Cambridge IGCSE Mathematics - International 0607 — 2023 May/June Paper 2 · Variant 2
0607/22/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 paper12 pages
Mark scheme6 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Write down (a) a square number between 101 and 150…
1 Write down (a) a square number between 101 and 150 ................................................. [1] 2 3 (b) a fraction between and 3 4 ................................................. [1] (c) an irrational number between 6 and 7. ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1(a) 121 or 144 1 1(b) Any correct fraction 1 1(c) Any correct irrational number 1
Question 2
2 Work out. (a) - 7 ' - 2 ................................................. [1] (b) ( 0. 3) 2 ................................................. [1]
Mark scheme: 2(a) 1 1 3.5 or 3 2 2(b) 0.09 1
Q3 · Solve x + 9 2 6
3 (a) Solve x + 9 2 6 . ................................................. [1] (b) Show your answer to part (a) on this number line. x – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 [1]
Mark scheme: 3(a) x > –3 or –3 < x 1 3(b) 1 FT their inequality from (a) –3 Correct line with correct end oe
Q4 · Aklima records the masses, m kg, of 120 parcels
4 Aklima records the masses, m kg, of 120 parcels. The results are shown in the table. Mass, m kg 0 1 m G 2 2 1 m G 4 4 1 m G 6 6 1 m G 8 8 1 m G 10 Frequency 35 30 40 12 3 Find (a) the modal class .................. 1 m G .................. [1] (b) the class which contains the median. .................. 1 m G .................. [1]
Mark scheme: 4(a) 4 [< m ⩽] 6 1 4(b) 2 [< m ⩽] 4 1
Q5 · 12 11 1 NOT TO 10 2 SCALE 9 3 8 4 7 5 6 The clock shows the time 09 30
5 12 11 1 NOT TO 10 2 SCALE 9 3 8 4 7 5 6 The clock shows the time 09 30. Work out the obtuse angle between the hands of the clock. ................................................. [2]
Mark scheme: 5 105 2 360 B1 for or 30 [for 1 hour] 12 or 15 [for half an hour] or 255 seen
Q6 · Find the value of 643
6 Find the value of 643. ................................................. [1]
Mark scheme: 6 4 cao 1
Q7 · Lee cycles for 60 km at an average speed of 30 km/h
7 Lee cycles for 60 km at an average speed of 30 km/h. He then returns along the same route at an average speed of 20 km/h. Find Lee’s average speed for the whole journey. ......................................... km/h [3]
Mark scheme: 7 24 3 B2 for 3[h] and 2[h] soi by 5 [h] or B1 for 60/30 or 60/20 or 3[h] If B0 or B1 scored, then M1 for 120 ÷ their total time (their total time MUST be greater than 2)
Q8 · Salma spins a biased spinner with sectors labelled 1, 2, 3, 4 and 5
8 Salma spins a biased spinner with sectors labelled 1, 2, 3, 4 and 5. The table shows the relative frequencies of each of her scores. Score 1 2 3 4 5 Relative frequency 0.1 0.05 0.3 0.35 p (a) Find the value of p. ................................................. [2] (b) Salma spins the spinner 4000 times. Work out an estimate for the number of times she scores 3. ................................................. [1]
Mark scheme: 8(a) 0.2 oe 2 M1 for 1 – (0.1 + 0.05 + 0.3 + 0.35) or B1 for 0.8 seen 8(b) 1200 1
Q9 · On the Venn diagrams, shade the given subsets
9 On the Venn diagrams, shade the given subsets. U U A B P Q A , B ( P l + Q ) , ( P + Q l ) [2]
Mark scheme: 9 Correct shading 2 B1 for each
Q10 · There is correlation between quantity p and quantity q
10 There is correlation between quantity p and quantity q. The regression equation is p = 80 - 5.2q . What type of correlation is there between p and q? ................................................. [1]
Mark scheme: 10 Negative 1
Q11 · Solve the simultaneous equations
11 Solve the simultaneous equations. 1 1 x - y = 7 2 3 3x + y = 6 x = ................................................. y = ................................................. [3]
Mark scheme: 11 x = 6, y = –12 3 M1 for correct method to eliminate one variable B1 for x = 6 B1 for y = –12 If 0 scored, SC1 for a pair of solutions that satisfy one equation.
Q12 · B NOT TO SCALE 35° C E 22° A D F A, B, C and D are points on the circle
12 B NOT TO SCALE 35° C E 22° A D F A, B, C and D are points on the circle. EF is a tangent to the circle at A. Angle DBC = 35° and angle ACD = 22° . Find (a) angle ABD Angle ABD = ................................................. [1] (b) angle ADC Angle ADC = ................................................. [1] (c) angle CAF. Angle CAF = ................................................. [1]
Mark scheme: 12(a) 22 1 12(b) 123 1 FT 145 – their(a) 12(c) 57 1 FT 35 + their(a)
Q13 · Rationalise the denominator and simplify
13 Rationalise the denominator and simplify. 2 3 - 5 ................................................. [3]
Mark scheme: 13 3 5 3 2(3 5) 6 2 5 cao final answer B2 for or 2 4 4 3 5 or M1 for 3 5
Q14 · Y varies inversely as the square of ( x - 3 )
14 y varies inversely as the square of ( x - 3 ) . When x = 6 , y = 20 . Find the value of y when x = 9 . ................................................. [3]
Mark scheme: 14 5 3 k M1 for y oe ( x 3) 2 A1 for k = 180 OR (9 3) 2 M2 for 20 oe (6 3) 2 1 y (9 3) 2 or M1 for oe 20 1 (6 3) 2
Q15 · Write down the value of log 10 ( 0 .01 )
15 (a) Write down the value of log 10 ( 0 .01 ) . ................................................. [1] (b) Find the value of 2 log 4 + log 5 - 3 log 2 . ................................................. [3]
Mark scheme: 15(a) –2 1 15(b) 1 3 B2 for log 10 OR M1 for any correct use of alogb = logba or loga + logb = logab a or loga – logb = log b
Q16 · A NOT TO SCALE D E B C ABC is a triangle
16 A NOT TO SCALE D E B C ABC is a triangle. DE is parallel to BC. (a) Show that triangle ADE is similar to triangle ABC. ..................................................................................................................................................... ..................................................................................................................................................... ..................................................................................................................................................... ..................................................................................................................................................... ..................................................................................................................................................... [2] (b) AD : DB = 2 : 3 . Find the ratio Area of triangle ADE : Area of triangle ABC. ...................... : ...................... [1]
Mark scheme: 16(a) Two from 2 B1 for 1 pair with a reason ADE = ABC Corresponding s or 2 pairs with no/incorrect reason AED = ACB Corresponding s DAE = BAC common oe [And Angles equal] 16(b) 4 : 25 1
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 2. A higher threshold means an easier paper — the bar moves with how the cohort did.