Cambridge IGCSE Mathematics 0580 — 2015 Oct/Nov Paper 1 · Variant 3
0580/13/O/N/15 · 23 questions · 56 marks · ≈63 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 scheme3 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · Write in figures the number six thousand and fifty four
1 Write in figures the number six thousand and fifty four. Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: Question Answer Mark Part marks 1 6054 1
Q2 · Measure the length of this line in centimetres
2 Measure the length of this line in centimetres. Answer .......................................... cm [1] __________________________________________________________________________________________
Mark scheme: 2 6.7 1
Q3 · Write down the order of rotational symmetry of this shape
3 Write down the order of rotational symmetry of this shape. Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: 3 3 1
Q4 · Write 168.9 correct to 2 significant figures
4 Write 168.9 correct to 2 significant figures. Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: 4 170 cao 1
Q5 · 07 - 1.89 .5 Calculate 5.71 - 3.92 Answer ...............................................
2.07 - 1.89 .5 Calculate 5.71 - 3.92 Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: 5 [0].101 or [0].1005 to [0].1006 1
Q6 · The probability that it will rain on any day is
16 The probability that it will rain on any day is . 5 Calculate an estimate of the number of days it will rain in a month with 30 days. Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: 6 6 1
Q7 · 11 12 13 14 15 16 From the list of numbers, write down (a) the factors of 60, Answer(a)…
7 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: 7 (a) 12, 15 1 (b) 11, 13 1
Q8 · These are the first four terms in a sequence
8 These are the first four terms in a sequence. 21 17 13 9 (a) Write down the next number in this sequence. Answer(a) ................................................ [1] (b) Write down the rule for continuing the sequence. Answer(b) ........................................................................................................................................... [1] __________________________________________________________________________________________
Mark scheme: 8 (a) 5 1 (b) Subtract 4 oe 1
Question 9
9 Simplify. 1 – 2u + u + 4 Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 9 5 – u final answer 2 B1 for 5 + ku or j – u , k ≠ 0 as final answer
Q10 · At 9 am the temperature was –3°C
10 (a) At 9 am the temperature was –3°C. At 1pm the temperature had risen by 5°C. Work out the temperature at 1pm. Answer(a) ............................................°C [1] (b) Work out –7 – 2. Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 10 (a) 2 1 (b) −9 1 2
Q11 · NOT TO 5 cm SCALE 2 cm x° Calculate the value of x
11 NOT TO 5 cm SCALE 2 cm x° Calculate the value of x. Answer x = ................................................ [2] __________________________________________________________________________________________
Mark scheme: 2 11 23.6 or 23.57 to 23.58 2 M1 for sin [ =] oe 5
Q12 · Write 72 as a product of its prime factors
12 Write 72 as a product of its prime factors. Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 12 23 × 32 or 2 × 2 × 2 × 3 × 3 2 B1 for 2, 2, 2, 3, 3
Q13 · NOT TO SCALE x cm 18 cm 26 cm Calculate the value of x
13 NOT TO SCALE x cm 18 cm 26 cm Calculate the value of x. Answer x = ................................................ [2] __________________________________________________________________________________________
Mark scheme: 13 31.6 [2....] 2 M1 for 18 2 + 26 2
Q14 · In this question use a ruler and compasses only and show all your construction arcs
14 In this question use a ruler and compasses only and show all your construction arcs. Using a scale of 1 centimetre to represent 50 metres, construct a triangle with sides 550 m, 450 m and 300 m. The 300 m side has been drawn for you. [2] __________________________________________________________________________________________
Mark scheme: 14 Correct triangle with correct 2 B1 for correct triangle without arcs or 1 correct side arcs with arcs
Q15 · NOT TO SCALE 5 cm 9 cm 12.5 cm Calculate the volume of this cuboid
15 NOT TO SCALE 5 cm 9 cm 12.5 cm Calculate the volume of this cuboid. Give the units of your answer. Answer ............................ ................ [3] __________________________________________________________________________________________
Mark scheme: 15 562.5 2 M1 for 5 × 12.5 × 9 cm3 1 8 2 3
Q16 · 1 116 Work out + – , giving your answer as a fraction in its lowest terms
2 1 116 Work out + – , giving your answer as a fraction in its lowest terms. 3 6 4 Do not use a calculator and show all the steps of your working. Answer ................................................ [3] __________________________________________________________________________________________
Mark scheme: 8 2 3 16 Any two of , or oe M1 M1 for any 2 correct over a common denominator, 12 12 12 4 1 eg and 6 6 8 2 3 + − oe M1 12 12 12 13 1 or SC2 for final answer or 1 with full working 12 12 7 A1 12
