Cambridge IGCSE Mathematics 0580 — 2015 Oct/Nov Paper 2 · Variant 1
0580/21/O/N/15 · 18 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 · At midnight the temperature in Newtown was –8 °C
1 At midnight the temperature in Newtown was –8 °C. At noon the next day the temperature in Newtown was 9 °C. Work out the rise in temperature from midnight to noon. Answer ........................................... °C [1] __________________________________________________________________________________________
Mark scheme: Question Answer Mark Part Marks 1 [+]17 1
Q2 · A B In the Venn diagram shade the region A B'
2 A B In the Venn diagram shade the region A B'. [1] __________________________________________________________________________________________
Mark scheme: 2 1
Q3 · Y 4 3 2 A 1 x –4 –3 –2 –1 0 1 2 3 4 5 –1 –2 –3 2 Draw the image of shape A after a…
3 y 4 3 2 A 1 x –4 –3 –2 –1 0 1 2 3 4 5 –1 –2 –3 2 Draw the image of shape A after a translation by the vector [2] e - 3 o.__________________________________________________________________________________________
Mark scheme: 3 Triangle (3, –2), (4, –2), 2 B1 for movement 2 right or 3 down (4, –1) 785 [ ]
Q4 · Pip and Ali share $785 in the ratio Pip : Ali = 4 : 1
4 Pip and Ali share $785 in the ratio Pip : Ali = 4 : 1. Work out Pip’s share. Answer $ ................................................ [2] __________________________________________________________________________________________
Mark scheme: 785 4 628 2 M1 for [× 4 ] 1 + 4
Q5 · Jim scores the following marks in 8 tests
5 Jim scores the following marks in 8 tests. 7 8 8 y 6 9 10 5 His mean mark is 7.5 . Calculate the value of y. Answer y = ................................................ [2] __________________________________________________________________________________________
Mark scheme: 5 7 nfww 2 M1 for 5.7 × 8 or for ( 7 + 8 + 8 + y + 6 + 9 + 10 + 5) ÷ 8 = 5.7 or better oe 4 × 30
Q6 · 9 # 29.36 By writing each number correct to 1 significant figure, estimate the value of
3.9 # 29.36 By writing each number correct to 1 significant figure, estimate the value of . 8.9 - 2.7 Show all your working. Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 4 × 30 6 M1 Allow one error and 2 for 4 and 6 for 9 – 3 9 − 3 10 nfww A1
Q7 · Work out the highest common factor (HCF) of 36 and 90
7 Work out the highest common factor (HCF) of 36 and 90. Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 7 18 2 M1 for 36 = 2 × 2 × 3 × 3 soi or 90 = 2 × 3 × 3 × 5 soi or listing the correct factors of 36 and 90 showing a minimum of 2, 3, 6, 9 and 18
Q8 · P 11 cm NOT TO SCALE 37° A O In the diagram, AP is a tangent to the circle at P
8 P 11 cm NOT TO SCALE 37° A O In the diagram, AP is a tangent to the circle at P. O is the centre of the circle, angle PAO = 37° and AP = 11 cm. (a) Write down the size of angle OPA. Answer(a) Angle OPA = ................................................ [1] (b) Work out the radius of the circle. Answer(b) .......................................... cm [2] __________________________________________________________________________________________
Mark scheme: 8 (a) 90 1 OP o (b) 8.29 or 8.289… to 8.29 2 M1 for = tan 37 oe 11
Question 9
9 Factorise completely. (a) ax + ay + 3cx + 3cy Answer(a) ................................................ [2] (b) 3a2 – 12b2 Answer(b) ................................................ [3] __________________________________________________________________________________________
Mark scheme: 9 (a) ( a + 3c )( x + y ) final answer 2 B1 for a ( x + y ) + 3c ( x + y ) or x ( a + 3c ) + y ( a + 3c ) (b) (3 a − 2b )( a + 2b ) final answer 3 B2 for (3 a − 2b )( a + 2b ) seen and then spoiled or (3a − 6b )( a + 2b ) or ( a − 2b )(3a + 6b ) or ( a − 2b )( a + 2b ) or B1 for 3( a 2 − 4b 2 )
Q10 · Write the recurring decimal .015o as a fraction
10 Write the recurring decimal .015o as a fraction. [ .015o means 0.1555...] Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 14 10 oe must be fraction 2 M1 for 155. − 5.1 oe 90 or k B1 for 90 2
Q11 · NOT TO SCALE 6.1 cm A protractor is a semi-circle of radius 6.1 cm
11 NOT TO SCALE 6.1 cm A protractor is a semi-circle of radius 6.1 cm. Calculate the perimeter of the protractor. Answer .......................................... cm [3] __________________________________________________________________________________________
Mark scheme: 2 11 31.4 or 31.36 to 31.37 3 M2 for × 1.6 × π + 2 × 1.6 oe 2 or B2 for 19.16 to 19.17 or 19.2 or M1 for 1.6 × π or for 12 2. × π 3
Q14 · A car travels at 56 km/h
14 A car travels at 56 km/h. Find the time it takes to travel 300 metres. Give your answer in seconds correct to the nearest second. Answer .............................................. s [4] __________________________________________________________________________________________
Mark scheme: 14 & &
Question 15
15 Simplify. 2 x - 16 x 2 - 3x - 4 Answer ................................................ [4] __________________________________________________________________________________________
