Cambridge IGCSE Mathematics - International 0607 — 2021 Oct/Nov Paper 2 · Variant 2
0607/22/O/N/21 · 20 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 scheme5 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Question 1
1 Work out. 3 + 7 # 2 + 5 ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1 22 1
Question 2
2 Complete the statement. A parallelogram has rotational symmetry of order ..................... and ..................... lines of symmetry. [2]
Mark scheme: 2 2 2 B1 for each 0 oe
Q3 · A number is greater than 1
3 (a) A number is greater than 1. The number is also both a square number and a cube number. Write down a possible value of this number. ................................................. [1] (b) Write down a prime number between 90 and 100. ................................................. [1]
Mark scheme: 3(a) 64 1 3(b) 97 only 1
Q4 · X – 4 – 3 – 2 – 1 0 1 2 3 4 Write down the inequality shown on the number line
4 x – 4 – 3 – 2 – 1 0 1 2 3 4 Write down the inequality shown on the number line. ................................................. [1]
Mark scheme: 4 –3 < x ≤ 2 1
Question 5
5 Work out. 3 8 ' 4 9 ................................................. [2]
Mark scheme: 5 27 2 3 9 27 32 M1 for × or ÷ oe 32 4 8 36 36
Q6 · X 1 2 Write down all the integer values of x
6 x 1 2 Write down all the integer values of x. ................................................. [1]
Mark scheme: 6 –1, 0, 1 1
Q7 · The bearing of P from Q is 110°
7 The bearing of P from Q is 110°. Find the bearing of Q from P. ................................................. [2]
Mark scheme: 7 290 2 M1 for 180 + 110 or for a diagram with a correct angle at P.
Q8 · On the diagram, sketch the graph of y =
8 On the diagram, sketch the graph of y = . x y x O [2]
Mark scheme: 8 Correct sketch 2 B1 for each branch 4444 2222 4444 -2-2-2-2 0000 0000 2222 4444 -2-2-2-2 -4-4-4-4
Q9 · NOT TO SCALE 40° O r cm The diagram shows an arc of a circle, centre O, radius r cm
9 NOT TO SCALE 40° O r cm The diagram shows an arc of a circle, centre O, radius r cm. The length of the arc is krr cm. Find the value of k. Give your answer as a fraction in its simplest form. k = ................................................ [2]
Mark scheme: 9 2 2 40 cao M1 for [× 2 πr ] oe 9 360
Q10 · Shade the region ( P , Q ) l
10 (a) Shade the region ( P , Q ) l. U P Q [1] (b) The Venn diagram shows the number of elements in each region. U R T 8 9 10 7 Find n( R + T l) . ................................................. [1] (c) Use set notation to describe the shaded region. U A B ................................................. [1]
Mark scheme: 10(a) Correct shading 1 10(b) 8 1 10(c) A ∪ B ′ oe 1
Q11 · Y = 2 Rearrange the formula to make w the subject
11 y = 2 Rearrange the formula to make w the subject. w = ................................................ [1]
Mark scheme: 11 2y final answer 1
Q12 · 2 Work out the value of 32 2
512 Work out the value of 32 2. ................................................. [1]
Mark scheme: 12 4 1
Q13 · A 40° T x° 77° NOT TO SCALE B AB is a tangent to the circle at T
13 A 40° T x° 77° NOT TO SCALE B AB is a tangent to the circle at T. Find the value of x. x = ................................................ [2]
Mark scheme: 13 63 2 M1 for other angle at tangent = 63˚ or other angle in triangle = 40˚
Question 14
14 Simplify. 125 + 80 ................................................. [2]
Mark scheme: 14 9 5 2 B1 for 5 5 or 4 5
Question 15
15 Solve. 8 - x x + 1 = 3 2 x = ................................................ [3]
Mark scheme: 15 2.6 oe 3 B2 for 16 – 3 = 3x + 2x or better or M1 for 2(8 − x ) = 3( x + 1)
Question 16
16 Factorise. 3x + 6 - 2xy - 4y ................................................. [2]
Mark scheme: 16 ( x + 2 )( 3 − 2 y ) final answer 2 B1 for 3( x + 2) − 2 y ( x + 2) or x (3 − 2 y ) + 2(3 − 2 y )
Q17 · 3 x = 27 x + 2 Find the value of x
17 3 x = 27 x + 2 Find the value of x. x = ................................................ [2]
Mark scheme: 17 –3 2 M1 for 33( x + 2) oe or better
Question 18
18 Simplify. w 2 - 9 2w 2 + 5w - 3 ................................................. [4]
Mark scheme: 18 w − 3 4 B1 for ( w − 3)( w + 3) final answer 2 w − 1 B2 for ( w + 3 )( 2 w − 1) or B1 for ( w + a )( 2 w + b ) where ab = –3 or 2a + b = 5 or 2 w( w + 3) − ( w + 3) or w(2 w − 1) + 3(2 w − 1)
Q19 · Log 48 + log 18 - 2 log 24 = logt Find the value of t
19 log 48 + log 18 - 2 log 24 = logt Find the value of t. t = ................................................ [3]
Mark scheme: 19 1 3 3 M1 for correct use of log p ± log q 1.5 or 12 or 2 M1 for correct use of n log p
Q20 · Tanx = k 0° 1 x 1 90° Find, in terms of k, (a) tan ( 180° - x)…
20 tanx = k 0° 1 x 1 90° Find, in terms of k, (a) tan ( 180° - x) , ................................................. [1] (b) tan ( 90° - x) . ................................................. [1]
Mark scheme: 20(a) –k 1 20(b) 1 1 k
What was in this paper
The subtopics covered by these 20 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 2021 Oct/Nov, Paper 2 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.