IGCSE 2021 0580/42 Feb/Mar (pdf)
- These are the rates charged by a painter, a plumber and an electrician who do some work for Mr Sharma.
(a) The painter works for 7 hours.
Calculate the amount Mr Sharma pays the painter.
(b) Mr Sharma pays the plumber $252.
Calculate how many hours the plumber works.
(c) Mr Sharma pays the electrician $224.
Calculate how many hours the electrician works
- (a) Describe fully the single transformation that maps
(i) triangle A onto triangle B,
(ii) triangle A onto triangle C.
- (a) The diagram shows two straight lines intersecting two parallel lines.
Find the values of a, b and c.
Points R and S lie on a circle with diameter PQ.
RQ is parallel to PS.
Angle RPQ = 58°.
Find the value of x, giving a geometrical reason for each stage of your working.
Points A, B and C lie on a circle, centre O.
Angle AOC = 142°.
Find the value of y.
- (a) A shop gives each of 1000 people a voucher.
28 people use their voucher.
The shop now gives each of 16500 people a voucher.
Calculate how many of these 16500 people are expected to use their voucher.
(b) In a class activity, all the 15 students wear hats.
7 students wear red hats, 6 students wear green hats and 2 students wear white hats.
(i) One of these students is picked at random.
Find the probability that this student wears a red hat.
(ii) Two of the 15 students are picked at random.
Show that the probability that these two students wear hats of the same colour is 37/105.
(iii) Three of the 15 students are picked at random.
Find the probability that at least two of these three students wear red hats.
- (a) Calculate angle ADB.
(b) Calculate DC.
(c) Calculate the shortest distance from C to BD
- (a) The grid shows the graph of y = a + bx2.
The graph passes through the points with coordinates (0, 4) and (1, 1).
(i) Find the value of a and the value of b.
(ii) Write down the equation of the tangent to the graph at (0, 4).
(iii) The equation of the tangent to the graph at x =-1 is y = 6x + 7.
Find the equation of the tangent to the graph at x = 1.
- (a) The box-and-whisker plot shows information about the marks scored by some students in a test.
(i) Write down the median mark.
(ii) Work out the range.
(iii) Jais scored a mark in the test that was higher than the marks scored by 75% of the students.
Write down a possible mark for Jais.
(iv) This box-and-whisker plot shows information about the marks scored by the same students in
a second test.
Make one comparison between the distributions of marks in the two tests.
- The diagram shows a sector OXY of a circle with centre O and radius 9.5cm.
The sector angle is 53°.
A lies on OX, B lies on OY and OA = OB.
(i) Show that the area of the sector is 41.7 cm2, correct to 1 decimal place.
The diagram shows a sector OPQ of a circle with centre O and radius 24cm.
The sector angle is 60°.
A cone is made from this sector by joining OP to OQ.
- (a) Factorise.
- (a) A box is a cuboid with length 45cm, width 30cm and height 42cm.
The box is completely filled with 90.72kg of sand.
Calculate the density of this sand in kg/m3
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