Cambridge IGCSE Mathematics 0580 — 2016 Oct/Nov Paper 2 · Variant 2
0580/22/O/N/16 · 20 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 · Write 14 835 correct to the nearest thousand
1 (a) Write 14 835 correct to the nearest thousand. ................................................. [1] (b) Write your answer to part (a) in standard form. ................................................. [1]
Mark scheme: Question Answer Mark Part marks 1 (a) 15000 cao 1 (b) 1.5 × 10 4 1FT FT their (a)
Q2 · 67° NOT TO SCALE a° 42° Find the value of a
2 67° NOT TO SCALE a° 42° Find the value of a. a = ................................................ [2]
Mark scheme: 2 25 2 B1 for 67 or 113 seen once in correct position or M1 for a + 42 = 67 or a + 42 + 113 = 180 or better
Question 3
3 Solve the equation. 6(k – 8) = 78 k = ................................................ [2]
Mark scheme: 3 21 2 M1 for k – 8 = 13 or 6k – 48 = 78 or better (13 + 16 ) × 4
Q4 · 13 cm NOT TO 5 cm SCALE 4 cm 16 cm Calculate the area of this trapezium
4 13 cm NOT TO 5 cm SCALE 4 cm 16 cm Calculate the area of this trapezium. ........................................ cm2 [2]
Mark scheme: (13 + 16 ) × 4 14 58 2 M1 for or 4 × 13 + 2 × 4 × 3 oe 2
Question 5
5 Simplify. 36y 5 ' 4y 2 ................................................. [2]
Mark scheme: 5 9y 3 final answer 2 B1 for 9yk, 9 × y3 or ky3 (k ≠ 0) as final answer
Q6 · The sides of a square are 8 cm, correct to the nearest centimetre
6 The sides of a square are 8 cm, correct to the nearest centimetre. Calculate the upper bound for the area of the square. ........................................ cm2 [2]
Mark scheme: 6 72.25 cao 2 M1 for 8 + 0.5 or better seen
Q7 · Find the positive integers that satisfy the inequality t + 2 2 3 t - 6
7 Find the positive integers that satisfy the inequality t + 2 2 3 t - 6 . ................................................. [3]
Mark scheme: 7 1, 2, 3 3 B2 for t < 4 or M1 for 2 + 6 > 3t – t oe or better If zero scored, SC1 for answer 0, 1, 2, 3 or 1, 2, 3, 4
Q8 · Solve the simultaneous equations
8 Solve the simultaneous equations. You must show all your working. 1 2 x + y = 8 x - 2y = 2 x = ............................................... y = ................................................ [3]
Mark scheme: 8 correctly eliminating one variable M1 [x = ] 9 A1 [y = ] 3.5 A1 If zero scored, SC1 for 2 values satisfying one of the original equations SC1 if no working shown but 2 correct answers given 300
Q9 · From the top of a building, 300 metres high, the angle of depression of a car, C, is 52°
9 From the top of a building, 300 metres high, the angle of depression of a car, C, is 52°. NOT TO SCALE 300 m C Calculate the horizontal distance from the car to the base of the building. ........................................... m [3]
Mark scheme: 300 9 234 or 234.3 to 234.4 3 M2 for [dist = ] oe tan52 or M1 for correct implicit trig statement allow M1 if they use their 52 or their 38 provided it is marked on the diagram or B1 for 52 or 38 correctly placed If zero scored, SC1 for final answer 384
Q10 · The length of a backpack of capacity 30 litres is 53 cm
10 The length of a backpack of capacity 30 litres is 53 cm. Calculate the length of a mathematically similar backpack of capacity 20 litres. .......................................... cm [3]
Mark scheme: 20 10 46.3 or 46.29 to 46.30 3 M2 for 53 × 3 oe 30 20 30 53 3 30 or or M1 for 3 or 3 or = 30 20 x 20 better
Q11 · B A C (a) Using compasses and a straight edge only, construct the bisector of angle BAC
11 B A C (a) Using compasses and a straight edge only, construct the bisector of angle BAC. [2] (b) Complete the statement. The bisector of angle BAC is the locus of points that are .................................................................... .............................................................................................................................................................. [1]
Mark scheme: 11 (a) Accurate angle bisector with correct 2 B1 for accurate angle bisector arcs or correct arcs with no/wrong line (b) Equidistant (oe) from AB and AC 1
Q12 · Ralf and Susie share $57 in the ratio 2 : 1
12 Ralf and Susie share $57 in the ratio 2 : 1. (a) Calculate the amount Ralf receives. $ ................................................ [2] (b) Ralf gives $2 to Susie. Calculate the new ratio Ralf’s money : Susie’s money. Give your answer in its simplest form. ..................... : .....................[2]
Mark scheme: 12 (a) 38 2 M1 for 57 ÷ (2 + 1) or better (b) 12 : 7 2 M1FT for their 38 – 2 and their 19 + 2 seen dep on sum = 57 If M0 SC1 for answer 7 : 12 2 ( )
Question 13
13 Factorise. (a) m 3 + m ................................................. [1] (b) 25 - y 2 ................................................. [1] (c) x 2 + 3 x - 28 ................................................. [2]
Mark scheme: 13 (a) m m 2 + 1 final answer 1 ( ) (b) ( 5 − y )( 5 + y ) final answer 1 (c) ( x − 4 )( x + 7 ) final answer 2 B1 for ( x − 4 )( x + 7 ) seen then spoiled or M1 for ( x + a )( x + b ) where ab = − 28 or a + b = 3 or for x ( x + 7) − 4( x + 7) or x ( x − 4) + 7( x − 4)
