Cambridge IGCSE Mathematics 0580 — 2018 Oct/Nov Paper 2 · Variant 2
0580/22/O/N/18 · 25 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 23 000 in standard form
1 Write 23 000 in standard form. ................................................ [1]
Mark scheme: Question Answer Marks Partial Marks 1 2.3 × 104 1
Q2 · B M NOT TO SCALE A O D N E The diagram shows a circle, centre O
2 B M NOT TO SCALE A O D N E The diagram shows a circle, centre O. AB and DE are chords of the circle. M is the mid-point of AB and N is the mid-point of DE. AB = DE = 9 cm and OM = 5 cm. Find ON. ON = ......................................... cm [1]
Mark scheme: 2 5 1
Q3 · Calculate .0125 - 2
33 Calculate .0125 - 2 . ................................................ [1]
Mark scheme: 3 4 1
Question 4
4 Expand. 2x 3 - x 2 ^ h ................................................ [2]
Mark scheme: 4 6x – 2x3 final answer 2 B1 for 6x or –2x3
Q5 · 25 Without using a calculator, work out +
1 25 Without using a calculator, work out + . 15 5 Write down all the steps of your working and give your answer as a fraction in its simplest form. ................................................ [2]
Mark scheme: 5 1 2 × 3 M1 1 6 + or better e.g. + 15 5 × 3 15 15 Allow any correct common denominator 15k 7 A1 cao 15
Question 6
6 Solve. 7m - 2 H 19 ................................................ [2]
Mark scheme: 6 m ⩾ 3 final answer 2 M1 for correct first step e.g. 7m ⩾ 19 + 2
Q7 · C = x | x is an integer and 5 1 x 1 12 D = 5 , 10 " , " , (a) Put a ring around the…
7 C = x | x is an integer and 5 1 x 1 12 D = 5 , 10 " , " , (a) Put a ring around the correct statement from the list below. D = Q C k D = 10 6 ! D D f C [1] " , (b) Find n C j D ^ h. ................................................ [1]
Mark scheme: 7(a) C ∩ D = {10} 1 7(b) 7 1
Question 8
8 Factorise. xy + 5y + 2x + 10 ................................................ [2]
Mark scheme: 8 (x + 5)(y + 2) final answer 2 B1 for y(x + 5) + 2(x + 5) or x(y + 2) + 5(y + 2)
Q9 · There are 30 000 lions in Africa
9 There are 30 000 lions in Africa. The number of lions in Africa decreases exponentially by 2% each year. Find the number of lions in Africa after 6 years. Give your answer correct to the nearest hundred. ................................................ [2]
Mark scheme: 9 26 600 cao 2 6 2 M1 for 30 000 × 1 − oe 100
Q10 · Find the mid-point of AB where A = (w, r) and B = (3w, t)
10 Find the mid-point of AB where A = (w, r) and B = (3w, t). Give your answer in its simplest form in terms of w, r and t. (..................... , .....................) [2]
Mark scheme: 10 r +t 2 r +t 2 w, final answer B1 for 2w oe nfww or oe 2 2
Q11 · An equilateral triangle has side length 12 cm, correct to the nearest centimetre
11 An equilateral triangle has side length 12 cm, correct to the nearest centimetre. Find the lower bound and the upper bound of the perimeter of the triangle. Lower bound = ......................................... cm Upper bound = ......................................... cm [2]
Mark scheme: 11 34.5 and 2 B1 for 11.5 or 12.5 seen 37.5 final answers or M1 for (12 – 0.5) × 3 or (12 + 0.5) × 3
Q12 · X° is an obtuse angle and sin x° = 0.43
12 x° is an obtuse angle and sin x° = 0.43 . Find the value of x. x = ............................................... [2]
Mark scheme: 12 154.5 or 154.5… 2 B1 for 25.5 or 25.46 to 25.47 or M1 for 180 – sin–1(0.43) oe