Question 17
17 (a) Multiply out. 3(x + 7) Answer(a) ................................................ [1] (b) Factorise completely. 2x – 4x2 Answer(b) ................................................ [2] __________________________________________________________________________________________
Mark scheme: 17 (a) 3x + 21 final answer 1 (b) 2x (1 − 2x) final answer 2 B1 for 2(x − 2x2) or x(2 – 4x) as final answer
Q18 · This scale drawing shows the positions of two towns, A and B, on a map
18 This scale drawing shows the positions of two towns, A and B, on a map. North A B (a) Measure the bearing of town B from town A. Answer(a) ................................................ [1] (b) On the map, town C is 8 cm from town A on a bearing of 155°. Mark the position of town C on the scale drawing. [2] __________________________________________________________________________________________
Mark scheme: 18 (a) 230 1 (b) C marked in correct position 2 B1 for correct distance 8 cm or correct bearing 155°
Q19 · Write 1.7 × 10–4 as an ordinary number
19 (a) Write 1.7 × 10–4 as an ordinary number. Answer(a) ................................................ [1] (b) Work out (3.8 × 104) × (2.7 × 10–8). Give your answer in standard form. Answer(b) ................................................ [2] __________________________________________________________________________________________
Mark scheme: 19 (a) [0].00017 1 (b) 1.026 × 10–3 2 B1 for 10.26 ×10−4 oe
Q20 · The diagram shows a quadrilateral with one side extended
20 (a) The diagram shows a quadrilateral with one side extended. 98° NOT TO 112° SCALE 66° x° Find the value of x. Answer(a) x = ................................................ [2] (b) Find the sum of the interior angles of a 25-sided polygon. Answer(b) ................................................ [2] __________________________________________________________________________________________
Mark scheme: 20 (a) 96 2 M1 for 360 – (66 + 98 +112) 360 (b) 4140 2 M1 for (25 – 2) × 180 or 25 × 180 − 25 10
Q21 · A P NOT TO x cm 10 cm 7.5 cm SCALE 6.25 cm B 6 cm C Q y cm R The diagram shows two…
21 A P NOT TO x cm 10 cm 7.5 cm SCALE 6.25 cm B 6 cm C Q y cm R The diagram shows two similar triangles ABC and PQR. Find the value of (a) x, Answer(a) x = ................................................ [2] (b) y. Answer(b) y = ................................................ [2] __________________________________________________________________________________________
Mark scheme: x 10 21 (a) 12 nfww 2 M1 for = oe 5.7 .625 y .625 (b) 3.75 cao 2 M1 for = oe 6 10
Q22 · Solve the simultaneous equations
22 Solve the simultaneous equations. You must show all your working. 5x + 2y = 8 2x – 3y = 26 Answer x = ................................................ y = ................................................ [4] __________________________________________________________________________________________
Mark scheme: 22 Correctly equating one set of M1 eg 10x + 4y = 16 and 10x − 15y = 130 coefficients or 15x + 6y = 24 and 4x – 6y = 52 Correct method to eliminate one M1 eg 19y = k or hx = 114 or 19x = m or ny = 76 variable [x =] 4 A1 [y =] −6 A1 If zero scored SC1 for 2 values satisfying one of the original equations. SC1 if no working shown, but 2 correct answers given
Q23 · The pie chart shows how 120 students travel to school
23 (a) The pie chart shows how 120 students travel to school. Car Bus 138° Cycle Walk (i) Measure the sector angle for the students who travel to school by car. Answer(a)(i) ................................................ [1] (ii) What fraction of the students cycle to school? Answer(a)(ii) ................................................ [1] (iii) Calculate how many students walk to school. Answer(a)(iii) ................................................ [2] (b) Wei records the number of children living in each of the houses in a street. Her results are recorded in the table. Number of Frequency children 0 3 1 3 2 8 3 5 4 4 5 2 Calculate the mean number of children per house. Answer(b) ................................................ [3] __________________________________________________________________________________________
Mark scheme: 23 (a) (i) 60 1 90 (ii) oe 1 360 (iii) 46 2 M1 for 138 × 120 360 (b) 2.4 nfww 3 M1 for (0 × 3)+ (1 × 3) + (2 × 8) + (3 × 5) + (4 × 4) + (5 × 2) implied by 60 M1dep for their 60 ÷ 25
What was in this paper
The subtopics covered by these 23 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
3Algebraic manipulation2The four operations2Angles1Equations1Fractions, decimals and percentages1Geometrical constructions1Introduction to probability1Limits of accuracy1Pythagoras’ theorem1Right-angled triangles1Scale drawings1Sequences1Similarity1Standard form1Statistical charts and diagrams1Surface area and volume1Symmetry1Units of measure1What you needed in this session
Cambridge’s own grade thresholds for 2015 Oct/Nov, Paper 1 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.