Question 12 marks
Question
x° NOT TO SCALE 34° The diagram shows an isosceles triangle. Find the value of x. x = …… [2]
Mark scheme
1 112 2 M1 for 180 – 34 × 2 oe
Mathematics 0580/22 October/November 2022: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 2 Extended, October/November 2022. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
0580_w22_qp_220580_w22_ms_220580/22/O/N/22
- Paper
- Paper 2 Extended
- Total marks
- 70
- Time
- 1 hour 30 minutes
- Code on the paper
- 0580/22/O/N/22
0580/22 mark scheme, question by question
Each question as it's printed, and the mark scheme's points for it, as text. Diagrams, tables and graphs are in the PDFs above.
Question 21 mark
Question
Simplify. y # 27 - y # 77 …… [1]
Mark scheme
2 –50y 1
Question 31 mark
Question
Find the sum of 3 2 and - 3 2 . …… [1]
Mark scheme
3 0 1
Question 42 marks
Question
Expand. x (3 + x 2) …… [2]
Mark scheme
4 3x + x3 final answer 2 B1 for one correct term from two in final answer or for correct answer then spoilt
Question 53 marks
Question
Jenna buys 2.4 m of ribbon and 4.8 m of fabric. The total cost is $33.48 . Ribbon costs $0.85 per metre. Find the cost of 1 m of fabric. $ …… [3]
Mark scheme
5 6.55 3 M2 for (33.48 – 2.4 × 0.85) oe or M1 for 2.4 × 0.85
Question 66 marks
Question
(a) These are the first five terms of a sequence. 27 26 23 18 11 Find the next two terms in the sequence. …… , …… [2] (b) The table shows information about two different sequences. First five terms of sequence nth term Sequence A 3 10 17 24 31 Sequence B 2 11 26 47 74 Complete the table. [4] 5 1
Mark scheme
6(a) 2 –9 2 B1 for one correct 6(b) Sequence A 2 B1 for 7n + c or kn – 4 k ≠ 0 7n – 4 oe final answer or for correct answer seen then spoilt Sequence B 2 M1 for finding second differences of 6 3n2 – 1 oe final answer or has an answer that is a quadratic sequence or for correct answer seen then spoilt
Question 72 marks
Question
Without using a calculator, work out - . 9 6 You must show all your working and give your answer as a fraction in its simplest form. …… [2]
Mark scheme
7 10 3 M1 Allow any correct common denominator and 18k 18 18 7 A1 cao 18
Question 83 marks
Question
Daryl records the number of hours in a week 8 people spend exercising. 5 2 1.5 3 18 4.5 2 4 (a) Find the median. …… h [2] (b) Explain why the mean may not be a suitable average to use. …… [1]
Mark scheme
8(a) 3.5 2 M1 for values in correct order 1.5 2 2 3 4 4.5 5 18 or 3 and 4 identified as middle numbers 8(b) One extreme value oe 1
Question 92 marks
Question
The diagram shows three triangles A, B and C. 60° 60° 6 cm NOT TO 60° 25° SCALE 6 cm 6 cm 25° 25° A B C (a) Which two of the triangles A, B and C are congruent with each other? …… [1] (b) Draw a ring around the congruence criterion that can be used to support your answer to part (a). SSS ASA SAS RHS [1]
Mark scheme
9(a) A and C 1 9(b) ASA 1
Question 103 marks
Question
Calculate. (a) 2000 # 1.2 3 …… [1] 1 6 (b) 2 # 8 17 …… [1] 4.5 (cos 30°) (c) -2 3 …… [1]
Mark scheme
10(a) 3456 1 10(b) 3 1 0.75 or oe 4 10(c) 1 1 0.25 or 4
Question 113 marks
Question
The graph of y = (x - 3) (x + b) (x + 2) intersects the y-axis at - 30 . (a) Find the value of b. b = …… [2] (b) When x 2 0 the graph crosses the x-axis once. Write down the coordinates of this point. ( …… , …… ) [1]
Mark scheme
11(a) 5 2 M1 for (0 – 3)(0 + b)(0 + 2) = –30 oe or better 11(b) (3, 0) 1
Question 122 marks
Question
x = 3 2 # 5 2 # 7 # 199 57 when written as a product of its prime factors. Write x ' 315 as a product of its prime factors. …… [2]
Mark scheme
12 5 × 19957 2 M1 for [315 =] 32 × 5 × 7 oe or 32 × 52 × 7 ÷ 315 = 5
Question 136 marks
Question
The table shows information about the mass of each of 50 children. Cumulative Mass (k kg) Frequency k G 20 0 k G 22 7 k G 24 23 k G 28 35 k G 32 43 k G 36 47 k G 42 50 (a) Draw a cumulative frequency diagram to show this information. 50 40 30 Cumulative frequency 20 10 0 k 20 24 28 32 36 40 44 Mass (kg) [3] (b) Use your graph to find an estimate of the 90th percentile. …… [1] 14 136 girls and 144 boys each measure the distance they jump in centimetres. The box-and-whisker plots show the distributions of these distances. Girls Boys 100 120 140 160 180 200 Distance jumped (cm) Each child who jumps a distance greater than 160 cm gets a certificate. Work out an estimate of the total number of children who get a certificate. …… [2]
Mark scheme
13(a) A correct cumulative frequency diagram 3 B1 for correct horizontal placement for 7 plots B1 for correct vertical placement for 7 plots B1FT dep on at least B1 for reasonable increasing curve or polygon through their 7 points If 0 scored SC1 FT for 6 out of 7 points correctly plotted 13(b) 33 to 34.5 1 FT their increasing cumulative frequency graph
Question 14
Question
In the question paper above.
