HIGHER GCSE MATHEMATICS by DAVID RAYNER (shown here) is an excellent textbook, recommended for all Higher-tier GCSE students.
KS3 (School Years 7, 8 and 9)
Key Stage Three MAY be a good time to start maths tuition. The key factors to consider are MOTIVATION, ATTITUDE and MATURITY. What is the motivation behind starting tuition: to consolidate shaky topics covered at school? To move up a set at school? To explore the syllabus ahead of school?
I recommend to parents of younger students to think very carefully about WHEN to start tuition. And after starting, I make sure to regularly review progress and discuss further goals with student and parent.
GCSE (School Years 10 and 11)
The current higher-tier GCSE syllabus is one big, hairy beast! There's a lot to cover and some topics are extremely challenging. I take the syllabus section-by-section:
Number 1 - fractional and decimal calculations (non-calculator), basic percentages, estimation
Number 2 - harder percentages, laws of powers, surds, bounds
Algebra 1 - expanding and factorising, linear equations and inequalities, straight-line graphs
Algebra 2 - quadratic equations, functions, proportion using k, sequences
Algebra 3 - iteration, advanced simultaneous equations, quadratic inequalities, circle equations
Shape 1 - angle theorems, transformations, areas and volumes, Pythagoras, basic trig, similarity
Shape 2 - circle theorems, advanced trig, vector geometry
Data - cumulative frequency, histograms etc.
Probability - Venns, tree diagrams etc.
For each section, I assess the student's strengths and weaknesses and make a plan of attack. Key topics may be covered over several lessons: I want the student to feel that nothing is beyond them, provided they work systematically and with a positive attitude! At the end of each section, I re-assess the student to evaluate their progress.
The overall aim is to finish as much of the syllabus as possible before Easter of Year 11, so that the student can go on tackle past papers with confidence.
Past Paper Practice
Once the main parts of the syllabus have been understood, the student is ready to start practising past papers. When doing papers, it is important to mark your work carefully and to analyse where you have lost marks. The following marksheets can be useful for this.