IGCSE 2021 Maths 0580/23 May/June

IGCSE 2021 0580/23 May/June (pdf)

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1. Write down the number that is 23 less than -1.6.
2. Write as a fraction in its simplest form.
   (a) 72%
   (b) 0.004
3. The diagram shows a pair of parallel lines and a straight line.
   Complete the statement with the correct geometrical reason.
4. Find the value of y.
5. Jo invests $600 for 7 years at a rate of 1.5% per year simple interest.
   Calculate the total interest earned during the 7 years.
6. Maria buys n pencils that cost p cents each.
   She pays with a $y note.
   Find, in terms of n, p and y, the amount of change Maria receives.
   Give your answer in cents.
7. 12 18 29 49 91 125
   From the list of numbers, write down
   (a) a cube number,
   (b) a prime number
8. Alex changes 190 euros (€) into pounds (£) when £1 = €1.1723 .
   Calculate the amount Alex receives.
   Give your answer correct to 2 decimal places.
9. Without using a calculator, work out

10. (a) Describe fully the single transformation that maps triangle T onto triangle A.
    (b) Draw the image of triangle T after an enlargement, scale factor -1/2 , centre (0, 0).
    
11. Simplify
12. x is an integer and - ≤ 2x - 1 < 3.
    Find the values of x.
13. Expand and simplify.
    6(t - q) - 2(t - 3q)
14. The magnitude of the vector
15. In the diagram, AB is parallel to CD.
    AD and BC intersect at X.
    AB = 6 cm, CD = 12 cm, CX = 8 cm and DX = 7 cm.
    (a) Complete the statement.
    Triangle ABX is ………. to triangle DCX.
    (b) Work out the length of BX.
    (c) The area of triangle DCX is 26.906 cm².
    Use this value to find the area of
    (i) triangle ABX,
    (ii) triangle ACX.
16. The sides of a regular hexagon are 80mm, correct to the nearest millimetre.
    Calculate the lower bound of the perimeter of the hexagon.
17. The interior angle of a regular polygon is 175°.
    Calculate the number of sides.
18. A car starts from rest and accelerates at a rate of 3m/s² for 4 seconds.
    The car then travels at a constant speed for 10 seconds.
    The diagram shows the speed–time graph for this journey.
    (a) Find the value of V.
    (b) Calculate the total distance travelled by the car during the 14 seconds
19. (a) P, Q and T are points on a circle.
    ATB is a tangent to the circle at T and PT = PQ.
    Find angle TPQ
    (b) The diagram shows a cyclic quadrilateral with an exterior angle of 68°.
    Find the value of w and the value of x.
20. Simplify
21. The shortest distance from B to AC is 12.8cm.
    Calculate BC
22. z is inversely proportional to the square of (y - 2).
    When y = 5, z = 9.
    Find z in terms of y.
23. A triangle has sides of length 11cm, 10 cm and 9cm.
    Calculate the largest angle in the triangle.
24. On the axes, sketch the graph of each of these functions.
25. Find the x-coordinates of the points on the graph of
26. Malik goes to a shop every day to buy bread.
    On any day, the probability that Malik goes to the shop in the morning is 0.7 .
    If he goes in the morning, the probability that there is bread for Malik to buy is 0.95 .
    If he goes later, the probability that there is bread for Malik to buy is 0.6 .
    Calculate the probability that, on any day, there is bread for Malik to buy.

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