Q14 · 2 114 Without using your calculator, work out + -
3 2 114 Without using your calculator, work out + - . 4 3 8 You must show all your working and give your answer as a mixed number in its simplest form. ................................................. [4]
Mark scheme: 14 Common denominator 24 B1 accept k × 24 18 16 3 18k 16 k 3k Two correct from , and oe M1 accept , and 24 24 24 24 k 24 k 24 k 7 31 31k 7 k 124 cao A2 A1 for 24 or 24 k or 124 k
Q15 · F M 8 2 4 3 1 0 2 2 R The Venn diagram shows the number of people who like films (F)…
15 F M 8 2 4 3 1 0 2 2 R The Venn diagram shows the number of people who like films (F), music (M) and reading (R). (a) Find (i) n (M) , ................................................. [1] (ii) n ( R , M ) . ................................................. [1] (b) A person is chosen at random from the people who like films. Write down the probability that this person also likes music. ................................................. [1] (c) On the Venn diagram, shade M l + (F , R) . [1]
Mark scheme: 15 (a) (i) 9 1 (ii) 12 1 5 (b) 1 14 (c) 1
Q16 · - 5 16 BC = BA = c 3 m c 6 m (a) Find CA
2 - 5 16 BC = BA = c 3 m c 6 m (a) Find CA. CA = [2] f p (b) Work out BA . ................................................. [2]
Mark scheme: 7 G 2 16 (a) 2 M1 for CB = 3 − 3 or for correct route allow e.g. BA – BC, CB + BA (b) 7.81 or 7.810…. 2 M1 for ( −5 ) 2 + 6 2
Q17 · 8 cm 32 cm 40 cm 125° NOT TO SCALE 48 cm The diagram shows the cross section of part of a…
17 8 cm 32 cm 40 cm 125° NOT TO SCALE 48 cm The diagram shows the cross section of part of a park bench. It is made from a rectangle of length 32 cm and width 8 cm and a curved section. The curved section is made from two concentric arcs with sector angle 125°. The inner arc has radius 40 cm and the outer arc has radius 48 cm. Calculate the area of the cross section correct to the nearest square centimetre. ........................................ cm2 [5]
Mark scheme: 17 1024 cao 5 B4 for 1023 to 1024.0… or 1020 or 125 2 125 2 M3 for × π × 48 − × π × 40 + 32 × 8 360 360 or 125 2 125 2 M1 for × π × 48 or × π × 40 360 360 and M1 for 32 × 8 + k π If B0 scored B1 for their more accurate decimal answer rounded correctly to an integer
Q18 · Y 6 5 4 3 B A 2 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 –4 –5 –6 (a) Describe fully…
18 y 6 5 4 3 B A 2 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 –4 –5 –6 (a) Describe fully the single transformation that maps triangle A onto triangle B. .............................................................................................................................................................. .............................................................................................................................................................. [3] 1 0 (b) Draw the image of triangle A after the transformation represented by . [3] c0 - 1m
Mark scheme: 18 (a) Enlargement 1 1 [s.f.] 1 2 [centre] ( −1 , 3 ) 1 (b) Triangle at (3 ,−1) (5,−1) (5,−5) 3 M2 for 2 correct vertices on grid or in working or M1 for identifying matrix as a reflection in 1 0 3 5 5 the x-axis or for oe 0 − 1 1 1 5 1 − 4 3 − 4 3
Q19 · - 3 19 (a) Find the inverse of
2 - 3 19 (a) Find the inverse of . c5 - 4m [2] f p w - 9 (b) The matrix does not have an inverse. f 4 w - 12p Calculate the value of w. w = ................................................ [4]
Mark scheme: 1 4 3 4 3 19 (a) oe isw 2 B1 for k or det = 7 soi 7 − 5 2 −5 2 (b) 6 nfww 4 M3 for ( w − 6 ) 2 = 0 or M2 for w 2 − 12 w + 36[ = 0] or M1 for w ( w − 12 ) − 4 × ( −9 ) [ = 0] oe or clear attempt at determinant = 0 oe
Q20 · Y 7 A 6 5 4 3 2 B 1 x 0 1 2 3 4 5 6 7 8 Point A has co-ordinates (3, 6)
20 y 7 A 6 5 4 3 2 B 1 x 0 1 2 3 4 5 6 7 8 Point A has co-ordinates (3, 6). (a) Write down the co-ordinates of point B. ( ....................... , ....................... ) [1] (b) Find the gradient of the line AB. ................................................. [2] (c) Find the equation of the line that • is perpendicular to the line AB and • passes through the point (0, 2). ................................................. [3]
Mark scheme: 20 (a) ( 7 , 1 ) 1 5 1 (b) ‒1.25 or − or −14 2 M1 for rise/run 4 4 4 −1 (c) y = x + 2 oe 3 B2 for x + 2 or y = x + 2 oe 5 5 their(b) 1 or M1 for −their ( b ) oe 4 or B1 for x seen or [ y = ] mx + 2 (m ≠ 0) 5
What was in this paper
The subtopics covered by these 20 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Equations2Limits of accuracy2Angles1Area and perimeter1Compound shapes and parts of shapes1Equations of linear graphs1Fractions, decimals and percentages1Geometrical constructions1Inequalities1Introduction to algebra1Introduction to probability1Ratio and proportion1Right-angled triangles1Similarity1Transformations1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2016 Oct/Nov, Paper 2 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.