Skills Audits for Maths and Stats

Rewriting a trigonometric expression of the form $A\sin(\theta)-B\cos(\theta)$ to $R\sin(\theta-\alpha)$ by calculating $R$ and $\alpha$.

Match the graphs to the functions. No randomisation. Multiple choice.

Draws a triangle based on 3 side lengths.  Randomises asking angle or side.

Draws a triangle based on 3 side lengths.  Randomises asking angle or side.

Find the diagonal or one side of a rectangle using Pythagoras' theorem.

Find the volume of a prism with a trapezium as a cross section from a diagram.

Find the volume of a semicylinder from a diagram.

Calculate the volume of different 3D shapes, given the units and measurements required. The formulae for the volume of each shape are available as steps if required.

Calculate the volume of different 3D shapes, given the units and measurements required. The formulae for the volume of each shape are available as steps if required.

Finding the area of a circle when given the diameter of the circle.

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

Find the missing angle in a triangle using the fact that the angles add to 180 degrees.

Calculating the integral of a function of the form $ax^2 \cos(bx)$ using integration by parts.

Calculating the integral of a function of the form $\frac{nx^{n-1}}{x^n+a}$ using integration by substitution.

Using the various versions of $\cos{2x}$ identity to integrate $\sin^2{x}$ and $\cos^2{x}$.

Calculating the integral of a function of the form $\frac{c}{(x+a)(x+b)}$ using partial fractions.

Calculating the derivative of a function of the form $\frac{ax^n}{bx+c}$ using the quotient rule.

Calculating the derivative a function of the form $ax^n \sin(bx)$ using the product rule.

Calculating the derivative of a function of the form $\sin(ax^m+bx^n)$ using the chain rule.

Calculating the derivative of an exponential function of the form $ae^{bx}$, using a table of derivatives.

Find the derivative of a function of the form $y=a \tan(bx+c)$ using a table of derivatives.

Find the derivative of a function of the form $y=a \sin(bx+c)$ using a table of derivatives.

Find the derivative of a function of the form $y=a \cos(bx+c)$ using a table of derivatives.

Finding the stationary points of a cubic equation and determining their nature.

Calculating the definite integral $\int_{n_1}^{n_2}a_1x^{b_1}+a_2x^{b_2}+a_3x^{b_3} dx$.

Calculating the integral of a function of the form $a_1x^{b_1}+a_2x^{b_2}+a_3x^{b_3}$ using a table of integrals. 

Differentiate a polynomial expression involving coefficients and, negative and fractional indices. 

Calculating the derivative of a function of the form $a \ln(bx)$ using a table of derivatives.

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

Solving $a\log(x)+\log(b)=\log(c)$ for $x$, where $a$, $b$ and $c$ are positive integers.