Cambridge IGCSE Mathematics 0580 — 2020 Oct/Nov Paper 2 · Variant 2
0580/22/O/N/20 · 26 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 · Write two hundred thousand and seventeen in figures
1 Write two hundred thousand and seventeen in figures. ................................................. [1]
Mark scheme: Question Answer Marks Partial Marks 1 200 017 1
Q2 · Insert one pair of brackets to make this calculation correct
2 Insert one pair of brackets to make this calculation correct. 7 - 5 - 3 + 4 = 9 [1]
Mark scheme: 2 7 – (5 – 3) + 4 1
Question 3
3 Solve the equation. 6 - 2x = 3x x = ................................................. [2]
Mark scheme: 3 1 6 2 M1 for 6 = 2x + 3x or better 1.2 or 15 or 5
Q4 · X° y° NOT TO SCALE 140° 120° The diagram shows a triangle drawn between a pair of…
4 x° y° NOT TO SCALE 140° 120° The diagram shows a triangle drawn between a pair of parallel lines. Find the value of x and the value of y. x = ................................................. y = ................................................. [3]
Mark scheme: 4 [x =] 60 3 B1 for [x =] 60 [y =] 80 B2 for [y =] 80 or B1 for 40 in a correct place on diagram If 0 scored SC1 for their x + their y = 140
Q5 · Increase 42 by 16%
5 Increase 42 by 16%. ................................................. [2]
Mark scheme: 5 48.72 2 16 M1 for × 42 oe or better 100
Question 6
6 Factorise completely. 4 - 8 x ................................................. [1]
Mark scheme: 6 4(1 – 2x) 1
Q7 · C NOT TO SCALE h cm A 6 cm B The area of triangle ABC is 27 cm2 and AB = 6 cm
7 C NOT TO SCALE h cm A 6 cm B The area of triangle ABC is 27 cm2 and AB = 6 cm. Calculate the value of h. h = ................................................. [2]
Mark scheme: 7 9 2 1 M1 for × 6 × h = 27 oe 2
Q8 · Calculate the size of one interior angle of a regular polygon with 40 sides
8 Calculate the size of one interior angle of a regular polygon with 40 sides. ................................................. [2]
Mark scheme: 8 171 2 M1 for 180 – (360 ÷ 40) oe or ( 40 − 2 ) × 180 oe 40
Q9 · Solve the simultaneous equations
9 Solve the simultaneous equations. 2x + y = 7 3x - y = 8 x = ................................................. y = ................................................. [2]
Mark scheme: 9 [x =] 3 2 B1 for each [y =] 1
Q10 · 110 Without using a calculator, work out ' 1
5 110 Without using a calculator, work out ' 1 . 6 3 You must show all your working and give your answer as a fraction in its simplest form. ................................................. [3]
Mark scheme: 10 5 3 5 8 M2 4 5 3 × or ÷ oe M1 for seen or for × their 6 4 6 6 3 6 4 5 their 8 or for ÷ 6 6 5 A1 dep on M2 cao 8
Question 11
11 Simplify. 2x 2 # 5x 5 ................................................. [2]
Mark scheme: 11 10x7 final answer 2 B1 for kx7 or 10xk final answer or for correct answer then spoilt
Q12 · Alex and Chris share sweets in the ratio Alex : Chris = 7 : 3
12 Alex and Chris share sweets in the ratio Alex : Chris = 7 : 3. Alex receives 20 more sweets than Chris. Work out the number of sweets Chris receives. ................................................. [2]
Mark scheme: 12 15 2 M1 for 4 [parts] = 20 soi or x + 20 x a correct equation e.g. = oe 7 3
Q13 · The length of one side of a rectangle is 12 cm
13 The length of one side of a rectangle is 12 cm. The length of the diagonal of the rectangle is 13 cm. Calculate the area of the rectangle. .......................................... cm2 [3]
Mark scheme: 13 60 3 2 2 M2 for 12 × 13 − 12 or M1 for 132 – 122 or for 12 × their 5 from Pythagoras or trig
Q14 · Work out ( 3 # 10 199 ) + ( 2 # 10 201 )
14 Work out ( 3 # 10 199 ) + ( 2 # 10 201 ) . Give your answer in standard form. ................................................. [2]
Mark scheme: 14 2.03 × 10201 2 B1 for figs 203 or [0].03 × 10201 or 200 × 10199
Q15 · NOT TO SCALE 60° 7.5 cm Calculate the area of this sector of a circle
15 NOT TO SCALE 60° 7.5 cm Calculate the area of this sector of a circle. .......................................... cm2 [2]
Mark scheme: 15 29.5 or 29.45 to 29.46 2 60 2 M1 for × π× 7.5 oe 360
Q16 · The selling price of a shirt is $26.50
16 The selling price of a shirt is $26.50 . This includes a tax of 6%. Calculate the price of the shirt before the tax was added. $ ................................................. [2]
Mark scheme: 16 25 2 6 M1 for x × 1 + = 26.50 oe or better 100
Q17 · 4 3 Speed 2 (m/s) 1 0 0 10 20 30 40 Time (seconds) The diagram shows the speed–time graph…
17 4 3 Speed 2 (m/s) 1 0 0 10 20 30 40 Time (seconds) The diagram shows the speed–time graph for the first 40 seconds of a cycle ride. (a) Find the acceleration between 20 and 40 seconds. ......................................... m/s2 [1] (b) Find the total distance travelled. .............................................. m [3]
