Cambridge IGCSE Mathematics 0580 — 2010 Oct/Nov Paper 1 · Variant 3
0580/13/O/N/10 · 21 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 · For Examiner's Use Write down the name of the solid that can be made from the net shown…
1 For Examiner's Use Write down the name of the solid that can be made from the net shown in the diagram. Answer [1]
Mark scheme: Qu. Answers Mark Part Marks 1 Pyramid 1
Q2 · Write down all the square numbers which are factors of 100
2 Write down all the square numbers which are factors of 100. Answer [2]
Mark scheme: 2 1, 4, 25, 100 2 B1 for any two and none incorrect. −1 each incorrect
Q3 · For the diagram, write down (a) the number of lines of symmetry, Answer(a) [1] (b) the…
3 For the diagram, write down (a) the number of lines of symmetry, Answer(a) [1] (b) the order of rotational symmetry. Answer(b) [1]
Mark scheme: 3 (a) 2 1 (b) 2 1
Q4 · In a desert the temperature at noon was 38°C
4 In a desert the temperature at noon was 38°C. At midnight the temperature was –3°C. (a) Find the change in temperature between noon and midnight. Answer(a) °C [1] (b) At 02 00 the temperature was 4°C below the midnight temperature. Write down the temperature at 02 00. Answer(b) °C [1]
Mark scheme: 4 (a) 41 or −41 1 (b) −7 1 2 2
Q5 · Multiply out the brackets
5 Multiply out the brackets. For x(2x + y) Examiner's Use Answer [2]
Mark scheme: 5 2x2 + xy final answer 2 B1 for 2x2 or xy seen in working
Question 6
6 Solve the equation. 2 x + 1 = 4 3 Answer x = [2]
Mark scheme: 6 5.5 2 M1 for 2x + 1 = 3 × 4 or better 2x 1 or = 4 − 3 3
Q7 · Work out 3 7.2 3 − 100
7 Work out 3 7.2 3 − 100 . Give your answer correct to 3 decimal places. Answer [2]
Mark scheme: 7 6.489 2 B1 for 6.5 or 6.49 or 6.4891….
Q8 · Chris and Max share $45 in the ratio Chris:Max = 7 : 2
8 Chris and Max share $45 in the ratio Chris:Max = 7 : 2 . Calculate how much Chris receives. Answer $ [2]
Mark scheme: 8 35 2 M1 for 45 ÷ (7 + 2) SC1 for answer = 10
Q9 · When Valentina was 10 years old, her mass was 32 kg
9 When Valentina was 10 years old, her mass was 32 kg. Two years later her mass had increased by 45%. Calculate Valentina’s mass when she was 12 years old. Answer kg [2]
Mark scheme: 9 46.4 2 M1 for 32 × 1.45 oe or B1 for answer of 14.4 3 1875
Q10 · Change 18.75% into a fraction
10 Change 18.75% into a fraction. For Examiner's Write your answer in its lowest terms. Use Answer [2]
Mark scheme: 3 1875 10 2 B1 for or any equivalent fraction. 16 10000
Question 11
11 Factorise completely. 3ac – 6ad Answer [2]
Mark scheme: 11 3a(c − 2d) 2 B1 for a(3c − 6d) or 3(ac − 2ad) or 3a(jc − kd) where j and k are non-zero. 8 1 3
Q12 · 1 12 Simplify 1 2
1 12 Simplify 1 2 . Give your answer as a fraction. Answer [2]
Mark scheme: 8 1 12 2 M1 for 1 ÷ (1 )3 oe 27 2 27 or SC1 for 8
Q13 · Solve the simultaneous equations
13 Solve the simultaneous equations. 3x + y = 5 5x + y = 9 Answer x = y = [2]
Mark scheme: 13 (x =) 2, (y =) −1 2 M1 for correct method for eliminating one variable. Subtract or multiply by 3 and 5, then subtract IGCSE – October/November 2010 0580 13
Q14 · 14 17 27 17 0.294 17 From the list of numbers, write down (a) a prime number, Answer(a)…
5 14 17 27 17 0.294 17 From the list of numbers, write down (a) a prime number, Answer(a) [1] (b) an irrational number, Answer(b) [1] (c) the smallest number. Answer(c) [1]
Mark scheme: 14 (a) 17 1 (b) √17 or 4.12(….) 1 (c) 0.294 1 2
Q15 · Amiria invests $200 for 2 years at 3% per year compound interest
15 Amiria invests $200 for 2 years at 3% per year compound interest. For Examiner's Calculate the total amount Amiria has at the end of the two years. Use Answer $ [3]
Mark scheme: 15 212.18 final answer cao 3 M2 for 200 × 1.032 oe or M1 for (200 × 1.03) × 0.03 oe
Q16 · B NOT TO SCALE O T A C U In the diagram, TAU is a tangent to the circle at A
