Cambridge IGCSE Mathematics 0580 — 2015 Feb/March Paper 1 · Variant 2
0580/12/F/M/15 · 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 · Write down the number seventy one thousand and seventy two in figures
1 Write down the number seventy one thousand and seventy two in figures. Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: Qu Answers Mark Part marks 1 71 072 1
Q2 · Write down the order of rotational symmetry of this shape
2 Write down the order of rotational symmetry of this shape. Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: 2 8 1
Q3 · Measure the reflex angle at B
3 Measure the reflex angle at B. B Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: 3 332 or 330 to 334 1
Q4 · Work out of 153
44 Work out of 153. 9 Answer ................................................ [1] __________________________________________________________________________________________
Mark scheme: 4 68 1
Q5 · 1 euro = $1.234
5 1 euro = $1.234 . Change 155 euros into dollars. Answer $ ................................................ [1] __________________________________________________________________________________________
Mark scheme: 5 191.27 cao 1 9
Q6 · 006 (a) Write as a fraction in its simplest form
45006 (a) Write as a fraction in its simplest form. 5500 Answer(a) ................................................ [1] (b) Write 0.73 as a fraction. Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 96 (a) 1 11 (b) 1 73 100
Q7 · The probability that Raju arrives on time at school is 0.72
7 The probability that Raju arrives on time at school is 0.72 . (a) Write down the probability that he will not arrive on time. Answer(a) ................................................ [1] (b) Raju attends school on 200 days. Work out the expected number of days he will arrive on time. Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 7 (a) 0.28 oe 1 (b) 144 1
Q8 · The diagram shows a circle, centre O
8 The diagram shows a circle, centre O. A NOT TO A, B and C are points on the circumference. SCALE B O C Write down the mathematical name of the straight line (a) OC, Answer(a) ................................................ [1] (b) AB. Answer(b) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 8 (a) radius 1 (b) chord 1
Q9 · 9 The point P has co-ordinates (2, –5) and = e- 7 o
6 9 The point P has co-ordinates (2, –5) and = e- 7 o. (a) Write down the co-ordinates of Q. Answer(a) (...................... , ......................) [1] (b) Write 4 as a column vector. Answer(b) [1] f p __________________________________________________________________________________________
Mark scheme: 9 (a) (8, –12) 1 24 (b) 1 −28
Q10 · Find the lowest common multiple (LCM) of 24 and 32
10 Find the lowest common multiple (LCM) of 24 and 32. Answer ................................................ [2] __________________________________________________________________________________________
Mark scheme: 10 96 2 B1 for 96k or 25 × 3 or for listing multiples of each up to 96
Q11 · The volume, V, of a cylinder with radius r and height h is V = πr2h
11 The volume, V, of a cylinder with radius r and height h is V = πr2h. Calculate the volume of a cylinder with radius 7 cm and height 8 cm. Answer ......................................... cm3 [2] __________________________________________________________________________________________
Mark scheme: 11 1230 or 1231 to 1232 2 M1 for π × 7 × 7 × 8 or better 4 5
Q12 · $760 is invested for 3 years at a rate of 4.5% per year simple interest
12 $760 is invested for 3 years at a rate of 4.5% per year simple interest. Work out the total interest at the end of the 3 years. Answer $ ................................................ [2] __________________________________________________________________________________________
Mark scheme: 5.4 12 102.6[0] 2 M1 for 760 × 3 × or better 100
Q13 · Simplify (i) x0, Answer(a)(i) ...............................................
