Solve a pair of linear equations by writing an equivalent matrix equation.

Questions which rely on knowledge of standard integrals.

Use the quotient rule to differentiate various functions.

Use the product rule to differentiate various functions.

Use the chain rule to differentiate various functions.

Solve a pair of linear equations by writing an equivalent matrix equation.

Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

$g: \mathbb{R} \rightarrow \mathbb{R}, g(x)=\frac{ax}{x^2+b^2}$. Find stationary points and local maxima, minima. Using limits, has $g$ a global max, min? 

Solve a pair of linear equations by writing an equivalent matrix equation.

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Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

6 questions on numerical reasoning using percentages and ratios.

3 questions. Finding the stationary points of functions of 2 variables.

Partial differentiation.

Three questions on using the Student $t$ distribution to perform hypothesis tests.

5 questions on using substitution to find indefinite integrals.

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3 questions. Finding the stationary points of functions of 2 variables.

Partial differentiation.

8 questions using logarithms. 7 questions use logarithms to solve equations.

26 questions: Product Rule, Quotient Rule and Chain Rule. For those that want a thorough testing of their basic differentiation using the standard rules.

5 questions on using substitution to find indefinite integrals.

4 questions on using partial fractions to solve indefinite integrals.

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

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Using trig identities to find solutions to equations

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $0$ and $2 \pi$ and careful with quadrants!

Let $x_n=\frac{an+b}{cn+d},\;\;n=1,\;2\ldots$. Find  $\lim_{x \to\infty} x_n=L$ and find least $N$ such that $|x_n-L| \lt 10^{-r},\;n \geq N,\;r \in \{2,\;3,\;4\}$.

Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.