IGCSE 2021 0580/21 May/June

IGCSE 2021 0580/21 May/June (pdf)

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1. (a) Write down the order of rotational symmetry of this diagram.
   (b) On the diagram, draw all the lines of symmetry.
2. The probability that a train is late is 0.15 .
   Write down the probability that the train is not late.
3. The stem-and-leaf diagram shows the number of hours that each of 16 students studied last week.
   Find
   (a) the median,
   (b) the mode,
   (c) the range
4. The diagram shows two parallel lines intersected by two straight lines.
   Find the values of a, b and c.
5. Work out.
6. (a) The nth term of a sequence is n² + 3n.
   Find the first three terms of this sequence.
   (b) These are the first five terms of a different sequence.
   25 18 11 4 -3
   Find the nth term of this sequence.
7. Solve the simultaneous equations.
   You must show all your working.
   2x + y = 3
   x - 5y = 40
8. Without using a calculator, work out
9. A is the point (5, -5) and B is the point (9, 3).
   (a) Find the coordinates of the midpoint of AB.
   (b) Find the length of AB.
   

10. (a) Describe fully the single transformation that maps
    (i) triangle A onto triangle B,
    (ii) triangle A onto triangle C.
11. (a) Simplify fully
12. The profit a company makes decreases exponentially at a rate of 0.9% per year.
    In 2014, the profit was $9500.
    Calculate the profit in 2019.
13. On a map, a lake has an area of 32 cm².
    The scale of the map is 1 : 24000.
    Calculate the actual area of the lake.
    Give your answer in km².
14. (y is directly proportional to the square root of (x - 3).
    When x = 28, y = 20.
    Find y when x = 39.
15. Make h the subject of the formula 2 mh = g(1 - h).
16. (a) Find the gradient of line l.
    (b) Find the equation of line l in the form y = mx + c.
    (c) Find the equation of the line that is perpendicular to line l and passes through the point (12, -7).
    Give your answer in the form y = mx + c.
17. A bag contains 3 blue buttons, 8 white buttons and 5 red buttons.
    Two buttons are picked at random from the bag, without replacement.
    Work out the probability that the two buttons are either both red or both white.
18. S is a point on PQ such that PS : SQ = 4 : 5.
19. (a) Sketch the graph of y x = tan x for 0° ≤ x ≤ 360°.
    (b) Solve the equation 5 tan x = 1 for 0° ≤ x ≤ 360°.
20. The distance between two towns is 600 km, correct to the nearest 10km.
    A car takes 8 hours 40 minutes, correct to the nearest 10 minutes, to travel this distance.
    Calculate the lower bound for the average speed of the car in km/h.

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