Cambridge IGCSE Mathematics 0580 — 2015 May/June Paper 1 · Variant 1
0580/11/M/J/15 · 22 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 scheme4 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · There are 31 days in January
1 There are 31 days in January. January 21st 2015 was a Wednesday. What day of the week was February 8th 2015? Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: Qu Answer Mark 1 Sunday 1
Q2 · The temperature in Berlin is –7 °C and the temperature in Istanbul is –3 °C
2 The temperature in Berlin is –7 °C and the temperature in Istanbul is –3 °C. (a) Write down how many degrees colder it is in Berlin than it is in Istanbul. Answer(a) ........................................... °C [1] (b) Sydney is 23 degrees warmer than Berlin. Write down the temperature in Sydney. Answer(b) ........................................... °C [1] __________________________________________________________________________________________
Mark scheme: 2 (a) 4 1 (b) 16 1
Q3 · A mass of 300 kg is increased by 8%
3 (a) A mass of 300 kg is increased by 8%. Work out the increase in mass. Answer(a) ........................................... kg [1] (b) Nelson scores 27 out of 40 in a history test. Work out his score as a percentage. Answer(b) ............................................ % [1] __________________________________________________________________________________________
Mark scheme: 3 (a) 24 final answer 1 (b) 67.5 1
Q4 · The total mass of 38 spoons is 1824 g
4 The total mass of 38 spoons is 1824 g. Work out the mass of 53 spoons. Answer ............................................. g [2] __________________________________________________________________________________________
Mark scheme: 4 2544 2 M1 for 1824 ÷ 38 [×53] oe 3000 × 5 × 4
Q5 · Prince Charming invests $3000 for 5 years at a rate of 4% per year simple interest
5 Prince Charming invests $3000 for 5 years at a rate of 4% per year simple interest. Calculate the total interest he will receive. Answer $ ................................................. [2] __________________________________________________________________________________________
Mark scheme: 3000 × 5 × 4 5 600 2 M1 for oe 100 If zero scored, SC1 for answer 3600
Q6 · Using a ruler and compasses only, construct a triangle with sides 5 cm, 6 cm and 7 cm
6 Using a ruler and compasses only, construct a triangle with sides 5 cm, 6 cm and 7 cm. The 5 cm side has been drawn for you. [2] __________________________________________________________________________________________
Mark scheme: 6 Correct triangle 2 M1 for a triangle with one other side correct with correct pair of arcs or for correct pair of arcs
Q7 · Equilateral triangle square regular pentagon parallelogram regular hexagon circle From…
7 equilateral triangle square regular pentagon parallelogram regular hexagon circle From the list write down (a) the shape which has more than 6 lines of symmetry, Answer(a) ................................................ [1] (b) the shape which has both acute and obtuse interior angles. Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 7 (a) circle 1 (b) parallelogram 1
Q8 · 3 - 8 a = b = 5 e o e 7 o Write each of the following as a single vector
8 3 - 8 a = b = 5 e o e 7 o Write each of the following as a single vector. (a) 3a Answer(a) [1] f p (b) a – b Answer(b) [1] f p __________________________________________________________________________________________
Mark scheme: 8 (a) 1 9 15 (b) 1 11 −2
Q9 · The scatter diagram shows the number of sun hats and ice creams sold by a shop each day…
9 The scatter diagram shows the number of sun hats and ice creams sold by a shop each day for two weeks. 40 30 Number of ice creams 20 sold 10 0 0 2 4 6 8 10 12 Number of sun hats sold (a) Write down the type of correlation shown by the diagram. Answer(a) ................................................ [1] (b) Describe the relationship between the number of sun hats sold and the number of ice creams sold. Answer(b) ........................................................................................................................................... ............................................................................................................................................................. [1] __________________________________________________________________________________________
Mark scheme: 9 (a) positive 1 (b) More ice creams sold, 1 more sun hats sold oe
Question 10
10 Simplify. 6uw–3 × 4uw6 Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 10 24u2w3 final answer 2 B1 for 2 correct elements in final answer AB
Q11 · A NOT TO SCALE 11.2 cm 37° B C Calculate AB
11 A NOT TO SCALE 11.2 cm 37° B C Calculate AB. Answer AB = .......................................... cm [2] __________________________________________________________________________________________
Mark scheme: AB 11 6.74[0…] 2 M1 for = sin 37 or better 112.
