Cambridge IGCSE Mathematics 0580 — 2017 Oct/Nov Paper 2 · Variant 2
0580/22/O/N/17 · 27 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 scheme5 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · One day, at noon, in Maseru, the temperature was 17 °C
1 One day, at noon, in Maseru, the temperature was 17 °C. At midnight the temperature was 20 °C lower. Work out the temperature at midnight. .........................................°C [1]
Mark scheme: Question Answer Marks Partial marks 1 – 3 1
Q2 · Write .517 # 10 -3 as an ordinary number
2 Write .517 # 10 -3 as an ordinary number. .............................................. [1]
Mark scheme: 2 [0].00517 1
Q3 · C N L A B M In the diagram, BL is the bisector of angle ABC and MN is the perpendicular…
3 C N L A B M In the diagram, BL is the bisector of angle ABC and MN is the perpendicular bisector of AB. Complete the statement. The shaded region contains the points, inside triangle ABC, that are • nearer to B than to A and • nearer to ....................... than to ....................... [1]
Mark scheme: 3 BC AB oe 1
Q4 · 1 and 12 are factors of 12
4 (a) 1 and 12 are factors of 12. Write down all the other factors of 12. .............................................. [1] (b) Write down the multiples of 9 between 20 and 40. .............................................. [1]
Mark scheme: 4(a) 2, 3, 4, 6 1 4(b) 27, 36 cao 1
Q5 · NOT TO 80° SCALE 120° y° x° A B In the diagram, AB is a straight line
5 NOT TO 80° SCALE 120° y° x° A B In the diagram, AB is a straight line. Find the value of x and the value of y. x = ....................................... y = ....................................... [2]
Mark scheme: 5 [x = ] 60 2 B1 for each or for two numbers that add to 100 [y =] 40
Q6 · Write 55 g as a percentage of 2.2 kg
6 Write 55 g as a percentage of 2.2 kg. ..........................................% [2]
Mark scheme: 6 2.5 2 B1 for 2200 or 0.055 seen or SC1 for answer figs 25
Q7 · The area of a triangle is 528 cm2
7 The area of a triangle is 528 cm2. The length of its base is 33 cm. Calculate the perpendicular height of the triangle. ........................................ cm [2]
Mark scheme: 7 32 2 1 M1 for × 33 × h = 528 oe 2
Q8 · Amar cycles at a speed of 18 km/h
8 Amar cycles at a speed of 18 km/h. It takes him 55 minutes to cycle between two villages. Calculate the distance between the two villages. ........................................ km [2]
Mark scheme: 8 16.5 2 55 M1 for 60 or speed × time (numerical)
Q9 · Work out, giving your answer in standard form
9 Work out, giving your answer in standard form. 1.2 # 10 40 + 1. 2 # 10 41 .............................................. [2]
Mark scheme: 9 1.32 × 1041 2 M1 for 0.12 × 1041 or 12 × 1040 or SC1 for figs 132
Q10 · The sides of a triangle are 5.2 cm, 6.3 cm and 9.4 cm, each correct to the nearest…
10 The sides of a triangle are 5.2 cm, 6.3 cm and 9.4 cm, each correct to the nearest millimetre. Calculate the lower bound of the perimeter of the triangle. ........................................ cm [2]
Mark scheme: 10 20.75 final answer cao 2 B1 for one of 5.15, 6.25 or 9.35 seen or M1 for (5.2 – 0.05) + (6.3 – 0.05) + (9.4 – 0.05)
Q11 · Write the recurring decimal .048o o as a fraction
11 Write the recurring decimal .048o o as a fraction. Show all your working. .............................................. [2]
Mark scheme: 11 48.48 – 0.48 oe M1 48 16 SC1 for or or equivalent fraction with 99 33 no/insufficient working 48 16 A1 or or equivalent fraction 99 33
