IGCSE Mathematics - Additional (0606) — October–November 2024, Paper 21

Show that tan θ + cot θ can be written as sec θ cosec θ.

Given that y = tan x − x, find dy/dx. Write your answer in terms of tan x.

Solve the equation 8^(1/x) − 2 × 8^(−1/x) = 1.

The diagram shows the triangle OAC. The point B lies on AC such that AB : BC = p : q, where p and q are constants (p ≠ −q). OA = a, OB = b and OC = c. Show that b = (qa + pc)/(q +…

Given that loga(p + 1) + 1/(logp a) − loga(p + 2) + loga 5 = loga 12, find the value of p.

In this question all lengths are in metres. The diagram shows a shape ABCDEF. AB, BD and DE are three sides of a rectangle. O is the mid-point of BD. AFE is an arc of a circle…

A curve has equation y = 2x cos x. The normal to the curve at (π, −2π) meets the x-axis and y-axis at points P and Q. Find the exact area of triangle POQ.

A particle moves in a straight line so that its displacement from a fixed point O at time t seconds is x metres, where x = t³ + t² − t + 8 and t ≥ 0. Find the time when the…

A curve has equation y = x² − 8x + c, where c is a constant. Find the value of c given that the curve crosses the x-axis at x = 2.

A class contains 7 girls and 8 boys. A group of 6 is selected from the class. The group must contain at least 3 girls and at least 2 boys. Find the number of different groups that…

f(x) = x/(x − 1) for −10 ≤ x ≤ 10, x ≠ 1. The diagram shows the graph of y = f(x). Use the diagram to explain why f is a function.

Two arithmetic progressions, A and B, each have 100 terms. Their terms are denoted by a₁, a₂, a₃, a₄, … a₁₀₀ and b₁, b₂, b₃, b₄, … b₁₀₀ respectively. It is given that a₁ = b₁₀₀ =…