Cambridge IGCSE Mathematics 0580 — 2018 Oct/Nov Paper 1 · Variant 1
0580/11/O/N/18 · 23 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 · Work out 8% of 140
1 Work out 8% of 140. .................................................[1]
Mark scheme: Question Answer Marks Partial Marks 1 11.2 oe 1
Q2 · The exchange rate between dollars and euros (€) is $1 = €0.88
2 The exchange rate between dollars and euros (€) is $1 = €0.88 . Change $350 into euros. € ................................................[1]
Mark scheme: 2 308 1
Q3 · A 5 .3 Simplify 2 a .................................................[1]
a 5 .3 Simplify 2 a .................................................[1]
Mark scheme: 3 a 3 cao 1
Q4 · Write these in order of size, starting with the smallest
4 Write these in order of size, starting with the smallest. 3 7 0.38 30 % 8 20 ..................... 1 ..................... 1 ..................... 1 ..................... [2] smallest
Mark scheme: 4 7 3 2 B1 for three in correct order 30%, , , 0.38 or M1 for 0.35 and 0.375 20 8
Q5 · O Measure the radius of the circle, centre O
5 (a) O Measure the radius of the circle, centre O. Give your answer in centimetres. .......................................... cm [1] (b) Write down the mathematical name of this polygon. ................................................. [1]
Mark scheme: 5(a) 3.7 1 5(b) [Regular] hexagon 1
Q6 · Write 257 964 correct to the nearest thousand
6 (a) Write 257 964 correct to the nearest thousand. ................................................. [1] (b) Write 0.060 31 correct to 2 significant figures. ................................................. [1]
Mark scheme: 6(a) 258 000 1 6(b) [0].060 cao 1
Q7 · Draw the line of symmetry on the shape below
7 (a) Draw the line of symmetry on the shape below. [1] (b) Shade one more square so that this pattern has rotational symmetry of order 2. [1]
Mark scheme: 7(a) 1 7(b) 1
Q8 · A bag contains 50 counters
8 A bag contains 50 counters. 10 of the counters are red. One of the counters is taken from the bag at random. (a) Draw an arrow ( ) on the scale to show the probability that this counter is red. 0 0.5 1 [1] (b) Find the probability that the counter is not red. ................................................. [1]
Mark scheme: 8(a) Arrow at 0.2 1 8(b) 0.8 oe 1
Q9 · On Monday, the lowest temperature was –12 °C
9 (a) On Monday, the lowest temperature was –12 °C. The highest temperature was 4 °C. Work out the difference between these temperatures. ........................................... °C [1] (b) On Tuesday, the highest temperature was –3 °C. The lowest temperature was 8 °C lower than this. Work out the lowest temperature on Tuesday. ........................................... °C [1]
Mark scheme: 9(a) 16 1 9(b) –11 1
Q10 · Shape A is shown on the grid
10 Shape A is shown on the grid. A On the grid, enlarge shape A by scale factor 3. [2]
Mark scheme: 10 Correct ruled enlargement 2 B1 for two sides correct or for enlargement incorrect scale factor
Question 11
11 Work out. 2 (a) 6 c- 1m [1] f p 5 2 (b) - c- 3m c4m [1] f p
Mark scheme: 11(a) 12 1 −6 11(b) 3 1 −7
Q12 · P A 8 cm 14 cm NOT TO SCALE B Q 12 cm C x cm R Triangle ABC is similar to triangle PQR
12 P A 8 cm 14 cm NOT TO SCALE B Q 12 cm C x cm R Triangle ABC is similar to triangle PQR. Find the value of x. x = ................................................ [2]
Mark scheme: 12 21 nfww 2 x 12 B1 for = oe, or better 14 8 4 or scale factor, i.e. 1.75 or oe seen 7
Q13 · Calculate the size of one exterior angle of a regular 15-sided polygon
13 Calculate the size of one exterior angle of a regular 15-sided polygon. ................................................. [2]
Mark scheme: 13 24 nfww 2 M1 for 360 ÷ 15 If zero scored, SC1 for answer of 156
Q14 · Shohan cycles from home to the library
14 Shohan cycles from home to the library. He stops at the post office on the way. The travel graph shows his journey. 10 Library 8 Distance 6 from home (km) 4 2 Home 0 10 00 10 15 10 30 10 45 11 00 11 15 11 30 11 45 12 00 Time (a) Write down the time Shohan arrives at the post office. ................................................. [1] (b) Shohan stays at the library for 25 minutes. He then cycles home at a constant speed of 18 km/h. Complete the travel graph. [2]
Mark scheme: 14(a) 10 25 1 14(b) Graph completed correctly 2 B1 for line from (10 55, 9) to (11 20, 9) B1 FT for line from (their 11 20, 9) to (their 11 20 + 30 min, 0)
Q15 · The diagram shows the top of a table
15 The diagram shows the top of a table. 1.2 m NOT TO 0.4 m SCALE 0.9 m 0.7 m (a) Calculate the perimeter. ............................................ m [1] (b) Calculate the area. ........................................... m2 [2]
Mark scheme: 15(a) 4.2 1 15(b) 0.83 [m2] or 8300 cm2 2 M1 for 0.4 × 1.2 + (0.9 – 0.4) × 0.7 or 0.7 × 0.9 + (1.2 – 0.7) × 0.4 or 1.2 × 0.9 – (0.9 – 0.4) × (1.2 – 0.7) or for one of the above, consistently using cm e.g. 40 × 120 + (90 – 40) × 70
