Cambridge IGCSE Mathematics - International 0607 — 2018 Oct/Nov Paper 2 · Variant 2
0607/22/O/N/18 · 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 49 059 300 correct to 3 significant figures
1 (a) Write 49 059 300 correct to 3 significant figures. .................................................... [1] (b) Write your answer to part (a) in standard form. .................................................... [1]
Mark scheme: Question Answer Marks Partial Marks 1(a) 49 100 000 1 1(b) 4.91 1 FT their (a)
Question 2
2 Find 3 3 . 8 .................................................... [2]
Mark scheme: 2 3 1 2 27 2 or 12 or 1.5 B1 for 8 seen
Q3 · Shade two small squares so that the shape has exactly one line of symmetry
3 Shade two small squares so that the shape has exactly one line of symmetry. [1]
Mark scheme: 3 1
Q4 · P = 5 (a) Find the column vector 3p
4 p = 5 (a) Find the column vector 3p. [1] f p (b) Find p , giving your answer in surd form. .................................................... [2]
Mark scheme: 4(a) −9 1 15 4(b) 2 M1 for (–3)2 + 52 oe 34
Q5 · F ()x = 2x - 7 for all real x
5 f ()x = 2x - 7 for all real x. (a) Find f (2 ) . .................................................... [1] (b) Write down the range of f ()x . .................................................... [1]
Mark scheme: 5(a) 3 1 5(b) f(x) ⩾ 0 1
Q6 · The line with equation 2x + 3y = 6 is drawn on the grid
6 The line with equation 2x + 3y = 6 is drawn on the grid. y 6 5 4 3 2 1 x 0 –4 –3 –2 –1 1 2 3 4 5 6 7 8 –1 –2 –3 –4 On the grid, show clearly the single region defined by these three inequalities. 2x + 3y G 6 x H- 3 y G- 1 [3]
Mark scheme: 6 x = –3 ruled 3 B1 for each y = –1 ruled Correct region clearly shown
Question 7
7 Factorise. (a) 64x 2 - 1 .................................................... [1] (b) 2y 2 - y - 6 .................................................... [2]
Mark scheme: 7(a) (8x + 1)(8x – 1) 1 7(b) (2y + 3)(y – 2) 2 B1 for (2y + a)(y + b) where ab = –6 or a + 2b = –1 or 2y(y – 2) + 3(y – 2) or y(2y + 3) – 2(y + 3)
Q8 · 2 3 ' 2 7 = 2 p Find the value of p
8 (a) 2 3 ' 2 7 = 2 p Find the value of p. .................................................... [1] (b) 2 5 = 2q Find the value of q. .................................................... [1]
Mark scheme: 8(a) –4 1 8(b) 2.5 oe 1
Q9 · An archer shoots 150 arrows at a target with sections coloured gold, red, blue, black and…
9 An archer shoots 150 arrows at a target with sections coloured gold, red, blue, black and white. The table shows her results. Colour Gold Red Blue Black White Frequency 30 60 36 15 9 Complete the compound bar chart to show these results as percentages. Gold Red 0 10 20 30 40 50 60 70 80 90 100 Percentage [3]
Mark scheme: 9 Labelled chart 3 B2 for three correct rectangles or B1 for one correct rectangle B1 for labels or for 24, 10, 6 Gold Red Blue BlaW 0 10 20 30 40 50 60 70 80 90 100
Question 10
10 Solve. 4x + 9 G 3 (2x - 1) .................................................... [3]
Mark scheme: 10 x ⩾ 6 3 B2 for ⩽ , <, >, = or M2 for 9 + 3 ⩽ 6x – 4x or M1 for 4x + 9 ⩽ 6x – 3 4 x or + 3 = 6x – 3 3
Q11 · The diagram shows nine sketch graphs
11 The diagram shows nine sketch graphs. A y B y C y x x x O O O D y E y F y x x x O O O G y H y I y x x x O O O Write the letter of the graph which shows each of these functions. f ()x = 2x - 3 Graph ................ f ()x = x 2 - 3 Graph ................ f ()x = 3 - x 3 Graph ................ f (x) = (x - 3 ) 2 Graph ................ [4]
Mark scheme: 11 H, B, C, G 4 B1 for each
Q12 · A B Q NOT TO O SCALE 40° 20° D C P A, B, C and D are points on the circle centre O
12 A B Q NOT TO O SCALE 40° 20° D C P A, B, C and D are points on the circle centre O. PQ is a tangent to the circle at C. Find these angles. (a) Angle DAC Angle DAC = ................................................... [2] (b) Angle ABC Angle ABC = ................................................... [1] (c) Angle ACQ Angle ACQ = ................................................... [2] Question 13, 14 and 15 are printed on the next page.
Mark scheme: 12(a) 70 2 B1 for ∠DOC = 140 (12b) 120 1 12(c) 60 2 B1 for reflex∠ COD = 220 or ∠OCA = 30
Question 13
13 Simplify. (5 + 2 3) 2 .................................................... [3]
Mark scheme: 13 37 + 20 3 3 B2 for 37 + a 3 or b + 20 3 , a, b ≠ 0 or M1 for 52 + 10 3 + 10 3 + 2 3 × 2 3
Q14 · Find the value of n when log 5 + log 3 - log 2 = logn
14 (a) Find the value of n when log 5 + log 3 - log 2 = logn . .................................................... [1] (b) Find log 3 (3 1.4 ) . .................................................... [1]
Mark scheme: 14(a) 7.5 1 14(b) 1.4 1
Q15 · F (x) = 3 sin 2x° (a) Write down the amplitude of the graph of f ()x
15 f (x) = 3 sin 2x° (a) Write down the amplitude of the graph of f ()x . .................................................... [1] (b) The graph of y = f ( x) goes through the points (75, 1.5) and (a, 1.5) . Find a possible value of a, greater than 75. .................................................... [1]
Mark scheme: 15(a) 3 1 15(b) 195 or 255 or 375 or 435 etc. 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 2018 Oct/Nov, Paper 2 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.