IGCSE Mathematics - Additional (0606) — October–November 2023, Paper 13

On the axes provided, sketch the graphs of y = 2x + 5 and y = 4x − 3, stating the intercepts with the coordinate axes.

The perpendicular bisector of the line joining the points (−3, 4/3) and (6, −7/3) passes through the point (2, k). Find the value of k.

On the axes provided, draw the graph of y = 2 sin(x/3) − 1 for −360° ≤ x ≤ 360°.

The polynomial P is given by P(x) = ax³ + bx² + 3x + 2, where a and b are integers. P(x) has a factor of 2x + 1. P(x) has a remainder of −6 when divided by x + 1. Find the values…

A 5-character password is to be formed from the following 10 characters: Letters A B C X Y Z and Symbols $ &. No character can be used more than once in any 5-character password.…

The polynomial q(x) is given by q(x) = −(1/3)(2x − 1)(x + 3)². Find the x-coordinates of the stationary points on the curve y = q(x).

Solve the equation 6x^(1/3) − 2x^(−1/3) − 1 = 0. Give your answers in exact form.

The first three terms, in descending powers of x, in the expansion of (2x² − 1/(4x))ⁿ can be written in the form 256x¹⁶ + ax¹³ + bx^c, where n, a, b and c are integers. Find the…

Given that y = (5x + 2)^(1/3)/(x − 1)² (i.e. cube root of (5x + 2) over (x − 1)²), show that dy/dx can be written in the form −(Ax + B)/(3(5x + 2)^(2/3)(x − 1)³), where A and B…

In this question, all lengths are in centimetres and all angles are in radians. The diagram shows the sector OAB of a circle with centre O and radius 20. The perimeter of this…

In the triangle OAB, OA = a and OB = b. The straight line XYZ is such that: OX = (4/5)b; AY = (1/3)AB; YZ = m·XY, where m is a constant. Show that XY = (2/3)a − (7/15)b.

Solve the equation 3 cosec²(2x/3 − π/3) = 4, for 0 < x ≤ 3π. Give your answers in terms of π.