Q13 · These are the first five terms of a sequence
13 These are the first five terms of a sequence. - 4 2 8 14 20 Find an expression for the nth term of this sequence. ................................................ [2]
Mark scheme: 13 6n – 10 oe 2 B1 for 6n + c or kn – 10 (k ≠ 0)
Q14 · Y 8 7 6 5 4 3 2 1 0 1 2 3 4 x By shading the unwanted regions of the grid, find and label…
14 y 8 7 6 5 4 3 2 1 0 1 2 3 4 x By shading the unwanted regions of the grid, find and label the region R that satisfies the following four inequalities. x G 3 x H 2 y G 2x + 1 y H 4 - x [3]
Mark scheme: 14 Correct reggion identifieed 3 B marks or SC1 for 1 2 1 2 3 2 R 0 1 2 1
Q15 · - 3 15 M = e- 1 2o (a) Find 3M
5 - 3 15 M = e- 1 2o (a) Find 3M. 3M = [1] f p (b) Find M -1 . M -1 = [2] f p
Mark scheme: 15(a) 15 −9 1 − 3 6 15(b) 1 2 3 2 2 3 oe isw B1 for k soi or det = 7 soi 7 1 5 1 5
Q16 · X 2 - 12x + a = ( x + b) 2 Find the value of a and the value of b
16 x 2 - 12x + a = ( x + b) 2 Find the value of a and the value of b. a = ............................................... b = ............................................... [3]
Mark scheme: 16 (a = ) 36 3 B2B for a = 366 (b = ) –6 oro M1 for b == –6 oro x2 + bx + bx + b2 or better oro b2 = a
Q17 · Y D NOT TO SCALE C O x The diagram shows the points C(–1, 2) and D(9, 7)
17 y D NOT TO SCALE C O x The diagram shows the points C(–1, 2) and D(9, 7). Find the equation of the line perpendicular to CD that passes through the point (1, 3). Give your answer in the form y = mx + c . y = ............................................... [4]
Mark scheme: 17 –2x + 5 4 7 − 2 M1M for oe 9 −−−1 −1 M1M for gradiient of perpeendicular = theirt 0.5 M1M for (1, 3)) correctly suubstituted intto their y = –2x + c
Q18 · 120 students choose what they want to do when they leave school
18 120 students choose what they want to do when they leave school. Their choices are shown in the table. Choice Number of students University 57 Training 45 Work 18 Complete the pie chart to show this information. Label each sector clearly. [4]
Mark scheme: 18 Correct pie chart e.g. 4 B3B for correcct chart no laabels oro for 2 correect sectors wwith or withouut labels oro B2 for 3 correctc angless seen (171°, 135° and 54°)5 oro 3 correct percentagesp ((47.5%, 37.55% and 15%)) oro M1 for method 57 57 e.g.e × 360,3 57 × 33 or ×× 100 oe 120 120 or one correctc sectorr on the pie chartc
Q19 · The diagram shows a pentagon ABCDE
19 The diagram shows a pentagon ABCDE. A E B D C (a) Using a straight edge and compasses only, construct the bisector of angle BCD. [2] (b) Draw the locus of the points inside the pentagon that are 3 cm from E. [1] (c) Shade the region inside the pentagon that is • less than 3 cm from E and • nearer to DC than to BC. [1]
Mark scheme: 19(a) Correct rulled bisector withw two 2 B1B for correcct ruled bisecctor with no//wrong arcs pairs of arccs 19(b) Correct arcc centre E raadius 3 cm 1 inside penttagon 19(c) Correct reggion shaded 1 DependentD ono at least B11 in part (a) anda 1 mark in partp (b) and a closed regiion
Q20 · Make m the subject of the formula
20 Make m the subject of the formula. 3 m x = 2 - m m = ............................................... [4]
Mark scheme: 20 2 x 4 M1 for correctly clearing the denominator and oe final answer 3+ x expanding bracket M1 for correctly collecting terms in m on one side and terms not in m on the other M1 for correct factorising M1 for correct division dependent on m appearing only once in a factorised expression
