Skills Audits for Maths and Stats

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.

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 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. 

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.

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

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.

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

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

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

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

Factorising a quadratic expression of the form $a^2x^2-b^2$ to $(ax+b)(ax-b)$, using the difference of two squares formula.

Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation

Rearrange expressions in the form $ax^2+bx+c$ to $a(x+b)^2+c$.

Solving a quadratic equation via factorisation (or otherwise) with the $x^2$-term having a coefficient of 1.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Solve linear equations with unkowns on both sides. Including brackets and fractions.

Solving a pair of simultaneous equations of the form $a_1x+y=c_1$ and $a_2x^2+b_2xy=c_2$ by forming a quadratic equation.

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