Cambridge IGCSE Mathematics 0580 — 2020 Feb/March Paper 2 · Variant 2
0580/22/F/M/20 · 21 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 scheme7 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · 3.56 5 196 8 7 12 From the list, write down a number that is (a) a multiple of 3…
1 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: Question Answer Marks Partial Marks 1(a) 12 1 1(b) 8 1 1(c) 5 1 1(d) 7 1
Q2 · The number of people swimming in a pool is recorded each day for 12 days
2 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
Q3 · Point A has coordinates (6, 4) and point B has coordinates (2, 7)
3 Point A has coordinates (6, 4) and point B has coordinates (2, 7). Write AB as a column vector. AB = [1] f p
Mark scheme: 3 − 4 1 3
Q4 · Find the interior angle of a regular polygon with 24 sides
4 Find the interior angle of a regular polygon with 24 sides. ................................................. [2]
Mark scheme: 4 165 2 ( 24 − 2 ) × 180 360 M1 for or 180 − 24 24
Q5 · 45 Without using a calculator, work out '
15 45 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
Q6 · The table shows the marks scored by 40 students in a test
6 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
Q7 · NOT TO 8.5 cm SCALE 10.8 cm The diagram shows a right-angled triangle
7 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 2 2 M2 for 8.5 + 10.8 + 8.5 + 10.8 oe or M1 for 8.5 2 + 10.8 2 oe
Q8 · Calculate the value of ( 2.3 # 10 -3 ) + ( 6
8 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 9
9 (a) Factorise completely. 3x 2 - 12xy ................................................. [2] (b) Expand and simplify. ( m - 3)( m + 2) ................................................. [2]
Mark scheme: 9(a) 3 x ( x − 4 y ) final answer 2 B1 for 3( x 2 − 4 xy ) or x (3 x − 12 y ) 9(b) m 2 − m − 6 final answer 2 M1 for 3 terms from m 2, − 3m, + 2 m, − 6
Q10 · Sketch the graph of each function
10 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
Q11 · 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…
11 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)
Q12 · The population of a town decreases exponentially at a rate of 1.7% per year
12 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 1.7 5 M1 for 250 000 × 1 − oe 100 B1 for their more accurate answer correctly rounded to the nearest 100
Q13 · Write the recurring decimal .026o as a fraction
13 Write the recurring decimal .026o 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
Q14 · The box-and-whisker plot gives information about the heights, in centimetres, of some…
14 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
Q15 · A NOT TO SCALE D B 64° P C Q A, B, C and D lie on the circle
15 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
Q16 · Solve the simultaneous equations
16 Solve the simultaneous equations. You must show all your working. x = 7 - 3y x 2 - y 2 = 39 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 2 7 − x or x − = 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
Q17 · A is the point (3, 5) and B is the point ( 1, - 7)
17 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
Q18 · A car travels at a constant speed
18 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
Q19 · Y 1 0 x 90° 180° 270° 360° – 1 (a) On the diagram, sketch the graph of y = cos x for 0° G…
19 y 1 0 x 90° 180° 270° 360° – 1 (a) On the diagram, sketch the graph of y = cos x for 0° G x G 360° . [2] (b) Solve the equation 4 cosx + 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 or M1 for cos x = oe 284.4 to 284.5 4 If 0 scored, SC1 for two answers with a sum of 360
Q20 · X 2 - 12x + a = ( x + b) 2 Find the value of a and the value of b
20 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
Q21 · XY = 3a + 2b and ZY = 6a + 4b
21 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
What was in this paper
The subtopics covered by these 21 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Averages and measures of spread2Fractions, decimals and percentages2Vectors in two dimensions2Angles1Area and perimeter1Circle theorems I1Equations1Equations of linear graphs1Exponential growth and decay1Graphs of functions1Limits of accuracy1Standard form1Statistical charts and diagrams1Transformations1Trigonometric functions1Types of number1What you needed in this session
Cambridge’s own grade thresholds for 2020 Feb/March, Paper 2 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.