Cambridge IGCSE Mathematics - International 0607 — 2018 Oct/Nov Paper 2 · Variant 3
0607/23/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 · Y = mx + c 1 (a) Find y when m = , x = -2 and c = 4
1 y = mx + c 1 (a) Find y when m = , x = -2 and c = 4. 2 y = .................................................... [2] (b) Rearrange the formula to write m in terms of x, y and c. m = .................................................... [2]
Mark scheme: Question Answer Marks Partial Marks 1(a) 3 2 1 M1 for × ( −2 ) + 4 2 1(b) y − c 2 M1 for correct rearrangement to oe final answer isolate the m term x M1 for correct division by x
Question 2
2 Solve. 6 - 2t =-12 t = .................................................... [2]
Mark scheme: 2 9 2 B1 for correct equation in form ax= b or b = ax
Q3 · X –6 –5 –4 –3 –2 –1 0 1 2 3 4 Write down the inequality shown above
3 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 Write down the inequality shown above. ..................................................... [1]
Mark scheme: 3 −<3 x - 2 1
Q4 · Danny stands to watch a train go past
4 Danny stands to watch a train go past. The train has a length of 120 m and takes 3 seconds to pass. Find the speed of the train (a) in m/s, .............................................. m/s [1] (b) in km/h. ............................................km/h [2]
Mark scheme: 4(a) 40 1 4(b) 144 2 FT their (a) 60 × 60 M1 for their 40 × oe or 1000 120 × 60 × 60 oe 1000 × 3
Question 5
5 Work out ' . 6 16 Give your answer in its lowest terms. ..................................................... [2]
Mark scheme: 5 8 2 5 16 80 M1 for × oe implied by or 9 6 15 90 better seen
Question 6
6 (a) Simplify 98 . ..................................................... [1] (b) Rationalise the denominator. 1 3 - 5 ..................................................... [2]
Mark scheme: 6(a) 7 2 1 6(b) 3 + 5 2 3 + 5 M1 for × 4 3 + 5
Q7 · Solve the simultaneous equations
7 Solve the simultaneous equations. 3t - u = -5 3t + 2u = 1 t = .................................................... u = .................................................... [2]
Mark scheme: 7 [t =] –1 2 B1 for each [u =] 2 If 0 scored, SC1 for their answers satisfying one equation.
Question 8
8 Simplify. (a) 12v 12 # 3v 3 ..................................................... [2] 3 (b) 100x 100 2 ` j ..................................................... [2]
Mark scheme: 8(a) 36v15 2 B1 for 36 kv or k v15 8(b) 1000 x150 2 B1 for 1000 kx or k x150
Q9 · For the diagram, write down (a) the number of lines of symmetry…
9 For the diagram, write down (a) the number of lines of symmetry, ..................................................... [1] (b) the order of rotational symmetry. ..................................................... [1]
Mark scheme: 9(a) 0 1 9(b) 2 1
Q10 · The volume of a sphere is 36r cubic centimetres
10 The volume of a sphere is 36r cubic centimetres. Find the radius of the sphere. ............................................... cm [2]
Mark scheme: 10 3 2 4 3 M1 for × π× r = 36 π oe 3
Q11 · Q T, U and V lie on a circle, centre O
11 (a) Q T, U and V lie on a circle, centre O. PQ is a tangent to the circle at T. NOT TO TU is a diameter. T SCALE O x° Find the value of x and the value of y. U 42° y° P V x = .................................................... y = .................................................... [2] (b) D C 44° q° ABCD is a cyclic quadrilateral. NOT TO SCALE Find the value of p and the value of q. 85° p° A B p = .................................................... q = .................................................... [2]
Mark scheme: 11(a) [x =] 48 2 B1 for each [y =] 42 FT 90 − their x 11(b) [p =] 44 2 B1 for each [q =] 51
Q12 · Sin i =- and 0° G i G 360°
12 sin i =- and 0° G i G 360° . 2 Find the two values of i. i = ...................... or i = ................. [2]
Mark scheme: 12 225, 315 2 B1 for each If 0 scored, M1 for 45 seen
Q13 · Find the equation of the straight line perpendicular to the line y = 2x + 1 that passes…
13 Find the equation of the straight line perpendicular to the line y = 2x + 1 that passes through the point (2, 5). Give your answer in the form y = mx + c. y = .................................................... [3]
Mark scheme: 13 1 3 1 − x + 6 B1 for gradient = − 2 2 M1 for substitution of (2, 5) into y = ( their m ) x + c
Q14 · NOT TO SCALE The two solids are mathematically similar
14 NOT TO SCALE The two solids are mathematically similar. The larger solid has a volume of 64 cm3. The smaller solid has a volume of 8 cm3 and a height of 5 cm. Work out the height of the larger solid. ............................................... cm [3] Question 15 is printed on the next page.
Mark scheme: 14 10 3 3 5 8 oe M2 for = h 64 8 or M1 for (scale factor)3 = or 64 64 or better 8
Q15 · Write as a single fraction in its simplest form
15 Write as a single fraction in its simplest form. 7 5 - x - 1 2x + 3 ..................................................... [3]
Mark scheme: 15 9 x + 26 3 M1 for denominator ( x − 1)( 2 x + 3 ) final answer ( x − 1)( 2 x + 3 ) B1 for 7 ( 2 x + 3 ) − 5 ( x − 1) oe seen or SC2 for final answer 9 x + 16 ( x − 1)( 2 x + 3 ) If expanded denominator must be 2 x 2 + x − 3
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 3. A higher threshold means an easier paper — the bar moves with how the cohort did.