Cambridge IGCSE Mathematics - International 0607 — 2023 Oct/Nov Paper 2 · Variant 1
0607/21/O/N/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 · 105° NOT TO SCALE x° The diagram shows a straight line crossing two parallel lines
1 105° NOT TO SCALE x° The diagram shows a straight line crossing two parallel lines. Find the value of x. x = ................................................ [1]
Mark scheme: Question Answer Marks Partial Marks 1 105 1
Q2 · Priya rolls a die 10 times
2 Priya rolls a die 10 times. The table shows the results. Score 1 2 3 4 5 6 Frequency 2 1 0 2 0 5 (a) Find the mode. ................................................. [1] (b) Find the interquartile range. ................................................. [2]
Mark scheme: 2(a) 6 1 2(b) 4 2 M1 for [u.q. =] 6 or [l.q. =] 2 identified
Q3 · A is the point (0, 7) and B is the point (-2, 1)
3 A is the point (0, 7) and B is the point (-2, 1). M is the mid-point of AB. Find the coordinates of M. ( ...................... , ...................... ) [2]
Mark scheme: 3 (–1, 4) 2 B1 for each
Q4 · Write 1.8796 correct to 4 significant figures
4 (a) Write 1.8796 correct to 4 significant figures. ................................................. [1] 4 (b) Work out 5 . ` j ................................................. [1] (c) x is an integer and x G 1. Write down the values of x. ................................................. [1] (d) Find the highest common factor (HCF) of 24 and 42. ................................................. [1]
Mark scheme: 4(a) 1.880 cao 1 4(b) 25 1 4(c) –1, 0, 1 1 4(d) 6 1
Q5 · A taxi fare, $F, consists of a fixed charge of $x plus $0.65 per kilometre travelled
5 A taxi fare, $F, consists of a fixed charge of $x plus $0.65 per kilometre travelled. Find a formula for F for a journey of y kilometres. ................................................. [2]
Mark scheme: 5 F = x + 0.65y 2 B1 for x + 0.65y or F = x + ky, k ≠ 0 or F = c + 0.65y, c ≠ 0
Q6 · Find the next term and the nth term of this sequence
6 Find the next term and the nth term of this sequence. 0 1 4 9 16 .... next term = ................................................ nth term = ................................................ [3]
Mark scheme: 6 25 1 (n – 1)2 oe 2 B1 for any quadratic or M1 for second differences = 2 (at least two)
Q7 · J = h 3 + k 3 (a) Find the value of J when h = 3 and k = 4
7 J = h 3 + k 3 (a) Find the value of J when h = 3 and k = 4 . J = ................................................ [2] (b) Rearrange the formula to write h in terms of J and k. h = ................................................ [2]
Mark scheme: 7(a) 91 2 M1 for 27 or 64 or 33 + 43 7(b) 3 3 2 M1 for correct rearrangement for J − k final answer h3 = ... or h = ... M1 for correct cube root Max 1 mark if answer incorrect
Q8 · 8 cm NOT TO 10 cm SCALE The length of the diagonal of the rectangle is 10 cm
8 8 cm NOT TO 10 cm SCALE The length of the diagonal of the rectangle is 10 cm. The length of the rectangle is 8 cm. Work out the width of the rectangle. ............................................ cm [3]
Mark scheme: 8 6 3 2 2 M2 for 10 − 8 or M1 for 82 + w2 = 10 2 oe
Q9 · A A B C C C D Ulrich has these cards
9 A A B C C C D Ulrich has these cards. He picks 2 cards at random without replacement. Find the probability that both cards have the letter A. .................................................. [2]
Mark scheme: 9 1 2 2 1 oe final answer M1 for or seen 21 7 6
Q10 · 5 w ' 5 13 = 25 Find the value of w
10 5 w ' 5 13 = 25 Find the value of w. w = ................................................ [1]
Mark scheme: 10 15 1
Q11 · The volume of a cone is 18r cm 3
11 The volume of a cone is 18r cm 3 . The height of the cone is the same as the diameter of its base. Find the radius of the base. ............................................ cm [3]
Mark scheme: 11 3 3 3 18 3 M2 for r = 2 or 1 2 M1 for πr (2 r ) = 18π oe or better 3
Q12 · T C NOT TO 55° U SCALE D x° 100° V y° B A ABCD is a cyclic quadrilateral
12 T C NOT TO 55° U SCALE D x° 100° V y° B A ABCD is a cyclic quadrilateral. ABV is a straight line and TU is a tangent to the circle at C. Find the value of x and the value of y. x = ................................................ y = ................................................ [2]
Mark scheme: 12 [x = ] 100 2 B1 for each [y = ] 55
Q13 · Y varies inversely as the square root of ( x + 1)
13 y varies inversely as the square root of ( x + 1) . When x = 8 , y = 5 . Find y in terms of x. y = ................................................ [2]
Mark scheme: 13 15 2 k M1 for y = oe x + 1 x + 1
Q14 · The line L is perpendicular to the line 2y = 5 - x and passes through the point (2, 3)
14 The line L is perpendicular to the line 2y = 5 - x and passes through the point (2, 3). Find the equation of line L. Give your answer in the form y = mx + c . y = ................................................ [4] Questions 15 and 16 are printed on the next page.
Mark scheme: 14 2x – 1 4 1 B1 for grad of given line = − 2 1 M1 for grad of L = − 1 their − 2 M1 for 3 = their grad × 2 + c y − 3 or = their (grad) x − 2 1 (their grad not − ) 2
Question 15
15 Rationalise the denominator. 5 5 - 1 ................................................. [2]
Mark scheme: 15 2 5 + 1 5 5 + 1 5 + 5 ( ) M1 for or 5 + 1 4 4
Q16 · Log 20 + logx = 2 Find the value of x
16 log 20 + logx = 2 Find the value of x. x = ................................................ [2]
Mark scheme: 16 5 2 M1 for 2 = log100 or for log(20x) = 2
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 Oct/Nov, Paper 2 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.