Cambridge IGCSE Mathematics 0580 — 2006 Oct/Nov Paper 1 · Variant 1
0580/11/O/N/06 · 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 paper8 pages
Mark scheme4 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · At noon one day the temperature is −9.5 °C
1 At noon one day the temperature is −9.5 °C. For By midnight the temperature has fallen by 3.6 °C. Examiner's What is the temperature at midnight? Use Answer °C [1]
Mark scheme: Question Answers Mark Notes 1 −13.1 1
Q2 · Insert brackets to make the following statement correct
2 Insert brackets to make the following statement correct. 2 × 3 – 4 + 5 = 3 [1]
Mark scheme: 2 2 × ( 3 − 4 ) + 5 = 3 1 & no other brackets
Q3 · Which word describes the correlation in the scatter graph below?
3 Which word describes the correlation in the scatter graph below? positive negative none Answer [1]
Mark scheme: 3 Negative (allow –ve) 1 Not allow ‘N’ or ‘n’ or ‘No’
Q4 · The nth term of a sequence is given by n2+2
4 The nth term of a sequence is given by n2+2. Work out the 4th term. Answer [1]
Mark scheme: 4 18 1
Q5 · $1 = 0.78 euros Use this exchange rate to change $15.50 into euros
5 $1 = 0.78 euros Use this exchange rate to change $15.50 into euros. Answer euros [1]
Mark scheme: 5 12.09 or 12.1 1 Not 12.10
Q6 · Factorise completely 2a2b − 6a
6 Factorise completely 2a2b − 6a. For Examiner's Use Answer [2]
Mark scheme: 6 2a( ab − 3 ) final answer. 2 SC1 for 2( a 2 b − 3a ) or a( 2ab − 6 ) or 2a( ab + 3 ) or 2a( ab – 6 ) final answer.
Q7 · Change 56.1 metres into kilometres
7 (a) Change 56.1 metres into kilometres. Answer(a) km [1] (b) Change 15.3 metres into millimetres. Answer(b) mm [1]
Mark scheme: 7 (a) 0.0561 1 (Answers may be in standard form) (b) 15300 1
Q8 · Simplify 3x2y × x4y2
8 Simplify 3x2y × x4y2. Answer [2]
Mark scheme: 8 3x 6y 3 or 3(x 2y) 3 2 SC1 for x 6or y 3 seen in final answer
Q9 · Work out 433 , giving (a) your full calculator display, Answer(a) [1] (b) your answer…
9 Work out 433 , giving (a) your full calculator display, Answer(a) [1] (b) your answer correct to the nearest thousand. Answer(b) [1]
Mark scheme: 9 (a) 79507 1 (b) 80000 1ft ft provided (a) > 500 and not a multiple of 1000.
Q10 · Write these fractions in order with the smallest first
10 Write these fractions in order with the smallest first. 33 2 6 50 3 10 Answer < < [2]
Mark scheme: 10 6 33 2 2 SC1 for reverse order. M1- at least 2 fractions correctly compared in 10 50 3 the same form. (decimal, percentage or common denominator) 15
Q11 · Solve the equation 5x − 2 = 10x − 8
11 Solve the equation 5x − 2 = 10x − 8. For Examiner's Use Answer x = [2]
Mark scheme: 11 6 2 M1 for -2 + 8 = 10x – 5x oe or better. (x = ) oe isw 5
Q12 · Only two of the following five statements are correct
12 Only two of the following five statements are correct. A 0.07077 0.07707 B 0.07077 ≠ 0.07707 C 0.07077 = 0.07707 D 0.07077 < 0.07707 E 0.07077 > 0.07707 Write down the letters which correspond to the two correct statements. Answer and [2]
Mark scheme: 12 B (and) D 1,1 Either way round. -1 each extra letter.
Q13 · Work out 2.6 × 10−3 + 9.1 × 10−4
13 Work out 2.6 × 10−3 + 9.1 × 10−4. Write your answer in standard form. Answer [2]
Mark scheme: 13 3.51 × 10 −3 2 B1 for figures 351 seen
Q14 · The length of a mirror is 15.6 centimetres correct to the nearest millimetre
14 The length of a mirror is 15.6 centimetres correct to the nearest millimetre. Complete the statement below about the length of the mirror. Answer cm length < cm[2]
Mark scheme: 14 15.55 ( ≤ length < ) 15.65 2 1 mark for each. SC1 for fully correct but reversed.
Q15 · A truck uses 2.5 litres of fuel to travel 8 kilometres
15 A truck uses 2.5 litres of fuel to travel 8 kilometres. (a) How far will the truck travel on 1 litre of fuel? Answer(a) km [1] (b) How far will the truck travel on 120 litres of fuel? Answer(b) km [1]
Mark scheme: 15 (a) 3.2 1 (b) 384 1 ft their (a) × 120.
