Cambridge IGCSE Mathematics 0580 — 2005 Oct/Nov Paper 1 · Variant 1

1 The distance from Buenos Aires to Wellington is approximately 10 100 kilometres. For Write this number in standard form. Examiner's Use Answer km [1]

Mark scheme: Question Answers Mark Notes 1 1.01(00) x 1044 1

More questions on Standard form

2 Factorise 3xy – 2x. Answer [1]

Mark scheme: 2 x(3y – 2) 1

More questions on Algebraic manipulation

3 The highest mountain in Argentina is Aconcagua. Its height is 6960 metres, correct to the nearest twenty metres. Write down the smallest possible height of Aconcagua. Answer m [1]

Mark scheme: 3 6950 1 √

More questions on Limits of accuracy

4 Which one of the numbers below is not a rational number? 7 23 5 –1 12 81 Answer [1]

Mark scheme: 4 √5 1

More questions on Types of number

5 Solve the equation 5x – 7 = 8. Answer x = [2]

Mark scheme: 5 5x = 8 + 7 or better seen. M1 (Correct first step) (x = ) 3 A1

More questions on Equations

6 A bottle of lemonade contains 1 1 litres. 2 1 A glass holds litre. 8 How many glasses can be filled from one bottle of lemonade? Answer [2]

Mark scheme: 6 12 2 SC1 correct method seen 1 1 1 ÷ or better. 2 8

More questions on Ratio and proportion

7 The table below shows the average monthly temperatures (°C) in the Islas Orcadas, Argentina. Examiner's Use Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 1 1 0.5 –1 –5 –8 –9 –8 –5 –3 –1 0.5 (a) Work out the difference between the highest and the lowest average monthly temperature. Answer(a) °C [1] (b) The highest recorded temperature for July is x °C. This is 21 °C above the average for July shown in the table. Work out the value of x. Answer(b) x = [1]

Mark scheme: 7 (a) 10 (allow –10) 1 (b) 12 1

More questions on The four operations

8 The formula for the perimeter, P, of a rectangle with length a and width b is P = 2a + 2b. Make a the subject of the formula. Answer a = [2]

Mark scheme: 8 P – 2b = 2a M1 P − 2b A1 oe 2

More questions on Algebraic manipulation

9 0.072 72% 0.702 7 7 7.2% 10 100 From the values listed above, write down (a) the smallest, Answer(a) [1] (b) the largest, Answer(b) [1] (c) the two which are equal. Answer(c) and [1]

Mark scheme: 9 (a) 7 1 Allow 0.07 or 7% 100 (b) 72% 1 72 Allow 0.72 or 100 (c) 0.072 and 7.2% 1 In this form. [15]

More questions on Fractions, decimals and percentages

10 An integer n is such that 60 n 70. For Write down a value of n which is Examiner's Use (a) a prime number, Answer(a) [1] (b) a multiple of 9, Answer(b) [1] (c) a square number. Answer(c) [1]

Mark scheme: 10 (a) 61 or 67 1 (b) 63 1 (c) 64 1

More questions on Types of number

11  2   3  p =   and q =   .  −3   1  (a) Write p + q as a column vector.     Answer (a) p + q =   [2]     (b) The point O is marked on the grid below. Draw the vector where = p. y 3 2 1 x –3 –2 –1 O 1 2 3 –1 –2 –3 [1]

Mark scheme: 11 (a)  5  2 1 mark for each correct component.    −2  (b) Correct Vector Drawn 1

More questions on Vectors in two dimensions

12 Examiner's T Use NOT TO 1.2 km SCALE S 21o The diagram shows a path, ST, up a hill. The path is 1.2 kilometres long and slopes at an angle of 21° to the horizontal. Calculate the height of the hill, showing all your working. Give your answer in metres. Answer m [3]

Mark scheme: 12 ° height M1 (alt. method) 1200 seen B1 sin 21 = oe or better 1 . 2 C’s 1200 sin 21o M1 430 (.0...) A1 f.t. 0.43(0……) A1 430(.0….) B1ft

More questions on Right-angled triangles

13 The population of Latvia in 1989 was 2 700 000. In 1994 it was 2 500 000. Calculate the percentage decrease in the population between 1989 and 1994. Answer % [3]

Mark scheme: 13 (Decrease) 200 000 B1 2500000 (alt. method) x 100 or 92.5 B1 2700000 subtract answer from 100 M1 Their 200 000 M1 × 100 2700 000 7.41 or 7.40(7….) A1

More questions on Percentages

14 = < > Choose one of the symbols given above to complete each of the following statements. When x = 6 and y = –7, then (a) x y [1] (b) x² y² [1] (c) y - x x - y [1]