Q12 · Expand the brackets and simplify
12 Expand the brackets and simplify. (5 - n) (3 + n) .............................................. [2]
Mark scheme: 12 15 + 2n − n 2 final answer 2 M1 for three terms of 15 + 5n − 3n − n 2 correct
Q13 · 13 (a) Write as a mixed number
1113 (a) Write as a mixed number. 3 .............................................. [1] 1 5 (b) Without using a calculator, work out + . 4 12 Show all the steps of your working and give your answer as a fraction in its lowest terms. .............................................. [2]
Mark scheme: 13(a) 2 1 3 cao 3 13(b) 3 5 M1 For correct method to find common denominator [and ] oe 12 12 12 20 e.g. and 48 48 2 A1 cao 3
Q14 · Find the integers which satisfy the inequality
14 Find the integers which satisfy the inequality. - 5 1 2n - 1 G 5 .............................................. [3]
Mark scheme: 14 –1, 0, 1, 2, 3 3 B2 for −<2 n - 3 or list with one error or omission or M1 for –5 + 1 < 2n or 2n ⩽ 5 + 1 or a list with 3 correct and no more than 1 incorrect or if zero scored, SC1 for 5, 3, 1, –1, –3
Q15 · Write as a single fraction in its simplest form
15 Write as a single fraction in its simplest form. x + 1 y - 1 - x y .............................................. [3]
Mark scheme: 15 y + x 3 B1 for y ( x + 1) − x ( y − 1) final answer xy B1 for common denominator xy y − x or SC2 for final answer xy
Q16 · Here are the first four terms of a sequence
16 Here are the first four terms of a sequence. 23 17 11 5 (a) Find the next term. .............................................. [1] (b) Find the nth term. .............................................. [2]
Mark scheme: 16(a) –1 1 16(b) –6n + 29 oe 2 M1 for −6n + k (any k ) or − kn + 29 ( k ≠ 0 )
Q17 · NOT TO 29x° SCALE x° The diagram shows part of a regular polygon
17 NOT TO 29x° SCALE x° The diagram shows part of a regular polygon. The exterior angle is x°. The interior angle is 29x°. Work out the number of sides of this polygon. .............................................. [3]
Mark scheme: 17 60 3 B2 for x = 6 or M1 for 29x + x = 180 oe and M1 for 360 ÷ 6 or 360 ÷ their x or 180(n – 2) = their x × 29n
Q18 · Solve the simultaneous equations
18 Solve the simultaneous equations. You must show all your working. x y = 2 2x - y = 1 x = ....................................... y = ....................................... [3]
Mark scheme: 18 Correctly eliminating one M1 variable 2 A1 [x =] or 0.667 or 0.6666… 3 1 A1 If zero scored, SC1 for [y =] or 0.333 or 0.333… 2 values satisfying one of the original equations 3 or if no working shown but 2 correct answers given
Q19 · Make x the subject of the formula
19 Make x the subject of the formula. y = x 2 + 1 x = ....................................... [3]
Mark scheme: 19 2 3 M1 for correct squaring [ ± ] y − 1 final answer M1 for correct rearranging for x or x2 term M1 for correct square root
Q20 · 12 Speed NOT TO (m/s) SCALE 0 0 3 10 15 Time (s) The diagram shows a speed-time graph
20 12 Speed NOT TO (m/s) SCALE 0 0 3 10 15 Time (s) The diagram shows a speed-time graph. Calculate the total distance travelled. .......................................... m [3]
Mark scheme: 20 132 3 1 M2 for (7 + 15) ×12 2 or M1 for any correct area
Q21 · B K b NOT TO SCALE O A a O is the origin and K is the point on AB so that AK : KB = 2 : 1
21 B K b NOT TO SCALE O A a O is the origin and K is the point on AB so that AK : KB = 2 : 1. OA = a and OB = b . Find the position vector of K. Give your answer in terms of a and b in its simplest form. .............................................. [3]