16 B NOT TO SCALE O T A C U In the diagram, TAU is a tangent to the circle at A. AB is a diameter of the circle and AC = BC. Find (a) angle BCA, Answer(a) Angle BCA = [1] (b) angle ABC, Answer(b) Angle ABC = [1] (c) angle CAU. Answer(c) Angle CAU = [1]
Mark scheme: 16 (a) 90 1 1 (b) 45 1ft ft (180 − their (a)) 2 (c) 45 1ft ft 90 − their (b)
Q18 · Y 7 C 6 B 5 4 3 A 2 1 x 0 1 2 3 4 5 6 7 The diagram shows three points, A(1, 2), B(7, 5)…
18 y 7 C 6 B 5 4 3 A 2 1 x 0 1 2 3 4 5 6 7 The diagram shows three points, A(1, 2), B(7, 5) and C(5, 7). (a) Write as column vectors (i) AC, Answer(a)(i) AC = [1] (ii) CB. Answer(a)(ii) CB = [1] (b) Use two of the symbols +, –, = in the spaces to make a correct statement. AC CB AB [1]
Mark scheme: 4 18 (a) (i) 5 1 2 (ii) −2 1 (b) (AC) + (CB) = (AB) 1 1 1
Q19 · For y Examiner's Use 2 x 0 6 The diagram shows a straight line passing through the points…
19 For y Examiner's Use 2 x 0 6 The diagram shows a straight line passing through the points (0, 2) and (6, 0). Find the equation of this line in the form y = mx + c. Answer y = [3]
Mark scheme: 1 1 19 (y =) −3 x + 2 cao 3 B1 for gradient of ± 3 oe (Allow ±0.33 or better) B1 ind for mx + 2 where m ≠ 0.
Q20 · 4 4 5 6 8 (a) The diagram shows 5 discs
20 4 4 5 6 8 (a) The diagram shows 5 discs. One disc is chosen at random. (i) Which number is most likely to be chosen? Answer(a)(i) [1] (ii) What is the probability that the number on the disc is even? Answer(a)(ii) [1] (iii) What is the probability that the number on the disc is even and a factor of 20? Answer(a)(iii) [1] (b) A disc is chosen at random from the discs with even numbers. What is the probability that the number on the disc is a factor of 20? Answer(b) [1] Questions 21 and 22 are printed on the next page
Mark scheme: 20 (a) (i) 4 1 4 (ii) oe 1 5 2 (iii) oe 1 5 2 (b) oe 1 4
Q21 · For 0 0 0 1 2 2 4 4 5 9 Examiner's Use The list shows the number of days absent in a…
21 For 0 0 0 1 2 2 4 4 5 9 Examiner's Use The list shows the number of days absent in a school term for each of 10 students. Find the mode, the median and the mean for the number of days absent. Answer Mode = Median = Mean = [4]
Mark scheme: 21 (Mode =) 0 1 (Median =) 2 1 (Mean =) 2.7 2 M1 (0 + 0 + 0) + 1 + 2 + 2 + 4 + 4 + 5 + 9 IGCSE – October/November 2010 0580 13
Q22 · School NOT TO SCALE Distance Shop (kilometres) Home 08 00 08 05 08 10 08 15 08 20 08 25…
22 School NOT TO SCALE Distance Shop (kilometres) Home 08 00 08 05 08 10 08 15 08 20 08 25 08 30 Time Rob walks to school each morning. One day, he leaves home at 08 00. He stops at a shop at 08 10 and stays there for 5 minutes. He then continues to school and arrives at 08 30. (a) Draw the travel graph for Rob’s journey from home to school. [3] (b) Rob’s average speed for the whole journey from home to school is 3.3 km/h. Calculate the distance from Rob’s home to school. Answer(b) km [2]
Mark scheme: 22 (a) Lines connecting 3 (08 00, home) to (08 10, shop) B1 home to shop (their 08 10, shop) to B1ft horizontal and 5 minute period (their 08 15, shop) (their 08 15, shop) to B1ft for line to 08 30 and school (08 30, school) (b) 1.65 2 M1 for use of speed × time SC1 for 1.375 or 1.376 to 1.38
What was in this paper
The subtopics covered by these 21 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
2Equations2Fractions, decimals and percentages2Percentages2Types of number2Averages and range1Equations of linear graphs1Graphs in practical situations1Introduction to probability1Powers and roots1Ratio and proportion1Right-angled triangles1Surface area and volume1Symmetry1The four operations1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2010 Oct/Nov, Paper 1 · Variant 3. A higher threshold means an easier paper — the bar moves with how the cohort did.