GCSE Maths Revision Higher Tier (Number)

Explore prime decomposition of x = 2^2 × 5^3 × 7 with a band diagram to reveal trailing zeros, square status, and related factors such as 14 and 25.

Use the table method to find the highest common factor and lowest common multiple by dividing by common factors and using the L-shape, illustrated with 20 and 8.

Explore calculating HCF and LCM using prime decomposition and Venn diagrams, with step-by-step examples for 20 and 8, 20 and 90, and 28, 30, 35.

Discover how to extract the highest common factor and lowest common multiple from prime decompositions, using 72 and 2016 to illustrate shared and non shared prime powers.

This lecture walks through exam questions on finding the highest common factor and the lowest common multiple using prime decomposition, focusing on common prime factors and their lowest powers.

Access carefully selected recent GCSE maths exam questions to deepen practice and mastery of the topic, with answers included on the final page to check understanding.

Learn to convert recurring decimals to fractions by setting x, multiplying by the repeating-length power of ten, and subtracting; examples include 0.54 recurring = 6/11 and 0.13 recurring = 2/15.

Recap of multipliers for percentage changes, converting percentages to decimals and applying them to increase or decrease values. Includes examples like 60% to 1.6 and 33% to 0.67.

Explore reverse percentages by using multipliers and division to recover original amounts from reduced values, with examples of 30% losses and 20% decreases.

Explore compound interest using yearly multipliers, compare it with simple interest, and analyze depreciation as a value shrinking over years.

Explore exam questions on fractions and percentages using multipliers and compound interest. Practice calculating end-of-period values from growth and declines across currencies.

The GCSE maths revision higher tier number course offers recent exam questions to challenge your understanding, with answers included on the final page for continued practice.

Explore direct proportion in GCSE maths by deriving y = kx, identifying the constant of proportionality, and solving for k using examples like hours on a computer and electricity.

Explore indirect proportion and inverse relationships, including reciprocal graphs and the equation y equals k over x, with practice solving for y and x.

Practice with carefully selected recent GCSE maths exam questions to challenge your understanding and master this topic, with answers included on the document’s final page.

Explore the laws of indices and master index rules for multiplying with the same base, dividing by subtracting exponents, and raising powers (power to a power), with practical equation examples.

Understand negative indices in exponents and how a^-n equals 1/(a^n). Practice converting decimals to fractions and applying the reciprocal rule to compute powers.

Explore fractional indices and exponents, turning roots into powers and solving examples like 64 and 32. Learn handling negatives and combining root and power rules.

Apply indices to powers by multiplying exponents when raising a base, and by applying the power to each factor in a product. Explore fractional exponents and roots.

Practice change of base by rewriting numbers as powers with a common base, substitute into equations, and equate indices to solve for x, using bases 5, 3, and 2.

Master techniques to solve exponential equations by changing bases and expressing terms as a single power. Practice matching bases and applying index rules to solve equations with examples.

Explore exam-style questions on indices and fractional powers, apply base and exponent rules, solve linear equations, and express results in standard form.

Practice with recent exam questions to master number concepts. Answers are included on the final page of the document.

Explore surds and radicals through quick Pythagoras examples, identifying rational and irrational numbers, and tracing how natural numbers, whole numbers, integers, and rationals relate to surds.

Learn to simplify and multiply radical expressions by using square-root rules, factoring into square numbers, and handling outside versus inside the radical, including algebra cases.

Learn to add and subtract square roots by simplifying them, combining like roots, and rewriting expressions such as sqrt8 and sqrt12 to produce correct totals.

Explore expanding brackets with surds, multiply and simplify square roots, handle cancellations and difference of squares, and apply the triangle area formula half the base times the height.

Learn to rationalize denominators by multiplying by conjugates, using the difference of squares to remove irrationals, and applying these steps to fractions like 1/√2 and 3/√2.

Learn bonus material on simplifying radicals, expanding brackets, and solving for a and b by matching rational and irrational parts in binomial squares like (a + b√2).

Practice exam questions on rationalising denominators, showing how to express the result as x plus y fractions, with x equals one half and y equals one tenth.

Practice with a curated set of recent exam questions to deepen understanding and master the concepts, with answers included on the final page for self-check.