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Cambridge IGCSE Mathematics (0580), Paper 2 (Extended), February/March 2020. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
0580_m20_qp_220580_m20_ms_220580/22/F/M/20
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
3.56 5 196 8 7 12 From the list, write down a number that is (a) a multiple of 3, …… [1] (b) a cube number, …… [1] (c) a prime number, …… [1] (d) an irrational number. …… [1]
Mark scheme
1(a) 12 1 1(b) 8 1 1(c) 5 1 1(d) 7 1
Question
The number of people swimming in a pool is recorded each day for 12 days. 24 28 13 38 15 26 45 21 48 36 18 38 (a) Complete the stem-and-leaf diagram. 1 2 3 4 Key: 1 3 represents 13 swimmers [2] (b) Find the median number of swimmers. …… [1]
Mark scheme
2(a) 1 3 5 8 2 M1 for correct but not ordered or for two 2 1 4 6 8 correct rows ordered 3 6 8 8 4 5 8 2(b) 27 1
Question
Point A has coordinates (6, 4) and point B has coordinates (2, 7). Write AB as a column vector. AB = f p [1]
Mark scheme
3 −4 1 3
Question
Find the interior angle of a regular polygon with 24 sides. …… [2] 15 4
Mark scheme
4 165 2 M1 for ( 24 − 2 ) × 180 or 180 − 360 24 24
Question
Without using a calculator, work out ' . 28 7 You must show all your working and give your answer as a fraction in its simplest form. …… [3]
Mark scheme
5 15 7 15 16 M1 × or ÷ oe 28 4 28 28 15 A2 105 cao A1 for oe 16 112
Question
The table shows the marks scored by 40 students in a test. Mark 5 6 7 8 9 10 Frequency 8 5 11 7 5 4 Calculate the mean mark. …… [3]
Mark scheme
6 7.2 3 M1 for 5 × 8 + 6 × 5 + 7 × 11 + 8 × 7 + 9 × 5 + 10 × 4 M1dep for ÷ 40
Question
NOT TO 8.5 cm SCALE 10.8 cm The diagram shows a right-angled triangle. (a) Calculate the area. …… cm2 [2] (b) Calculate the perimeter. …… cm [3]
Mark scheme
7(a) 45.9 2 M1 for 0.5 × 8.5 × 10.8 oe 7(b) 33[.0] or 33.04… 3 M2 for 8.5 + 10.8 + 8.52 + 10.82 oe or M1 for 8.52 + 10.82 oe
Question
Calculate the value of (2.3 # 10 -3) + (6.8 # 10 -4) . Give your answer in standard form. …… [1]
Mark scheme
8 2.98 × 10−3 1
Question
(a) Factorise completely. 3x 2 - 12xy …… [2] (b) Expand and simplify. (m - 3) (m + 2) …… [2]
Mark scheme
9(a) 3x( x − 4 y ) final answer 2 B1 for 3( x 2 − 4 xy ) or x(3x − 12 y ) 9(b) m2 − m − 6 final answer 2 M1 for 3 terms from m2 , − 3m, + 2m, − 6
Question
Sketch the graph of each function. (a) y = x - 3 y O x [1] 1 (b) y = x y O x [2]
Mark scheme
10(a) Correct sketch 1 Line with positive gradient and negative y intercept 10(b) Correct sketch 2 B1 for only one branch or attempt at correct shape
Question
y 7 6 5 4 C 3 2 D 1 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 x –1 B –2 A –3 –4 –5 Describe fully the single transformation that maps (a) shape A onto shape B, …… [3] (b) shape A onto shape C, …… [2] (c) shape A onto shape D. …… [3]
Mark scheme
11(a) Rotation 3 B1 for each 90° clockwise oe (0, 2) 11(b) Reflection 2 B1 for each y=x 11(c) Enlargement 3 B1 for each 1 [sf] 2 (4, 6)
Question
The population of a town decreases exponentially at a rate of 1.7% per year. The population now is 250 000. Calculate the population at the end of 5 years. Give your answer correct to the nearest hundred. …… [3]
Mark scheme
12 229 500 cao 3 B2 for 229 460… OR 5 1.7 M1 for 250 000 × 1 − oe 100 B1 for their more accurate answer correctly rounded to the nearest 100
Question
Write the recurring decimal 0.26o as a fraction. You must show all your working. …… [2]
Mark scheme
13 2.6 − 0.26 oe M1 4 A1 k oe fraction nfww If M0 scored SC1 for 15 90
Question
