Cambridge IGCSE Mathematics 0580 — 2018 May/June Paper 1 · Variant 1
0580/11/M/J/18 · 25 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 · Write 4647 correct to the nearest 100
1 Write 4647 correct to the nearest 100. .............................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1 4600 1
Q2 · Write 0.007 as a fraction
2 Write 0.007 as a fraction. .............................................. [1]
Mark scheme: 2 7 1 1000
Q3 · The diagram shows a quadrilateral
3 The diagram shows a quadrilateral. x° NOT TO 47° 95° SCALE 82° Find the value of x. x = ....................................... [1]
Mark scheme: 3 136 1
Q4 · The nth term of a sequence is 5n - 3
4 The nth term of a sequence is 5n - 3. Write down the first three terms of the sequence. ................... , ................... , ................... [1]
Mark scheme: 4 2 7 12 cao 1
Q5 · Write 0.002 68 correct to 2 significant figures
5 (a) Write 0.002 68 correct to 2 significant figures. .............................................. [1] (b) Write 0.000 038 7 in standard form. .............................................. [1]
Mark scheme: 5(a) [0].0027 1 5(b) 3.87 × 10–5 1
Q6 · Find the value of 7x + 3y when x = 12 and y = -6
6 Find the value of 7x + 3y when x = 12 and y = -6. .............................................. [2]
Mark scheme: 6 66 2 B1 for 84 or −18 seen
Q7 · Q T A 43° C x° NOT TO SCALE P B S The diagram shows two parallel lines PAQ and SBCT
7 Q T A 43° C x° NOT TO SCALE P B S The diagram shows two parallel lines PAQ and SBCT. AB = AC and angle QAC = 43°. Find the value of x. x = ....................................... [2]
Mark scheme: 7 94 2 B1 for ACB or PAB or ABC = 43 or M1 for 180 − 2 × 43 or 12 x = 90 − 43
Q8 · Solve the equation 8x - 5 = 7
8 Solve the equation 8x - 5 = 7. x = ....................................... [2]
Mark scheme: 8 1.5 oe 2 5 7 M1 for 8x = 7 + 5 or x − = oe 8 8
Q9 · Change 6.54 kilometres into metres
9 (a) Change 6.54 kilometres into metres. ..........................................m [1] (b) Change 7850 cm3 into litres. .................................... litres [1]
Mark scheme: 9(a) 6540 1 9(b) 7.85[0] 1
Q10 · The height, h metres, of a boy is 1.72 m, correct to the nearest centimetre
10 The height, h metres, of a boy is 1.72 m, correct to the nearest centimetre. Complete this statement about the value of h. ..................... G h 1 ..................... [2]
Mark scheme: 10 1.715, 1.725 2 B1 for one correct in correct place If zero scored, SC1 for both correct but reversed or for 171.5 and 172.5
Question 11
11 Expand and simplify. 6(2y - 3) - 5(y + 1) .............................................. [2]
Mark scheme: 11 7y − 23 final answer 2 M1 for 12 y − 18 or −5 y − 5 or B1 for answer 7y − k or cy − 23 c ≠ 0
Q12 · 2 - 3 g = h = c 5 m c 4 m Write as a single vector (a) g + h, [1] f p (b) -h
12 2 - 3 g = h = c 5 m c 4 m Write as a single vector (a) g + h, [1] f p (b) -h. [1] f p
Mark scheme: 12(a) − 1 1 9 12(b) 3 1 − 4
Q13 · Work out the lowest common multiple (LCM) of 18 and 21
13 Work out the lowest common multiple (LCM) of 18 and 21. .............................................. [2]
Mark scheme: 13 126 2 M1 for at least 3 multiples of 18 and 21 or 3 × 6 × 7 as final answer or 3 [×] 6 and 3 [×] 7 in working or B1 for final answer 126k, integer k >1
Q14 · Work out the size of one exterior angle of a regular octagon
14 Work out the size of one exterior angle of a regular octagon. .............................................. [2]
Mark scheme: 14 45 2 360 M1 for 8 If zero scored, SC1 for answer 135
Q15 · Calculate 2.38 + 6.42 , writing down your full calculator display
15 (a) Calculate 2.38 + 6.42 , writing down your full calculator display. .............................................. [1] (b) Write your answer to part (a) correct to 4 decimal places. .............................................. [1]
Mark scheme: 15(a) 6.58331… 1 15(b) 6.5833 1 FT their (a) correctly rounded to 4 dp
Q16 · Enlarge the rectangle using a scale factor of 3 and centre of enlargement O
16 Enlarge the rectangle using a scale factor of 3 and centre of enlargement O. O [2]
Mark scheme: 16 Correct enlargement drawn 2 B1 for correct sf but wrong position
Q17 · A box contains 3 blue pens, 4 red pens and 8 green pens only
