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.

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 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.

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

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

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

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

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

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

Find the highest scoring people over a course of days using the MAX, MATCH and INDEX functions

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Factorising a quadratic expression of the form $ax^2+bx+c$ by completing the square.

Factorising a quadratic expression of the form $x^2+bx+c$ by completing the square.

Factorising a quadratic expression with the $x^2$-term having a coefficient of 1.

Factorising a quadratic expression with the $x^2$-term having a coefficient of 1.

Solving simple linear equations in $\mathbb{Q}$ and $\mathbb{Z}_n$ for $n= 13, \;17$ or $19$.

Multiple choice. Students need to select the correct simplification for a given expression. 

This question has four versions. Skills required are: using Pythagorean identities, converting to sine or cosine. Some also require fraction division.

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A question which asks students to encrypt a number using RSA, then to factor a small public key and find the decryption exponent.

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Questions to test if the student knows the inverse of an even power (and how to solve equations that contain a single power that is even). 

Questions to test if the student knows the inverse of an odd power (and how to solve equations that contain a single power that is odd). 

Recognising the equation of a semi-circle centred at the origin. Top, bottom, left and right.

Recognising the equation of a circle.

Recognising that $(x-a)^2+(y-b)^2=r^2$ is a circle of radius $r$ with centre $(a,b)$ 

Here you need to choose which trigonometric function is the red dashed side divided by the solid green side. Your goal is to get twenty correct answers quickly. Incorrect answers show a highlight of the correct answer to select to continue.  The timer starts as soon as you choose your first answer and continues until you get 20 correct.  Select save answer after your results show in the applet.