Cambridge IGCSE Mathematics 0580 — 2014 May/June Paper 1 · Variant 3
0580/13/M/J/14 · 26 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 scheme5 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · –3°C 8°C –19°C 42°C –7°C Write down the lowest temperature from this list
1 –3°C 8°C –19°C 42°C –7°C Write down the lowest temperature from this list. Answer ........................................... °C [1] __________________________________________________________________________________________
Mark scheme: Question Answers Mark Part Marks 1 –19 1
Q2 · Change 6450 cm into metres
2 Change 6450 cm into metres. Answer ............................................ m [1] __________________________________________________________________________________________
Mark scheme: 2 64.5[0] 1
Q3 · NOT TO 52° SCALE x° In the diagram, a straight line intersects two parallel lines
3 NOT TO 52° SCALE x° In the diagram, a straight line intersects two parallel lines. Find the value of x. Answer x = ................................................ [1] __________________________________________________________________________________________
Mark scheme: 3 128 1
Question 4
4 Calculate. 56.2 - 34.8 - 0.2 Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: 4 −107 1
Q5 · Write down the value of 70
5 Write down the value of 70. Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: 5 1 1
Q6 · Write 45 000 in standard form
6 Write 45 000 in standard form. Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: 6 4.5 × 104 1
Q7 · Four faces of a cube are drawn on the grid
7 Four faces of a cube are drawn on the grid. Complete the net of this cube. [1] __________________________________________________________________________________________
Mark scheme: 7 Cube net drawn correctly 1
Q8 · Write down all the prime numbers that are greater than 30 and less than 40
8 Write down all the prime numbers that are greater than 30 and less than 40. Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: 8 31, 37 1 −6
Q9 · - 3 2 a = b = 4 e o e 6 o Write each of the following as a single vector
9 - 3 2 a = b = 4 e o e 6 o Write each of the following as a single vector. (a) 2a Answer(a) [1] f p (b) a – b Answer(b) [1] f p __________________________________________________________________________________________
Mark scheme: 6 9 (a) 1 8 − 5 (b) 1 − 2
Q10 · 1 4 8 12 27 40 Write down the number from this list which is both a cube number and has a…
10 (a) 1 4 8 12 27 40 Write down the number from this list which is both a cube number and has a factor of 4. Answer(a) ................................................ [1] (b) 1258 is a multiple of 34. Write down a different multiple of 34 between 1200 and 1300. Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 10 (a) 8 1 (b) 1 1224 or 1292
Q11 · –3 –5 1 0 3 Three different numbers from the list are added together to give the smallest…
11 –3 –5 1 0 3 Three different numbers from the list are added together to give the smallest possible total. Complete the sum below. ................. + ................. + ................. = ................. [2] __________________________________________________________________________________________
Mark scheme: 11 –3, –5, 0 [=] –8 2 B1 for –3, –5 and 0 in any order seen on left hand side. or B1 for –8 seen on answer line in correct position
Q12 · The area of a square is 36 cm2
12 The area of a square is 36 cm2. Calculate the perimeter of this square. Answer .......................................... cm [2] __________________________________________________________________________________________
Mark scheme: 12 24 2 M1 for √36 × 4 oe or B1 for 6 seen
Q13 · The mean of fi ve numbers is 6
13 The mean of fi ve numbers is 6. Four of the numbers are 3, 4, 5, and 10. Work out the number that is missing from the list. Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 13 8 2 B1 for 6 × 5 or better
Q14 · Find the value of 3a – 5b when a = –4 and b = 2
14 Find the value of 3a – 5b when a = –4 and b = 2 . Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 14 –22 2 M1 for 3×(–4) –5×2 or B1 for −12 or −10 seen in the working. IGCSE – May/June 2014 0580 13 13
Q15 · Celine buys a bag of 24 tulip bulbs
15 Celine buys a bag of 24 tulip bulbs. There are 8 red bulbs and 5 white bulbs. All of the other bulbs are yellow. Celine chooses a bulb at random from the bag. (a) Write down the probability that the bulb is red or white. Answer(a) ................................................ [1] (b) Write down the probability that the bulb is yellow. Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 13 15 (a) oe 1 24 11 (b) oe 1 24 7 7 3 4
Q16 · 2 16 Find the fraction that is half-way between and
1 2 16 Find the fraction that is half-way between and . 2 3 Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 7 7 3 4 16 oe 2 B1 for or ( and ) 12 6 6 6 6 8 or etc., 12 and12 5.3 or 6
Q17 · Using a straight edge and compasses only, construct the perpendicular bisector of AB
17 Using a straight edge and compasses only, construct the perpendicular bisector of AB. All construction arcs must be clearly shown. A B [2] __________________________________________________________________________________________
Mark scheme: 17 Perpendicular bisector with 2 pairs of correct arcs. 2 B1 for correct line or B1 for 2 pairs of correct arcs 7
Q18 · Michelle sells ice cream
18 Michelle sells ice cream. The table shows how many of the different fl avours she sells in one hour. Flavour Vanilla Strawberry Chocolate Mango Number sold 6 8 9 7 Michelle wants to show this information in a pie chart. Calculate the sector angle for mango. Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 7 18 84 2 M1 for or 6 + 8 + 9 + 7 360 6 + 8 + 9 + 7
