IGCSE Maths 2020 0580/42 May/June

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Questions and Worked Solutions for IGCSE 2020 0580/42 May/June Paper 4.

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IGCSE 2020 0580/42 May/June (pdf)

  1. (a) (i) Divide $24 in the ratio 7 : 5.
    (ii) Write $24.60 as a fraction of $2870.
    Give your answer in its lowest terms.
    (iii) Write $1.92 as a percentage of $1.60 .
    (b) In a sale the original prices are reduced by 15%.
    (i) Calculate the sale price of a book that has an original price of $12.
    (ii) Calculate the original price of a jacket that has a sale price of $38.25 .
    (c) (i) Dean invests $500 for 10 years at a rate of 1.7% per year simple interest.
    Calculate the total interest earned during the 10 years.
    (ii) Ollie invests $200 at a rate of 0.0035% per day compound interest.
    Calculate the value of Ollie’s investment at the end of 1 year.
    (1 year = 365 days.)
    (iii) Edna invests $500 at a rate of r% per year compound interest.
    At the end of 6 years, the value of Edna’s investment is $559.78 .
    Find the value of r.
  2. (a) (i) Find 2p + q
    (ii) Find |p|.
    (b) A is the point (4, 1) and AB =
    Find the coordinates of B.
    (c) The line y = 3x - 2 crosses the y-axis at G.
    Write down the coordinates of G.
    (d) In the diagram, O is the origin, OT = 2TD and M is the midpoint of TC.
    OC = c and OD = d.
    Find the position vector of M.
    Give your answer in terms of c and d in its simplest form.
  3. The speed, vkm/h, of each of 200 cars passing a building is measured.
    The table shows the results.
    (a) Calculate an estimate of the mean.
    (b) (i) Use the frequency table to complete the cumulative frequency table.
    (ii) On the grid, draw a cumulative frequency diagram.
    (iii) Use your diagram to find an estimate of
    (a) the upper quartile,
    (b) the number of cars with a speed greater than 35km/h.
    (c) Two of the 200 cars are chosen at random
    . Find the probability that they both have a speed greater than 50km/h.
    (d) A new frequency table is made by combining intervals.
    On the grid, draw a histogram to show the information in this table.

  1. The diagram shows two triangles.
    (a) Calculate QR.
    (b) Calculate RS.
    (c) Calculate the total area of the two triangles.
  2. The diagram shows a field ABCD.
    The bearing of B from A is 140°.
    C is due east of B and D is due north of C.
    AB = 400m, BC = 350m and CD = 450m.
    (a) Find the bearing of D from B.
    (b) Calculate the distance from D to A.
    (c) Jono runs around the field from A to B, B to C, C to D and D to A.
    He runs at a speed of 3m/s.
    Calculate the total time Jono takes to run around the field.
    Give your answer in minutes and seconds, correct to the nearest second.
  3. f(x) = 3x + 2
    g(x) = x2 + 1
    h(x) = 4x
    (a) Find h(4).
    (b) Find fg(1).
    (c) Find gf(x) in the form ax2 + bx + c
    (d) Find x when f(x) = g(7).
    (e) Find f-1(x)
    (f) Find g(x)/f(x) + x
    Give your answer as a single fraction, in terms of x, in its simplest form.
    (g) Find x when h-1(x) = 2
  4. Tanya plants some seeds.
    The probability that a seed will produce flowers is 0.8 .
    When a seed produces flowers, the probability that the flowers are red is 0.6 and the probability that the flowers are yellow is 0.3 .
    (a) Tanya has a seed that produces flowers.
    Find the probability that the flowers are not red and not yellow.
    (b) (i) Complete the tree diagram.
    (ii) Find the probability that a seed chosen at random produces red flowers.
    (iii) Tanya chooses a seed at random.
    Find the probability that this seed does not produce red flowers and does not produce yellow flowers.
    (c) Two of the seeds are chosen at random.
    Find the probability that one produces flowers and one does not produce flowers.
  5. (a) Triangle ABC is mathematically similar to triangle PQR.
    The area of triangle ABC is 16 cm2.
    (i) Calculate the area of triangle PQR.
    (ii) The triangles are the cross-sections of prisms which are also mathematically similar.
    The volume of the smaller prism is 320cm3.
    Calculate the length of the larger prism.
    (b) A cylinder with radius 6cm and height hcm has the same volume as a sphere with radius 4.5cm.
    Find the value of h.
    (The volume, V, of a sphere with radius r is V = 4/3 πr3)
    (c) A solid metal cube of side 20 cm is melted down and made into 40 solid spheres, each of radius r cm.
    Find the value of r.
    (The volume, V, of a sphere with radius r is V = 4/3 πr3)
    (d) A solid cylinder has radius x cm and height 7x/2 cm.
    The surface area of a sphere with radius Rcm is equal to the total surface area of the cylinder.
    Find an expression for R in terms of x.
    (The surface area, A, of a sphere with radius r is A = 4πr2.)
  6. (a) (i) Write x2 + 8x - 9 in the form (x + k)2 + h .
    (ii) Use your answer to part (a)(i) to solve the equation x2 + 8x - 9 = 0
    (b) The solutions of the equation x2 + bx + c = 0 are
    Find the value of b and the value of c.
    (c) (i) On the diagram,
    (a) sketch the graph of y = (x - 1)2
    (b) sketch the graph of y = 1/2 x + 1
    (ii) The graphs of y = (x - 1)2 and y = 1/2 x + 1 intersect at A and B.
    Find the length of AB.
  7. (a) y = x4 - 4x3
    (i) Find the value of y when x = -1.
    (ii) Find the two stationary points on the graph of y = x4 - 4x3
    (b) y = xp + 2xq
    Find the value of p and the value of q.

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