Question 12 marks
Question
Write 24.07839 (a) correct to 2 decimal places …… [1] (b) correct to the nearest 10. …… [1]
Mark scheme
1(a) 24.08 cao 1 1(b) 20 cao 1
Mathematics 0580/22 October/November 2023: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 2 (Extended), October/November 2023. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
0580_w23_qp_220580_w23_ms_220580/22/O/N/23
- Paper
- Paper 2 (Extended)
- Total marks
- 70
- Time
- 1 hour 30 minutes
- Code on the paper
- 0580/22/O/N/23
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
Write down the number that is 9 greater than - 23. …… [1]
Mark scheme
2 –14 1
Question 32 marks
Question
v = u + at Find the value of v when u = 30 , a =- 2 and t = 7 . v = …… [2]
Mark scheme
3 16 2 B1 for –14 or M1 for 30 – 2 × 7
Question 41 mark
Question
Change 62 000 millimetres into kilometres. …… km [1]
Mark scheme
4 0.062 1
Question 52 marks
Question
50° x° NOT TO SCALE 114° The diagram shows two intersecting straight lines crossing two parallel lines. Find the value of x. x = …… [2]
Mark scheme
5 64 2 B1 for any of these angles labelled on the diagram or M1 for x + 50 = 114 or better
Question 62 marks
Question
(a) Explain why 111 is not a prime number. …… [1] (b) Find a prime number between 110 and 120. …… [1]
Mark scheme
6(a) Multiple of 3 or multiple of 37 1 6(b) 113 1
Question 72 marks
Question
North NOT TO North SCALE P 39° Q East Find the bearing of Q from P. …… [2] 1 3
Mark scheme
7 231 2 B1 for any of these angles in correct place on diagram 51 or 129 or 141 between east line drawn from P and QP or 39 between west line drawn from P and QP or indicating the correct bearing of Q from P on the diagram or M1 for 180 + (90 – 39) oe or 360 – (90 + 39) oe
Question 83 marks
Question
Without using a calculator, work out 3 - 1 . 8 4 You must show all your working and give your answer as a mixed number in its simplest form. …… [3]
Mark scheme
8 B1 Correct step for dealing with mixed numbers 25 7 1 3 or 2 − 25k 7k 8 4 8 4 Allow or 8k 4k M1 Correct method to find common denominator 25 14 1 6 and 2 and oe 1 6 100 − 56 8 8 8 8 e.g. 3 − 1 , 8 8 32 3 A1 1 cao 8
Question 92 marks
Question
Write 90 as a product of its prime factors. …… [2]
Mark scheme
9 2 × 3 × 3 × 5 or 2 × 32 × 5 2 B1 for 2, 3, 3, 5 or M1 for correct factor tree/diagram/list/table.
Question 102 marks
Question
Expand and simplify. 2 (t + w) + 3 (w - t) …… [2]
Mark scheme
10 5w – t final answer 2 B1 for 2t + 2w or 3w – 3t or for 5w – t seen then spoiled or for 5w or – t in the final answer
Question 114 marks
Question
6.3 cm NOT TO h cm SCALE 5 cm 9 cm The two shapes are mathematically similar. (a) Find the value of h. h = …… [2] (b) The area of the smaller shape is 16 cm 2 . Calculate the area of the larger shape. …… cm 2 [2]
Mark scheme
11(a) 3.5 2 9 6.3 M1 for = oe 5 h 11(b) 51.84 2 9 2 5 2 M1 for or oe 5 9 their ( a ) 2 2 6.3 or or oe their ( a ) 6.3
Question 123 marks
Question
10 Speed NOT TO (m/s) SCALE 0 0 12 16 Time (seconds) The diagram shows a speed–time graph for 16 seconds of a car journey. (a) Find the deceleration of the car in the final 4 seconds. …… m/s 2 [1] (b) Find the total distance travelled during the 16 seconds. …… m [2]
Mark scheme
12(a) 2.5 oe 1 12(b) 140 2 M1 for a correct area 1 e.g. 10 × 12, × 4 × 10 , 0.5 × (16 + 12) × 10 2
Question 134 marks
Question
(a) 3 3p # 3 2p = 729 Find the value of p. p = …… [2] (b) Simplify. 1 (32x 10) 5 …… [2]
Mark scheme
13(a) 1.2 oe 2 B1 for 32 p +3 p or 36 soi 13(b) 2x2 final answer 2 B1 for kx 2 or 2 xk as final answer or correct answer spoiled
Question 143 marks
Question
y = 2w 2 - x Rearrange the formula to make w the subject. w = …… [3]
Mark scheme
14 y+x 3 M1 for isolating term in w [±] oe final answer M1 for division by 2 2 M1 for square root Max 2 marks if answer incorrect
Question 153 marks
Question
(a) On the Venn diagram, shade the region P , Q l . P Q [1] (b) n () = 20 n (A , B) l = 1 n (A) = 12 n (B) = 10 Complete the Venn diagram. A B [2]
Mark scheme
15(a) 1 15(b) A B 2 B1 for two correct or for n(A) =12 and n(B) = 10 and n( A B ) ≠ 9 3 7 0 1
Question 162 marks
Question
Find the lowest common multiple (LCM) of 12x 8 and 8x 12 . …… [2]