Q12 · Write down the co-ordinates of the point where the line y = 3x + 5 crosses the y-axis
12 (a) Write down the co-ordinates of the point where the line y = 3x + 5 crosses the y-axis. Answer(a) (...................... , ......................) [1] (b) Write down the equation of a line that is parallel to the line y = 3x + 5. Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 12 (a) ( 0 , 5 ) 1 (b) y = 3x + k 1 k must be a number, ≠ 5
Question 13
13 (a) Factorise. 3w2 – 2w Answer(a) ................................................ [1] (b) Expand and simplify. x (2x + 3) + 5(x – 7) Answer(b) ................................................ [2] __________________________________________________________________________________________
Mark scheme: 13 (a) w (3w – 2) 1 (b) 2x2 + 8x – 35 final answer 2 B1 for 2 terms correct in final answer or M1 for 2x2 + 3x or 5x – 35
Q14 · Six donkeys are each given two 5 ml spoons of medicine three times each day
14 Six donkeys are each given two 5 ml spoons of medicine three times each day. Calculate the number of whole days a 2 litre bottle of medicine will last. Answer ........................................ days [3] __________________________________________________________________________________________
Mark scheme: 14 11 3 B1 for 2000[ml] or 0.005[litres] soi M1 for figs 2 ÷ (6 × 2 × 5 × 3) or better or figs 111…. seen
Q15 · A cuboid has volume 288 cm3
15 A cuboid has volume 288 cm3. (a) The cuboid has length 12 cm and width 5 cm. Calculate the height of the cuboid. Answer(a) .......................................... cm [2] (b) 1 cm3 of the cuboid has a mass of 4 g. Work out the mass of the cuboid. Answer(b) ............................................. g [1] __________________________________________________________________________________________
Mark scheme: 15 (a) 4.8 2 M1 for 288 ÷ (12 × 5) oe (b) 1152 1 9 63
Q16 · 3 .16 Without using a calculator, work out 1 5 ÷ 7 Show all your working and give your…
4 3 .16 Without using a calculator, work out 1 5 ÷ 7 Show all your working and give your answer as a fraction in its lowest terms. Answer ................................................ [3] __________________________________________________________________________________________
Mark scheme: 9 63 16 B1 or 5 35 63 15 9 7 9 × 7 M1 or their ÷ or equivalent division with their × or 35 35 5 3 5 × 3 fractions with common denominators 21 1 A1 or 4 cao 5 5
Q17 · Write 82 600 in standard form
17 (a) Write 82 600 in standard form. Answer(a) ................................................ [1] 6.02 # 10 8 - 5 # 10 6 (b) Calculate 6 . 3 # 10 Give your answer in standard form. Answer(b) ................................................ [2] __________________________________________________________________________________________
Mark scheme: 17 (a) 8.26 × 104 1 (b) 1.99 × 102 2 B1 for figs 199
Question 18
18 Solve the equation. 5(3y – 2) = 35 Answer y = ................................................ [3] __________________________________________________________________________________________
Mark scheme: 18 3 3 B1 for 15y − 10 seen or M1 for 3y – 2 = 35 ÷ 5 and M1 for 15y = 35 + their (5 × 2) or 3y = their (35 ÷ 5) + 2
Q19 · In this question use a ruler and compasses
19 In this question use a ruler and compasses. A B D C Shade the region inside rectangle ABCD that is • more than 2 cm from AD and • more than 4 cm from B. [3] __________________________________________________________________________________________
Mark scheme: 19 correct shaded region 3 B1 for ruled line 2cm from and parallel to AD and B1 for arc centre B, radius 4cm and B1 for correct shaded region between their vertical line and their arc centre B
Q20 · 2, 3, 6, 11, 18,
20 (a) 2, 3, 6, 11, 18, . . . (i) Write down the next two terms in this sequence. Answer(a)(i) ....................... , ....................... [2] (ii) Describe, in words, the rule for continuing this sequence. Answer(a)(ii) ............................................................................................................................... [1] (b) The nth term of a different sequence is 4n – 3. Work out the first three terms in this sequence. Answer(b) ....................... , ....................... , ....................... [1] __________________________________________________________________________________________
Mark scheme: 20 (a) (i) 27, 38 2 B1 for 27 and B1FT for their 27 + 11 (ii) Add the next odd number oe 1 (b) 1, 5, 9 1
Q21 · Write 30 as a product of its prime factors
21 (a) Write 30 as a product of its prime factors. Answer(a) ................................................ [2] (b) Find the lowest common multiple (LCM) of 30 and 45. Answer(b) ................................................ [2] __________________________________________________________________________________________
Mark scheme: 21 (a) 2 × 3 × 5 2 B1 for 2, 3, 5 as prime factors (b) 90 2 B1 for 90k or for listing multiples of each up to 90 or 2 × 32 × 5 6
Q22 · B E NOT TO SCALE 8 cm 10 cm 6 cm x cm A y cm C D 9 cm F Triangle ABC is similar to…
22 B E NOT TO SCALE 8 cm 10 cm 6 cm x cm A y cm C D 9 cm F Triangle ABC is similar to triangle DEF. Calculate the value of (a) x, Answer(a) x = ................................................ [2] (b) y. Answer(b) y = ................................................ [2] __________________________________________________________________________________________
Mark scheme: 6 22 (a) 7.5 2 M1 for [10] × oe 8 8 10 (b) 12 cao 2 M1 for 9× oe or 9 × 6 their (a)
What was in this paper
The subtopics covered by these 22 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Geometrical constructions2Percentages2Rates2Equations1Equations of linear graphs1Fractions, decimals and percentages1Right-angled triangles1Scatter diagrams1Sequences1Similarity1Standard form1Surface area and volume1Symmetry1The four operations1Time1Types of number1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2015 May/June, Paper 1 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.