Cambridge IGCSE Mathematics - International 0607 — 2023 May/June Paper 2 · Variant 3
0607/23/M/J/23 · 16 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 · 29 31 41 49 51 59 From this list, write down all the numbers that are prime numbers
1 29 31 41 49 51 59 From this list, write down all the numbers that are prime numbers. ............................................................................... [2]
Mark scheme: Question Answer Marks Partial Marks 1 29 31 41 59 2 B1 for at least two correct
Q2 · NOT TO SCALE x° 64° 37° Find the value of x
2 NOT TO SCALE x° 64° 37° Find the value of x. x = ................................................ [1]
Mark scheme: 2 79 1
Question 3
3 Work out. (a) 0.04 # 0.06 ................................................. [1] 0.02 (b) 0.8 ................................................. [1]
Mark scheme: 3(a) 0.0024 oe 1 3(b) 0.025 oe 1
Q4 · A bag contains 3 blue balls and 7 green balls
4 A bag contains 3 blue balls and 7 green balls. One ball is chosen at random. Find the probability the ball chosen is (a) white ................................................. [1] (b) not blue. ................................................. [1]
Mark scheme: 4(a) 0 1 4(b) 0.7 oe 1
Q5 · Change 12 millimetres into metres
5 Change 12 millimetres into metres. ............................................. m [1]
Mark scheme: 5 0.012 cao 1
Question 6
6 Expand. 3x ( 2x 4 - 5) ................................................. [2]
Mark scheme: 6 6 x 5 15 x final answer 2 M1 for 6x 5 kx or px k 15 x oe
Q7 · Write 0.003 08 in standard form
7 (a) Write 0.003 08 in standard form. ................................................. [1] (b) Work out 7 # 10 6 # 3 # 10 -8 ` j ` j. Give your answer in standard form. ................................................. [2]
Mark scheme: 7(a) 3.08 103 cao 1 7(b) 2.1 101 cao 2 M1 for correct answer not in standard form
Q8 · Find the next term and the nth term for this sequence
8 Find the next term and the nth term for this sequence. 1, 7, 17, 31, 49, … next term ................................................ nth term ................................................ [3]
Mark scheme: 8 71 B1 2 n 2 1 B2 M1 for any quadratic or 2nd differences of 4 seen
Q9 · The total cost of 5 pens and 7 pencils is $6.75
9 The total cost of 5 pens and 7 pencils is $6.75 . Each pencil costs $0.45 . Find the cost of one pen. $ ................................................ [3]
Mark scheme: 9 0.72 3 6.75 their (7 0.45) M2 for oe 5 or M1 for 6.75 7 0.45 oe if 0 scored, SC2 for 72
Q10 · Write 48 as a product of its prime factors
10 Write 48 as a product of its prime factors. ................................................. [2]
Mark scheme: 10 2 4 3 or 2 2 2 2 3 2 M1 for 2k and 3 seen
Q11 · The range of ten numbers is 30
11 (a) The range of ten numbers is 30. The range of eight other numbers is 13. Find the smallest possible value of the range of all eighteen numbers. ................................................. [1] (b) The mean of twelve numbers is 25. The mean of ten of these numbers is 16. Find the mean of the other two numbers. ................................................. [2]
Mark scheme: 11(a) 30 1 11(b) 70 2 M1 for 12 25 or 10 16
Question 12
12 Factorise fully. (a) ( 3)y 2 - 16 ................................................. [1] (b) 15ab - 1 - 3a + 5b ................................................. [2]
Mark scheme: 12(a) (3 y 4)(3 y 4) final answer 1 12(b) (5b 1)(3a 1) oe final answer 2 M1 for 5b (3a 1) 1 3a or 3a(5b – 1) + 5b – 1
Q13 · Shade the given region on the Venn diagram
13 Shade the given region on the Venn diagram. (a) Al + B l U A B [1] (b) ( A , B l) l U A B [1]
Mark scheme: 13(a) Correct sketch 1 13(b) Correct sketch 1
Q14 · An archer shoots three arrows at a target
14 An archer shoots three arrows at a target. 7 The probability that she hits the target with each arrow is . 10 Find the probability she hits the target exactly twice. ................................................. [3]
Mark scheme: 14 441 3 7 7 3 M2 for 3 oe 1000 10 10 10 7 7 3 or M1 for oe 10 10 10
Q15 · Rearrange the equation to make x the subject
15 Rearrange the equation to make x the subject. A + 4y = A ( 2 - 3x) x = ................................................ [3] Question 16 is printed on the next page.
Mark scheme: 15 A 4 y 3 B1 for 2 A 3 Ax [ x ] oe 3 A M1 for correctly isolating their x term M1 for correct division to find their x in a 3-term equation Maximum of 2 if answer not fully correct
Q16 · The point A has coordinates (2, 3) and the point B has coordinates (6, 5)
16 The point A has coordinates (2, 3) and the point B has coordinates (6, 5). The point C lies on the line AB. The point D has coordinates (2, 5.5). CD is perpendicular to AB. Find the coordinates of C. ( ...................... , ...................... ) [5]
Mark scheme: 16 (3, 3.5) oe 5 5 3 M1 for grad AB = oe or better 6 2 M1 for equation of AB y 0.5 x 2 oe 1 M1 for grad CD = their grad AB M1 for 5.5 their (0.5 p 2) their grad CD 2 p oe where ‘p’ is x-coordinate of C If 0 scored, SC1 for (3, k ) or ( k , 3.5)
What was in this paper
The subtopics covered by these 16 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 May/June, Paper 2 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.