IGCSE Maths 2022 0580/42 May/June

IGCSE 2022 0580/42 May/June (pdf)

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1. (a) Find the lowest common multiple (LCM) of 30 and 75.
   (b) Share $608 in the ratio 4 : 5 : 7
   
2. The points P, Q, R and S lie on a circle with diameter PR.
   Work out the size of angle PSQ, giving a geometrical reason for each step of your working.
3. A line, l, joins point F (3, 2) and point G (- 5, 4).
   (a) Calculate the length of line l.
   (b) Find the equation of the perpendicular bisector of line l in the form y = mx + c.
   (c) A point H lies on the y-axis such that the distance GH = 13 units.
   Find the coordinates of the two possible positions of H.
4. ABCD is a trapezium with DC parallel to AB.
   DC = 6.4cm, DB = 10.9 cm, angle CDB = 38° and angle DAB = 45°.
   (a) Find CB.
5. (a) Draw the lines of symmetry of the rectangle.
6. (a) At a festival, 380 people out of 500 people questioned say that they are camping.
   There are 55300 people at the festival.
   Calculate an estimate of the total number of people camping at the festival.
7. Information about the mass, mkg, of each of 150 children is recorded in the frequency table.
8. (a) Solve.
   10 - 3p = 3 + 11p
9. In triangle PQR, M lies on QR and S lies on PR.
   Explain, giving reasons, why triangle PMR is similar to triangle MSR.
10. (a) Find all the positive integers which satisfy the inequality.
    3n - 8 > 5n -15
11. (a) A rectangular sheet of paper ABCD is made into an open cylinder with the edge AB meeting the edge DC.
    AD = 28cm and AB = 20cm
12. A curve has equation y = x³ - kx² + 1
    When x = 2, the gradient of the curve is 6.
    (a) Show that k = 1.5.

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