Cambridge IGCSE Mathematics 0580 — 2018 Oct/Nov Paper 1 · Variant 2
0580/12/O/N/18 · 20 questions · 56 marks · ≈63 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 down the type of angle shown in the diagram
1 Write down the type of angle shown in the diagram. ................................................ [1]
Mark scheme: Question Answer Marks Partial Marks 1 Obtuse 1
Q2 · Write down the size of one angle in an equilateral triangle
2 Write down the size of one angle in an equilateral triangle. ................................................ [1]
Mark scheme: 2 60[°] 1
Q3 · Write 23 000 in standard form
3 Write 23 000 in standard form. ................................................ [1]
Mark scheme: 3 2.3 × 104 1
Question 4
4 Work out. - 2 - 1 (a) - e 5o e 1o [1] f p - 3 (b) 7 e 4o [1] f p
Mark scheme: 4(a) − 1 1 4 4(b) − 21 1 28
Question 5
5 Expand. 2x 3 - x 2 ^ h ................................................ [2]
Mark scheme: 5 6x – 2x3 final answer 2 B1 for 6x or –2x3
Q6 · Triangle ABC and triangle DEF are similar
6 Triangle ABC and triangle DEF are similar. E NOT TO SCALE B 16 cm A C D F 18 cm 27 cm Find DE. DE = ......................................... cm [2]
Mark scheme: 6 24 2 DE 16 M1 for = oe or scale factor, 1.5 27 18 2 or seen 3
Q7 · The diagram shows a right-angled triangle
7 The diagram shows a right-angled triangle. NOT TO 16 cm SCALE 52° x cm Use trigonometry to calculate the value of x. x = ............................................... [2]
Mark scheme: 7 9.85 or 9.850 to 9.851 2 x M1 for cos 52 = oe or better 16
Q8 · T = a 2 + 4b Find the value of T when a = 5 and b = 3
8 T = a 2 + 4b Find the value of T when a = 5 and b = 3. T = ............................................... [2]
Mark scheme: 8 37 2 B1 for 25 or 12
Question 9
9 Complete the table. Fraction Percentage 1 = 4 = 47% 3 = 5 [3]
Mark scheme: 9 25% 3 B1 for each 47 100 60%
Q10 · The scale drawing shows the positions of town A and town B
10 The scale drawing shows the positions of town A and town B. The scale is 1 centimetre represents 12 kilometres. North B North Scale: 1 cm to 12 km A (a) Work out the actual distance from town A to town B. .......................................... km [2] (b) Measure the bearing of town B from town A. ................................................ [1]
Mark scheme: 10(a) 102 2 B1 for 8.3 to 8.7 10(b) [0]64[°] 1
Q11 · A bag contains 6 blue counters and 2 red counters only
11 (a) A bag contains 6 blue counters and 2 red counters only. A counter is taken from the bag at random. Draw an arrow (↓) on the probability scale to show the probability of taking (i) a blue counter, 0 1 [1] (ii) a yellow counter. 0 1 [1] (b) Another bag contains green counters and black counters only. A counter is taken from the bag at random. The probability of taking a green counter is 0.64 . Work out the probability of taking a black counter. ................................................ [1]
Mark scheme: 11(a)(i) 3 1 Clear indication Arrow at 4 11(a)(ii) Arrow at 0 1 Clear indication 11(b) [0].36 oe 1
Q12 · Samit invests $1800 at a rate of 4.5% per year simple interest
12 Samit invests $1800 at a rate of 4.5% per year simple interest. Work out the value of his investment at the end of 4 years. $ ............................................... [3]
Mark scheme: 12 2124 3 1800 × 4.5 × 4 M2 for 1800 + 100 1800 × 4.5 × 4 or M1 for 100
Q13 · The diagram shows a conversion graph between pounds (£) and dollars ($)
13 The diagram shows a conversion graph between pounds (£) and dollars ($). 30 20 Pounds (£) 10 0 0 10 20 30 40 Dollars ($) Ana finds the same watch on sale in a shop and on the internet. The shop price is $120. The internet price is £90. Use the conversion graph to find which price is lower. Show your working clearly. The ........................ price is lower. [3]
