Cambridge IGCSE Mathematics 0580 — 2019 Oct/Nov Paper 2 · Variant 2
0580/22/O/N/19 · 23 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 paper12 pages
Mark scheme6 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · The lowest temperature recorded at Scott Base in Antarctica is -57.0 °C
1 The lowest temperature recorded at Scott Base in Antarctica is -57.0 °C. The highest temperature recorded at Scott Base is 63.8 °C more than this. What is the highest temperature recorded at Scott Base? ................................................°C [1]
Mark scheme: Question Answer Marks Partial Marks 1 6.8 1
Question 2
2 Calculate. 5 3 + 340 8 .................................................... [1]
Mark scheme: 2 7.6[0] or 7.604 to 7.605 1
Question 3
3 Expand. a ( a 3 + 3) .................................................... [1]
Mark scheme: 3 a4 + 3a final answer 1
Q4 · On the Venn diagram, shade the region (A + B) l
4 On the Venn diagram, shade the region (A + B) l. A B [1]
Mark scheme: 4 1
Q5 · The mass, correct to the nearest kilogram, of each of 11 parcels is shown below
5 The mass, correct to the nearest kilogram, of each of 11 parcels is shown below. 24 23 23 26 25 27 18 96 16 17 32 (a) Find the mode. ............................................... kg [1] (b) Give a reason why the mean would be an unsuitable average to use. ............................................................................................................................................................ [1]
Mark scheme: 5(a) 23 1 5(b) One extreme value oe 1
Q6 · The table shows how children in Ivan’s class travel to school
6 The table shows how children in Ivan’s class travel to school. Travel to school Number of children Walk 12 Car 7 Bicycle 9 Bus 4 Ivan wants to draw a pie chart to show this information. Find the sector angle for children who walk to school. .................................................... [2]
Mark scheme: 6 135 2 12 M1 for [× 360 ] 12 + 7 + 9 + 4 360 or [× 12 ] oe 12 + 7 + 9 + 4
Q7 · Rashid changes 30 000 rupees to dollars when the exchange rate is $1 = 68.14 rupees
7 Rashid changes 30 000 rupees to dollars when the exchange rate is $1 = 68.14 rupees. How many dollars does he receive? $ ................................................... [2]
Mark scheme: 7 440 or 440.2 to 440.3 2 M1 for 30 000 ÷ 68.14
Q8 · North NOT TO SCALE 102° B P The bearing of P from B is 102°
8 North NOT TO SCALE 102° B P The bearing of P from B is 102°. Find the bearing of B from P. .................................................... [2]
Mark scheme: 8 282 2 M1 for 180 + 102 or 360 – (180 – 102)
Question 9
9 Solve the inequality. x - 13 2 12 + 3x 2 .................................................... [2]
Mark scheme: 9 x < –10 final answer 2 x M1 for –12 –13 > 3x – oe 2
Q10 · Write the recurring decimal .067o as a fraction
10 Write the recurring decimal .067o as a fraction. Show all your working and give your answer in its simplest form. .................................................... [2]
Mark scheme: 10 67.7 – 6.7 oe M1 61 A1 k If 0 scored, SC1 for 90 90
Q11 · 211 Without using a calculator, work out 3 - 1
5 211 Without using a calculator, work out 3 - 1 . 8 3 You must show all your working and give your answer as a mixed number in its simplest form. .................................................... [3]
Mark scheme: 11 29 5 5 2 M1 29 k 5 k or 8 3 28 − 3 Allow 8k or 3k Correct step for dealing with mixed numbers 87 40 16 M1 Correct method to find common and [ 2 ]15 and 15 16 24 24 24 24 denominator e.g. 324 and 124 23 A1 124 cao
Q12 · A regular polygon has an interior angle of 176°
