Cambridge IGCSE Mathematics 0580 — 2016 Oct/Nov Paper 2 · Variant 1
0580/21/O/N/16 · 19 questions · 70 marks · ≈79 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
Q1 · Write down the temperature which is 5 °C below –2 °C
1 Write down the temperature which is 5 °C below –2 °C. ......................................... °C [1]
Mark scheme: Question Answer Mark Part marks 1 –7 1
Q2 · Write 0.040 190 7 correct to (a) 3 significant figures…
2 Write 0.040 190 7 correct to (a) 3 significant figures, .................................................[1] (b) 3 decimal places. .................................................[1]
Mark scheme: 2 (a) [0].0402 1 (b) [0].040 1
Q3 · The price of a toy is 12 euros (€) in Germany and 14 Swiss francs in Switzerland
3 The price of a toy is 12 euros (€) in Germany and 14 Swiss francs in Switzerland. 1 Swiss franc = €0.905 Calculate the difference between these two prices. Give your answer in euros. € ................................................[2]
Mark scheme: 3 [0].67 2 M1 for 14 × 0.905 [–12] or 12.67 If zero scored, SC1 for answer [0].74[0] 8 3
Q4 · 14 Work out - , giving your answer as a fraction in its lowest terms
2 14 Work out - , giving your answer as a fraction in its lowest terms. 3 4 Do not use a calculator and show all the steps of your working. .................................................[2]
Mark scheme: 8 3 4 and oe M1 Correct fractions with common denominator 12 12 5 cao 12 A1 1
Q5 · Write 5 -3 as a fraction
5 (a) Write 5 -3 as a fraction. ................................................. [1] (b) Write 0.004 56 in standard form. ................................................. [1]
Mark scheme: 5 (a) 1 125 (b) 1 4.56 × 10–3
Q6 · P NOT TO SCALE 42°42° Q T W In the diagram, PT is a tangent to the circle at P
6 P NOT TO SCALE 42°42° Q T W In the diagram, PT is a tangent to the circle at P. PW is a diameter and angle TPQ = 42°. Find angle PWQ. Angle PWQ = ................................................ [2]
Mark scheme: 6 42 2 M1 for Q = 90 or WPQ = 90 – 42 or WPQ =48 x 2 + 2 y 2 x 2 y
Question 7
7 Simplify. 3 3 x y + 2xy x 2 y 2 ................................................. [2]
Mark scheme: x + 2 y x 2 y 2 27 or + 2 B1 for xy ( x + 2 y ) xy y x final answer x 2 y + 2 y 3 x 3 + 2 xy 2 or M1 for or xy 2 x 2 y pt 2t 3 p 2t + 3 p
Q8 · Write as a single fraction
8 Write as a single fraction. 2 3 1 - - p t ................................................. [2]
Mark scheme: pt − 2t − 3 p 2t + 3 p 8 final answer 2 B1 for pt − 2t − 3 p or 1 − pt pt
Q9 · D NOT TO x° SCALE O 110° A y° C B A, B, C and D lie on the circle, centre O
9 D NOT TO x° SCALE O 110° A y° C B A, B, C and D lie on the circle, centre O. Find the value of x and the value of y. x = ................................................ y = ................................................ [2]
Mark scheme: 9 [x =] 55 1 [y =] 125 1FT correct or FT (180 – their x)
Question 10
10 Simplify. 1 ^36x 16h2 ................................................. [2]
Mark scheme: 10 6x 8 final answer 2 B1 for 6 kx , 6× x 8 or kx 8 (k ≠ 0) as final answer
Q11 · Solve the simultaneous equations
11 Solve the simultaneous equations. You must show all your working. 2x + 3y = 13 x + 2y = 9 x = ................................................ y = ................................................ [3]
Mark scheme: 11 Correctly eliminating one variable M1 [x =] −1 and A1 If zero scored, SC1 for 2 values that satisfy one of the original [y = ] 5 A1 equations or SC1 if no working shown, but 2 correct answers given 1
Q12 · Write $0.70 as a fraction of $5.60, giving your answer in its lowest terms
12 (a) Write $0.70 as a fraction of $5.60, giving your answer in its lowest terms. ................................................. [1] (b) Write the recurring decimal .018o o as a fraction in its lowest terms. [ .018o o means 0.181818… ] ................................................. [2]
