Cambridge IGCSE Mathematics 0580 — 2007 Oct/Nov Paper 1 · Variant 1
0580/11/O/N/07 · 18 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 paper25 pages
Mark scheme7 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · On a winter’s day in Vienna the maximum temperature was –2°C
1 On a winter’s day in Vienna the maximum temperature was –2°C. For The minimum temperature was 11°C lower than this. Examiner's Write down the minimum temperature. Use Answer °C [1]
Mark scheme: Question Answers Mark Notes 1 −13 1 Not 13–
Q2 · Chris and Roberto share $35 in the ratio 5:2
2 Chris and Roberto share $35 in the ratio 5:2. Calculate how much Roberto receives. Answer $ [2]
Mark scheme: 2 ($) 10 2 M1 for 35 ÷ (5 + 2) or better. SC1 for ($) 25 only or 25:10 or 25 and 10 in the answer space.
Q3 · Solve the equation 1 – 2x = x + 4
3 Solve the equation 1 – 2x = x + 4. Answer x = [2]
Mark scheme: 3 (x = ) − 1 2 M1 for 1 − 4 = x + 2x oe Not embedded unless x = –1 seen.
Q4 · In 2005, a toy cost 52.50 reals in Brazil
4 In 2005, a toy cost 52.50 reals in Brazil. In Argentina, 1 peso = 0.875 reals. Work out the cost of the toy in pesos. Answer pesos [2]
Mark scheme: 4 60 2 M1 for 52.50 ÷ 0.875. SC1 for answers 59.659 rot or 60.3448 rot (from rounding 0.875 to 0.88 or 0.87.)
Q5 · Factorise completely 4xy – 2x
5 Factorise completely 4xy – 2x. For Examiner's Use Answer [2]
Mark scheme: 5 2x(2y − 1) final answer 2 SC1 for x(4y − 2) or 2(2xy − x) or 2x(2y +1) Or SC1 for 2x(2y – 1) not as final answer.
Q6 · NOT TO SCALE 25 m pº 30 m The height of a tree is 25 metres
6 NOT TO SCALE 25 m pº 30 m The height of a tree is 25 metres. The shadow of the tree has a length of 30 metres. Calculate the size of the angle marked p° in the diagram. Answer p = [2]
Mark scheme: 6 art39.8 2 M1 for tan p = 2530 oe
Q7 · The distance, d kilometres, between Windhoek and Cape Town is 1300 km, correct to the…
7 The distance, d kilometres, between Windhoek and Cape Town is 1300 km, correct to the nearest 100 kilometres. Complete the statement about the value of d. Answer d < [2]
Mark scheme: 7 1250 (≤ d <) 1350 2 1 mark for each in correct order 13
Q8 · For Examiner's Use Draw all the lines of symmetry on the shape above
8 (a) For Examiner's Use Draw all the lines of symmetry on the shape above. [1] (b) A quadrilateral has rotational symmetry of order 2 and no lines of symmetry. Write down the geometrical name of this shape. Answer(b) [1]
Mark scheme: 8 1 Lines must be a minimum of length and height (a) Two correct lines of of the figure. symmetry, No extra lines (b) Parallelogram 1
Question 9
5 ... 9 (a) Write in the missing number. = 6 18 [1] (b) Without using your calculator and writing down all your working, show that 2 5 7 1 − = . 9 6 18 Answer(b) [2]
Mark scheme: 9 (a) 15 1 (b) 119 oe B1 Eg 5466 Allow 99 + 29 or better 18 22 − 1518 = 187 oe E1 Must be finally reduced to 187
Q10 · Each interior angle of a regular polygon is 150°
10 Each interior angle of a regular polygon is 150°. For (a) Work out the size of each exterior angle. Examiner's Use Answer(a) [1] (b) Work out the number of sides of this polygon. Answer(b) [2]
Mark scheme: 10 (a) 30 1 (b) 12 2ft M1 for 360 ÷ either 30 or their (a) ft. answer only when calculation gives an integer > 2
Q11 · North NOT TO SCALE 140º A 50 km B A ship travels 50 kilometres from A to B on a bearing…
11 North NOT TO SCALE 140º A 50 km B A ship travels 50 kilometres from A to B on a bearing of 140°, as shown in the diagram. Calculate how far south B is from A. Answer km [3]
Mark scheme: 11 art38.3 3 M1 for 50d = cos (180 – 140) oe soi M1dep. for ( d =) 50 cos (180 – 140) oe SC1 for 32.1 (distance east) 11
