Cambridge IGCSE Mathematics 0580 — 2017 May/June Paper 2 · Variant 1
0580/21/M/J/17 · 20 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 paper16 pages
Mark scheme5 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Question 1
1 Simplify. (x2) 5 .............................................. [1]
Mark scheme: Question Answer Mark Part marks 1 x10 1
Q2 · The thickness of one sheet of paper is 8 # 10-3 cm
2 The thickness of one sheet of paper is 8 # 10-3 cm. Work out the thickness of 250 sheets of paper. ........................................ cm [1]
Mark scheme: 2 2 1
Q3 · Write 23.4571 correct to (a) 4 significant figures…
3 Write 23.4571 correct to (a) 4 significant figures, .............................................. [1] (b) the nearest 10. .............................................. [1]
Mark scheme: 3(a) 23.46 cao 1 3(b) 20 cao 1
Q4 · The table shows the temperatures in five places at 10 am one day in January
4 The table shows the temperatures in five places at 10 am one day in January. Place Temperature (°C) Helsinki -7 Chicago -10 London 3 Moscow -4 Bangkok 26 (a) Which place was the coldest? .............................................. [1] (b) At 2 pm the temperature in Helsinki had increased by 4 °C. Write down the temperature in Helsinki at 2 pm. .........................................°C [1]
Mark scheme: 4(a) Chicago 1 4(b) − 3 1
Question 5
5 Factorise completely. 12n2 - 4mn .............................................. [2]
Mark scheme: 5 4n(3n – m) final answer 2 B1 for 4(3n2 – mn) or n(12n – 4m) or 2n(6n – 2m) or 2(6n2 – 2mn)
Q6 · R 16 (a) 2 = 16 Find the value of r
r 16 (a) 2 = 16 Find the value of r. r = ....................................... [1] (b) 3 t = 5 3 Find the value of t. t = ........................................ [1]
Mark scheme: 6(a) − 4 1 6(b) 1 1 or 0.2 5
Q7 · 57 Without using a calculator, work out 1 +
2 57 Without using a calculator, work out 1 + . 3 7 Write down all the steps of your working and give your answer as a mixed number in its simplest form. .............................................. [3]
Mark scheme: 7 14 ( or 35 ) 15 M1 14 k ( or 35k ) 15k + accept + 21 21 21k 21k 8 A2 50 8 29 29 2 cao or A1 for or 1 or or 1 21 21 21 21 21
Q8 · Simon has two boxes of cards
8 Simon has two boxes of cards. In one box, each card has one shape drawn on it that is either a triangle or a square. In the other box, each card is coloured either red or blue. Simon picks a card from each box at random. The probability of picking a triangle card is t. The probability of picking a red card is r. Complete the table for the cards that Simon picks, writing each probability in terms of r and t. Event Probability Triangle and red Square and red (1 - t) r Triangle and blue Square and blue [3]
Mark scheme: 8 3 B1 for each rt (1 – t) r (1 − r)t oe (1 – r)(1 – t) oe
Q9 · H is directly proportional to the square root of p
9 h is directly proportional to the square root of p. h = 5.4 when p = 1.44 . Find h when p = 2.89 . h = ....................................... [3]
Mark scheme: 9 7.65 3 M1 for h = k p oe M1 for h = their k p 5.4 h or M2 for = oe 1.44 2.89
Q10 · Y 5 4 3 2 1 x 0 1 2 3 4 5 6 –1 By shading the unwanted regions of the grid, find and…
10 y 5 4 3 2 1 x 0 1 2 3 4 5 6 –1 By shading the unwanted regions of the grid, find and label the region R that satisfies the following four inequalities. y G 2 y H 1 y G 2x - 1 y G 5 - x [3]
Mark scheme: 10 Correct regionn identified 3 0 1 1 2 2 3 2 1 2 1 RR SC1 foor
Q11 · The two barrels in the diagram are mathematically similar
11 The two barrels in the diagram are mathematically similar. NOT TO SCALE 90 cm h cm The smaller barrel has a height of h cm and a capacity of 100 litres. The larger barrel has a height of 90 cm and a capacity of 160 litres. Work out the value of h. h = ....................................... [3]
Mark scheme: 11 76.9 or 76.94 to 76.95 3 160 100 M2 forr 90 ÷ 3 or 90 × 3 100 160 160 100 or M1 for 3 sooi or 3 soi or 100 160 h 3 100 = oe 90 160
Q12 · A line has gradient 5
12 A line has gradient 5. M and N are two points on this line. M is the point (x, 8) and N is the point (k, 23). Find an expression for x in terms of k. x = ....................................... [3]
Mark scheme: 12 k – 3 or −+3 kk 3 23 − 8 M1 forr 5 = ooe k − x M1 forr 5(k – x) = 223 – 8 or bettter 23 − 88 e.g. [x =]= k − 5
Q13 · A B NOT TO SCALE 5 cm D C 13 cm F E 4 cm H G The diagram shows a cuboid ABCDEFGH
13 A B NOT TO SCALE 5 cm D C 13 cm F E 4 cm H G The diagram shows a cuboid ABCDEFGH. AE = 5 cm, EH = 4 cm and AG = 13 cm. Calculate the angle between the line AG and the base EFGH of the cuboid. .............................................. [3]
Mark scheme: 13 22.6 or 22.61 to 22.62 3 5 M2 forr sin [=] ooe 13 or M1 for identifyinng angle AGE
Q16 · Six students revise for a test