Q21 · A NOT TO M N SCALE C B 10 cm The diagram shows an equilateral triangle ABC with sides of…
21 A NOT TO M N SCALE C B 10 cm The diagram shows an equilateral triangle ABC with sides of length 10 cm. AMN is a sector of a circle, centre A. M is the mid-point of AC. Work out the area of the shaded region. ......................................... cm2 [4]
Mark scheme: 21 30.2 or 30.20 to 30.21… 4 2 1 60 10 M3 for × 10 × 10 × sin60 − × π × 2 360 2 k 10 2 or M1 for × π × oe 360 2 1 and M1 for × 10 × 10 × sin c oe 2
Q22 · B NOT TO 8 cm SCALE 5.5 cm A 16.2 cm The diagram shows a cuboid with dimensions 5.5 cm, 8…
22 B NOT TO 8 cm SCALE 5.5 cm A 16.2 cm The diagram shows a cuboid with dimensions 5.5 cm, 8 cm and 16.2 cm. Calculate the angle between the line AB and the horizontal base of the cuboid. ................................................ [4]
Mark scheme: 22 25.1 or 25.06… 4 8 M3 for tan = oe 16.2 2 + 5.5 2 or M2 for 16.2 2 + 5.5 2 or M1 for 16.2 2 + 5.5 2 or B1 for identifying correct angle
Q23 · Write 56 as a product of its prime factors
23 (a) Write 56 as a product of its prime factors. ................................................ [2] (b) Find the lowest common multiple (LCM) of 56 and 42. ................................................ [2]
Mark scheme: 23(a) 23 × 7 or 2 × 2 × 2 × 7 2 B1 for identifying 2 and 7 as the only prime factors 23(b) 168 2 B1 for 168k or 2 × 2 × 2 × 3 × 7 oe or for listing multiples of each up to 168
Q24 · The time, t minutes, 80 students each spend completing their homework is recorded
24 The time, t minutes, 80 students each spend completing their homework is recorded. The cumulative frequency diagram shows the results. 80 70 60 50 Cumulative 40 frequency 30 20 10 0 t 0 10 20 30 40 50 60 Time (minutes) Use the cumulative frequency diagram to find an estimate of (a) the median, ......................................... min [1] (b) the interquartile range, ......................................... min [2] (c) the number of students who spend more than 40 minutes completing their homework. ................................................ [2] Question 25 is printed on the next page.
Mark scheme: 24(a) 25 1 24(b) 12 2 B1 for 16 or 28 24(c) 5 2 B1 for 75
Q25 · F (x) = x 3 g ()x = 5x + 2 (i) Find gf ()x
25 (a) f (x) = x 3 g ()x = 5x + 2 (i) Find gf ()x . ................................................ [1] (ii) Find g -1 ()x . g -1 ()x = ............................................... [2] (b) h (x) = ax 2 + 1 Find the value of a when h (- 2) = 21. a = ............................................... [2]
Mark scheme: 25(a)(i) 5x3 + 2 final answer 1 25(a)(ii) x − 2 2 M1 for correct first step final answer y 2 5 e.g. y – 2 = 5x, x = 5y + 2, = x + 5 5 25(b) 5 2 M1 for a × (–2)2 + 1 = 21
What was in this paper
The subtopics covered by these 25 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
4Inequalities2Averages and measures of spread1Circles, arcs and sectors1Equations1Equations of linear graphs1Exponential growth and decay1Functions1Geometrical constructions1Length and midpoint1Limits of accuracy1Powers and roots1Pythagoras’ theorem1Right-angled triangles1Sequences1Sets1Standard form1Statistical charts and diagrams1The four operations1Trigonometric functions1Types of number1What you needed in this session
Cambridge’s own grade thresholds for 2018 Oct/Nov, Paper 2 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.