IGCSE Maths 2021 0580/42 Feb/Mar

IGCSE 2021 0580/42 Feb/Mar (pdf)

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1. 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
2. (a) Describe fully the single transformation that maps
   (i) triangle A onto triangle B,
   (ii) triangle A onto triangle C.
3. (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.

4. (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.
5. (a) Calculate angle ADB.
   (b) Calculate DC.
   (c) Calculate the shortest distance from C to BD
6. (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.
7. (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.
8. 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.
9. (a) Factorise.
10. (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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