Cambridge IGCSE Mathematics 0580 — 2019 Feb/March Paper 2 · Variant 2
0580/22/F/M/19 · 24 questions · 70 marks · ≈79 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 paper12 pages
Mark scheme5 pages
Answers below. Sit the paper first if you are practising.
Questions as text
Q1 · The temperature at 07 00 is -3 °C
1 The temperature at 07 00 is -3 °C. This temperature is 11 °C higher than the temperature at 01 00. Find the temperature at 01 00. ................................................°C [1]
Mark scheme: Question Answer Marks Partial Marks 1 −14 1
Q2 · Jodi swims 22 lengths of a swimming pool to raise money for charity
2 Jodi swims 22 lengths of a swimming pool to raise money for charity. She receives $15 for each length she swims. Calculate how much money Jodi raises for charity. $ .................................................. [1]
Mark scheme: 2 330 1
Q3 · Write the recurring decimal .023o o as a fraction
3 Write the recurring decimal .023o o as a fraction. .................................................... [1]
Mark scheme: 3 23 1 99
Q4 · Write 0.046 875 correct to 2 significant figures
4 (a) Write 0.046 875 correct to 2 significant figures. .................................................... [1] (b) Write 2 760 000 in standard form. .................................................... [1]
Mark scheme: 4(a) 0.047 1 4(b) 2.76 × 10 6 1
Q5 · A tourist changes $500 to euros (€) when the exchange rate is €1 = $1.0697
5 A tourist changes $500 to euros (€) when the exchange rate is €1 = $1.0697 . Calculate how many euros he receives. € .................................................. [2]
Mark scheme: 5 467.42 or 467 2 M1 for 500 ÷ 1.0697
Q6 · The probability that a sweet made in a factory is the wrong shape is 0.0028
6 The probability that a sweet made in a factory is the wrong shape is 0.0028 . One day, the factory makes 25 000 sweets. Calculate the number of sweets that are expected to be the wrong shape. .................................................... [2]
Mark scheme: 6 70 2 M1 for 25 000 × 0.0028 oe
Q7 · The bearing of Alexandria from Paris is 128°
7 The bearing of Alexandria from Paris is 128°. Calculate the bearing of Paris from Alexandria. .................................................... [2]
Mark scheme: 7 308 2 M1 for 180 + 128 oe or 52 seen
Q8 · O is the origin, OA = 2x + 3y and BA = x - 4y
8 O is the origin, OA = 2x + 3y and BA = x - 4y . Find the position vector of B, in terms of x and y, in its simplest form. .................................................... [2]
Mark scheme: 8 x + 7y 2 M1 for a correct route
Q9 · Y is directly proportional to (x - 4)
9 y is directly proportional to (x - 4) . When x = 16 , y = 3 . Find y in terms of x. y = .................................................... [2]
Mark scheme: 9 1 2 M1 for y = k ( x − 4 ) [y = ] ( x − 4) oe final answer 4
Q10 · 7.5 cm NOT TO SCALE 5 cm 12 cm Calculate the total surface area of the cuboid
10 7.5 cm NOT TO SCALE 5 cm 12 cm Calculate the total surface area of the cuboid. ..............................................cm2 [3]
Mark scheme: 10 375 3 M2 for 2 (12 × 5 + 12 × 7.5 + 5 × 7.5 ) oe or M1 for 12 × 5 or 12 × 7.5 or 5 × 7.5
Q11 · The number of passengers on a train increases from 63 to 77
11 The number of passengers on a train increases from 63 to 77. Calculate the percentage increase. .................................................% [3]
Mark scheme: 11 2 3 77 − 22 or 22.2 or 22.22... M2 for 63[× 100] oe or 9 63 77 × 100 [– 100] oe 63 77 or M1 for oe 63
Q12 · A cone with height 14.8 cm has volume 275 cm3
12 A cone with height 14.8 cm has volume 275 cm3. Calculate the radius of the cone. 1 2 [The volume, V, of a cone with radius r and height h is V = r r h .] 3 ............................................... cm [3]
Mark scheme: 12 4.21 or 4.212.... 3 275 × 3 M2 for oe 14.8 × π 1 2 or M1 for 275 = × π × r × 14.8 oe 3
Question 13
13 Factorise. (a) 7k 2 - 15 k .................................................... [1] (b) 12 (m + p ) + 8 (m + p ) 2 .................................................... [2]
Mark scheme: 13(a) k ( 7 k − 15 ) final answer 1 13(b) 4 ( m + p )( 3 + 2 m + 2 p ) 2 B1 for (m + p)(12 + 8(m + p)) or (m + p)(12 + 8m + 8p) final answer or (4m + 4p)(3 + 2m + 2p) or (2m + 2p)(6 + 4m + 4p) or 2(2m + 2p)(3 + 2m + 2p) or 2(m + p)(6 + 4m + 4p)
Q14 · Eric invests an amount in a bank that pays compound interest at a rate of 2.16% per year
14 Eric invests an amount in a bank that pays compound interest at a rate of 2.16% per year. At the end of 5 years, the value of his investment is $6 999.31 . Calculate the amount Eric invests. $ .................................................. [3]
Mark scheme: 14 6290[.0…] 3 6999.31 M2 for 2.16 5 1 + 100 2.16 5 or M1 for [ A] 1 + 100
Q15 · O NOT TO B SCALE 104° 21° P w° A C A, B and C are points on the circle, centre O
