IGCSE Maths 2021 0580/42 May/June

IGCSE 2021 0580/42 May/June (pdf)

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1. (a) A 2.5-litre tin of paint costs $13.50.
   In a sale, the cost is reduced by 14%.
   (i) Work out the sale price of this tin of paint.
   (ii) Work out the cost of buying 42.5 litres of paint at this sale price.
   (b) Henri buys some paint in the ratio red paint : white paint : green paint = 2 : 8 : 5.
   (i) Find the percentage of this paint that is white.
   (ii) Henri buys a total of 22.5 litres of paint.
   Find the number of litres of green paint he buys.
   (c) Maria paints a rectangular wall.
   The length of the wall is 20.5m and the height is 2.4m, both correct to 1 decimal place.
   One litre of paint covers an area of exactly 10m².
   Calculate the smallest number of 2.5-litre tins of paint she will need to be sure all the wall is painted.
   Show all your working.
2. The table shows some values for
   (a) (i) Complete the table.
   (ii) On the grid, draw the graph of
   (b) By drawing a suitable straight line, solve the equation
   (c) There are no solutions to the equation
   Complete the following statements.
   The highest possible value of k is
   The equation of the asymptote to the graph of
3. (a) Simplify, giving your answer as a single power of 7.

4. (a) The mass, m kg, of each of 40 parcels in a warehouse is recorded.
   The table shows information about the masses of these parcels.
   (i) Complete the histogram to show this information.
   (ii) Calculate an estimate of the mean mass of the parcels.
   (iii) A parcel is picked at random from the 40 parcels.
   Find the probability that this parcel has a mass of 2kg or less.
   (iv) Two parcels are picked at random without replacement from those with a mass greater than 2 kg.
   Work out the probability that one of them has a mass greater than 7 kg and the other has a mass of 4 kg or less.
   (b) A van delivers parcels from a different warehouse.
   The box-and-whisker plot shows information about the masses of the parcels in the van
   (i) Find the median
   (ii) Find the interquartile range.
   (iii) Two parcels are removed from the van at the first delivery.
   The masses of these parcels are 2.4kg and 5.8 kg.
   Describe the effect that removing these parcels has on the median mass of the remaining parcels.
   Give a reason for your answer.
5. (a)
6. The diagram shows a quadrilateral ABCD made from two triangles, ABD and BCD.
   (a) Show that BD = 16.9m, correct to 1 decimal place.
   (b) Calculate angle CBD.
   (c) Find the area of the quadrilateral ABCD.
   (d) Find the shortest distance from B to AD.
7. (a) On the grid, draw the image of
8. (a) A cuboid has length Lcm, width Wcm and height Hcm.
   The diagram shows the net of this cuboid.
   The ratio W : L = 1 : 2.
   Find the value of L, the value of W and the value of H.
   (b) The diagram shows a solid pyramid with a rectangular base ABCD.
   E is vertically above D.
9. (a) (i) The equation
10. The table shows four sequences A, B, C and D.

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