MASH Bath: Question Bank

Rewrite the expression $\frac{n}{(x+a)(x+b)(x+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+\frac{C}{x+c}$.

Rewrite the expression $\frac{cx+d}{kx^2+mx+n}$ as partial fractions in the form $\frac{A}{kx+a}+\frac{B}{x+b}$, where the quadratic $kx^2+mx+n=(kx+a)(x+b)$.

Rewrite the expression $\frac{cx+d}{x^2+mx+n}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}$, where the quadratic $x^2+mx+n=(x+a)(x+b)$.

Rewrite the expression $\frac{cx+d}{(x+a)(x+b)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}$.

Rewrite the expression $\frac{c}{x^2+mx+n}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}$, where the quadratic $x^2+mx+n=(x+a)(x+b)$.

Rewrite the expression $\frac{c}{(x+a)(x+b)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}$.

Rewrite the expression $\frac{c}{kx^2+mx+n}$ as partial fractions in the form $\frac{A}{kx+a}+\frac{B}{x+b}$, where the quadratic $kx^2+mx+n=(kx+a)(x+b)$.

Rewrite the expression $\frac{c}{(kx+a)(x+b)}$ as partial fractions in the form $\frac{A}{kx+a}+\frac{B}{x+b}$.

Match the greek letter to its pronunication.  15 common letters.

Simplifying an expression of the form $\frac{a^4b^3}{\sqrt{a^4b^2}}$ to $a^2b^2$, for integers $a$ and $b$.

Simplifying an expression of the form $a^3 \times (a^4)^{1/2}$ to $a^5$, where $a$ is an integer. 

Using indices rules to rewrite an expression from $\left(\frac{a^n}{b^n}\right)^{-1/n}$ to $\frac{b}{a}$.

Using indices rules to rewrite an expression from $a^\frac{m}{n}$ to $\frac{1}{b}$, for integers $a$, $b$, $m$ and $n$.

Simplifying expressions from $\left(\frac{x^m}{x^n}\right)^p$ to $x^{(m-n)p}$.

Simplifying expressions from $\frac{x^mx^n}{x^p}$ to $x^{m+n-p}$. 

Simplifying expressions from $(ax^n)^m$ to $a^mx^{mn}$, where $a$, $m$ and $n$ are positive integers.

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Finding composite functions of a quadratic function and a logarithmic function.

Find the derivative of a function of the form $y=ax^b$ using a table of derivatives.

Calculating the missing side-length of a triangle using the cosine rule.

Given two angles and a side-length of a triangle, use the sine rule to calculate an unknown side-length.

Draws a triangle based on 3 side lengths and randomises asking for hypotenuse or not.

Solving a differential equation of the form $\frac{dy}{dx}=\frac{ax^n}{y}$ using separation of variables.

Solving a differential equation of the form $\frac{dy}{dx}=axy^2$ using separation of variables.

Solving a differential equation of the form $\frac{dy}{dx}=axy$ using separation of variables.

Calculating the integral of a function of the form $4ax(ax^2+b)^n$ using integration by substitution.

Calculating the angle between two vectors.

Calculating several linear combinations of three 2-dimensional vectors. 

Calculating several linear combinations of three 3-dimensional vectors. 

Calculate the magnitude of a 3-dimensional vector, where $\mathbf v$ is written in the form $\pmatrix{v_1\\v_2\\v_3}$.