Mark scheme: 1 12 (a) cao 1 8 2 . . . . (b) 2 M1 for 18.18 − 0.18 oe 11 2 k or B1 for (k not 0 or 1) 11k
Question 13
13 Factorise completely. (a) 4p 2 - 9 ................................................. [1] (b) 2ax - 4bx - ay + 2by ................................................. [2]
Mark scheme: 13 (a) (2 p − 3)(2 p + 3) final answer 1 (b) ( a − 2b )(2 x − y ) oe final answer 2 B1 for 2 x ( a − 2b ) − y ( a − 2b ) or a (2 x − y ) − 2b (2 x − y )
Q14 · Y is directly proportional to the square root of (x + 2)
14 y is directly proportional to the square root of (x + 2). When x = 7, y = 2. Find y when x = 98. y = ................................................ [3]
Mark scheme: 14 6 23 oe 3 M1 for y = k x + 2 oe or better e.g. 2 = k 7 + 2 M1 for [y = ] their k × 98 + 2 or y 98 + 2 M2 for = 2 7 + 2 5
Question 15
15 Work out. 3 1 (a) 2 - c m c m 5 2 ................................................. [1] 2 (b) (1 2 ) c 3 m ................................................. [2]
Mark scheme: 5 15 (a) 1 8 (b) (8) final answer 2 B1 for final answer 8 without brackets Page 4 Mark Sccheme Syllabuss Paper Cambridge IGCSE – Occtober/November 2016 0580 21
Q21 · Y 4 NOT TO SCALE R x 0 1 4 Write down the three inequalities that define the unshaded…
21 y 4 NOT TO SCALE R x 0 1 4 Write down the three inequalities that define the unshaded region, R. ................................................. ................................................. ................................................. [4]
Mark scheme: 21 y ⩾ 0 and x ⩾ 1 oe 4 SC3 for y > 0, x > 1 and x + y < 4 oe and or x + y ⩽4 oe B1 for y ⩾ 0 B1 for x ⩾ 1 oe and B2 for x + y ⩽ 4 oe or M1 for grad = –1 soi If B0 scored for first two B marks, SC1 for y = 0 and x = 1 or with incorrect inequality sign
Q22 · N() = 10, n(A) = 7, n(B) = 6, n ( A , B) l = 1
22 (a) n() = 10, n(A) = 7, n(B) = 6, n ( A , B) l = 1. A B (i) Complete the Venn diagram by writing the number of elements in each subset. [2] (ii) An element of is chosen at random. Find the probability that this element is an element of Al + B . ................................................. [1] (b) On the Venn diagram below, shade the region C l + D l. C D [1]
Mark scheme: 22 (a) (i) 2 B1 for n( A ∩ B ) = 4 A B 3 4 2 1 2 their 2 (ii) oe 1FT allow correct answer or FT 10 10 (b) C D 1 3 2
Q23 · Solve the equation 2x 2 + 3 x - 3 = 0
23 Solve the equation 2x 2 + 3 x - 3 = 0 . Show all your working and give your answers correct to 2 decimal places. x = ........................... or x = ........................... [4] Question 24 is printed on the next page.
Mark scheme: 2 3 23 (3) − 4(2)( −3) oe or better B1 If completing the square, B1 for x + oe 4 −+3 k −−3 k 3 3 3 2 3 3 3 2 or oe B1 B1 for − + + or − − + oe 2(2) 2(2) 4 2 4 4 2 4 –2.19, 0.69 B1B1 SC1 for –2.2 or –2.186… and 0.7 or 0.686.. or –2.19 and 0.69 seen but not final answer or 2.19 and –0.69 Maximum score without working is 2 2 2 2
Q24 · S R NOT TO P Q 8 cm SCALE D C 8 cm A 8 cm B The diagram shows a cube of side length 8 cm
24 S R NOT TO P Q 8 cm SCALE D C 8 cm A 8 cm B The diagram shows a cube of side length 8 cm. (a) Calculate the length of the diagonal BS. BS = ......................................... cm [3] (b) Calculate angle SBD. Angle SBD = ................................................ [2]
Mark scheme: 24 (a) 13.9 or 13.85 to 13.86 3 M2 for 8 2 + 8 2 + 8 2 oe or M1 for 82 + 82 or better for one face 8 8 2 + 8 2 (b) 35.1 to 35.5[4…] 2 M1 for sin = or cos = their(a) their(a) 8 or tan = oe 8 2 + 8 2
What was in this paper
The subtopics covered by these 19 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 2016 Oct/Nov, Paper 2 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.