Mark scheme: 13 Any example of equivalence from the M1 Examples conversion graph Dollars ($) Pounds (£) 5 3.5 10 7 20 14 30 21 40 28 7 5 14 to 14.5 10 21 15 28 to 29 20 Shop and [£]81 to [£]87 A2 A1 for [£]81 to [£]87 or [$]126 to or [$]126 to [$]138 nfww [$]138 If M0 allow SC1 for [$]120 = [£]81 to [£]87 or [£]90 = [$]126 to [$]138 with ‘shop’ as the answer
Q14 · The expression for the nth term of a sequence is 5n 2
14 (a) The expression for the nth term of a sequence is 5n 2. Work out the third term in this sequence. ................................................ [1] (b) 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: 14(a) 45 1 14(b) 6n – 10 oe 2 B1 for 6n + c or kn – 10 (k ≠ 0)
Q15 · 120 students choose what they want to do when they leave school
15 120 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: 15 Correct pie chart 4 B3 for correct chart no labels e.g. or for 2 correct sectors with or without labels or B2 for 3 correct angles seen (171°, 135° and 54°) or 3 correct percentages (47.5%, 37.5% and 15%) or M1 for method 57 57 e.g. × 360, 57 × 3 or × 100 oe 120 120 or one correct sector on the pie chart
Question 16
16 Calculate. (a) .413 ................................................ [1] (b) - 4 - 5 2 - 2 # 4 # - 3 ^ h ................................................ [1] 4.88 - 2.36 (c) 5.3 + 1.9 ................................................ [1] (d) 56.25 - 3 15.625 ................................................ [1]
Mark scheme: 16(a) 68.921 1 16(b) –53 1 16(c) [0].35 1 16(d) 5 1
Q17 · Write 56 as a product of its prime factors
17 (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: 17(a) 23 × 7 or 2 × 2 × 2 × 7 2 B1 for identifying 2 and 7 as the only prime factors 17(b) 168 2 B1 for 168k or 2 × 2 × 2 × 3 × 7 oe or for listing multiples of each up to 168
Q18 · The diagram shows a pentagon ABCDE
18 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: 18(a) Correct ruled bisector with two pairs of 2 B1 for correct ruled bisector with arcs no/wrong arcs 18(b) Correct arc centre E radius 3 cm inside 1 pentagon 18(c) Correct region shaded 1 Dependent on at least B1 in part (a) and 1 mark in part (b) and a closed region
Q19 · Solve the simultaneous equations
19 Solve the simultaneous equations. You must show all your working. 2x + 5y = 60 3x - 2y = 14 x = ............................................... y = ............................................... [4]
Mark scheme: 19 multiplying both equations to get a M1 common coefficient correctly adding or subtracting their M1 equations [x = ] 10 A1 [y = ] 8 A1 If zero scored then SC1 for two answers which satisfy one of the original equations or for 2 correct answers with no working
Q20 · Y 4 3 L A 2 1 −4 −3 −2 −1 0 1 2 3 4 x −1 −2 −3 −4 (a) Write down the co-ordinates of…
20 y 4 3 L A 2 1 −4 −3 −2 −1 0 1 2 3 4 x −1 −2 −3 −4 (a) Write down the co-ordinates of point A. (.................... , ....................) [1] (b) On the grid, plot point B (1, –3). [1] (c) Find the gradient of line L. ................................................ [2] (d) Find the equation of line L in the form y = mx + c . y = ............................................... [1]
Mark scheme: 20(a) –3, 2 1 20(b) B plotted at (1, –3) 1 20(c) 1 2 Rise 2 2 −− 1 or 0.5 M1 for e.g. or 2 Run 4 2 −− 4 20(d) 1 1 FT their (c) e.g.[ y =] their (c) x + 1 oe y = x + 1 oe 2
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.
2Algebraic manipulation1Angles1Coordinates1Equations1Fractions, decimals and percentages1Geometrical constructions1Geometrical terms1Introduction to probability1Money1Powers and roots1Ratio and proportion1Right-angled triangles1Scale drawings1Sequences1Similarity1Standard form1Statistical charts and diagrams1Types of number1What you needed in this session
Cambridge’s own grade thresholds for 2018 Oct/Nov, Paper 1 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.