16 Six students revise for a test. The scatter diagram shows the time, in hours, each student spent revising and their mark in the test. 50 45 40 Mark 35 30 25 0 1 2 3 4 5 6 7 8 9 10 Time (hours) (a) The data for two more students is shown in the table. Time (hours) 4.5 6.5 Mark 33 35 Plot these two points on the scatter diagram. [1] (b) What type of correlation is shown on the scatter diagram? .............................................. [1] (c) Draw a line of best fit on the scatter diagram. [1] (d) Another student spent 5.5 hours revising. Estimate a mark for this student. .............................................. [1]
Mark scheme: 16(b) Positive 1 16(c) Correct ruled line 1 16(d) 33.5 to 37.5 1FT FT from their line providing positive gradient
Q17 · In this Venn diagram, shade the region F , G l
17 (a) In this Venn diagram, shade the region F , G l. F G [1] (b) = {1, 2, 3, 4, 5, 6, 7, 8, 9} A = {x: x is an odd number} B = {x: x is a square number} C = {x: x is a multiple of 3} (i) Write all the elements of in the Venn diagram below. A B C [2] (ii) Another number is included in the set . This number is in the regionAl + B + C . Write down a possible value for this number. .............................................. [1]
Mark scheme: 17(a) 1 F G 17(b)(i) 2 B1 for four out of the eight regions correct A B 1 5 7 4 9 3 2 8 6 C 17(b)(ii) Any even square number that is also a 1 multiple of 3
Q18 · The diagram shows a parallelogram OCEG
18 The diagram shows a parallelogram OCEG. C D E NOT TO SCALE B F H b O A G a O is the origin, OA = a and OB = b . BHF and AHD are straight lines parallel to the sides of the parallelogram. OG = 3 OA and OC = 2 OB . (a) Write the vector HE in terms of a and b. HE = .................................. [1] (b) Complete this statement. a + 2b is the position vector of point ......................... [1] (c) Write down two vectors that can be written as 3a - b. ............................... and ............................... [2]
Mark scheme: 18(a) 2a + b 1 18(b) D 1 uuur uuur18(c) CF and BG 2 B1 for each
Q19 · ABCD is a rhombus with side length 10 cm
19 ABCD is a rhombus with side length 10 cm. A NOT TO 10 cm SCALE D 40° B C Angle ADC = 40°. DAC is a sector of a circle with centre D. BAC is a sector of a circle with centre B. Calculate the shaded area. ...................................... cm2 [4]
Mark scheme: 19 5.53 or 5.54 or 5.534 to 5.543… 4 M3 for 40 1 2 × {( × π × 102)– ( × 102 × sin 40)} 360 2 or M2 for 1 40 × 102 × sin 40 and [2 ×] × π × 102 2 360 or M1 for 1 40 × 102 × sin 40 or [2 ×] × π × 102 2 360
Q20 · The diagram shows a fair spinner
20 The diagram shows a fair spinner. 1 6 3 4 3 Anna spins it twice and adds the scores. (a) Complete the table for the total scores. Score on first spin 1 3 3 4 6 1 2 4 4 5 7 3 4 6 6 7 9 Score on 3 4 6 6 7 9 second spin 4 6 [1] (b) Write down the most likely total score. .............................................. [1] (c) Find the probability that Anna scores (i) a total less than 6, .............................................. [2] (ii) a total of 3. .............................................. [1]
Mark scheme: 20(a) 5 7 7 8 10 1 7 9 9 10 12 20(b) 7 1 20(c)(i) 7 2FT their 7 or 0.28 or 28% FT 25 25 k B1 for 25 2 6 If zero scored, then SC1 for or if no 5 15 values in the bottom two rows of the table. 20(c)(ii) 0 1FT their 0 FT 25
Q21 · D NOT TO SCALE v° C 35° A X u° B A, B, C and D are points on the circle
21 (a) D NOT TO SCALE v° C 35° A X u° B A, B, C and D are points on the circle. AD is parallel to BC. The chords AC and BD intersect at X. Find the value of u and the value of v. u = ....................................... v = ....................................... [3] (b) NOT TO SCALE 210° H p° O F G F, G and H are points on the circle, centre O. Find the value of p. p = ....................................... [2]
Mark scheme: 21(a) [u =] 35 1 [v =] 110 2 B1 for ACB or ADB = 35 21(b) 75 2 B1 for 150 360 − 210 or M1 for 2
Q22 · Write as a single fraction in its simplest form
22 Write as a single fraction in its simplest form. x 2 - 3x (a) 2 x - 9 .............................................. [3] 3 2 (b) + x - 4 2x + 5 .............................................. [3]
Mark scheme: 22(a) x 3 B1 for x(x – 3) final answer B1 for (x – 3)(x + 3) x + 3 22(b) 8 x + 7 3 B1 for common denominator of (x − 4)(2x + 5) final answer oe ( x − 4)(2 x + 5) M1 for 3(2x + 5) + 2(x − 4) oe with an attempt to expand the brackets
What was in this paper
The subtopics covered by these 20 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Algebraic fractions1Algebraic manipulation1Circle theorems I1Circles, arcs and sectors1Fractions, decimals and percentages1Gradient of linear graphs1Indices I1Indices II1Inequalities1Introduction to probability1Limits of accuracy1Ordering1Probability of combined events1Pythagoras’ theorem and trigonometry1Scatter diagrams1Sets1Similarity1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2017 May/June, Paper 2 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.