A-Level CAIE Mathematics A2 3.1 Algebra Question Bank

Expand $(1+3 x)^{\frac{2}{3}}$ in ascending powers of x, up to and including the term in $x^{3}$, simplifying the coefficients.

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

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

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

Expand $(1+2 x)^{-3}$ in ascending powers of x, up to and including the term in $x^{2}$, simplifying the coefficients.

Solve the inequality |2 x-5|>3|2 x+1|.

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

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

Expand $(3+x)(1-2 x)^{\frac{1}{2}}$ in ascending powers of x, up to and including the term in $x^{2}$, simplifying the coefficients.

Find the coefficient of $x^{3}$ in the expansion of $(3-x)(1+3 x)^{\frac{1}{3}}$ in ascending powers of x.