Mark scheme
16 24x12 final answer 2 B1 for 24 x k or kx12 in final answer
Question 174 marks
Question
(a) C NOT TO O SCALE 28° A B A, B and C are points on a circle, centre O. Angle OBA = 28° . Find angle ACB. Angle ACB = …… [2] (b) Q NOT TO SCALE R 52° 47° T U P P, Q and R are points on a circle. TU is a tangent to the circle at P. Angle TPR = 47° and angle PRQ = 52° . Find angle RPQ. Angle RPQ = …… [2]
Mark scheme
17(a) 62 2 B1 for angle AOB = 124 180 − 28 − 28 or M1 for oe 2 17(b) 81 2 B1 for angle RQP = 47 or QPU = 52 or M1 for 180 – 52 – 47
Question 184 marks
Question
A solid cylinder has radius 5 cm and height 8 cm. Calculate the total surface area of the cylinder. …… cm 2 [4]
Mark scheme
18 408 or 408.4 to 408.5 4 M3 for 2 × π × 5 × 8 + 2 × π × 52 oe OR M1 for 2 × π × 5 × 8 M1 for [ 2] × π × 52
Question 194 marks
Question
Find the nth term of each sequence. (a) 11, 8, 5, 2, -1, … …… [2] (b) 1, 5, 25, 125, 625, … …… [2]
Mark scheme
19(a) 14 – 3n oe final answer 2 B1 for 14 – kn or c – 3n or 14 – 3n seen then spoiled 19(b) 5n −1 oe 2 B1 for 5an + b where a > 0 or 5k for any integer k > 1
Question 203 marks
Question
The area of a rectangle is 55.2 cm 2 , correct to 1 decimal place. The length of the rectangle is 9 cm, correct to the nearest cm. Calculate the upper bound of the width of the rectangle. …… cm [3]
Mark scheme
20 6.5 nfww 3 55.2 + 0.05 55.2 to 55.3 M2 for or 8 to 9 9 − 0.5 or M1 for 9 + 0.5 or 9 – 0.5 or 55.2 + 0.05 or 55.2 – 0.05
Question 216 marks
Question
The line y = x + 1 intersects the curve y = x 2 + x - 3 at two points. Find the coordinates of the two points. ( …… , …… ) ( …… , …… ) [4] 22 x is inversely proportional to the square root of w. When w = 16 , x = 3. Find x in terms of w. x = …… [2]
Mark scheme
21 (2, 3) and (–2, –1) 4 B3 for x = 2 and x = –2 or B2 for x2 − 4[= 0] or better or for (2, 3) or (–2, –1) or M1 for x + 1 = x 2 + x − 3 oe
Question 22
Question
In the question paper above.
Mark scheme
22 12 2 k oe final answer M1 for x = oe w w
Question 232 marks
Question
Some students record their reaction times. The table shows the results. Reaction time 01tG6 6 1 t G 10 (t seconds) Frequency 18 16 On a histogram, the height of the block for the 0 1 t G 6 interval is 7.5 cm. Calculate the height of the block for the 6 1 t G 10 interval. …… cm [2]
Mark scheme
23 10 2 7.5 M1 for oe or better 18 ÷ 6 or [frequency densities] 3 and 4 or 45 and 4h or 45 and 40
Question 244 marks
Question
Simplify. ax - 2a - x + 2 a2 - 1 …… [4]
Mark scheme
24 x –2 4 B2 for ( x − 2 )( a − 1) final answer a +1 or M1 for a ( x − 2 ) − ( x − 2 ) or x ( a − 1) − 2 ( a − 1) B1 for ( a − 1)( a + 1)
Question 252 marks
Question
The derivative of 2ax 7 + 3x k is 42x 6 + 15x k - 1 . Find the value of a and the value of k. a = …… k = …… [2] Question 26 is printed on the next page.
Mark scheme
25 a=3 2 B1 for each k=5 or M1 for 2 × 7ax6 + 3kx k −1 or better
Question 263 marks
Question
T Q X K NOT TO b SCALE O a P The diagram shows a parallelogram OPQT. The position vector of P is a and the position vector of T is b. K is on PQ so that PK : KQ = 3 : 1. The lines OK and TQ are extended to meet at X. Find the position vector of X in terms of a and b. Give your answer in its simplest form. …… [3]
Mark scheme
26 4 3 B2 for correct unsimplified answer b+ a 3 1 or QX = a seen 3 or B1 for a correct route for OX or answer b + ka where k > 1 3 or OK = a + b seen 4 1 or QX = OP 3 4 or OX = × OK 3
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0580/22 questions
Where can I find the 0580/22 October/November 2023 mark scheme?
On this page, free: the mark scheme for IGCSE Mathematics 0580/22, October/November 2023 (0580_w23_ms_22), and the question paper (0580_w23_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 2023 is out of 70 marks, with 1 hour 30 minutes to answer it.
Can I get my 0580/22 answers marked?
Yes. Upload your answers to 0580/22/O/N/23 as a PDF or photos, and CIE Buddy marks every question against this paper's official mark scheme, using Cambridge's marking rules. You get your score, each lost mark explained on your own script, and the topics to revise. It's a guide, not an official Cambridge grade.