IGCSE 2020 0580/23 Nov/Dec

IGCSE 2020 0580/23 Nov/Dec (questions)

IGCSE 2020 0580/23 Nov/Dec (mark scheme)

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1. Write down the cube number that is greater than 50 but less than 100.
2. Calculate.
3. In triangle ABC, BC = 7.6cm and AC = 6.2cm.
   Using a ruler and compasses only, construct triangle ABC.
   Leave in your construction arcs.
   The side AB has been drawn for you.
4. Simplify.
   a² ÷ a⁶
5. Thor changes 40 000 Icelandic Krona into dollars when the exchange rate is 1 krona = $0.0099.
   Work out how many dollars he receives.
6. The diagram shows triangle ABC.
   The triangle is reflected in the line BC to give a quadrilateral ABDC.
   (a) Write down the mathematical name of the quadrilateral ABDC.
   (b) Find angle ACD.
7. Change 457000 cm² into m².
8. The length, l cm, of a line is 18.3cm, correct to the nearest millimetre.
   Complete this statement about the value of l.
9. Without using a calculator, work out 1 1/7 × 2 1/10
   You must show all your working and give your answer as a mixed number in its simplest form.

10. Solve the simultaneous equations.
    You must show all your working.
    3x - 8y = 22
    x + 4y = 4
11. Simplify.
    2x² × 5x⁵
12. A straight line, l, has equation y = 5x + 12.
    (a) Write down the gradient of line l.
    (b) Find the coordinates of the point where line l crosses the x-axis.
    (c) A line perpendicular to line l has gradient k.
    Find the value of k.
13. Use set notation to describe the shaded region.
14. N = 2⁴ × 3 &times 7⁵
    PN = K, where P is an integer and K is a square number.
    Find the smallest value of P.
15. Make x the subject of this formula.
16. A paperweight has height 4cm and volume 38.4cm³.
    A mathematically similar paperweight has height 7cm.
    Calculate the volume of this paperweight.
17. Adil and Brian are paid the same wage.
    Adil is given a 7% pay decrease and his new wage is $427.80 .
    Brian is given a 7% pay increase.
    Work out Brian’s new wage.
18. (a) Simplify.
    (4xy²)³
    (b) 25 = 125^k
    Find the value of k.
19. The diagram shows the speed–time graph for the final 40 seconds of a car journey.
    At the start of the 40 seconds the speed is v m/s.
    (a) Find the acceleration of the car during the first 24 seconds.
    (b) The total distance travelled during the 40 seconds is 1.24 kilometres.
    Find the value of v.
20. Factorise.
    3x + 8y - 6ax - 16ay
21. OAB is the sector of a circle, centre O.
    OB = 8cm and angle AOB = 30°.
    BP is perpendicular to OA.
    (a) Calculate AP.
    (b) Work out the area of the shaded region APB.
22. The table shows information about the times, t seconds, taken by each of 100 students to solve a puzzle.
23. y is inversely proportional to the square root of x.
    When y = 7, x = 2.25.
    Write y in terms of x.
24. Simplify.
25. Solve 3 tan x = -4 for 0° ≤ x ≤ 360°

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