Mark scheme: 17(a) 1 1 0.1 or 10 17(b) 90 3 M2 for 1 1 × 10 × 2 + 10 × 2 + ( 2 + 4 ) × 20 oe 2 2 or M1 for one area calculation or indicated on diagram
Q18 · The sides of an isosceles triangle are measured correct to the nearest millimetre
18 The sides of an isosceles triangle are measured correct to the nearest millimetre. One side has a length of 8.2 cm and another has a length of 9.4 cm. Find the largest possible value of the perimeter of this triangle. ............................................ cm [3]
Mark scheme: 18 27.15 cao 3 M2 for (9.4 + 0.05) × 2 + 8.2 + 0.05 or better or M1 for 8.2 + 0.05 or 9.4 + 0.05 or better seen OR SC2 for answer 25.95 or SC1 for answer 26.85
Q19 · 100° NOT TO 8 cm SCALE x° 9 cm (a) Calculate the value of x
19 100° NOT TO 8 cm SCALE x° 9 cm (a) Calculate the value of x. x = ................................................. [3] (b) Calculate the area of the triangle. .......................................... cm2 [3]
Mark scheme: 19(a) 61.1 or 61.08 to 61.09... 3 8sin100 M2 for [sin x =] oe or better 9 9 8 or M1 for = oe sin100 sin x 19(b) 11.7 or 11.66 to 11.67 3 M2 for 1 × 9 × 8 × sin(180 − 100 − their (a)) oe 2 or M1 for 180 – 100 – their (a)
Q20 · A model of a statue has a height of 4 cm
20 A model of a statue has a height of 4 cm. The volume of the model is 12 cm3. The volume of the statue is 40 500 cm3. Calculate the height of the statue. ............................................ cm [3]
Mark scheme: 20 60 3 40500 M2 for 4 × 3 oe 12 4 =3 12 oe or M1 for l 40500 40500 12 or 3 oe or 3 oe 12 40500
Q21 · Differentiate 6 + 4x - x 2
21 (a) Differentiate 6 + 4x - x 2 . ................................................. [2] (b) Find the coordinates of the turning point of the graph of y = 6 + 4x - x 2 . ( ...................... , ...................... ) [2]
Mark scheme: 21(a) 4 – 2x 2 B1 for 4 or – 2x 21(b) (2, 10) 2 B1 for x-coordinate of 2 or M1 for their 4 – 2x = 0
Q22 · C A NOT TO SCALE a M O B b The diagram shows a triangle OAB and a straight line OAC
22 C A NOT TO SCALE a M O B b The diagram shows a triangle OAB and a straight line OAC. OA : OC = 2 : 5 and M is the midpoint of AB. OA = a and OB = b . Find, in terms of a and b, in its simplest form (a) AB, AB = ................................................. [1] (b) MC. MC = ................................................. [3]
Mark scheme: 22(a) –a + b 1 22(b) 1 3 1 1 2a – b B2 for answer 2a + pb or qa – b q ≠ 2 2 2 or correct unsimplified answer in terms of a and b 3 5 or M1 for AC = a or OC = a or 2 2 correct route 1 If 0 scored SC1 for answer a + b 2
Q23 · Write as a single fraction in its simplest form
23 Write as a single fraction in its simplest form. 2x - 1 2 - x + 1 ................................................. [3]
Mark scheme: 23 3 3 B1 for 2( x + 1) − (2 x − 1) oe final answer x + 1 B1 for common denominator x + 1
Q24 · 4 A line from the point (2, 3) is perpendicular to the line y = x + 1
124 A line from the point (2, 3) is perpendicular to the line y = x + 1. 3 The two lines meet at the point P. Find the coordinates of P. ( ...................... , ...................... ) [5] Questions 25 and 26 are printed on the next page.
Mark scheme: 24 (2.4, 1.8) oe 5 1 M1 for [gradient =] –1 ÷ oe 3 M1 for substituting (2, 3) into y = (their m)x + c oe 1 M1 for x + 1 = their ( mx + c ) with 3 1 their m ≠ 3 M1 for substituting their x-coord into either equation to find y or for substituting their y-coord into either equation to find x
Q25 · Solve the equation tanx = 2 for 0° G x G 360°
25 Solve the equation tanx = 2 for 0° G x G 360° . x = ........................ or x = ........................ [2]
Mark scheme: 25 63.4 or 63.43... 2 B1 for each 243.4 or 243.4... If 0 scored SC1 for two answers with a difference of 180
Question 26
26 Simplify. ux - 2u - x + 2 u 2 - 1 ................................................. [4]
Mark scheme: 26 x − 2 4 B2 for ( x − 2)(u − 1) oe final answer u + 1 or B1 for u ( x − 2) − ( x − 2) or x (u − 1) − 2(u − 1) B1 for (u − 1)( u + 1)
What was in this paper
The subtopics covered by these 26 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Angles2Area and perimeter2Equations2Percentages2Ratio and proportion2Algebraic fractions1Circles, arcs and sectors1Differentiation1Equations of linear graphs1Fractions, decimals and percentages1Indices I1Limits of accuracy1Pythagoras’ theorem1Standard form1Surface area and volume1The four operations1Trigonometric functions1Types of number1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2020 Oct/Nov, Paper 2 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.