Cambridge IGCSE Mathematics 0580 — 2014 Oct/Nov Paper 2 · Variant 1
0580/21/O/N/14 · 20 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 scheme4 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Use your calculator to fi nd the value of 1.357
1 Use your calculator to fi nd the value of 1.357. Give your answer correct to 5 signifi cant fi gures. Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 1 8.1722 cao 2 B1 for 8.17 or 8.172 or 8.1721 or 8.17215… 22
Q2 · Write the following in order of size, smallest fi rst
2 Write the following in order of size, smallest fi rst. 22 π 3.14 3.142 3 7 Answer ..................... < ..................... < ..................... < ..................... < ..................... [2] smallest __________________________________________________________________________________________
Mark scheme: 22 2 3 3.14 π 3.142 2 B1 for 3.141[5...] to 3.1416 7 and 3.1428 to 3.1429 or 3.143 seen or SC1 for 4 in correct order
Q3 · Write down the letters in the word above that have (a) exactly one line of symmetry…
3 Write down the letters in the word above that have (a) exactly one line of symmetry, Answer(a) ................................................ [1] (b) rotational symmetry of order 2. Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 3 (a) E B A cao 1 (b) Z cao 1
Q4 · Cheryl recorded the midday temperatures in Seoul for one week in January
4 Cheryl recorded the midday temperatures in Seoul for one week in January. Day Mon Tue Wed Thu Fri Sat Sun Temperature (°C) –4 –5 –3 –11 –8 –3 –1 (a) Write down the mode. Answer(a) ........................................... °C [1] (b) On how many days was the temperature lower than the mode? Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 4 (a) –3 1 (b) 4 1FT FT their numerical mode 3 2
Q5 · Without using a calculator, work out 1 + 1
5 Without using a calculator, work out 1 + 1 . 4 6 Write down all the steps in your working and give your answer as a fraction in its simplest form. Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 5 3 and 2 M1 Equivalent denominators can be used, 12 12 working must be shown. 5 cao A1 12
Q6 · Write 15.0782 correct to (a) one decimal place, Answer(a)…
6 Write 15.0782 correct to (a) one decimal place, Answer(a) ................................................ [1] (b) the nearest 10. Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 6 (a) 15.1 cao 1 (b) 20 cao 1 ( )
Q7 · The population of Dubai at the end of 2012 was 2.1 million
7 The population of Dubai at the end of 2012 was 2.1 million. This was predicted to increase at a rate of 6% each year. Calculate the predicted population of Dubai at the end of 2015. Answer .................................... million [3] __________________________________________________________________________________________
Mark scheme: 6 )3 oe7 2.5[0] or 2.501… nfww 3 M2 for 1.2 × (1 + 100 6 )n oe where n ≥ 2 or M1 for 1.2 × (1 + 100 6 3 or for figs 21 × (1 + 100 ) oe
Q8 · On a ship, the price of a gift is 24 euros (€) or $30
8 On a ship, the price of a gift is 24 euros (€) or $30. What is the difference in the price on a day when the exchange rate is €1 = $1.2378? Give your answer in dollars, correct to the nearest cent. Answer $ ................................................. [3] __________________________________________________________________________________________
Mark scheme: 8 0.29 cao 3 M2 for 30 − (24 × .12378) or (24 × .12378) − 30 or M1 for 24× .12378
Q9 · Write 2.8 × 102 as an ordinary number
9 (a) Write 2.8 × 102 as an ordinary number. Answer(a) ................................................ [1] (b) Work out 2.5 × 108 × 2 × 10–2. Give your answer in standard form. Answer(b) ................................................ [2] __________________________________________________________________________________________
Mark scheme: 9 (a) 280 1 (b) 5 × 106 2 B1 for 5 000 000 oe or B1 for answer k × 10 6 or 5× 10 k
Question 10
10 Solve the equation. x + 5 7 = x 3 Answer x = ................................................ [3] __________________________________________________________________________________________
Mark scheme: 10 3.75 oe 3 M2 for 3 × 5 = 7 x − 3 x oe or M1 for 3( x + 5 ) = 7 x or x + 5 = 73 x or 1 + 5x = 73 or better
Q11 · Simplify x8 ÷ x2
11 (a) Simplify x8 ÷ x2. Answer(a) ................................................ [1] x6 13 (b) Simplify . 27 ` j Answer(b) ................................................ [2] __________________________________________________________________________________________
Mark scheme: 11 (a) x6 1 2 x (b) 2 B1 for answer kx2 or x3k or 13 3 5
Q12 · Solve the simultaneous equations
12 Solve the simultaneous equations. 0.4x – 5y = 27 2x + 0.2y = 9 Answer x = ................................................ y = ................................................ [3] __________________________________________________________________________________________
Mark scheme: 5 12 nfww 3 M1 for correctly eliminating one variable − 5 A1 for x = 5 A1 for y = −5 If zero scored SC1 for correct substitution and evaluation to find the other variable
Q13 · Y varies directly with x + 5
13 y varies directly with x + 5 . y = 4 when x = –1. Find y when x = 11. Answer y = ................................................ [3] __________________________________________________________________________________________
Mark scheme: 13 [±] 8 nfww 3 M1 for y = k x + 5 A1 for k = [±] 2 or 4 y M2 for = oe − 1 + 5 11 + 5 4 16 12 48 8 32
Q14 · 2 8 A = 1 4 f p Work out A2 – 4A