12 A regular polygon has an interior angle of 176°. Find the number of sides of this polygon. .................................................... [3]
Mark scheme: 12 90 3 M2 for 360 ÷ (180 – 176) oe or M1 for 180(n – 2) = 176n oe or 180 – 176
Q13 · Two mathematically similar containers have heights of 30 cm and 75 cm
13 Two mathematically similar containers have heights of 30 cm and 75 cm. The larger container has a capacity of 5.5 litres. Calculate the capacity of the smaller container. Give your answer in millilitres. ............................................... ml [3]
Mark scheme: 13 352 3 B2 for figs 352 75 3 30 3 or M1 for oe or oe 30 75 OR 30 3 M2 for 5.5 × × 1000 75
Q14 · Show that the line 4y = 5x - 10 is perpendicular to the line 5y + 4x = 35
14 Show that the line 4y = 5x - 10 is perpendicular to the line 5y + 4x = 35 . [3]
Mark scheme: 14 5 M1 M marks can be in any order Gradient = oe 4 4 4 M1 y = k − x oe and gradient = − oe 5 5 Use of product of gradients is −1 oe M1
Q15 · Esme buys x magazines at $2.45 each and y cards at $3.15 each
15 Esme buys x magazines at $2.45 each and y cards at $3.15 each. (a) Write down an expression, in terms of x and y, for the total cost, in dollars, of the magazines and the cards. $ ................................................... [2] (b) Esme spends $60.55 in total. She buys 8 magazines. How many cards does she buy? .................................................... [2]
Mark scheme: 15(a) 2.45x + 3.15y final answer 2 B1 for one correct term in final answer If 0 scored, SC1 for 245x + 315y 15(b) 13 2 M1 for 60.55 – 2.45 × 8 oe
Q16 · Y 6 5 4 3 2x + y = 6 2 1 0 1 2 3 4 5 x By shading the unwanted regions of the grid, find…
16 y 6 5 4 3 2x + y = 6 2 1 0 1 2 3 4 5 x By shading the unwanted regions of the grid, find and label the region R that satisfies the following inequalities. y G 5 2x + y H 6 y H x + 1 [4]
Mark scheme: 16 y = 5 ruled 4 B2 for two correct lines y = x + 1 ruled or B1 for one correct line Correct region indicated B2 for indication of correct region or B1 for shading that satisfies two of the inequalities
Q17 · The diagram shows a scale drawing of Lei’s garden, PQRS
17 The diagram shows a scale drawing of Lei’s garden, PQRS. The scale is 1 centimetre represents 2 metres. P Q S R Scale: 1 cm to 2 m Lei has a bird table in the garden that is • equidistant from PQ and QR and • 13 m from R. On the diagram, construct the position of the bird table. Use a ruler and compasses only and show all your construction arcs. [4]
Mark scheme: 17 Bisector of angle Q accurate with two 4 M2 for bisector of angle Q accurate with pairs of correct arcs two pairs of correct arcs or M1 for accurate bisector with no/wrong and arcs Arc centre R, radius 6.5 cm M2 for arc centre R, radius 6.5 cm or M1 for arc centre R With bird table correctly indicated or implied by correct intersecting Maximum 3 marks if constructions incorrect position/region is labelled, or there is no label and a region is shaded, or their constructions do not intersect
Q18 · Harris is taking a driving test
18 Harris is taking a driving test. The probability that he passes the driving test at the first attempt is 0.6 . If he fails, the probability that he passes at any further attempt is 0.75 . Calculate the probability that Harris (a) passes the driving test at the second attempt, .................................................... [2] (b) takes no more than three attempts to pass the driving test. .................................................... [2]
Mark scheme: 18(a) 0.3 oe 2 M1 for 0.4 × 0.75 18(b) 0.975 oe 2 M1 for 1 – 0.4 × 0.25 × 0.25 oe or 0.6 + 0.4 × 0.75 + 0.4 × 0.25 × 0.75 or 0.6 + their (a) + 0.4 × 0.25 × 0.75
