IGCSE Maths 2021 0580/42 Oct/Nov

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Questions and Worked Solutions for IGCSE 2021 0580/42 Oct/Nov Paper 4.

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IGCSE 2021 0580/42 Oct/Nov Questions (pdf)

  1. (a) Malena has 450 fruit trees.
    The fruit trees are in the ratio apple : pear : plum = 8 : 7 : 3.
    (i) Show that Malena has 200 apple trees.
    (ii) Find the number of plum trees.
    (iii) Malena wants to increase the number of pear trees by 32%.
    Calculate the number of extra pear trees she needs.
    (iv) Each apple tree produces 48.5kg of apples.
    The apples have an average mass of 165g each.
    Calculate the total number of apples produced by the 200 trees.
    Give your answer correct to the nearest 1000 apples
    (b) Malena’s land is valued at three million and seventy-five thousand dollars.
    (i) Write this number in figures.
    (ii) Write your answer to part (b)(i) in standard form
    (c) In 2020, each plum tree produced 37.7kg of plums.
    This was 16% more than in 2019.
    Calculate the mass of plums produced by each plum tree in 2019.
    (d) Malena invests $1800 at a rate of 2.1% per year compound interest.
    Calculate the value of her investment at the end of 15 years.
  2. (a) The cumulative frequency diagram shows information about the floor area, a m2, of each of 80 houses.
    Use the diagram to find an estimate of
    (i) the median,
    (ii) the lower quartile,
    (iii) the interquartile range,
    (iv) the number of houses with a floor area greater than 120 m2
    (b) The information about the 80 floor areas is shown in this frequency table
    (i) Calculate an estimate of the mean floor area
    (ii) Complete the histogram to show the information in the frequency table.
    (iii) Two of the houses are picked at random.
    Find the probability that one of the houses has a floor area greater than 130m2 and the other has a floor area 60m2 or less
  3. ABCDE is a pentagon.
    (i) Calculate AD and show that it rounds to 94.5m, correct to 1 decimal place.
    (ii) Calculate angle BAC.
    (iii) Calculate the largest angle in triangle CAD.
    Triangle PQR has the same area as triangle LMN.
    Calculate the shortest distance from R to the line PQ.

  1. (a) On the grid, draw the image of triangle A after
    (b) Describe fully the single transformation that maps triangle A onto triangle B
  2. The table shows some values for
  3. (a) Solve
    (i) 4(2x - 3) = 14
  4. (a) The diagram shows a container for storing grain.
    The container is made from a hemisphere, a cylinder and a cone, each with radius 2m.
    The height of the cylinder is 5.2m and the height of the cone is h m.
    (i) Calculate the volume of the hemisphere.
    Give your answer as a multiple of r.
    (iii) The container is full of grain.
    Grain is removed from the container at a rate of 35000kg per hour. 1m3 of grain has a mass of 620kg.
    Calculate the time taken to empty the container.
    Give your answer in hours and minutes
    A and B are points on a circle, centre O, radius r cm.
    The area of the shaded segment is 65cm2.
    Calculate the value of r.
  5. (a) Kaito runs along a 12km path at an average speed of x km/h.
    (i) Write down an expression, in terms of x, for the number of hours he takes.
    (ii) Yuki takes 1.5 hours longer to walk along the same path as Kaito.
    She walks at an average speed of (x - 4) km/h.
    (b) A bus travels 440 km, correct to the nearest 10km.
    The time taken to complete the journey is 6 hours, correct to the nearest half hour.
    Calculate the lower bound of the speed of the bus
  6. (a) F is the point (5, -2)
  7. (a) Find the coordinates of the turning points of the graph of
  8. (a) Triangle PQR is mathematically similar to triangle XYZ.
    (i) Find YZ.

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