Maths

Focus on fluency, accuracy, and securing the key skills that appear across all three papers.

Secure your number and arithmetic basics

You must be confident with:

• adding, subtracting, multiplying, dividing (without a calculator)
• negative numbers
• fractions (equivalence, simplifying, four operations)
• decimals and percentages
• converting between fractions, decimals, and percentages

These skills appear everywhere on the exam.

Master the “Foundation essentials”

Revisit the key topics that unlock many Grade 4 marks:

• area and perimeter
• basic algebraic manipulation
• solving one-step and two-step equations
• ratio and proportion
• substitution
• reading and interpreting tables, charts, and graphs
• basic probability

Aim for secure, consistent working.

Learn simple method steps

Show every step clearly. Even if your final answer is wrong, method marks can lift you towards Grade 4.

Practise interpreting the question

Know what terms mean: “estimate”, “approximate to…”, “work out”, “solve”, “simplify”, “express as a ratio”. Misreading command words is a major barrier at Grade 3.

Use diagrams, workings, and labels

Drawing a quick sketch for angles, transformations, or area questions often secures marks.

Use all three papers to your advantage

• Foundation Paper 1 (non-calculator)
• Foundation Papers 2 and 3 (calculator)

Use your calculator efficiently but do not rely on it for basic arithmetic.

Focus on multi-step problems and showing clear mathematical reasoning.

Strengthen your algebra

You must be secure with:

• expanding and factorising single brackets
• solving linear equations
• straight line graphs
• forming expressions

Algebra underpins many Grade 5 questions.

Develop confidence with multi-step questions

Show each stage clearly, especially when dealing with:

• percentage increase/decrease
• compound interest
• reverse percentages
• scale drawings
• bearings
• standard form

Clarity means more method marks.

Improve your reasoning on problem-solving questions

For worded questions: underline key numbers, decide which operation is needed, show clear working, and check your answer is sensible. Maths is marked for process as well as accuracy.

Strengthen geometry and measure

Be confident with:

• angle rules
• area and circumference of a circle
• Pythagoras' theorem (Foundation and Higher)
• transformations (reflections, rotations, translations, enlargements)

These topics often push students from Grade 4 to 5.

Use mathematical vocabulary correctly

Such as “proportion”, “gradient”, “hypotenuse”, “factorise”, “estimate”. Correct language supports clearer method steps.

Use your calculator effectively

Practise using it for squares and square roots, fractions, standard form, and trigonometric values (if on Higher). Calculator efficiency supports Grade 5 accuracy.

Focus on precision, algebraic fluency, and advanced reasoning, especially on the Higher tier.

Stick strictly to exam timings

Top performers do not lose time on early items. You must protect time for the final long problems on Papers 2 and 3.

Know the full specification demands

Be confident with Higher-tier topics such as:

• quadratic equations (solve, factorise, complete the square)
• simultaneous equations (including graphically)
• inequalities (single and double)
• advanced ratio and proportion
• trigonometry in non-right-angled triangles (sine rule, cosine rule, area rule)
• vectors
• gradient and area under a graph
• compound probability

These are the questions that separate Grades 6, 7, 8, and 9.

Build algebra fluency

High-grade students confidently manipulate surds, work with indices accurately, rearrange formulae, simplify algebraic fractions, and expand double brackets and factorise quadratics. Algebra is the backbone of Grade 7–9 success.

Write mathematically precise solutions

Top answers show clearly structured steps, justified reasoning, accurate units, appropriate rounding, and a final statement that answers the question. Marker-friendly layouts earn marks.

Use efficient problem-solving strategies

Top students draw diagrams, annotate questions, try different approaches if stuck, check answers against context, and look for patterns or shortcuts. Reasoning matters as much as calculation.

Demonstrate insightful understanding

Grades 8 and 9 reward students who explain why a method works, compare strategies, break down unfamiliar problems, apply mathematical ideas in new contexts, and make logical connections between topics (e.g. algebra and area problems, ratio and probability).

Insightful means flexible, logical, calm, and well-reasoned.