IGCSE 2021 0580/21 May/June (pdf)
- (a) Write down the order of rotational symmetry of this diagram.
(b) On the diagram, draw all the lines of symmetry.
- The probability that a train is late is 0.15 .
Write down the probability that the train is not late.
- The stem-and-leaf diagram shows the number of hours that each of 16 students studied last week.
(a) the median,
(b) the mode,
(c) the range
- The diagram shows two parallel lines intersected by two straight lines.
Find the values of a, b and c.
- Work out.
- (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.
- Solve the simultaneous equations.
You must show all your working.
2x + y = 3
x - 5y = 40
- Without using a calculator, work out
- 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.
- (a) Describe fully the single transformation that maps
(i) triangle A onto triangle B,
(ii) triangle A onto triangle C.
- (a) Simplify fully
- 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.
- 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.
- (y is directly proportional to the square root of (x - 3).
When x = 28, y = 20.
Find y when x = 39.
- Make h the subject of the formula 2 mh = g(1 - h).
- (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.
- 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.
- S is a point on PQ such that PS : SQ = 4 : 5.
- (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°.
- 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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