13 (a) Simplify (i) x0, Answer(a)(i) ................................................ [1] (ii) m4 × m3. Answer(a)(ii) ................................................ [1] (b) Solve 5x3 = 40 . Answer(b) x = ................................................ [1] __________________________________________________________________________________________
Mark scheme: 13 (a) (i) 1 1 (ii) m7 1 (b) 2 1 1000
Q14 · Ahmed, Batuk and Chand share $1000 in the ratio 8 : 7 : 5
14 Ahmed, Batuk and Chand share $1000 in the ratio 8 : 7 : 5. Calculate the amount each receives. Answer Ahmed $ ................................................ Batuk $ ................................................ Chand $ ................................................ [3] __________________________________________________________________________________________
Mark scheme: 1000 14 400 350 250 3 M1 for implied by 50 8 + 7 + 5 A1 for one clearly assigned correct answer or SC2 for 3 correct answers in wrong order
Q15 · NOT TO 44° SCALE x° The diagram shows an isosceles triangle
15 (a) NOT TO 44° SCALE x° The diagram shows an isosceles triangle. Find the value of x. Answer(a) x = ................................................ [1] (b) (i) The exterior angle of a regular polygon is 24°. Find the number of sides of this regular polygon. Answer(b)(i) ................................................ [2] (ii) Write down the mathematical name for a 5-sided polygon. Answer(b)(ii) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 15 (a) 68 1 360 (b) (i) 15 2 M1 for = 24 or (n − 2 )180 = 156n n (ii) pentagon 1 25 25
Q16 · Without using your calculator, work out 2 97 ÷ 56
16 Without using your calculator, work out 2 97 ÷ 56 . Give your answer as a fraction in its lowest terms. You must show each step of your working. Answer ................................................ [4] __________________________________________________________________________________________
Mark scheme: 25 25 16 B1 (Alt) 9 9 a 6 their 25 × 2 5 × 3 × where a > b M1 ÷ oe b 5 9 × 2 6 × 3 150 their 25 × 2 Their oe or M1FT oe or 45 dep 5 × 3 their correct full cancelling 50 15 ÷ oe with 18’s cancelled 18 18 10 1 A1 or 3 nfww 3 3
Q17 · 6 8 14 36 47 50 130 From the list of numbers, write down one number for each of the…
17 6 8 14 36 47 50 130 From the list of numbers, write down one number for each of the following. (a) An odd number. Answer(a) ................................................ [1] (b) A square number. Answer(b) ................................................ [1] (c) A factor of 70. Answer(c) ................................................ [1] (d) A multiple of 26. Answer(d) ................................................ [1] __________________________________________________________________________________________
Mark scheme: 17 (a) 47 1 (b) 36 1 (c) 14 1 (d) 130 1
Q18 · Solve the simultaneous equations
18 (a) Solve the simultaneous equations. You must show all your working. 4x + 2y = 31 6x – 2y = 34 Answer(a) x = ................................................ y = ................................................ [2] (b) Factorise 14p2 + 21pq. Answer(b) ................................................ [2] __________________________________________________________________________________________
Mark scheme: 18 (a) [x =] 6.5 [y =] 2.5 2 B1 for x = 6.5 B1 for y = 2.5 If zero scored, SC1 for correct substitution and evaluation to find other variable or SC1 no working, 2 correct answers given. (b) 7p(2p + 3q) 2 B1 for 7(2p2 + 3pq) or p(14p + 21q)
Q19 · Idris has c toy cars
19 Idris has c toy cars. Fadl has twice as many cars as Idris. Baasim has three more cars than Fadl. (a) Write down an expression, in terms of c, to complete each statement. Fadl has ....................................... cars. Baasim has ....................................... cars. [2] (b) Write down an expression, in terms of c, for the total number of cars the three children have. Give your answer in its simplest form. Answer(b) ................................................ [2] __________________________________________________________________________________________
Mark scheme: 19 (a) 2c 1 2c + 3 1FT FT is their 2c + 3 provided linear (b) 5c + 3 2FT M1 for c + their 2c + their(2c+3) provided linear
Q20 · Ravi cycles from home to the bank
20 Ravi cycles from home to the bank. It takes him 15 minutes, cycling at a constant speed of 14 km/h. (a) Work out how far Ravi cycles from home to the bank. Answer(a) .......................................... km [1] (b) Ravi stays at the bank for 18 minutes. He then cycles home at a constant speed for 12 minutes. Draw the travel graph to show Ravi’s journey since he left home. 4.5 4 3.5 3 Distance 2.5 (km) 2 1.5 1 0.5 Ravi’s home 0 5 10 15 20 25 30 35 40 45 50 Time (minutes) [3] __________________________________________________________________________________________ Question 21 is printed on the next page.
Mark scheme: 20 (a) 3.5 1 (b) straight line from (0,0) to (15,their 3.5) 1FT FT from (a) horiz line from (their 15, their 3.5) to 1FT FT is horizontal line length 18 mins (their 33, their 3.5) 1FT FT is from (their x, their y) to straight line from (their 33, their 3.5) to (their x + 12, 0) (their 33 + 12, 0)
Q21 · Y 9 8 7 6 5 4 3 2 A B 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 C –2 –3 –4 –5 Three shapes A, B…
21 y 9 8 7 6 5 4 3 2 A B 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 C –2 –3 –4 –5 Three shapes A, B and C are shown on the grid. (a) Describe fully the single transformation that maps shape A onto (i) shape B, Answer(a)(i) ................................................................................................................................ ..................................................................................................................................................... [2] (ii) shape C. Answer(a)(ii) ............................................................................................................................... ..................................................................................................................................................... [3] (b) Enlarge shape A by scale factor 2 from the centre (4, 0). [2]
Mark scheme: 21 (a) (i) reflection 1 x = 3 1 (ii) rotation 1 [centre] (0,0) oe 1 180 1 (b) correct enlargement 2 B1 for correct scale factor used, wrong centre (−2, 0), (−4, 0), (−2, 6), (−4, 8)
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.
What you needed in this session
Cambridge’s own grade thresholds for 2015 Feb/March, Paper 1 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.