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Cambridge IGCSE Mathematics (0580), Paper 2 (Extended), October/November 2019. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
0580_w19_qp_220580_w19_ms_220580/22/O/N/19
Each question as it's printed, and the mark scheme's points for it, as text. Diagrams, tables and graphs are in the PDFs above.
Question
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
1 6.8 1 1 cao 24
Question
Calculate. 5 3 + 340 8 …… [1]
Mark scheme
2 7.6[0] or 7.604 to 7.605 1
Question
Expand. a (a 3 + 3) …… [1]
Mark scheme
3 a4 + 3a final answer 1
Question
On the Venn diagram, shade the region (A + B)l . A B [1]
Mark scheme
4 1
Question
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
Question
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
Question
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
Question
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
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
Question
Write the recurring decimal 0.67o as a fraction. Show all your working and give your answer in its simplest form. …… [2] 5 2
Mark scheme
10 67.7 – 6.7 oe M1 61 A1 k If 0 scored, SC1 for 90 90
Question
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 29k 5k or 2 − Allow or 8 3 8 3 8k 3k Correct step for dealing with mixed numbers 87 40 15 16 M1 Correct method to find common and [ 2] and 15 16 24 24 24 24 denominator e.g. 3 and 1 24 24 23 A1
Question
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
Question
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 3 3 75 30 or M1 for oe or oe 30 75 OR 3 30 M2 for 5.5 × × 1000 75
Question
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
Question
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
Question
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. yG5 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
Question
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
Question
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
Question
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
(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)
Question
(a) 3 -2 # 3 x = 81 Find the value of x. x = …… [2] 1 (b) x - 3 = 32x -2 Find the value of x. x = …… [3] 3 2 -2 5
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 1 = or better x2 x3 1 − −− 2 or x 3 = 32 or better
Question
A =e o B =e o C = (- 1 k) -5 0 4 1 (a) Find AB. f p [2] (b) CA = (- 13 - 2) Find the value of k. k = …… [2] (c) Find A-1. f p [2]
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
Question
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
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Mark my 0580/22Examiners follow the generic marking principles at the front of the scheme, then each question's points: method (M), accuracy (A) and independent (B) marks, error carried forward where the scheme allows it, and positive marking, so you're credited for what you got right.
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On this page, free: the mark scheme for IGCSE Mathematics 0580/22, October/November 2019 (0580_w19_ms_22), and the question paper (0580_w19_qp_22), to read or download, with each question's marking points written out underneath.
Mathematics 0580/22 for October/November 2019 is out of 70 marks, with 1 hour 30 minutes to answer it.
Yes. Upload your answers to 0580/22/O/N/19 as a PDF or photos, and CIE Buddy marks every question against this paper's official mark scheme, using Cambridge's marking rules. You get your score, each lost mark explained on your own script, and the topics to revise. It's a guide, not an official Cambridge grade.