A-Level CAIE Mathematics AS 2.1 Algebra Question Bank

Solve the inequality |2 x+1|<|2 x-5|.

Solve the inequality |5 x+7|>|2 x-3|.

Solve the inequality 3|2 x-1|>|x+4|.

Find the quotient and remainder when $x^{4}$ is divided by $x^{2}+2 x-1$.

Find the quotient and remainder when $2 x^{4}+1$ is divided by $x^{2}-x+2$.

Solve the inequality |3 x-2|<|x+5|.

Solve the inequality 2|x-2|>|3 x+1|.

The polynomial f(x) is defined by

Find the quotient and remainder when f(x) is divided by $\left(x^{2}+2\right)$.

Solve the inequality |x+3|<|2 x+1|.

The polynomial p(x) is defined by

where k and m are constants. Given that (x+1) is a factor of p(x), express m in terms of k.