Mark scheme: JJJG 21 1 2 3 B2 for correct unsimplified vector for OK in terms of a + b oe simplified 3 3 a and b JJJG or M1 for a correct route for OK JJJG JJJG or AB =− a + b or BA = – b + a JJJG or recognition of OK as a position vector
Q22 · NOT TO SCALE O 108° D w° A y° E 60° C x° B A, B, C and D are points on the circle, centre…
22 NOT TO SCALE O 108° D w° A y° E 60° C x° B A, B, C and D are points on the circle, centre O. BCE is a straight line. Angle AOC = 108° and angle DCE = 60°. Calculate the values of w, x and y. w = ...................................... x = ....................................... y = ....................................... [3]
Mark scheme: 22 [w =] 54 3 B1 for [w =] 54 [x =] 126 B1 for [x =] 126 [y =] 60 If B0 B0 for first two B marks then B1 for their w + their x = 180 B1 for [y =] 60 or for their w + their x + their y = 240
Q23 · 6 cm O 30° NOT TO SCALE The diagram shows a sector of a circle, centre O and radius 6 cm
23 6 cm O 30° NOT TO SCALE The diagram shows a sector of a circle, centre O and radius 6 cm. The sector angle is 30°. The area of the shaded segment is (kr – c) cm2, where k and c are integers. Find the value of k and the value of c. k = ....................................... c = ....................................... [3]
Mark scheme: 23 [k =] 3 3 30 2 M1 for × π × 6 [c =] 9 360 1 M1 for × 6 × 6 × sin30 2
Question 24
24 Solve the equations. (a) 7 - 3n = 11 n + 2 n = ....................................... [2] p - 3 (b) = 3 5 p = ....................................... [2]
Mark scheme: 24(a) 5 2 M1 for 7 – 2 = 11n + 3n oe or better or 0.357 or 0.357… 14 24(b) 18 2 p 3 M1 for p – 3 = 3 × 5 or = 3 + 5 5
Question 25
25 Factorise completely. (a) x 2 - x - 132 .............................................. [2] (b) x 3 - 4x .............................................. [2]
Mark scheme: 25(a) ( x − 12)( x + 11) final answer 2 B1 for ( x + a )( x + b ) where ab = –132 or a + b = –1 25(b) x ( x + 2)( x − 2) final answer 2 B1 for x ( x 2 − 4) or ( x + 2)( x 2 − 2 x ) or ( x − 2)( x 2 + 2 x )
Q26 · P Q NOT TO 2 cm SCALE D C 3 cm A 4 cm B The diagram shows a prism of length 4 cm
26 P Q NOT TO 2 cm SCALE D C 3 cm A 4 cm B The diagram shows a prism of length 4 cm. The cross section is a right-angled triangle. BC = 3 cm and CQ = 2 cm. Calculate the angle between the line AQ and the base, ABCD, of the prism. .............................................. [4]
Mark scheme: 26 21.8 or 21.80… 4 2 M3 for tan = oe 32 + 4 2 or M1 for 3 2 + 4 2 or 32 + 4 2 + 2 2 and M1 for recognising angle QAC
Question 27
27 Simplify. 3 (a) 814 .............................................. [1] 2 4 (b) x 3 ' x - 3 .............................................. [1] 1 8 - 3 (c) 6 c y m
Mark scheme: 27(a) 27 1 27(b) x2 final answer 1 1 2 −127(c) y 2 3 2 y 6 or 0.5y2 final answer 2 M1 for or 2 or better 8 y y 2 ky 2 or SC1 for answer or or c 2 y 2
What was in this paper
The subtopics covered by these 27 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
3Algebraic manipulation2Angles2Fractions, decimals and percentages2Rates2Standard form2Algebraic fractions1Area and perimeter1Circle theorems I1Circles, arcs and sectors1Geometrical terms1Inequalities1Limits of accuracy1Percentages1Powers and roots1Pythagoras’ theorem and trigonometry1Sequences1The four operations1Types of number1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2017 Oct/Nov, Paper 2 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.