Mark scheme
14 104 2 M1 for 0.5 × 136 oe or 0.25 × 144 oe
Question 151 mark
Question
95° NOT TO 101° SCALE 79° 85° The diagram shows a quadrilateral. Give a geometrical reason why this is a cyclic quadrilateral. …… [1]
Mark scheme
15 Opposite angles add up to 180 oe 1
Question 164 marks
Question
(a) Shade the region indicated in each Venn diagram. G ∩ H′ (J ∪ K ′ ) ∩ L G H J K L [2] (b) The Venn diagram shows some information about the number of elements in sets A, B, C and . A B 3 21 8 7 2 C Given the following information, complete the Venn diagram. n (A + B + C ) = 1 n (A , B , C )l = 17 n (C ) = 42 [2] x+5
Mark scheme
16(a) G H 2 B1 for each J K L 16(b) 2 B1 for 2 correct
Question 176 marks
Question
f (x) = x 2 g (x) = h (x) = 7x - 3 2 (a) Find f (- 3) . …… [1] (b) Find g -1 (x) . g -1 (x) = …… [2] (c) Solve gf (x) = hh -1 (63) where x 2 0 . x = …… [3] o o as a fraction in its simplest form.
Mark scheme
17(a) 9 1 17(b) 2x – 5 final answer 2 M1 for correct first step e.g. y +5 5 x x= or 2y = x + 5 or y – = or 2 2 2 better 17(c) 11 3 x2 + 5 M1 for 2 M1 for hh–1(63) = 63 soi
Question 183 marks
Question
Write 0.419 You must show all your working. …… [3]
Mark scheme
18 419.19 − 4.19 oe M1 83 A2 415 cao Al for oe 198 990 k If M0 scored SC1 for or correct 990 answer with insufficient working
Question 193 marks
Question
Katy picks a number at random from the numbers 2, 3 and 5. She then picks a number at random from the numbers 5, 6, 7 and 9. When she adds the two numbers the answer is even. Find the probability that exactly one of the numbers picked is a 5. …… [3]
Mark scheme
19 3 3 M1 for clearly identifying the 7 even oe outcomes 7 2 6, 3 5, 3 7, 3 9, 5 5, 5 7, 5 9 M1 for clearly identifying the 3 even outcomes with just one five 3 5, 5 7 and 5 9 1 If 0 scored SC1 for answer oe 4
Question 203 marks
Question
Simplify fully. 3 (a) (81x 16) 4 …… [2] 1 - 1 (b) e 2 o 2 y …… [1]
Mark scheme
20(a) 27x12 final answer 2 B1 for kx12 or 27xc final answer or for 27x12 then spoilt 20(b) [±] y 1
Question 214 marks
Question
12.5 cm NOT TO SCALE 5.5 cm 9.2 cm A solid is made by cutting a small cone from a larger cone, as shown in the diagram. The height of the larger cone is 12.5 cm. The height of the solid is 5.5 cm. The diameter of the base of the larger cone is 9.2 cm. Work out the volume of the solid. 1 [The volume, V, of a cone with radius r and height h is V = rr 2 h .] 3 …… cm 3 [4] Questions 22 and 23 are printed on the next page.
Mark scheme
21 228 or 228.3 to 228.4 4 1 9.2 2 M1 for × π× ×12.5 oe 3 2 9.2 diameter M1 for = oe or better 12.5 12.5 − 5.5 2 1 their 5.152 M1 for × π× × (12.5 − 5.5) 3 2 oe OR M2 for 2 π 9.2 π 2 × ×12.5 − × r × (12.5 − 5.5) oe 3 2 3 for any r < 4.6 If 0 scored SC1 for 913 or 913.3 to 913.5
Question 223 marks
Question
The volumes of two mathematically similar objects are 56 cm 3 and 875 cm 3 . The height of the smaller object is 18 cm. Find the height of the larger object. …… cm [3] 4 2
Mark scheme
22 45 3 875 M2 for 3 × 18 oe 56 875 56 or M1 for 3 or 3 oe or 56 875 183 56 = oe h3 875
Question 237 marks
Question
Solve + = 3. x + 1 2x - 5 You must show all your working. x = …… or x = …… [7]
Mark scheme
23 [0 =] 6x2 – 19x + 3 B5 B4 for 8x – 20 + 2x + 2 = 6x2 + 6x –15x – 15 or better OR M2 for 4(2x – 5) + 2(x + 1) = 3(x + 1)(2x – 5) oe or M1 for 4(2x – 5) + 2(x + 1) or better or common denominator (x + 1)(2x – 5) or better B1 for 2x2 + 2x – 5x – 5 or better seen M1 for correctly simplifying their quadratic to the form [0 =] ax2 + bx + c Correct method to solve their three term M1 e.g. (6x – 1)(x – 3) − ( −19 ) ± ( −19)2 − 4 × 6 × 3 quadratic 2× 6 1 B1 x = 3, x = oe 6
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Where can I find the 0580/22 October/November 2022 mark scheme?
On this page, free: the mark scheme for IGCSE Mathematics 0580/22, October/November 2022 (0580_w22_ms_22), and the question paper (0580_w22_qp_22), to read or download, with each question's marking points written out underneath.
How many marks is 0580/22 out of?
Mathematics 0580/22 for October/November 2022 is out of 70 marks, with 1 hour 30 minutes to answer it.
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