IGCSE 2020 0580/42 Feb/Mar

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Questions and Worked Solutions for IGCSE 2020 0580/42 Feb/Mar Paper 4.

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IGCSE 2020 0580/42 Feb/Mar (pdf)

  1. Dhanu has a model railway.
    (a) He has a train that consists of a locomotive and 4 coaches.
    The mass of the locomotive is 87g and the mass of each coach is 52g.
    (i) Work out the total mass of the train.
    (ii) Work out the mass of the locomotive as a percentage of the total mass of the train.
    (b) The train is 61cm long and travels at a speed of 18cm/s.
    It takes 4 seconds for the whole of the train to cross a bridge.
    Calculate the length of the bridge.
    (c) A new locomotive costs $64.
    Calculate the cost of the locomotive in rupees when the exchange rate is 1 rupee = $0.0154 .
    Give your answer correct to the nearest 10 rupees.
    (d) The cost of a railway magazine increases by 12.5% to $2.70 .
    Calculate the cost of the magazine before this increase.
    (e) Dhanu plays with his model railway from 0650 to 11 15.
    He then rides his bicycle for 3 hours.
    Find the ratio time playing with model railway : time riding bicycle.
    Give your answer in its simplest form.
    (f) The value of Dhanu’s model railway is $550.
    This value increases exponentially at a rate of r% per year.
    At the end of 5 years the value will be $736.
    Calculate the value of r.
  2. (a) The table shows some values for y = 2x3 - 4x2 + 3.
    (i) Complete the table.
    (ii) On the grid, draw the graph of y = 2x3 - 4x2 + 3 for -1 ≤ x ≤ 2
    (iii) Use your graph to solve the equation 2x3 - 4x2 + 3 = 1.5
    (iv) The equation 2x3 - 4x2 + 3 = k has only one solution for -1 ≤ x ≤ 2.
    Write down a possible integer value of k.
    (b) (i) On the grid, draw the tangent to the curve at x = 1.
    (ii) Use your tangent to estimate the gradient of the curve at x = 1.
    (iii) Write down the equation of your tangent in the form y = mx + c.
  3. (a) Manjeet uses 220 litres of water each day.
    She reduces the amount of water she uses by 15%.
    Calculate the number of litres of water she now uses each day.
    (b) Manjeet has two mathematically similar bottles in her bathroom.
    The large bottle holds 1.35 litres and is 29.7cm high.
    The small bottle holds 0.4 litres.
    Calculate the height of the small bottle.
    (c) Water from Manjeet’s shower flows at a rate of 12 litres per minute.
    The water from the shower flows into a tank that is a cuboid of length 90cm and width 75cm.
    Calculate the increase in the level of water in the tank when the shower is used for 7 minutes.

  1. A solid metal cone has radius 1.65cm and slant height 4.70 cm.
    (a) Calculate the total surface area of the cone.
    (The curved surface area, A, of a cone with radius r and slant height l is A = πrl.)
    (b) Find the angle the slant height makes with the base of the cone.
    (c) (i) Calculate the volume of the cone.
    (The volume, V, of a cone with radius r and height h is V = 1/3 πr2h)
    (ii) A metal sphere with radius 5cm is melted down to make cones identical to this one.
    Calculate the number of complete identical cones that are made.
    (The volume, V, of a sphere with radius r is V = 4/3 πr3)
  2. (a) Write as a single fraction in its simplest form.
    (b) Find the value of k.
    (c) Expand and simplify.
    (y + 3)(y - 4)(2y - 1)
    (d) Make x the subject of the formula.
  3. Suleika has six cards numbered 1 to 6.
    (a) She takes one card at random, records the number and replaces the card.
    (i) Write down the probability that the number is 5 or 6.
    (ii) Suleika does this 300 times.
    Find how many times she expects the number 5 or 6.
    (b) Suleika takes two cards at random, without replacement.
    (i) Find the probability that the sum of the numbers on the two cards is 5.
    (ii) Find the probability that at least one of the numbers on the cards is a square number.
  4. (a) Naga has n marbles.
    Panav has three times as many marbles as Naga.
    Naga loses 5 marbles and Panav buys 10 marbles.
    Together they now have more than 105 marbles.
    Write down and solve an inequality in n.
    (b) y is inversely proportional to x2.
    When x = 4, y = 7.5.
    Find y when x = 5.
    (c) Find the nth term of each sequence.
    (i) 4 2 0 -2 -4 …
    (ii) 1 7 17 31 49 …
  5. (a) The diagram shows a quadrilateral PQRS formed from two triangles, PQS and QRS.
    (i) QR,
    (ii) PS,
    (iii) the area of quadrilateral PQRS.
    (b) The diagram shows an open box ABCDEFGH in the shape of a cuboid.
    AB = = 20 cm, BC 18 cm and AE = 16 cm.
    A thin rod AGX rests partly in the box as shown.
    The rod is 40cm long.
    (i) Calculate GX, the length of the rod which is outside the box.
    (ii) Calculate the angle the rod makes with the base of the box.
  6. This year, 40 students have each travelled by one or more of plane (P), train (T) or boat (B).
    7 have travelled only by plane.
    11 have travelled only by train.
    9 have travelled only by boat.
    n(P ∩ T) = 8
    n(B ∩ T) = 3
    n(B ∩ P) = 6
    (a) Complete the Venn diagram.
    (b) Find n((P ∪ B)').
    (c) Use set notation to complete the statement.
    (P ∪ T ∪ B)' = ….
    (d) Two students are chosen at random.
    Calculate the probability that they both have travelled only by plane.
    (e) Two students are chosen at random from those who have travelled by train.
    Calculate the probability that they both have also travelled by plane.
  7. f(x) = 4x - 1
    g(x) = x2
    h(x) = 3-x
    (a) Find in its simplest form
    (i) f(x - 3)
    (ii) g(5x)
    (b) Find f-1(x)
    (c) Find the value of hh(l) , correct to 4 significant figures.
    (d) (i) Show that g(3x - 2) - h(-3) can be wrtiiten as 9x2 - 12x - 23
    (ii) Use the quadratic formula to solve 9x2 - 12x - 23 = 0
    Give your answers correct to 2 decimal places.
    (e) Find x when f(61) = h(x) .
  8. A curve has equation y = x3 - 3x + 4
    (a) Work out the coordinates of the two stationary points.
    (b) Determine whether each stationary point is a maximum or a minimum.
    Give reasons for your answers.

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