IGCSE Maths 2020 0580/11 May/June

IGCSE 2020 0580/11 May/June (pdf)

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1. Write down the value of the 7 in the number 570296.
   
2. The table shows the temperature, in °C, at midday on the first day of each month during one year in a city.
   Calculate the mean of these temperatures.
3. Write these numbers in order, starting with the smallest.
4. (a) On each shape draw all the lines of symmetry.
   (b) Write down the order of rotational symmetry of this shape.
5. In the triangle ABC, AB = AC and angle BAC = 38°.
   BCD is a straight line.
   Work out angle ACD.
6. (a) Diego flies from Madrid to Buenos Aires.
   His flight leaves at 20 55 and arrives at 03 50 local time.
   The local time in Buenos Aires is 5 hours behind the local time in Madrid.
   Work out, in hours and minutes, the time the flight takes.
   (b) Diego changes 200 euros into Argentine Peso.
   The exchange rate is 1 euro = 24.8 pesos.
   Work out how many pesos he receives.
   (c) The distance between Madrid and Buenos Aires is 10050km.
   Diego’s return flight takes 12 hours 30 minutes.
   Calculate the average speed, in km/h, for the return flight.

7. Rectangle A measures 3 cm by 8 cm.
   Five rectangles congruent to A are joined to make a shape.
   Work out the perimeter of this shape.
8. Find the highest odd number that is a factor of 60 and a factor of 90.
9. (a) Write PQ as a column vector.
   (b) Write 3PQ as a single vector.
10. Work out the size of one interior angle of a regular 9-sided polygon.
11. A cone has radius 4.5 cm and height 10.4cm.
    Calculate, in terms of r, the volume of the cone.
    (The volume, V, of a cone with radius r and height h is V = 1/3 πr²h)
12. (a) The nth term of a sequence is 60-8n.
    Find the largest number in this sequence.
    (b) Here are the first five terms of a different sequence.
    12 19 26 33 40
    Find an expression for the nth term of this sequence.
13. Factorise completely.
    21a² + 28ab
    
14. The diagram shows a trapezium.
    Work out the value of x.
15. Simplify.
    4p⁵q³ × p²q^-4
16. (a) Write the number 0.0605 in standard form.
    (b) Calculate (1.63 × 10¹²) × (2.47 × 10^-1).
    Give your answer in standard form.
17. Expand and simplify.
    (x - 5)(x - 7)
18. Mrs Salaman gives her class two mathematics tests.
    The scatter diagram shows information about the marks each student scored.
    (a) Write down the highest mark scored on test 1.
    (b) Write down the type of correlation shown in the scatter diagram.
    (c) Draw a line of best fit on the scatter diagram.
    (d) Hamish scored a mark of 40 on test 1.
    He was absent for test 2.
    Use your line of best fit to find an estimate for his mark on test 2.
19. The length, l cm, of a sheet of paper is 29.7 cm, correct to the nearest millimetre.
    Complete this statement about the value of l.
20. Without using a calculator, work out
    You must show all your working and give your answer as a fraction in its simplest form.
21. Lucia invests $5000 at a rate of 4.5% per year compound interest.
    Calculate the value of her investment at the end of 7 years.
22. (a) Find the equation of line L in the form y = mx + c.
    (b) On the grid, draw a line that is perpendicular to line L.
23. Explain why triangle ABC is similar to triangle PQR.

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