Q12 · For y Examiner's Use NOT TO 3 SCALE l x 0 1 A straight line, l, crosses the x-axis at (1…
12 For y Examiner's Use NOT TO 3 SCALE l x 0 1 A straight line, l, crosses the x-axis at (1, 0) and the y-axis at (0, 3). (a) Find the gradient of the line l. Answer(a) [1] (b) Write down the equation of the line l, in the form y = mx + c. Answer(b) y = [2]
Mark scheme: 12 (a) −3 1 B1 for their (a)x or +3 as intercept seen (b) (y =) −3x + 3 2ft in the equation. Not y = 3 Final answer
Q13 · A school has 240 students
13 A school has 240 students. (a) There are 131 girls. What percentage of the students are girls? Answer(a) [2] (b) One day 6.25% of the 240 students are absent. Work out the number of students who are absent. Answer(b) [2]
Mark scheme: 13 (a) 55 or art 54.6 2 M1 for 131 ÷ 240(× 100) implied by 54.5 (b) 15 2 M1 for 6.25 ÷ 100 × 240 SC1 for answer 225
Q14 · Calculate the circumference of a circle of diameter 8 cm
14 (a) Calculate the circumference of a circle of diameter 8 cm. For Examiner's Use Answer(a) cm [2] (b) Q NOT TO SCALE 29º A B AQB is a semi-circle. Angle QAB = 29°. Work out the size of angle ABQ. Answer(b) Angle ABQ = [2]
Mark scheme: 14 (a) art 25.1 www 2 M1 for π × 8 or 2π × 8 ÷ 2 implied by answer of 25 (b) 61 (Can be on 2 M1 for 90 – 29 or 180 – 90 – 29 diagram) SC1 for angle Q = 90° soi
Q15 · Simplify (a) a0, Answer(a) [1] 2 (b) ( 3x ) Answer(b) [1] -2 3 (c)
15 Simplify (a) a0, Answer(a) [1] 2 (b) ( 3x ) Answer(b) [1] -2 3 (c) . x Answer(c) [2]
Mark scheme: 15 (a) 1 1 (b) x 6 1 1 3 or better. E.g. ( x3) 2 )2 (c) x92 2 M1 for ( x B1 if answer contains x 2 as numerator or 3 2(or 9) as denominator. 15
Q16 · Write 17 598 correct to 2 significant figures
16 (a) (i) Write 17 598 correct to 2 significant figures. For Examiner's Use Answer(a)(i) [1] (ii) Write your answer to part (a)(i) in standard form. Answer(a)(ii) [1] (b) Write 5.649 × 10-2 as a decimal, correct to 3 decimal places. Answer(b) [2]
Mark scheme: 16 (a)(i) 18 000 1 (ii) 1.8 × 10 4 1 ft 1.7598 × 10 4 gets 0 (b) 0.056 2 B1 for 0.06 or 0.0565 or 0.05649 or 0.057 seen SC1 for final answer 0.0560(0)
Q17 · Alex invests $200 for 2 years at 4.05% per year simple interest
17 (a) Alex invests $200 for 2 years at 4.05% per year simple interest. Calculate how much interest Alex receives. Answer(a) $ [2] (b) Bobbie invests $200 for 2 years at 4% per year compound interest. Calculate how much interest Bobbie receives. Give your answer to 2 decimal places. Answer(b) $ [2]
Mark scheme: 17 (a) ($) 16.2(0) 2 M1 for (200 × 4.05 × 2)/100 SC1 for 216.2(0) (b) ($) 16.3(2) or 16.3(0) 2 M1 for 200(1.04) 2 − 200oe SC1 for 216.3(2). SC1 for both 8.(00) and 8.3(2) seen
Q18 · For y Examiner's Use 5 4 3 2 1 x –4 –3 –2 –1 0 1 2 3 4 5 6 K –1 –2 –3 –4 –5 − 3 (a) KL…
18 For y Examiner's Use 5 4 3 2 1 x –4 –3 –2 –1 0 1 2 3 4 5 6 K –1 –2 –3 –4 –5 − 3 (a) KL = . The point K is marked on the diagram. 3 (i) Draw KL on the diagram. [1] (ii) Write down the co-ordinates of the point L. Answer(a)(ii) ( , ) [1] (b) P is the point (−3, −3). 2 PR= and PS = 2PR. 1 Find the co-ordinates of S. Answer(b) ( , ) [2] Question 19 is printed on the next page.
Mark scheme: 18 (a)(i) Vector KL drawn 1 If arrow shown, it must be correct. Only ft their point if labelled L. (ii) (0,2) 1 ft M1 for vector PS drawn or for (b) (1, −1) 2 4 (PS =) 2 SC1 Point S on diagram at (1, –1) 12
What was in this paper
The subtopics covered by these 18 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
What you needed in this session
Cambridge’s own grade thresholds for 2007 Oct/Nov, Paper 1 · Variant 1. A higher threshold means an easier paper — the bar moves with how the cohort did.