IGCSE Mathematics - Additional (0606) — May–June 2024, Paper 22

On the axes provided, sketch the graph of y = (2x − 5)(x + 3)(1 − x), stating the intercepts with the coordinate axes.

Evaluate ∫₂^π... (specifically ∫ from 2 to π of cos(x/4) dx). You must show all your working.

Determine whether the equation (4x + 1)(3x + 2)/(5x − 3) = x + 1 has two distinct real roots, two equal roots or no real roots.

The polynomial p is such that p(x) = 6x³ + x² − 12x + 5. Find the remainder when p(x) is divided by x − 2.

A curve has equation y = 5e^(2x − 1) + e. The tangent to the curve at the point where x = 1 cuts the x-axis at the point P. Find the equation of the tangent in the form y = mx +…

Show that (sin³x · cosec x)/(cot x) can be written as sin²x tan x.

Find the number of different ways the 9 letters of the word POLYMATHS can be arranged when the O and A are not next to each other.

An experiment was carried out and values of y for certain values of x were recorded. The table shows the values recorded. x 15 30 45 60 75 --- ---- ---- ---- ---- ---- y 10 13 22…

The diagram shows part of the curve y = 32x − 4x² − 48 and the line AB. The curve and the line AB meet the x-axis at A and meet again at the point B(5, 12). The line CD extended…

The functions f and fg are defined by f(x) = e^(x²) + 3 for x < 0, and fg(x) = e^(2x) for x 3/2. Explain why f⁻¹ exists.

In the binomial expansion of (2 + x/2)ⁿ, the first three terms in increasing powers of x are b + abx + (9/8)abx². Find the values of the constants n, a and b.