IGCSE Maths 2020 0580/31 Oct/Nov Paper 3

IGCSE 2020 0580/31 Oct/Nov (pdf)

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1. Sean is the manager of a museum.
   (a) He buys a Chinese pot costing 1200 yuan.
   The exchange rate is $1 = 6.4 yuan.
   Work out the cost of this pot in dollars.
   (b) Sean records the maximum and minimum temperatures, in °C, at the museum.
   Some of the results for one week are shown in the table.
   (i) Find the difference between the maximum temperature and the minimum temperature on Wednesday
   (ii) The minimum temperature on Saturday was 2°C higher than the minimum temperature on Monday.
   Find the minimum temperature on Saturday
   (iii) In this week the range of temperatures was 23°C.
   Find the minimum temperature on Sunday.
   (c) These are the opening times for the museum.
   Monday to Friday 0900 to 1700
   Saturday and Sunday 10 00 to 16 00
   During opening hours the museum has 4 security guards working.
   Each guard works a maximum of 30 hours each week.
   Work out the smallest number of guards needed each week.
   (d) The entry price to the museum is $18.
   This price is increased by 28%.
   Find the increased entry price.
2. (a) Jian has a fair spinner in the shape of a regular hexagon.
   The spinner is numbered 2, 2, 3, 4, 4, 5.
   Jian spins the spinner.
   Find the probability that the spinner lands on
   (i) an even number,
   (ii) a number less than 6
   (iii) the number 1.
   (b) Mei has two fair square spinners, A and B.
   Spinner A is numbered 1, 2, 2, 4 and spinner B is numbered 3, 3, 4, 5
   She spins both spinners and adds the two numbers.
   (i) Complete the table to show all the possible outcomes.
   (ii) Use the table to write down the probability that the total is
   (a) 5,
   (b) more than 5.
   (c) Ning has a spinner numbered 1 to 6.
   She spins it 50 times and her results are shown in the table.
   (i) Write down the mode
   (ii) Find the median.
   (iii) Work out the mean.

3. (a)
   8 15 18 33 39 41 51 57 60 81
   From this list, write down
   (i) a factor of 54,
   (ii) a multiple of 19,
   (iii) a prime number
   (b) Write down the reciprocal of 64.
   (c) (i) Write 4.81 x 10^-3 as an ordinary number.
   (ii) Write 75000 in standard form.
4. (a) Simplify.
   6a - 3b + 2a - 4b
   (b) Expand.
   5(x - 3)
5. (a) Write one hundred and twenty thousand and twenty in figures.
6. The diagram shows a right-angled triangular prism.
   (a) On the 1 cm² grid, complete the net of the prism.
   One face has been drawn for you.
   (b) Work out the surface area of the prism.
   (c) Work out the volume of the prism.
7. (a) The diagram shows an isosceles triangle and a straight line.
   Work out the value of w
   (b) ABCD is a rectangle.
   AE is parallel to DBF.
   Find the value of x and the value of y.
   (c) A, B and C are points on a circle.
   AC is a diameter of the circle.
   Find the value of a
   (d) Two regular octagons and a square meet at point P.
   Show, by calculation, that the three interior angles at P add up to 360°.
8. (a) Describe fully the single transformation that maps
   (i) triangle A onto triangle B,
   (ii) triangle A onto triangle C,
   (iii) triangle A onto triangle D.
   (b) On the grid, draw the image of triangle A after a reflection in the line x =-2.
9. (a) Complete the table of values for y
10. (a) These are the first four terms of a sequence.
    8 15 22 29
    (i) Write down the next term.
    (ii) Write down the term to term rule for continuing this sequence.
    (iii) Find an expression for the nth term.
    (b) Find the next term in each of these sequences.
    (i) 18, 21, 26, 33, 42, …
    (ii) 18, 20, 24, 32, 48, …
    (c) Find the first three terms of the sequence with nth term n² + 5n

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