14 2 8 A = 1 4 f p Work out A2 – 4A. Answer [3] f p __________________________________________________________________________________________
Mark scheme: 4 16 12 48 8 32 14 3 M2 for and 2 8 6 24 4 16 12 48 8 32 or M1 for or for 6 24 4 16
Q15 · C A B (a) Using compasses and straight edge only, construct (i) the perpendicular…
15 C A B (a) Using compasses and straight edge only, construct (i) the perpendicular bisector of AC, [2] (ii) the bisector of angle ACB. [2] (b) Shade the region inside the triangle which is ● nearer to A than to C and ● nearer to AC than to BC. [1] __________________________________________________________________________________________
Mark scheme: 15 (a) (i) 2 B2 for correct ruled bisector with correct arcs or B1 for correct bisector with no/incorrect arcs (ii) 2 B2 for correct ruled bisector with correct arcs or B1 for correct bisector with no/incorrect arcs (b) 1 correct shading
Q16 · A helicopter fl ies from its base B to deliver supplies to two oil rigs at C and D
16 A helicopter fl ies from its base B to deliver supplies to two oil rigs at C and D. C is 6 km due east of B and the distance from C to D is 8 km. D is on a bearing of 120° from B. North North NOT TO 120° 6 km SCALE B C 8 km D Find the bearing of D from C. Answer ................................................ [5] __________________________________________________________________________________________
Mark scheme: 16 142 or 142.0… 5 B1 for CBD = 30 6 × sin theirB M2 for [sin D = ] oe 8 6 8 or M1 for = oe sin D sin(their 30) A1 for [D =] 22 or 22.0 or 22.02… B1FT for 90 + (their30 + their22) evaluated correctly for their final answer or for 360 – 90 – theirBCD evaluated correctly for their final answer 1 4
Q17 · The diagram shows a child’s toy
17 The diagram shows a child’s toy. 5 cm NOT TO SCALE 8 cm The shape of the toy is a cylinder of radius 5 cm and height 8 cm on top of a hemisphere of radius 5 cm. Calculate the volume of the toy. 4 [The volume, V, of a sphere with radius r is V = πr 3.] 3 Answer ......................................... cm3 [5] __________________________________________________________________________________________
Mark scheme: 1 4 3 217 890 or 890.1 to 890.2… 5 M4 for × × π × 5 + π × 5 × 8 2 3 1 4 3 2 or M3 for × × π × 5 and π × 5 × 8 2 3 1 4 3 2 or M2 for × × π × 5 or π × 5 × 8 2 3 4 3 or M1 for × π × 5 3
Q18 · If it rains today the probability that it will rain tomorrow is 0.4
18 If it rains today the probability that it will rain tomorrow is 0.4 . If it does not rain today the probability that it will rain tomorrow is 0.2 . On Sunday it rained. (a) Complete the tree diagram for Monday and Tuesday. Monday Tuesday Rain 0.4 Rain 0.4 0.6 No rain Rain ........ ........ No rain ........ No rain [2] (b) Find the probability that it rains on at least one of the two days shown in the tree diagram. Answer(b) ................................................ [3] __________________________________________________________________________________________
Mark scheme: 18 (a) 6.0 2.0 8.0 in correct places 2 B1 for 0.6 in correct place B1 for 0.2 and 0.8 in correct places (b) 0.52 oe nfww 3 M2FT for 1 – (their 0.6 × their 0.8) oe or M1FT for a correct product from their tree in (a)
Q19 · C NOT TO SCALE A B D Two circles, centres A and B, are each of radius 8 cm and intersect…
19 C NOT TO SCALE A B D Two circles, centres A and B, are each of radius 8 cm and intersect at C and D. Each circle passes through the centre of the other circle. (a) Explain why angle CBD is 120°. Answer(a) [1] C (b) For the circle, centre B, fi nd the area of the sector BCD. NOT TO 8 cm SCALE A 120° B 8 cm D Answer(b) ......................................... cm2 [2] (c) (i) Find the area of the shaded segment CAD. C NOT TO SCALE A B D Answer(c)(i) ......................................... cm2 [3] (ii) Find the area of overlap of the two circles. Answer(c)(ii) ......................................... cm2 [1] __________________________________________________________________________________________ Question 20 is printed on the next page.
Mark scheme: 19 (a) CBA and BDA are equilateral oe 1 (b) 67[.0] or 67.02 to 67.03 2 M1 for 120360 × π × 8 2 oe (c) (i) 3 M2FT for their (b ) − 12 × 82 × sin 120 oe 39.3 or 39.28 to 39.33 or M1 for 12 × 82 × sin 120 oe (ii) 1FT FT 2 × their(c)(i) correctly evaluated 78.6 or 78.7 or 78.56 to 78.66
Q20 · 0 f(x) = 3x – 2 g(x) = , x ≠ –1 x + 1 (a) Find gf(2)
220 f(x) = 3x – 2 g(x) = , x ≠ –1 x + 1 (a) Find gf(2). Answer(a) ................................................ [2] (b) Solve g(x) = 10. Answer(b) x = ................................................ [2] (c) Simplify. f(2x) – f(x + 2) Answer(c) ................................................ [3]
Mark scheme: 20 (a) 0.4 or 52 2 B1 for [f(2) =] 4 2 or M1 for or better (3 x − 2 ) + 1 (b) –0.8 or − 54 2 M1 for 2 = 10( x + )1 or better (c) 3 x − 6 or 3( x − 2 ) nfww 3 M2 for 3(2 x ) − 2 − (3( x + 2 ) − 2 ) or M1 for [f (2 x ) = ]3(2 x ) − 2 or [f ( x + 2 )] = 3( x + 2 ) − 2
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.
2Equations2Averages and measures of spread1Circles, arcs and sectors1Fractions, decimals and percentages1Geometrical constructions1Limits of accuracy1Non-right-angled triangles1Ordering1Percentages1Powers and roots1Probability of combined events1Proportion1Ratio and proportion1Standard form1Surface area and volume1Symmetry1Using a calculator1What you needed in this session
Cambridge’s own grade thresholds for 2014 Oct/Nov, Paper 2 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.