IGCSE 2020 Maths 0580/22 Feb/Mar

IGCSE 2020 0580/22 Feb/Mar (pdf)

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1. From the list, write down a number that is
   (a) a multiple of 3,
   (b) a cube number,
   (c) a prime number,
   (d) an irrational number.
2. The number of people swimming in a pool is recorded each day for 12 days.
   24 28 13 38 15 26
   45 21 48 36 18 38
   (a) Complete the stem-and-leaf diagram.
   (b) Find the median number of swimmers.
3. Point A has coordinates (6, 4) and point B has coordinates (2, 7).
   Write AB as a column vector.
4. Find the interior angle of a regular polygon with 24 sides.
5. Without using a calculator, work out 15/28 %divide; 4/7
   You must show all your working and give your answer as a fraction in its simplest form.
6. The table shows the marks scored by 40 students in a test.
   Calculate the mean mark.
7. The diagram shows a right-angled triangle.
   (a) Calculate the area.
   (b) Calculate the perimeter.
   
8. Calculate the value of (2.3 × 10^-3) + (6.8 × 10^-4.
   Give your answer in standard form.
9. (a) Factorise completely.
   3x² - 12xy
   (b) Expand and simplify.
   (m - 3)(m + 2)

10. Sketch the graph of each function.
    (a) y = x - 3
    (b) y = 1/x
11. Describe fully the single transformation that maps
    (a) shape A onto shape B,
    (b) shape A onto shape C,
    (c) shape A onto shape D.
12. The population of a town decreases exponentially at a rate of 1.7% per year.
    The population now is 250000.
    Calculate the population at the end of 5 years.
    Give your answer correct to the nearest hundred.
13. Write the recurring decimal 0.26
    You must show all your working.
14. The box-and-whisker plot gives information about the heights, in centimetres, of some plants.
    (a) Write down the median.
    (b) Find
    (i) the range,
    (ii) the interquartile range.
15. A, B, C and D lie on the circle.
    PCQ is a tangent to the circle at C.
    Angle ACQ = 64°.
    Work out angle ABC, giving reasons for your answer.
16. Solve the simultaneous equations.
    You must show all your working.
    x = 7 - 3y
    x² - y² = 39
17. A is the point (3, 5) and B is the point (1, -7).
    Find the equation of the line perpendicular to AB that passes through the point A.
    Give your answer in the form y = mx + c.
    
18. A car travels at a constant speed.
    It travels a distance of 146.2m, correct to 1 decimal place.
    This takes 7 seconds, correct to the nearest second.
    Calculate the upper bound for the speed of the car.
    
19. (a) On the diagram, sketch the graph of y = cos x for 0° < x < 360°.
    (b) Solve the equation 4 cos x + 2 = 3 for 0° < x < 360°.
20. x² - 12x + a = (x + b)²
    Find the value of a and the value of b.
21. XY = 3a + 2b and ZY = 6a + 4b
    Write down two statements about the relationship between the points X, Y and Z.

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