Cambridge IGCSE Mathematics 0580 — 2015 Oct/Nov Paper 2 · Variant 3
0580/23/O/N/15 · 26 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 168.9 correct to 2 significant figures
1 Write 168.9 correct to 2 significant figures. Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: Question Answer Mark Part marks 1 170 cao 1
Q2 · 07 - 1.89 .2 Calculate 5.71 - 3.92 Answer ...............................................
2.07 - 1.89 .2 Calculate 5.71 - 3.92 Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: 2 [0].101 or [0].1005 to [0].1006 1
Q3 · Write 1.7 × 10–4 as an ordinary number
3 Write 1.7 × 10–4 as an ordinary number. Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: 3 [0].00017 1
Q4 · The probability that it will rain on any day is 15
4 The probability that it will rain on any day is 15 . Calculate an estimate of the number of days it will rain in a month with 30 days. Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: 4 6 1
Q5 · 11 12 13 14 15 16 From the list of numbers, write down (a) the factors of 60, Answer(a)…
5 11 12 13 14 15 16 From the list of numbers, write down (a) the factors of 60, Answer(a) ................................................ [1] (b) the prime numbers. Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 5 (a) 12, 15 1 (b) 11, 13 1
Question 6
6 Simplify. 1 – 2u + u + 4 Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 6 5 − u final answer 2 B1 for 5 + ku or j – u , k ≠ 0 as final answer
Question 7
7 Factorise completely. 2x – 4x2 Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 2 ) or x ( 2 − 4 x ) as final answer7 2 x 1( − 2 x ) final answer 2 B1 for 2( x − 2 x 360
Q8 · Find the sum of the interior angles of a 25-sided polygon
8 Find the sum of the interior angles of a 25-sided polygon. Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 360 8 4140 2 M1 for ( 25 − 2) × 180 or 25 × 180 − 25 2
Q9 · NOT TO 5 cm SCALE 2 cm x° Calculate the value of x
9 NOT TO 5 cm SCALE 2 cm x° Calculate the value of x. Answer x = ................................................ [2] __________________________________________________________________________________________
Mark scheme: 2 9 23.6 or 23.57 to 23.58 2 M1 for sin[= ] oe 5
Q10 · Find the value of (a) ^ 5h8 , Answer(a) ...............................................
10 Find the value of (a) ^ 5h8 , Answer(a) ................................................ [1] 2 1 - 3 (b) . c 27 m Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 10 (a) 625 1 (b) 9 1 3x
Q11 · Write the following as single fractions
11 Write the following as single fractions. x (a) x + 2 Answer(a) ................................................ [1] 2 (b) x + x Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 3x 11 (a) oe final answer 1 2 x 2 + 2 (b) 1 oe final answer x
Q12 · P Q 3 5 10 9 The Venn diagram shows the number of elements in each set
12 P Q 3 5 10 9 The Venn diagram shows the number of elements in each set. (a) Find n (P' Q). Answer(a) ................................................ [1] (b) Complete the statement n (..................................) = 17. [1] __________________________________________________________________________________________
Mark scheme: 12 (a) 10 1 (b) P ∪ Q ′ oe 1
Q13 · U 13 M = and M = 1
7 u 13 M = and M = 1. e 2 3 o Find the value of u. Answer u = ................................................ [2] __________________________________________________________________________________________
Mark scheme: 13 10 2 B1 for 7 × 3 − 2 × u
Q14 · Two containers are mathematically similar
14 Two containers are mathematically similar. Their volumes are 54 cm3 and 128 cm3. The height of the smaller container is 4.5 cm. Calculate the height of the larger container. Answer .......................................... cm [3] __________________________________________________________________________________________
Mark scheme: 128 14 6 3 M2 for 5.4 × 3 oe or better 54 3 128 54 54 5.4 M1 for 3 or 3 oe or = oe 54 128 128 x 8 2 3