Mark scheme: 14 (a) > 1 (b) < 1 (c) < 1 [15] IGCSE – NOVEMBER 2005 0580/0581 1

More questions on Ordering

15 (a) Write 0.48 correct to 1 significant figure. For Examiner's Use Answer(a) [1] (b) (i) Find an approximate answer for the sum 9.87 – 5.79 × 0.48 by rounding each number to 1 significant figure. Show your working. Answer(b)(i) [1] (ii) Use your calculator to find the exact answer for the sum in part (b) (i). Write down all the figures on your calculator. Answer(b)(ii) [1]

Mark scheme: 15 (a) 0.5 not 0.50 1 (b) (i) 10 – 6 x c’s 0.5 = 7 1f.t. Only f.t. c’s (a) if it is 0.4 (0) or 0.50 or 0 (ii) 7.0908 1 Allow 7.6 or 8 from 0.4

More questions on Estimation

16 Simplify the following expressions. (a) 9r – 4s – 6r + s Answer(a) [1] (b) q4 ÷ q3 Answer(b) [1] (c) p6 × p−2 Answer(c) [1]

Mark scheme: 16 (a) 3r – 3s or 3(r – s) 1 (b) q or q1 1 (c) p4 1

More questions on Indices II

17 Three friends, Cleopatra, Dalila and Ebony go shopping. The money they each have is in the ratio Cleopatra : Dalila : Ebony = 5 : 7 : 8. Cleopatra has $15. (a) How many dollars do they have in total? Answer(a) [2] (b) Dalila spends $12 on a hat. How many dollars does she have left? Answer(b) [1]

Mark scheme: 17 (a) A clear attempt to multiply M1 each by 3 and add, or equivalent. 60 A1 (b) 9 1f.t. Must be a clear use of Dalila’s intended total from (a) subtract 12

More questions on Ratio and proportion

18 A 400 metre running track has two straight sections, each of length 120 metres, and two semicircular For ends. Examiner's Use 120 m NOT TO d SCALE (a) Calculate the total length of the curved sections of the track. Answer(a) m [1] (b) Calculate d, the distance between the parallel straight sections of the track. Answer(b) d = m [2]

Mark scheme: 18 (a) 160 1 (b) Their (a) ÷π M1 50.9(…..) or 51 A1

More questions on Area and perimeter

19 Joseph buys 45 kilograms of potatoes from a supplier for $0.65 per kilogram. (a) How much does he pay for the potatoes? Answer(a) $ [1] (b) He then puts the potatoes into bags which each hold 2.5 kilograms. How many bags can he fill with the potatoes? Answer(b) bags [1] (c) At the market he sells the bags of potatoes for $2.20 per bag. Calculate the smallest number of complete bags he needs to sell in order to make a profit. Answer(c) bags [2]

Mark scheme: 19 (a) 29.25 or 29.2 or 29.3 1 (b) 18 1 (c) Their (a) ÷ 2.20 M1 Implied by 13.3 or 13.2 (...) seen 14 A [16]

More questions on Rates

20 For Examiner's Use $900 Lorenzo saves money for a motorbike. The marked price of the motorbike is $900. He pays a deposit of 35% of the marked price. (a) Calculate his deposit. Answer(a) $ [2] (b) He then makes 12 monthly payments of $60 each. How much more than the $900 marked price does he pay altogether? Answer(b) $ [3]

Mark scheme: 20 (a) 35 ÷ 100 × 900 M1 =315 A1 (b) (Payments) 720 B1 Implied by 1035 seen Deposit + Payments – 900 M1 135 A1 f.t. No follow through for negative answer

More questions on Money

21 The graph below shows the amount a plumber charges for up to 6 hours work. For Examiner's Use 120 100 80 Charge ($) 60 40 20 0 1 2 3 4 5 6 Time (hours) (a) How much does he charge for 3 1 hours work? 2 Answer(a) $ [1] (b) The plumber charged $50. How many hours did he work? Answer(b) hours [1] (c) Another plumber charges $16 per hour. (i) Draw a line on the grid above to show his charges. Start your line at (0,0). [2] (ii) Write down the number of hours for which the two plumbers charge the same amount. Answer(c)(ii) hours [1]

Mark scheme: 21 (a) 62 1 (b) 1 1 2 2 (c) (i) Ruled line through (0, 0) and (1, 16) B1 Through and further than (5, 80) B1 Dependent (ii) 5 1f.t. Intersection of their line with the given line. [10]

More questions on Graphs in practical situations