Mark scheme: x + 4 15 final answer 4 B1 for ( x − 4)( x + 4) and x + 1 B2 for ( x − 4)( x + )1 or SC1 for ( x + a )( x + b ) where a + b = − 3 or ab = − 4
Q16 · Hazel invests $1800 for 7 years at a rate of 1.5% per year compound interest
16 Hazel invests $1800 for 7 years at a rate of 1.5% per year compound interest. Calculate how much interest she will receive after the 7 years. Give your answer correct to the nearest dollar. Answer $ ................................................ [4] __________________________________________________________________________________________
Mark scheme: 16 198 4 B3 for 197.7…. or answer 198.00 or 7 5.1 M2 for 1800 × + 1 – 1800 100 or B2 for answer 1998 or 7 5.1 M1 for 1800 × + 1 100 If B0 then B1 for seeing their answer in decimal form correctly written to the nearest integer
Q17 · Y 6 5 4 3 S 2 T 1 x 0 1 2 3 4 5 6 7 8 9 (a) Describe fully the single transformation that…
17 y 6 5 4 3 S 2 T 1 x 0 1 2 3 4 5 6 7 8 9 (a) Describe fully the single transformation that maps triangle S onto triangle T. Answer(a) ........................................................................................................................................... ............................................................................................................................................................. [3] (b) Find the matrix which represents the transformation that maps triangle S onto triangle T. Answer(b) [2] f p __________________________________________________________________________________________
Mark scheme: 17 (a) Enlargement 1 1 1 2 origin oe 1 12 0 k 0 (b) oe 2FT correct or FT their (a) allow for 2 marks 0 k 0 12 where k = their scale factor in (a) k 0 B1 for one correct row or correct column or 0 k ( k ≠ 0 or )1 − 9 − 5
Q19 · 25° 5 cm NOT TO SCALE 15 cm The diagram shows a wooden prism of height 5 cm
19 25° 5 cm NOT TO SCALE 15 cm The diagram shows a wooden prism of height 5 cm. The cross section of the prism is a sector of a circle with sector angle 25°. The radius of the sector is 15 cm. Calculate the total surface area of the prism. Answer ......................................... cm2 [5] __________________________________________________________________________________________
Mark scheme: 14 19 nfww 4 B3 19.3 or 19.28 to 19.29 or 300 × 60 2 M2 for oe 56 × 1000 or M1 for distance divided by speed 56× 1000 e.g. their 300 ÷ their 56 or 60 2 If B0 then B1 for seeing their answer in decimal form correctly written to the nearest integer x + 4
Q20 · The table shows the probability that a person has blue, brown or green eyes
20 The table shows the probability that a person has blue, brown or green eyes. Eye colour Blue Brown Green Probability 0.4 0.5 0.1 Use the table to work out the probability that two people, chosen at random, (a) have blue eyes, Answer(a) ................................................ [2] (b) have different coloured eyes. Answer(b) ................................................ [4] __________________________________________________________________________________________
Mark scheme: 20 (a) 0.16 oe 2 M1 for 4.0 × 4.0 If zero scored SC1 for fully correct evaluated method involving a without replacement method (b) 0.58 oe 4 M3 for 1 − ( 4.0 2 + 5.0 2 + 1.02 ) oe or M2 for 4.0 2 + 5.0 2 + 1.0 2 ALT method M3 for 4.0 × ( 5.0 + )1.0 + 5.0 × ( 4.0 + )1.0 + 1.0 × ( 4.0 + 5.0) oe or M2 for addition of any three of: 4.0 × ,5.0 4.0 × ,1.0 5.0 × ,4.0 0.5 × 0.1, 1.0 × 4.0 and 1.0 × 5.0 or M1 for addition of any two of: 4.0 × ,5.0 4.0 × ,1.0 5.0 × ,4.0 5.0 × ,1.0 1.0 × 4.0 and 1.0 × 5.0 If zero scored SC2 for fully correct evaluated method involving a without replacement method [ ]
Q21 · F(x) = x3 g(x) = 3x – 5 h(x) = 2x + 1 Work out (a) ff(2), Answer(a)…
21 f(x) = x3 g(x) = 3x – 5 h(x) = 2x + 1 Work out (a) ff(2), Answer(a) ................................................ [2] (b) gh(x) and simplify your answer, Answer(b) ................................................ [2] (c) h–1(x), the inverse of h(x). Answer(c) h–1(x) = ................................................ [2] __________________________________________________________________________________________
Mark scheme: 21 (a) 512 2 B1 for [f ( 2 ) = ]8 or M1 for (x 3) 3 or better (b) 6 x − 2 or 2(3 x − )1 final answer 2 B1 for (3 2 x + )1 − 5 or better (c) 1 M1 for correct first step ( x − )1 oe 2 2 y 1 eg y − 1 = 2 x or = x + 2 2 or x = 2 y + 1 or better
What was in this paper
The subtopics covered by these 18 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Transformations2Area and perimeter1Averages and measures of spread1Circles, arcs and sectors1Estimation1Fractions, decimals and percentages1Functions1Percentages1Probability of combined events1Rates1Ratio and proportion1Right-angled triangles1Sets1The four operations1Types of number1What you needed in this session
Cambridge’s own grade thresholds for 2015 Oct/Nov, Paper 2 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.