IGCSE Mathematics - International (0607) — October–November 2023, Paper 21

The diagram shows a straight line crossing two parallel lines. One marked angle is 105° and the angle x° is formed at the other parallel line. (NOT TO SCALE.) Find the value of x.

Find the mode.

A is the point (0, 7) and B is the point (−2, 1). M is the mid-point of AB. Find the coordinates of M.

Write 1.8796 correct to 4 significant figures.

A taxi fare, $F, consists of a fixed charge of $x plus $0.65 per kilometre travelled. Find a formula for F for a journey of y kilometres.

Find the next term and the nth term of this sequence. 0 1 4 9 16 ....

J = h³ + k³ Find the value of J when h = 3 and k = 4.

The length of the diagonal of a rectangle is 10 cm and the length of the rectangle is 8 cm. (NOT TO SCALE.) Work out the width of the rectangle.

Ulrich has these cards: A A B C C C D He picks 2 cards at random without replacement. Find the probability that both cards have the letter A.

5ʷ ÷ 5¹³ = 25 Find the value of w.

The volume of a cone is 18π cm³. The height of the cone is the same as the diameter of its base. Find the radius of the base.

ABCD is a cyclic quadrilateral. ABV is a straight line and TU is a tangent to the circle at C. The angle UCV (between the tangent and chord) is 55° and the exterior angle DBV at B…

y varies inversely as the square root of (x + 1). When x = 8, y = 5. Find y in terms of x.

The line L is perpendicular to the line 2y = 5 − x and passes through the point (2, 3). Find the equation of line L. Give your answer in the form y = mx + c.

Rationalise the denominator. 5 / (√5 − 1)

log 20 + log x = 2 Find the value of x.