equation 3 tanx + 5 = 1 for 0° G x G 360° . x = .................... or x = .................... [3]
Mark scheme: 21 126.9 and 306.9 3 B2 for one correct answer 4 or M1 for tan x = – oe 3 If M1 or 0 scored, SC1 for two angles with a difference of 180
Q22 · The graph of y = ( x + 2)( x - 1) 2 is shown on the grid
22 The graph of y = ( x + 2)( x - 1) 2 is shown on the grid. y 4 3 2 1 x -2 -1 0 1 2 -1 (a) Show that y = ( x + 2 )( x - 1 ) 2 can be written as y = x 3 - 3x + 2 . [2] (b) By drawing a suitable straight line, solve the equation 2x 3 - 5x = 0 . x = .................... or x = .................... or x = .................... [4] Question 23 is printed on the next page.
Mark scheme: 22(a) x2 – x – x + 1 M1 or x2 + 2x– x – 2 A correct unsimplified expansion A1 e.g. x3 + 2x2 –x2 –2x – x2 –2x + x + 2 oe leading to [y = ] x3 – 3x + 2 22(b) y = 2 – 0.5x ruled B2 B1 for [y =] 2 – 0.5x soi or for y = 2 – kx drawn or for y = k – 0.5x drawn –1.5 to –1.6 B2 B1 for two correct values 0 1.5 to 1.6
Q23 · ( x - 5) 2 + k = x 2 - px - 21 Find the value of p and the value of k
23 ( x - 5) 2 + k = x 2 - px - 21 Find the value of p and the value of k. p = ....................................................... k = ....................................................... [2]
Mark scheme: 23 [p = ] 10 2 B1 for each [k = ] –46
What was in this paper
The subtopics covered by these 23 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
What you needed in this session
Cambridge’s own grade thresholds for 2024 Oct/Nov, Paper 2 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.