MASH Bath: Question Bank

Solving a pair of linear simultaneous equations with integer solutions.

Solving a pair of linear simultaneous equations, giving answers as integers or fractions.

Rewriting fractions involving surds by rationalising the denominator.

Rewriting fractions involving surds by rationalising the denominator.

Rewriting expressions involving surds into the form $a+b \sqrt{c}$, where $a$, $b$ and $c$ are integers.

Rewiting expressions involving sums or differences of surds into the form $a \sqrt{b}$.

Rewiting expressions involving sums or differences of surds into the form $a \sqrt{b}$.

Simplifying expressions of the form $(a_1+b_1 \sqrt{c}) + (a_2 + b_2 \sqrt{c})$.

Rewriting expressions involving surds into the form $a+b \sqrt{c}$, where $a$, $b$ and $c$ are integers.

Rewriting expressions involving surds into the form $a+b \sqrt{c}$, where $a$, $b$ and $c$ are integers.

Simplifying expressions of the form $(a_1+b_1 \sqrt{c}) - (a_2 + b_2 \sqrt{c})$.

Simplifying surds from $a\sqrt{b^2c}$ to $ab\sqrt{c}$, where $a$, $b$ and $c$ are positive integers.

Simplifying surds from $\sqrt{a^2b}$ to $a\sqrt{b}$, where $a$ and $b$ are positive integers.

Rewriting fractional expressions involving $\sqrt[n]{x^m}$ using rules to combine and simplify indices. 

Rewriting fractions of the form $\frac{\sqrt[m]{x^n}}{\sqrt[p]{x^q}}$ to $x^{\frac{n}{m}-\frac{q}{p}}$.

Rewriting expressions from $\sqrt[m]{x^n}$ to $x^\frac{n}{m}$.

Simple exercise in collecting terms in different powers of \(x\)

No description given

Finding the product of a linear function of the form $mx+c$ and a cubic function of the form $ax^3+bx^2+cx+d$.

Finding the product of two linear functions of the form $mx+c$ and a quadratic function of the form $ax^2+bx+c$.

Finding the product of three linear functions of the form $mx+c$.

Finding the product of two linear functions of the form $mx+c$.

Given two quadratic expressions $f(x)$ and $g(x)$, calculate $f(x)(g(x)-f(x))$. 

Calculate the product of two quadratic expressions of the form $ax^2+bx+c$.

Calculating a quartic polynomial by squaring a quadratic expression of the form $ax^2+bx+c$.

Multiplying a linear expression of the form $mx+c$ by a quadratic expression of the form $ax^2+bx+c$. 

Finding linear combinations of two quadtratic expressions of the form $ax^2+bx+c$.

Solving a quadratic equation via factorisation, with the $x^2$-term having a coefficient of 1.

Solving a cubic equation of the form $ax^3+bx^2+cx+d=0$.

Factorise a cubic expression into the product of three linear factors of the form $mx+c$, where one of the factors is given.