Q19 · C x° D NOT TO SCALE O 2x° A B In the diagram, A, B, C and D lie on the circumference of a…
19 C x° D NOT TO SCALE O 2x° A B In the diagram, A, B, C and D lie on the circumference of a circle, centre O. Angle ACD = x° and angle OAB = 2x°. Find an expression, in terms of x, in its simplest form for (a) angle AOB, Angle AOB = ................................................... [1] (b) angle ACB, Angle ACB = ................................................... [1] (c) angle DAB. Angle DAB = ................................................... [2]
Mark scheme: 19(a) 180 – 4x 1 19(b) 90 – 2x 1 FT their (a) ÷ 2 in its simplest form dep on expression in x in (a) 19(c) 90 + x 2 FT 180 – their (b) – x oe dep on expression in x in (b) then fully simplified M1 for 180 – (90 – 2x + x) oe or 180 – their (b) – x oe dep on expression in x in (b)
Question 20
20 (a) Factorise. 18y - 3ay + 12x - 2ax .................................................... [2] (b) Factorise. 3x 2 - 48y 2 .................................................... [3]
Mark scheme: 20(a) (3y + 2x)(6 – a) oe final answer 2 M1 for 3y (6 – a) + 2x(6 – a) oe or 6(2x + 3y) – a(2x + 3y) oe 20(b) 3(x + 4y)(x – 4y) final answer 3 M2 for (3x + 12y)(x – 4y) or (3x – 12y)(x + 4y) or M1 for 3(x2 – 16y2) or for (x + 4y)(x – 4y)
Q21 · 3 -2 # 3 x = 81 Find the value of x
21 (a) 3 -2 # 3 x = 81 Find the value of x. x = ................................................... [2] 1 (b) x - 3 = 32 x -2 Find the value of x. x = ................................................... [3]
Mark scheme: 21(a) 6 2 B1 for 34 or 3x–2 or M1 for 3x = 81 × 32 or better 21(b) 8 3 5 M2 for x 3 = 32 or better 1 32 or M1 for = or better 1 x 2 x 3 1 − 2 or x 3 −−= 32 or better
Q22 · 2 - 2 5 22 A = B = C = (- 1 k) e- 5 0o e 4 1o (a) Find AB
3 2 - 2 5 22 A = B = C = (- 1 k) e- 5 0o e 4 1o (a) Find AB. [2] f p (b) CA = (- 13 - 2 ) Find the value of k. k = ................................................... [2] (c) Find A-1. [2] f p
Mark scheme: 22(a) 2 17 2 B1 for 2 correct elements 10 − 25 22(b) 2 2 M1 for –3 –5k = –13 oe 22(c) 1 0 − 2 2 0 − 2 oe isw M1 for k or for det = 10 or soi 10 5 3 5 3
Q23 · 4 3 Speed 2 (km/min) 1 0 0 5 10 15 20 25 30 t Time (minutes) The speed–time graph shows…
23 4 3 Speed 2 (km/min) 1 0 0 5 10 15 20 25 30 t Time (minutes) The speed–time graph shows information about a train journey. (a) By drawing a suitable tangent to the graph, estimate the gradient of the curve at t = 24 . .................................................... [3] (b) What does this gradient represent? ............................................................................................................................................................ [1] (c) Work out the distance travelled by the train when it is travelling at constant speed. .............................................. km [2]
Mark scheme: 23(a) Tangent ruled at t = 24 B1 – 0.7 to – 0.3 B2 B2 dep on correct tangent or close attempt at tangent M1 for rise/run also dep on correct tangent drawn or close attempt at tangent. Must see correct or implied calculation from a drawn tangent. 23(b) acceleration or deceleration oe 1 23(c) 68 2 M1 for (22 – 5) × 4
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.
3Fractions, decimals and percentages2Inequalities2Ratio and proportion2The four operations2Averages and measures of spread1Circle theorems I1Circles, arcs and sectors1Equations1Equations of linear graphs1Geometrical constructions1Geometrical terms1Interpreting statistical data1Money1Probability of combined events1Rates1Sets1What you needed in this session
Cambridge’s own grade thresholds for 2019 Oct/Nov, Paper 2 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.