You can use this workbook to practise your core mathematical skills. This will be very useful both whilst at school and when you move on to higher study, where a high degree of algebraic fluency is really useful.

- Don't be tempted to look at the answer if you think that you can do the question unless you have actually done the question, on paper with a pen.
- Try not to use your calculator for the simple arithmetical parts of a question - this is a bad habit to get into.
- If you are stuck, don't give up immediately. Think about the problem. Perhaps look at one or two answers and ask: how does this answer work?
- Accuracy is important, but speed is also important. This workbook is good for speed training.
- If your answer differs from the answer given then think: is my answer wrong, or is it merely represented in a different form?
- Use your skills in some interesting rich mathematical problems from NRICH. You might want to look at the core mathematics curriculum document for suggestions or just browse the stage 5 content on the site.
- Keep a record of your best times. See how quickly you can complete one of each question type from each section.

Fluency with mathematics means the ability to perform routine calculation BOTH quickly AND accurately. One without the other will hamper your progress, especially once you reach university.

To give you a feel for where you might be aiming, here are some average times for some of the questions as recorded by Judith, a second year mathematics undergraduate who worked with NRICH over the summer:

Algebra | Curve sketching | Differentiation | |||

Quadratic equations | 8s | Modulus function for linear | 20s | Stationary points for quadratic | 10s |

Completing the square | 8s | Modulus function for quadratic | 1m 10s | Stationary points for cubic | 50s |

Inequalities for quadratics | 10s | Implicit differentiation | 1m 10s | ||

Inequalities for cubics | 1m 10s | ||||

Partial fractions | 1m 30s | ||||

Powers | 1m | ||||

Logarithms | 20s | ||||

Solving trig equations | 40s | ||||

TOTAL | 5m 6s |

Can you match or beat Judith's times?

More times from other brave solvers will be posted periodically.