Cambridge CIE IGCSE Past Papers and solutions.

Questions and Worked Solutions for IGCSE 2021 0580/42 Feb/Mar Paper 4.

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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 + bx
^{2}.

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 cm^{2}, 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/m^{3}

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