Cambridge IGCSE Mathematics - International 0607 — 2019 Oct/Nov Paper 2 · Variant 3
0607/23/O/N/19 · 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
Question 1
1 Work out. (a) (- 4) 2 .................................................... [1] (b) (0.3) 2 .................................................... [1]
Mark scheme: Question Answer Marks Partial Marks 1(a) 16 1 1(b) [0].09 1
Q2 · Write down a prime number between 80 and 90
2 (a) Write down a prime number between 80 and 90. .................................................... [1] (b) Write down a triangle number between 30 and 50. .................................................... [1]
Mark scheme: 2(a) 83 or 89 1 2(b) 36 or 45 1
Q3 · Shade two squares so that this shape has exactly one line of symmetry
3 (a) Shade two squares so that this shape has exactly one line of symmetry. [1] (b) Shade two squares so that this shape has rotational symmetry of order 2. [1]
Mark scheme: 3(a) 1 or 3(b) 1
Q4 · A cat eats 1 tins of food each day
4 A cat eats 1 tins of food each day. 3 How many tins are needed for one week? .................................................... [2]
Mark scheme: 4 2 2 5 12 or 11 M1 for 7 × oe 3 3
Question 5
5 Factorise. (a) x 2 - 1 .................................................... [1] (b) 3x 2 - 6ax - axy + 2a 2 y .................................................... [2]
Mark scheme: 5(a) (x + 1)(x – 1) 1 5(b) (3x – ay)(x – 2a) oe 2 B1 for 3x( x – 2a) or –ay(x –2a) or ay(2a – x) or x(3x – ay) or 2a(–3x + ay) or –2a(3x – ay)
Q6 · Triangle ABC is isosceles and angle A = 40°
6 Triangle ABC is isosceles and angle A = 40°. Find the three possible values for angle B. .......................... , .......................... , .......................... [2]
Mark scheme: 6 40, 70, 100 2 B1 for any two.
Q7 · The mean of 10 numbers is 15
7 The mean of 10 numbers is 15. When an 11th number is included, the mean is 16. Find the 11th number. .................................................... [2]
Mark scheme: 7 26 2 B1 for 150 or 176 seen
Q8 · 200 students record the method they use most to travel to school
8 200 students record the method they use most to travel to school. The results are shown in the table. Method of travel Bus Car Walk Cycle Number of students 40 98 37 25 (a) Find, as a fraction, the relative frequency of a student travelling to school by bus. .................................................... [1] (b) Give a reason why it is reasonable to use your answer to part (a) to estimate the probability that a student travels to school by bus. ............................................................................................................................................................ [1] (c) The school has 1800 students. Estimate the number of students who travel to school by bus. .................................................... [1]
Mark scheme: 8(a) 40 1 oe 200 8(b) Large sample oe 1 8(c) 360 1 FT for their (a) × 1800
Q9 · Solve 3x - 2 2 7x + 6
9 (a) Solve 3x - 2 2 7x + 6 . .................................................... [2] (b) Show your solution to part (a) on this number line. x –5 –4 –3 –2 –1 0 1 2 3 4 5 [1]
Mark scheme: 9(a) x < –2 2 B1 for x = or ⩽ or ⩾ –2 or M1 for –2 – 6 > 7x – 3x oe 9(b) Line/arrow from –2 to left with 1 FT from their inequality in (a) empty circle at –2
Q10 · Rearrange this formula to make a the subject
10 Rearrange this formula to make a the subject. 3a - 2 y = a - 1 .................................................... [3]
Mark scheme: 10 y − 2 3 M1 for y(a – 1) = 3a – 2 oe oe M1 FT for ay – 3a = y – 2 y − 3 M1 FT for completion
Question 11
11 Expand and simplify. (3 2 + 7 ) 2 .................................................... [3]
Mark scheme: 11 67 + 42 2 3 B2 for a + 42 2 or 67 + b 2 or M1 for 3 2 × 3 2 + 21 2 + 21 2 + 49 or better
Q12 · The equation of the line L is y = 3 x - 2
12 The equation of the line L is y = 3 x - 2 . (a) Find the co-ordinates of the point A, where the line L crosses the y-axis. (................. , .................) [1] (b) Find the co-ordinates of the point B, where the line L crosses the x-axis. (................. , .................) [1] (c) The line M passes through the point A and is perpendicular to the line L. Find the equation of the line M. .................................................... [2]
Mark scheme: 12(a) (0, –2) 1 12(b) 2 1 , 0 oe 3 12(c) 1 2 FT their (a) y = – x – 2 oe 1 3 B1 for m = – 3
Q13 · A B P NOT TO SCALE Q D C ABCD is a parallelogram
13 A B P NOT TO SCALE Q D C ABCD is a parallelogram. AP = PQ = QC. Show that triangles BQC and DPA are congruent. Statement Reason ................................................ ............................................................................................................ ................................................ ............................................................................................................ ................................................ ............................................................................................................ ................................................ ............................................................................................................ [3]
Mark scheme: 13 BC = DA [opp] sides of 1 parallelogram ∠ BCQ = ∠ DAP Alternate angles 1 AP = QC and SAS 1 If 0 scored, SC1 for BC = DA and ∠ BCQ = ∠ DAP and AP = QC
Q14 · Y NOT TO SCALE O x P (2, –3) The diagram shows a sketch of the graph y = x 2 + bx + c
14 y NOT TO SCALE O x P (2, –3) The diagram shows a sketch of the graph y = x 2 + bx + c . The minimum point is at P (2, - 3) . Find the value of b and the value of c. b = ............................... c = ............................... [3] Question 15 is printed on the next page.
Mark scheme: 14 [b =] –4, 3 B2 for either value [c =] 1 or M1 for (x – 2)2 + p or (x + q)2 – 3
Q15 · The table shows the height, h cm, of some plants
15 The table shows the height, h cm, of some plants. Height (h cm) 0 1 h G 10 10 1 h G 40 40 1 h G 60 Frequency p q 44 (a) Complete the histogram to show this information. 6 5 4 Frequency density 3 2 1 0 0 10 20 30 40 50 60 h Height (cm) [1] (b) Find the value of p and the value of q. p = ................................................... q = ................................................... [2]
Mark scheme: 15(a) Bar from 40 to 60, height 2.2 1 15(b) [p =] 38 2 B1 for each [q = ] 150
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 2019 Oct/Nov, Paper 2 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.