Cambridge IGCSE Mathematics - International 0607 — 2023 Oct/Nov Paper 2 · Variant 3
0607/23/O/N/23 · 15 questions · 40 marks · ≈45 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 paper8 pages
Mark scheme5 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Write 0.030 149 7 (a) correct to 3 decimal places…
1 Write 0.030 149 7 (a) correct to 3 decimal places ................................................. [1] (b) correct to 4 significant figures. ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1(a) 0.030 1 1(b) 0.03015 1
Q2 · Write down the number of lines of symmetry of a kite
2 Write down the number of lines of symmetry of a kite. ................................................. [1]
Mark scheme: 2 1 1
Question 3
3 Work out - . 6 8 ................................................. [2]
Mark scheme: 3 5 2 M1 for common denominator with 1 or equivalent fraction numerator correct. 24
Q4 · Solve 11 + 2x 2 5
4 (a) Solve 11 + 2x 2 5 . ................................................. [2] (b) Show your solution to part (a) on this number line. x – 5 – 4 –3 –2 –1 0 1 2 3 4 [1]
Mark scheme: 4(a) x > –3 2 M1 for 2x > 5 – 11 or B1 for x * –3 where * is =, <, ⩽, ⩾ 4(b) 1 FT their (a) dep on (a) being an inequality –3
Q5 · One day Hassan surveys the number of people in the cars passing his house
5 One day Hassan surveys the number of people in the cars passing his house. The results for the first 100 cars are shown in the table. Number of people 1 2 3 4 5 6 Frequency 42 23 17 9 7 2 Relative frequency (a) Complete the table. [2] (b) A total of 1200 cars pass Hassan’s house that day. Calculate an estimate of the number of these cars with 5 people. ................................................. [1]
Mark scheme: 5(a) 0.42, 0.23, 0.17, 0.09, 0.07, 0.02 oe 2 B1 for 3 or more correct. 5(b) 84 1
Q6 · The angles of a triangle are in the ratio 2 : 3 : 7
6 The angles of a triangle are in the ratio 2 : 3 : 7. Find each angle. .................... , .................... , .................... [3]
Mark scheme: 6 30, 45, 105 3 180 180 180 M2 for two of 2 3 7 12 12 12 seen 180 or M1 for 2 + 3 + 7
Q7 · P = 5 # 107 Work out p3
7 p = 5 # 107 Work out p3. Give your answer in standard form. ................................................. [2]
Mark scheme: 7 1.25 × 1023 2 B1 for correct answer not in standard form seen
Q8 · For this sequence 1 6 11 16 21 … (a) find the next term…
8 For this sequence 1 6 11 16 21 … (a) find the next term ................................................. [1] (b) find an expression for the nth term. ................................................. [2]
Mark scheme: 8(a) 26 1 8(b) 5n – 4 oe final answer 2 B1 5n + k
Q9 · NOT TO SCALE 30 cm 24 cm The two bottles are mathematically similar
9 NOT TO SCALE 30 cm 24 cm The two bottles are mathematically similar. The height of the large bottle is 30 cm. The height of the small bottle is 24 cm. The volume of the large bottle is 250 cm3. Calculate the volume of the small bottle. ......................................... cm3 [3]
Mark scheme: 9 128 3 3 24 M2 for 250 oe 30 24 3 30 3 or M1 for or oe seen 30 24
Q10 · B NOT TO SCALE A 51° O Q C 64° D P A, B, C and D are points on the circle centre O
10 B NOT TO SCALE A 51° O Q C 64° D P A, B, C and D are points on the circle centre O. PDQ is a tangent to the circle at D. Angle BAD = 51° and angle PDA = 64° . Find (a) angle BCD Angle BCD = ................................................ [1] (b) angle ABD Angle ABD = ................................................ [1] (c) the obtuse angle BOD. Angle B O D = ................................................ [1]
Mark scheme: 10(a) 129 1 10(b) 64 1 10(c) 102 1
Question 11
11 Expand and simplify. ( 4 + 2 3)( 5 - 3) ................................................. [2]
Mark scheme: 11 14 + 6 3 oe 2 B1 for 14 + k 3 or k + 6 3 or M1 for 20 + 10 3 – 4 3 – 2 3 3
Q12 · Y is inversely proportional to x2
12 y is inversely proportional to x2. When x = 2 , y = 10 . Find y in terms of x. y = ................................................ [2]
Mark scheme: 12 40 2 k oe M1 for y = oe x 2 x 2
Q13 · NOT TO 6 cm SCALE 30° The area of the shaded segment is ( a r+ b ) cm2
13 NOT TO 6 cm SCALE 30° The area of the shaded segment is ( a r+ b ) cm2. Find the value of a and the value of b. a = ................................................ b = ................................................ [4] Questions 14 and 15 are printed on the next page.
Mark scheme: 13 a = 3 4 30 2 M1 for π 6 b = –9 360 1 M1 for × 62 × sin30 2 1 B1 for sin 30 = 2
Q14 · Solve 2 log x - 3 log 2 + log 5 = 3
14 Solve 2 log x - 3 log 2 + log 5 = 3 . x = ................................................ [4]
Mark scheme: 14 40 4 M1 for one correct use of log a + log b = log ab or a log a – log b = log b M1 for one correct use of n log a = logan B1 for [log]1000
Q15 · Write as a single fraction in its simplest form
15 Write as a single fraction in its simplest form. 3 2 - x - 1 2x + 5 ................................................. [3]
Mark scheme: 15 4 x + 17 3 B1 for common denominator oe final answer (x – 1)(2x + 5) ( x − 1)(2 x + 5) B1 for 3(2x + 5) – 2(x – 1)
What was in this paper
The subtopics covered by these 15 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 2023 Oct/Nov, Paper 2 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.