Q15 · 1 1 – +15 Work out 4 , giving your answer as a fraction in its lowest terms
2 1 1 – +15 Work out 4 , giving your answer as a fraction in its lowest terms. 3 6 Do not use a calculator and show all the steps of your working. Answer ................................................ [3] __________________________________________________________________________________________
Mark scheme: 8 2 3 15 Any two of , oe M1 M1 for any 2 correct over a common denominator 12 12 or12 4 1 e.g. and 6 6 8 2 3 13 1 + − oe M1 or SC2 for final answer or 1 with full working 12 12 12 12 12 7 A1 12 2 ( s ut )
Q16 · 16 Make a the subject of the formula s = ut + 2 at 2
1 16 Make a the subject of the formula s = ut + 2 at 2. Answer a = ................................................ [3] __________________________________________________________________________________________
Mark scheme: 2 ( s − ut )16 oe final answer 3 M1 for correctly isolating term in a 2 t M1 for correctly multiplying by 2 (or 2) M1 for correctly dividing by t2 (or t2)
Question 17
17 Simplify. 1 16 o e 16x y64 4 Answer ................................................ [3] __________________________________________________________________________________________
Mark scheme: 17 3 B2 for fraction as final answer with two of x16, 2, y4 x 16 final answer 4 correct and in correct position 2y or B1 for fraction as final answer with one of x16, 2, y4 correct and in correct position
Q18 · Samira takes part in two charity runs
18 Samira takes part in two charity runs. The probability that she finishes each run is 0.8 . First run Second run 0.8 finishes finishes 0.8 0.2 does not finish 0.2 0.8 finishes does not finish 0.2 does not finish Find the probability that Samira finishes at least one run. Answer ................................................ [3] __________________________________________________________________________________________
Mark scheme: 18 0.96 oe 3 M2 for 1 − 2.0 × 2.0 or 0.8 + 0.2 × 0.8 or 0.8 × 0.8 + 0.8 × 0.2 + 0.2 × 0.8 or B1 for one of 2.0 × 2.0 , 8.0 × ,8.0 8.0 × ,2.0 2.0 × 8.0 seen 18 k
Q19 · Y is inversely proportional to (x + 2)2
19 y is inversely proportional to (x + 2)2. When x = 1, y = 2. Find y in terms of x. Answer y = ................................................ [2] __________________________________________________________________________________________
Mark scheme: 18 k 19 oe 2 M1 for y = or better ( x + 22) ( x + 22) If zero scored k SC1 for final answer of y = ( x + 22) where k ≠0 or 18 877 5
Q20 · The volume of a cuboid is 878 cm3, correct to the nearest cubic centimetre
20 The volume of a cuboid is 878 cm3, correct to the nearest cubic centimetre. The length of the base of the cuboid is 7 cm, correct to the nearest centimetre. The width of the base of the cuboid is 6 cm, correct to the nearest centimetre. Calculate the lower bound for the height of the cuboid. Answer .......................................... cm [3] __________________________________________________________________________________________
Mark scheme: 8775. 20 18 cao nfww 3 M2 for 5.7 × 5.6 or B1 for any two of 877.5, 7.5 and 6.5 seen
Q21 · Solve the equation 3x2 + 4x – 5 = 0
21 Solve the equation 3x2 + 4x – 5 = 0. Show all your working and give your answers correct to 2 decimal places. Answer x = ........................ or x = ........................ [4] __________________________________________________________________________________________
Mark scheme: 21 ( 4) 2 − 4(3)( −5) or better seen B1 If completing the square p + q p − q 2 2 if or seen then B1 for x + oe r r 3 2 5 2 2 2 5 2 2 − + 2 or − 3 3 p = – 4 and r = 2(3) B1 B1 for −3 + 3 + 3 3 2 – 2.12 B1 0.79 final answers B1 If B0, SC1 for 0.786[299] and −2.119[632] – 2.1 and 0.8 or – 2.120 or – 2.119 and 0.786 or 2.12 and –0.79 final answers –2.12 and 0.79 seen not as final answers 1
Question 22
22 Simplify. 4 + 10 w 8 - 50 w 2 Answer ................................................ [4] __________________________________________________________________________________________