Q19 · Chris changes $1350 into euros (€) when €1 = $1.313
19 Chris changes $1350 into euros (€) when €1 = $1.313 . Calculate how much he receives. Answer € ................................................. [2] __________________________________________________________________________________________
Mark scheme: 19 1030 2 M1 for 1350 ÷ 1.313 k 3
Q20 · Y 7 6 5 4 A 3 2 1 x –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 –1 –2 –3 3 Draw the image of…
20 y 7 6 5 4 A 3 2 1 x –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 –1 –2 –3 3 Draw the image of triangle A after a translation by the vector [2] 4 e- o. __________________________________________________________________________________________
Mark scheme: k 3 20 Triangle at ( 2, −1) ( 2, 1) ( 1, −2) 2 B1 for translation by or −4 k
Q21 · Each exterior angle of a regular polygon is 30°
21 Each exterior angle of a regular polygon is 30°. Work out the number of sides the polygon has. Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 21 12 2 M1 for 360 ÷ 30
Q22 · 46° NOT TO 9.65 cm SCALE 8.69 cm 9.65 cm x° 74° 60° y cm 46° 7.22 cm These two triangles…
22 46° NOT TO 9.65 cm SCALE 8.69 cm 9.65 cm x° 74° 60° y cm 46° 7.22 cm These two triangles are congruent. Write down the value of (a) x, Answer(a) x = ................................................ [1] (b) y. Answer(b) y = ................................................ [1] __________________________________________________________________________________________
Mark scheme: 22 (a) 74 1 (b) 8.69 1 IGCSE – May/June 2014 0580 13 5
Q23 · 723 Without using a calculator, work out 1 –
1 723 Without using a calculator, work out 1 – . 4 9 Write down all the steps in your working. Answer ............................................... [3] __________________________________________________________________________________________
Mark scheme: 5 23 oe B1 Do not allow decimals for the B1, 4 M1 or A1 5 × 9 7 × 4 45 28 and oe or better M1 e.g. 36 and 36 4 × 9 9 × 4 17 5 oe working must be shown A1 Follow through their for the M1 36 4 mark. Alt method 1: B1 for 1 + 2 4 9 M1 for 1 × 9 and 2 × 4 oe e.g. 4 × 9 4 × 9 9 8 and 36 36 Alt method 2: B1 for 1 − 7 + 1 4 9 M1 for oe e.g. 9 and 8 36 36 ISW converting fraction answer to decimal.
Q24 · Solve the simultaneous equations
24 Solve the simultaneous equations. 2x + 3y = 29 5x + y = 27 Answer x = ................................................ y = ................................................ [3] __________________________________________________________________________________________
Mark scheme: 24 x = 4 3 M1 for correct method to eliminate y = 7 one variable or (substitution) correct rearrangement of one equation seen substituted into the second equation. A1 for one correct answer. If M0 SC1 for both answers satisfying one of the original equations
Q25 · William Toby Town 4 3 Distance 2 (km) 1 Home 0 10 00 10 04 10 08 10 12 10 16 10 20 10 24…
25 William Toby Town 4 3 Distance 2 (km) 1 Home 0 10 00 10 04 10 08 10 12 10 16 10 20 10 24 10 28 10 32 Time Toby and William cycled into town. Their journeys are shown on the travel graph. (a) For how many minutes did Toby stop on his journey into town? Answer(a) ......................................... min [1] (b) Explain what happened at 10 20. Answer(b) ........................................................................................................................................... [1] (c) Work out how long William took to cycle into town. Answer(c) ......................................... min [1] (d) Calculate William’s speed in km/h. Answer(d) ....................................... km/h [2] __________________________________________________________________________________________
Mark scheme: 25 (a) 6 1 (b) They are at the same place at the same time 1 (c) 16 1 (d) 15 cao 2 M1 FT for 4 × 60 oe their ( c ) IGCSE – May/June 2014 0580 13
Question 26
26 (a) Factorise completely. 15a3 – 5ab Answer(a) ................................................ [2] (b) Simplify. 3x2y3 × x4y Answer(b) ................................................ [2] (c) Multiply out the brackets and simplify. 3(x – 2) – 4(2x – 3) Answer(c) ................................................ [2] (d) Solve the equation. 8x + 9 = 3(x + 8) Answer(d) x = ................................................ [3] __________________________________________________________________________________________
Mark scheme: 26 (a) 5a(3a2−b) 2 B1 for a(15a2 − 5b) or 5(3a3− ab) (b) 3x6 y4 2 B1 for x6 or y4 in a product on answer line (c) 6 – 5x as final answer nfww 2 B1 for 3x – 6 or – 8x + 12 seen or SC1 for 6 or – 5x seen in final answer nfww (d) 3 nfww 3 M2 for 5x = 15 or B1 for 3x +24 seen or M1 for 8x – 3x = 3 × 8 − 9 or better. If zero, SC1 for answer [x =] − 1 5
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.
2Fractions, decimals and percentages2The four operations2Types of number2Vectors in two dimensions2Algebraic manipulation1Area and perimeter1Averages and range1Compound shapes and parts of shapes1Equations1Geometrical constructions1Indices I1Introduction to algebra1Introduction to probability1Ordering1Ratio and proportion1Similarity1Standard form1Statistical charts and diagrams1Time1Units of measure1What you needed in this session
Cambridge’s own grade thresholds for 2014 May/June, Paper 1 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.