A-level Maths 2027 predicted topics

Find the 6th term of the geometric sequence $5, 15, 45, \dots$

Find the sum to infinity of $12 + 9 + 6.75 + \dots$

$X \sim N(\mu, 10^2)$ and a sample of $25$ is taken. Find the standard deviation of $\bar{X}$.

A random sample of $25$ from $N(\mu, 15^2)$ has $\bar{x} = 106$. For $H_0: \mu = 100$, $H_1: \mu > 100$, find the $p$-value to 4 decimal places.

Expand $(1 + 3x)^{-2}$ up to the $x^2$ term.

State the values of $x$ for which the expansion of $(1 - 4x)^{\frac{1}{2}}$ is valid.

$f(x) = x^3 + x - 3$. Find $f(1.2)$.

$f(x) = \cos x - x$, with $x$ in radians. Find $f(0.8)$ to 3 decimal places.

Find the exact value of $\arcsin\left(\frac{1}{2}\right)$ in radians.

Solve $\csc x = 2$ for $0^\circ \le x < 360^\circ$.