Skills Audits for Maths and Stats

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

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

Solving an equation of the form $a^x=b$ using logarithms to find $x$.

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

Finding $x$ from a logarithmic equation of the form $\log_ax = b$, where $a$ and $b$ are positive integers.

Finding composite functions of 2 linear functions.

Finding the inverse of a function of the form $f(x)=\frac{mx+c}{x+a},\,x\neq-a$.

Determining the range of a function of the form $f = m|x| + a$.

Evaluating a linear function for a given value of $x$.

Match the relevant graph (sin, cos, tan) with its equation. 

Multiple choice - select the quadratic graph.

Calculating gradient and finding intercept from a geogebra graph.

Basic calculation from a sum given in Sigma notation.

Rewrite the expression $\frac{mx^2+nx+k}{(x+a)(x^2+bx+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{Bx+C}{x^2+bx+c}$.

Simplifying first is essential in terms of managing expressions that might need factorising.

Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place. 

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).

Simplify the sum of two algebraic fractions where spotting factorising of both numerators and denominators can reduce the work massively.

Simplify (qx+a)/(rx+b) +/- (sx+c)/(tx+d)

x is a randomised variable. a,b,c,d,q,r,s,t are randomised integers. a,b,c,d run from -5 to 5, including 0. q,r,s,t run from -3 to 3, and can be 0 if the constant term is nonzero, but are mostly 1.

Rearrange a specific formula. No randomisation.

Substitute values into an algebraic expression and calculate the result.

Fiind the Highest Common Factor of two algebraic expressions involving a coefficient and powers of $x$ and $y$.

Factorise an expression of 2 or 3 terms where the gcd is a letter times a number. Part of HELM Book 1.3.4

This question is made up of 10 exercises to practice the multiplication of brackets by a single term.

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

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

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

Expand two brackets involving powers of $x$.

Expanding two linear brackets multiplied together.

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