Q16 · 116 Without using your calculator, work out ' 2
3 116 Without using your calculator, work out ' 2 . 8 4 You must show all your working and give your answer as a fraction in its simplest form. ................................................. [3]
Mark scheme: 16 3 4 3 18 M2 9 × oe or ÷ oe with common B1 for oe seen 8 9 8 8 4 denominator 3 4 or M1 for ×their 8 9 1 A1 cao 6
Q17 · A teacher gives her Spanish students a test each week
17 A teacher gives her Spanish students a test each week. Some of the students’ marks for two weeks are shown in the scatter diagram. 40 35 30 25 Mark in week 2 20 15 10 5 0 0 5 10 15 20 25 30 35 40 Mark in week 1 (a) Leo scored 28 marks in week 1 and 30 marks in week 2. On the scatter diagram, plot a point to show Leo’s marks. [1] (b) On the scatter diagram, draw a line of best fit. [1] (c) Sonia scored 20 marks in week 1 but was absent in week 2. Use your line of best fit to estimate a mark for Sonia in week 2. ................................................. [1]
Mark scheme: 17(a) Point (28 , 30) marked 1 17(b) Ruled line of best fit 1 17(c) 22 to 26 1 FT their ruled line of best fit with positive gradient
Q18 · Jan invests $800 at a rate of 3% per year simple interest
18 Jan invests $800 at a rate of 3% per year simple interest. Calculate the value of her investment at the end of 4 years. $ ................................................ [3]
Mark scheme: 18 896 3 800 × 4 × 3 M2 for 800 + oe 100 800 × 4 × 3 or M1 for oe 100
Q19 · These are the first five terms in a sequence
19 These are the first five terms in a sequence. 8 11 14 17 20 (a) Find the next term. ................................................. [1] (b) Find an expression for the nth term. ................................................. [2]
Mark scheme: 19(a) 23 1 19(b) 3n + 5 oe 2 B1 for 3n + j or kn + 5, k ≠ 0
Q20 · A water tank in the shape of a cuboid has length 1.5 metres and width 1 metre
20 A water tank in the shape of a cuboid has length 1.5 metres and width 1 metre. The water in the tank is 60 centimetres deep. Calculate the number of litres of water in the tank. ....................................... litres [3]
Mark scheme: 20 900 3 150 × 100 × 60 M2 for oe 1000 or M1 for 150 × 100 × 60 or 1.5 [× 1] × 0.6 or B1 for figs 9
Q21 · In 2016, the population of Nigeria was 187 000 000
21 (a) In 2016, the population of Nigeria was 187 000 000. Write 187 000 000 in standard form. ................................................. [1] (b) In 2016, the population of South Africa was .550 # 107. In 2016, the population of Kenya was .472 # 107. Calculate the difference between the population of South Africa and the population of Kenya. Give your answer in standard form. ................................................. [2]
Mark scheme: 21(a) 1.87 × 108 1 21(b) 7.8 × 106 2 B1 for answer figs 78
Q22 · A B NOT TO x° SCALE 56° L M C y° N The diagram shows an isosceles triangle ABC with AB =…
22 A B NOT TO x° SCALE 56° L M C y° N The diagram shows an isosceles triangle ABC with AB = AC. LCM and BCN are straight lines and LCM is parallel to AB. Angle ACL = 56°. Find the value of x and the value of y. x = ................................................ y = ................................................ [4] Question 23 is printed on the next page.
Mark scheme: 22 [x = ] 62 2 B1 for 56 identified as angle A (180 − 56 ) or M1 for 2 [y = ] 118 2 FT for 2 marks their acute x + their y =180 or 56 + their acute x = their y or B1 for any of ACB, BCM or LCN = 62 or their acute x or M1 for 180 – 62 or 180 – their acute x or 56 + 62 or 56 + their acute x
Q23 · Expand the brackets and simplify fully
23 (a) Expand the brackets and simplify fully. 5 (x - 3) + 2 (3x + 1) ................................................. [2] (b) Solve the simultaneous equations. You must show all your working. 4x - y = 14 3x + 2y = 5 x = ................................................ y = ................................................ [3]
Mark scheme: 23(a) 11x – 13 final answer 2 B1 for 5x – 15 or 6x + 2 or for answer of 11x + j or kx – 13 23(b) Correctly eliminating one variable M1 [x = ] 3 A1 [y = ] –2 A1 If zero scored, SC1 for 2 values satisfying one of the original equations or for 2 correct answers with no working
What was in this paper
The subtopics covered by these 23 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Fractions, decimals and percentages2Rates2Angles1Equations1Indices II1Introduction to probability1Limits of accuracy1Percentages1Ratio and proportion1Scatter diagrams1Sequences1Similarity1Standard form1Surface area and volume1Symmetry1The four operations1Transformations1Units of measure1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2018 Oct/Nov, Paper 1 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.