Mark scheme: 1 22 final answer nfww 4 B1 for 2(2 + 5w) 2 − 5 w B1 for 2(4 – 25w2) B1 for [2](2 + 5w)(2 – 5w) ALT method 4 + 10 w B3 for ( 4 + 10 w)( 2 − 5 w) or B2 for (4 + 10w)(2 – 5w) 1 2
Q23 · B NOT TO SCALE b C A O a In the diagram, O is the origin, OA = a and OB = b
23 B NOT TO SCALE b C A O a In the diagram, O is the origin, OA = a and OB = b. C is on the line AB so that AC : CB = 1 : 2. Find, in terms of a and b, in its simplest form, (a) AC, Answer(a) AC = ................................................ [2] (b) the position vector of C. Answer(b) ................................................ [2] __________________________________________________________________________________________
Mark scheme: 1 2 23 (a) (– a + b) oe 2 M1 for any correct route eg AO+OB+ BA 3 3 or B1 for AB = – a + b oe 2 1 (b) a + b oe simplified 2FT FT their (a) + a simplified only if in terms of a and b. 3 3 M1 for identifying OCas position vector or correct route in any form or for correct unsimplified answer
Q24 · 80 70 60 50 Cumulative 40 frequency 30 20 10 0 1 2 3 4 5 6 7 8 9 10 Time (minutes) The…
24 80 70 60 50 Cumulative 40 frequency 30 20 10 0 1 2 3 4 5 6 7 8 9 10 Time (minutes) The cumulative frequency diagram shows information about the times, in minutes, taken by 80 students to complete a short test. Find (a) the median, Answer(a) ......................................... min [1] (b) the 30th percentile, Answer(b) ......................................... min [2] (c) the number of students taking more than 5 minutes. Answer(c) ................................................ [2] __________________________________________________________________________________________
Mark scheme: 24 (a) 6.2 1 (b) 5.8 2 M1 for 24 soi (c) 70 2 M1 for 10 soi 30
Q25 · B NOT TO SCALE 8 cm 30° O A C OAB is the sector of a circle, centre O, with radius 8 cm…
25 B NOT TO SCALE 8 cm 30° O A C OAB is the sector of a circle, centre O, with radius 8 cm and sector angle 30°. BC is perpendicular to OA. Calculate the area of the region shaded on the diagram. Answer ......................................... cm2 [5] __________________________________________________________________________________________ Question 26 is printed on the next page.
Mark scheme: 30 × π × 8 2 – 0.5×8cos30×8sin3025 2.9[0] or 2.898 to 2.901 5 M4 for 360 or 30 2 M1 for × π × 8 360 and M2 for [area of triangle =] 0.5×8cos30×8sin30 oe OC BC or M1 for = cos30 oe or = sin30 oe 8 8
Q26 · 45 NOT TO SCALE Speed (km/h) 0 10 20 30 Time (seconds) The diagram shows the speed-time…
26 45 NOT TO SCALE Speed (km/h) 0 10 20 30 Time (seconds) The diagram shows the speed-time graph of a car. The car travels at 45 km/h for 20 seconds. The car then decelerates for 10 seconds until it stops. (a) Change 45 km/h into m/s. Answer(a) ......................................... m/s [2] (b) Find the deceleration of the car, giving your answer in m/s2. Answer(b) ........................................ m/s2 [1] (c) Find the distance travelled by the car during the 30 seconds, giving your answer in metres. Answer(c) ............................................ m [3]
Mark scheme: 26 (a) 12.5 oe 2 M1 for 45 × 1000 ÷ 60 ÷ 60 oe (b) 1.25 oe 1FT FT their (a) ÷ 10 (c) 312.5 oe 3FT FT for 25 × their (a) M2 for 20 × their 12.5 + 0.5 × 10 × their 12.5 oe or M1 for one correct relevant area calculation or SC2 for final answer 1125
What was in this paper
The subtopics covered by these 26 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
4Fractions, decimals and percentages2Limits of accuracy2Powers and roots2Vectors in two dimensions2Angles1Circles, arcs and sectors1Equations1Interpreting statistical data1Introduction to probability1Probability of combined events1Rates1Ratio and proportion1Right-angled triangles1Sets1Similarity1Standard form1The four operations1Types of number1What you needed in this session
Cambridge’s own grade thresholds for 2015 Oct/Nov, Paper 2 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.