The box-and-whisker plot gives information about the heights, in centimetres, of some plants. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Height (cm) (a) Write down the median. …… cm [1] (b) Find (i) the range, …… cm [1] (ii) the interquartile range. …… cm [1]
Mark scheme
14(a) 11.5 1 14(b)(i) 12 1 14(b)(ii) 8.5 1
Question
A NOT TO SCALE D B 64° P C Q A, B, C and D lie on the circle. PCQ is a tangent to the circle at C. Angle ACQ = 64°. Work out angle ABC, giving reasons for your answer. Angle ABC = …… because …… …… [3]
Mark scheme
15 116° B1 alternate segment theorem B1 angles in opposite segments are B1 supplementary or cyclic quadrilateral or angles at a point on a straight line
Question
Solve the simultaneous equations. You must show all your working. x = 7 - 3y x - y 2 = 39 2 x = …… y = …… x = …… y = …… [6]
Mark scheme
16 8 y 2 − 42 y + 10[= 0] or M3 M1 for ( 7 − 3 y )2 − y 2 = 39 oe 8 x 2 + 14 x − 400[= 0] 2 7−x or x 2 − = 39 oe 3 M1 for 49 – 21y – 21y + 9y2 or better or 49 –7x –7x + x2 or better or for correct expansion of their quadratic binomial (8 y − 2 )( y − 5)[= 0] oe M1 M1 for correct method to solve their quadratic equation e.g. factors, quadratic formula, (8 x − 50 )( x + 8)[= 0] oe completing the square x = 6.25 oe y = 0.25 oe B2 B1 for x = 6.25, x = −8 or for y = 0.25, y = 5 x=−8 y=5 or for a correct pair of x and y values
Question
A is the point (3, 5) and B is the point (1, - 7) . Find the equation of the line perpendicular to AB that passes through the point A. Give your answer in the form y = mx + c . y = …… [4]
Mark scheme
17 1 11 4 5 − −7 [ y =] − x + oe M1 for [gradient of AB =] oe 6 2 3 −1 M1 for 1 [gradient of perpendicular =] − their grad AB M1 for substituting (3, 5) in their linear equation
Question
A car travels at a constant speed. It travels a distance of 146.2 m, correct to 1 decimal place. This takes 7 seconds, correct to the nearest second. Calculate the upper bound for the speed of the car. …… m/s [3]
Mark scheme
18 22.5 nfww 3 146.2 + 0.05 M2 for 7 − 0.5 or M1 for 146.2 + 0.05 or 7 – 0.5 or better seen
Question
y 1 0 90° 180° 270° 360° x –1 (a) On the diagram, sketch the graph of y = cos x for 0° G x G 360° . [2] (b) Solve the equation 4 cos x + 2 = 3 for 0° G x G 360° . x = …… and x = …… [3] Questions 20 and 21 are printed on the next page.
Mark scheme
19(a) Correct sketch 2 Needs all three features for 2 marks: • Correct curve shape • Maximum at (0, 1) and at (360, 1) and minimum at (180, − 1) • Passing through (90, 0) and (270, 0) only B1 for two correct features 19(b) 75.5 or 75.52… 3 B2 for one correct and 1 284.4 to 284.5 or M1 for cos x = oe 4 If 0 scored, SC1 for two answers with a sum of 360
Question
x 2 - 12x + a = (x + b) 2 Find the value of a and the value of b. a = …… b = …… [2]
Mark scheme
20 [a =] 36 2 B1 for each [b =] − 6 or SC1 for correct answers reversed
Question
XY = 3a + 2b and ZY = 6a + 4b . Write down two statements about the relationship between the points X, Y and Z. 1 …… 2 …… [2]
Mark scheme
21 X, Y and Z are collinear oe 1 Allow in a straight line X is the midpoint of ZY oe 1 Allow e.g. ZY = 2XY , ZX = XY oe
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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, February/March 2020 (0580_m20_ms_22), and the question paper (0580_m20_qp_22), to read or download, with each question's marking points written out underneath.
Mathematics 0580/22 for February/March 2020 is out of 70 marks, with 1 hour 30 minutes to answer it.
Yes. Upload your answers to 0580/22/F/M/20 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.