17 (a) A box contains 3 blue pens, 4 red pens and 8 green pens only. A pen is chosen at random from the box. Find the probability that this pen is green. .............................................. [1] (b) A cube has only one of its six faces painted yellow. This cube is rolled 240 times. Work out the expected number of times that it lands on the yellow face. .............................................. [1]
Mark scheme: 17(a) 8 1 oe 15 17(b) 40 1
Question 18
18 (a) Simplify. 4 (x3) .............................................. [1] w 1 (b) 4 = 16 Find the value of w. w = ...................................... [1]
Mark scheme: 18(a) x12 1 18(b) −2 1
Q19 · -2 419 r 3 3 33.3% 3 .03 3999 7 From this list, write down the two numbers that are…
-2 419 r 3 3 33.3% 3 .03 3999 7 From this list, write down the two numbers that are irrational. ...................... , .................... [2]
Mark scheme: 19 π 3 2 B1 for each
Q20 · Here is a description of a quadrilateral
20 (a) Here is a description of a quadrilateral. It has 4 right angles. It has 2 lines of symmetry. It has rotational symmetry of order 2. Write down the mathematical name of this quadrilateral. .............................................. [1] (b) Write down two geometrical properties of a parallelogram. 1. ....................................................................................................................................................... 2. ....................................................................................................................................................... [2]
Mark scheme: 20(a) Rectangle 1 20(b) Two correct properties 2 B1 for one correct property e.g. 2 pairs of parallel sides Opposite angles are equal Opposite sides are same length Rotational symmetry order 2 Diagonals are not equal
Q21 · The net of a solid is drawn on a 1 cm2 grid
21 The net of a solid is drawn on a 1 cm2 grid. (a) Write down the name of the solid made from this net. .............................................. [1] (b) Work out the volume of this solid. .......................................cm3 [2]
Mark scheme: 21(a) Cuboid 1 21(b) 24 2 M1 for 2 × 3 × 4
Question 22
22 Factorise completely. (a) 10 + 16w .............................................. [1] (b) 12tx - 8t2 .............................................. [2]
Mark scheme: 22(a) 2 ( 5 + 8w ) 1 22(b) 4t ( 3 x − 2t ) 2 B1 for answer 4(3tx − 2t 2 ) or t (12 x − 8t ) 2(6tx − 4t 2 ) or 2t (6 x − 4t )
Q23 · 623 Without using your calculator, work out 1 #
3 623 Without using your calculator, work out 1 # . 4 35 You must show all your working and give your answer as a fraction in its simplest form. .............................................. [3]
Mark scheme: 23 7 M1 k 6 or × where k > 4 4 4 35 3 A2 42 21 6 cao A1 for or or 10 140 70 20
Q24 · Solve the simultaneous equations
24 Solve the simultaneous equations. You must show all your working. 3x + 10y = 106 5x - 4y = 1 x = ....................................... y = ....................................... [4]
Mark scheme: 24 for correctly equating one set of M1 coefficients for correct method to eliminate one M1 variable [x =] 7 A1 [y =] 8.5 A1 If zero scored, SC1 for 2 values satisfying one of the original equations or SC1 for both answers correct but no working
Q25 · 40 people were asked how many times they visited the cinema in one month
25 40 people were asked how many times they visited the cinema in one month. The table shows the results. Number of cinema visits 0 1 2 3 4 5 6 7 Frequency 5 5 6 6 7 3 6 2 (a) (i) Find the mode. .............................................. [1] (ii) Calculate the mean. .............................................. [3] (b) Omar wants to show the information from the table in a pie chart. Calculate the sector angle for the people who visited the cinema 5 times. .............................................. [2]
Mark scheme: 25(a)(i) 4 1 25(a)(ii) 3.2 3 M1 for Σfx , allow one error or omission their128 and M1dep for 40 25(b) 27 2 3 360 M1 for or 40 40
What was in this paper
The subtopics covered by these 25 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
3Limits of accuracy3Algebraic manipulation2Equations2Fractions, decimals and percentages2Types of number2Averages and range1Geometrical terms1Indices I1Introduction to algebra1Introduction to probability1Sequences1Surface area and volume1Transformations1Units of measure1Using a calculator1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2018 May/June, Paper 1 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.