15 O NOT TO B SCALE 104° 21° P w° A C A, B and C are points on the circle, centre O. AB and OC intersect at P. Find the value of w. w = .................................................... [3]
Mark scheme: 15 73 3 B1 for angle PBC = 52 B1 for APO or BPC = 55 or APC or OPB = 125
Q16 · 4 3.5 3 2.5 2 1.5 P 1 0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 By drawing a suitable tangent…
16 4 3.5 3 2.5 2 1.5 P 1 0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 By drawing a suitable tangent, estimate the gradient of the curve at the point P. .................................................... [3]
Mark scheme: 16 tangent ruled at x = 2 B1 −0.7 to –0.3 B2 dep on B1 or a close attempt at tangent at x = 2 or M1 for rise/run for their tangent at x = 2 must see correct or implied calculation from a drawn tangent
Q17 · 17 (a) Find the value of n when 5 n = 125 n =…
1 .17 (a) Find the value of n when 5 n = 125 n = .................................................... [1] 1 64 - 3 (b) Simplify 3 . e m o .................................................... [2]
Mark scheme: 17(a) − 3 1 17(b) m 2 1 or 0.25m final answer B1 for or 0.25 or 4–1 or m correct in final 4 4 answer
Q18 · A pipe is full of water
18 A pipe is full of water. The cross-section of the pipe is a circle, radius 2.6 cm. Water flows through the pipe into a tank at a speed of 12 centimetres per second. Calculate the number of litres that flow into the tank in one hour. ............................................ litres [3]
Mark scheme: 18 917 or 918 or 917.4 to 917.6 3 M2 for π × 2.6 2 × 12 × 60 × 60 ÷ 1000 or M1 for π × 2.62 isw or 12 × 60 × 60 ÷ 1000 isw If 0 scored SC1 for figs 917 to 918
Question 19
19 Simplify. 2 ab - b a 2 - b 2 .................................................... [3]
Mark scheme: 19 b 3 B1 for b ( a − b ) final answer a + b B1 for ( a + b )( a − b )
Q20 · - 1 1 6 20 (a) Work out e4 3eo- 5 4o
2 - 1 1 6 20 (a) Work out e4 3eo- 5 4o. [2] f p 3 - 1 (b) Find the value of x when the determinant of is 5. e- 7 xo x = .................................................... [2]
Mark scheme: 20(a) 7 8 2 B1 for 2 correct elements −11 36 20(b) 4 2 M1 for 3 x −−( 1) × ( −7 ) = 5 or better
Q21 · 521 Without using a calculator, work out 3 '
1 521 Without using a calculator, work out 3 ' . 8 12 You must show all your working and give your answer as a mixed number in its simplest form. .................................................... [4]
Mark scheme: 21 25 B1 75 or 8 24 25 12 75 10 M1 75 24 their × or their ÷ oe × 8 5 24 24 24 10 300 M1 75 60 30 their oe oe e.g.1800 , , , ,15 40 240 10 8 4 2 1 A1 7 cao 2
Q22 · 25 NOT TO Speed SCALE (m/s) 0 0 15 50 Time (s) The speed–time graph shows the first 50…
22 25 NOT TO Speed SCALE (m/s) 0 0 15 50 Time (s) The speed–time graph shows the first 50 seconds of a journey. Calculate (a) the acceleration during the first 15 seconds, .............................................m/s2 [1] (b) the distance travelled in the 50 seconds. ................................................. m [3]
Mark scheme: 22(a) 2 1 13 or 1.67 or 1.666 to 1.667 22(b) 1062.5 3 25 M2 for ( 50 + 35 ) oe 2 or M1 for one area
Q23 · A is the point (2, 3) and B is the point (7, -5)
23 A is the point (2, 3) and B is the point (7, -5). (a) Find the co-ordinates of the midpoint of AB. ( ........................, ........................) [2] (b) Find the equation of the line through A that is perpendicular to AB. Give your answer in the form y = mx + c . y = .................................................... [4]
Mark scheme: 23(a) (4.5, − 1) 2 B1 for each 23(b) 5 7 4 −−5 3 [ y = ]8 x + 4 M1 for 7 − 2 oe 8 M1 for –1/ their − 5 M1 for 3 = 2 × their gradient + c oe
Q24 · R S 97° Q 7.4 cm NOT TO SCALE 8.5 cm 26° 53° P Calculate (a) SR, SR =…
24 R S 97° Q 7.4 cm NOT TO SCALE 8.5 cm 26° 53° P Calculate (a) SR, SR = ............................................... cm [3] (b) RQ. RQ = ............................................... cm [4]
Mark scheme: 24(a) 5.95 or 5.954... 3 7.4 M2 for × sin53 sin97 sin97 sin53 or M1 for = oe 7.4 SR 24(b) 3.73 or 3.733 to 3.734 4 M2 for 8.5 2 + 7.4 2 − 2 × 8.5 × 7.4 × cos26 or M1 for implicit form A1 for 13.9[4...]
What was in this paper
The subtopics covered by these 24 questions, and how many questions each got. Open one in a new tab to see every Cambridge question on it.
3Area and perimeter2Fractions, decimals and percentages2Percentages2Ratio and proportion2Circle theorems I1Equations of linear graphs1Graphs of functions1Limits of accuracy1Money1Powers and roots1Rates1Relative and expected frequencies1Right-angled triangles1Surface area and volume1The four operations1Time1Vectors in two dimensions1What you needed in this session
Cambridge’s own grade thresholds for 2019 Feb/March, Paper 2 · Variant 2. A higher threshold means an easier paper — the bar moves with how the cohort did.