Q16 · Write down the value of x when For Examiner's (a) 2 x = 8, Use Answer(a) x= [1] x 1 (b) 3…
16 Write down the value of x when For Examiner's (a) 2 x = 8, Use Answer(a) x= [1] x 1 (b) 3 = . 81 Answer(b) x= [1]
Mark scheme: 16 (a) 3 or 2 3 = 8 1 SC1 for 2 3 and 3 −4 in the answer spaces −4 1 (b) −4 or 3 = 81
Q17 · The surface area of a sphere with radius r is A = 4πr2
17 The surface area of a sphere with radius r is A = 4πr2. (a) Calculate the surface area of a sphere with a radius of 5 centimetres. Answer(a) cm2 [1] (b) Make r the subject of the formula A = 4πr2. Answer(b) r = [2]
Mark scheme: 17 (a) art 314 1 A A (b) oe 2 M1 for seen 4π 4π
Q18 · 100 B 80 60 Distance from A 40 (km) 20 A 10 00 11 00 12 00 13 00 14 00 15 00 Time of day…
18 100 B 80 60 Distance from A 40 (km) 20 A 10 00 11 00 12 00 13 00 14 00 15 00 Time of day (a) Carla drives from town A to a supermarket. At 11 00 she continues her journey to town B, driving at 80 km/h. The first part of the journey is shown on the grid above. (i) How many minutes is Carla at the supermarket? Answer(a) (i) min [1] (ii) Draw the rest of her journey to town B on the grid. [1] (b) Carla spends 1 hour in town B and then drives back to town A, at a constant speed, arriving at 14 30. Show this information on the grid. [2]
Mark scheme: 18 (a)(i) 30 1 (ii) Straight line from (11 00, 20) to (11 45, 80) 1 Ignore all beyond (11 45, 80) (b) ‘Correct’ horizontal line 1 Horizontal line @ 80, 4 units long. ‘Correct’ return journey line 1 Line to (14 30, 0) 19 IGCSE - OCT/NOV 2006 0580, 0581 1
Q19 · A shopkeeper buys some ready-made meals from a supplier
19 A shopkeeper buys some ready-made meals from a supplier. For Examiner's (a) Complete the bill shown below. Use Meal Cost of one meal Number of meals Total cost Chicken curry $3.48 15 $ Pizza $2.99 28 $ [1] (b) He sells all 15 Chicken curry meals for $4.00 each. Work out the total profit on these meals. Answer(b) $ [1] (c) He sells 15 Pizzas for $3.55 each but is unable to sell the rest. Calculate his loss on the Pizzas as a percentage of the total cost of the Pizzas. Answer(c) % [2]
Mark scheme: 19 (a) 52.2(0) 83.7(2) 1 (b) 7.8(0) 1ft 60 − their ($3.48 × 15) (c) art 36.4 allow –ve. 2ft M1 for ((their 83.72 − 15 × 3.55)/their 83.72) × Accept 36www 100 or 100 − ((15 × 3.55)/their 83.72) × 100
Q20 · Draw the lines of symmetry on the two letters below
20 (a) Draw the lines of symmetry on the two letters below. [2] (b) Write down the order of rotational symmetry for each of the figures below. Order Order [2]
Mark scheme: 20 (a) 2 correct lines on H 1 Ruled not essential in either. Judge by eye. 1 correct line on W 1 No extraneous lines on either. (b) 1 1 Allow 0 or indication of no rotational symmetry. 2 1
Q21 · Write the following as single vectors
21 Write the following as single vectors. For Examiner's Use 2 1 3 (a) + − − 1 3 0 Answer(a) [2] 5 (b) 6 −4 Answer(b) [2]
Mark scheme: 21 Ignore ‘fraction’ lines in (a) and (b) 0 Allow coordinate form (a) Final ans 2 1 mark for each correct component. 4 30 (b) Final ans 2 1 mark for each correct component. −24
Q22 · 13.5 + 16 4.8 − (22 ÷ 13 ) (a) Rewrite this calculation with each number rounded to 1…
22 13.5 + 16 4.8 − (22 ÷ 13 ) (a) Rewrite this calculation with each number rounded to 1 significant figure. Answer(a) [2] (b) Use your answer to part (a) to estimate the answer to the calculation. Show your working and write your answer correct to 1 significant figure. Answer(b) [1] (c) Use your calculator to find the answer to the original calculation correct to 3 significant figures. Answer(c) [2]
Mark scheme: 22 10 + 20 (a) 2 SC1 for 3 or 4 of the numbers given to 1 5 − ( 20 ÷ 10) significant figure. (b) 10 cao. 1 (c) 9.49 cao. 2 B1 for 9.485(5)… to 9.493 seen. (Allows for 22 ÷ 13 rounded to 3sf) If zero, SC1 for 9.5www as final answer 17 (Not 9.50 but check for possible B1)
Q23 · The diagram shows a six-sided spinner
23 The diagram shows a six-sided spinner. For Examiner's Use 6 1 5 2 4 3 5 (a) Amy spins a biased spinner and the probability she gets a two is . 36 Find the probability she (i) does not get a two, Answer(a) (i) [1] (ii) gets a seven, Answer(a) (ii) [1] (iii) gets a number on the spinner less than 7. Answer(a) (iii) [1] (b) Joel spins his blue spinner 99 times and gets a two 17 times. Write down the relative frequency of getting a two with Joel’s spinner. Answer(b) [1] 21 (c) The relative frequency of getting a two with Piero’s spinner is . 102 Which of the three spinners, Amy’s, Joel’s or Piero’s, is most likely to give a two? Answer(c) [1]
Mark scheme: 23 (a) (i) 3631 oe isw 1 Fraction, decimal or percentage only. (ii) 0 Final ans 1 06 , 360 , 0% or zero. Not allow ‘no’, none, 70 or 0/0. (iii) 1 1 Allow 66 or 3636 or 100%. (b) 1799 isw 1 If decimal, allow art 0.172 (c) Piero’s 1 Can be indicated by 10221 5 Total for the paper is 56 marks
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.
3Limits of accuracy2The four operations2Equations1Fractions, decimals and percentages1Indices I1Introduction to probability1Money1Ordering1Powers and roots1Rates1Ratio and proportion1Scatter diagrams1Sequences1Standard form1Symmetry1Time1Units of measure1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2006 Oct/Nov, Paper 1 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.