GCSE Edexcel Higher Tier Maths Revision Guide
Welcome to your comprehensive revision guide! This resource covers all the essential topics for the Higher Tier, from
foundational concepts like indices and fractions through to advanced material including trigonometry, vectors, and proof.
Each section provides clear explanations, step-by-step methods, worked examples, and practical tips to help you master the
content. Whether you're revising for mocks or preparing for your final exams, this guide will support your learning journey.
Let's dive in!
,Number: Core Concepts
Compound Interest & Depreciation Indices Rules
1
Use the formula: A = P (1 ± r)n where P is principal, r is am × an = am+n, (am)n = amn, and a−n = an
rate (as decimal), and n is years
Prime Factors, HCF & LCM Standard Form
Break numbers into prime factors using factor trees, then Write as A × 10n where 1 ≤ A < 10 and n is integer
use Venn diagrams to find HCF and LCM
These number skills form the foundation for many other topics. Practice converting between fractions, decimals, and
percentages regularly. Remember: for reverse percentages, divide by the multiplier rather than multiplying. For recurring
decimals to fractions, use algebra with 10x or 100x depending on the repeating pattern.
Common Mistake Alert!
Students often forget that depreciation uses a minus sign in the compound interest formula. Always check if the
value is increasing or decreasing before choosing + or -.
,Algebra: Equations & Graphs
Linear Equations Quadratics
Form and solve equations by balancing both sides. To find Expand brackets using FOIL, factorise by finding two
the nth term of a sequence, identify the common difference numbers that multiply to give c and add to give b in
and use an + b where a is the difference. x2 + bx + c.
Example: Find nth term of 5, 8, 11, 14... Example: Factorise x2 + 7x + 12
Common difference = 3, so 3n + b. First term: 3(1) + b = 5, so Need two numbers: multiply to 12, add to 7. 3 and 4 work.
b=2
Answer: (x + 3)(x + 4)
Answer: 3n + 2
01 02
Expanding & Simplifying Factorising
Expand brackets first, then collect like terms Find HCF or use double brackets for quadratics
03 04
Solving Equations Changing Subject
Balance both sides, isolate the variable Treat like solving, but isolate the required variable
, Geometry: Shapes & Measures
Pythagoras Circles Volume
a2 + b2 = c2 where c is hypotenuse Circumference: 2πr, Area: πr2 Prism: cross-sectional area × length
For surface area, find the area of each face and add them together. With cylinders, remember there are two circles and a
rectangle (the curved surface). For sectors and arcs, use fractions of the full circle: θ
360 × πr2 for area, θ
360 × 2πr for arc length.
Angles in Parallel Lines Angles in Polygons
Corresponding angles (F-shape), alternate angles (Z- Sum of interior angles: (n − 2) × 180°. For regular
shape), and co-interior angles (C-shape) help find polygons, divide by n to find each angle
missing angles
Welcome to your comprehensive revision guide! This resource covers all the essential topics for the Higher Tier, from
foundational concepts like indices and fractions through to advanced material including trigonometry, vectors, and proof.
Each section provides clear explanations, step-by-step methods, worked examples, and practical tips to help you master the
content. Whether you're revising for mocks or preparing for your final exams, this guide will support your learning journey.
Let's dive in!
,Number: Core Concepts
Compound Interest & Depreciation Indices Rules
1
Use the formula: A = P (1 ± r)n where P is principal, r is am × an = am+n, (am)n = amn, and a−n = an
rate (as decimal), and n is years
Prime Factors, HCF & LCM Standard Form
Break numbers into prime factors using factor trees, then Write as A × 10n where 1 ≤ A < 10 and n is integer
use Venn diagrams to find HCF and LCM
These number skills form the foundation for many other topics. Practice converting between fractions, decimals, and
percentages regularly. Remember: for reverse percentages, divide by the multiplier rather than multiplying. For recurring
decimals to fractions, use algebra with 10x or 100x depending on the repeating pattern.
Common Mistake Alert!
Students often forget that depreciation uses a minus sign in the compound interest formula. Always check if the
value is increasing or decreasing before choosing + or -.
,Algebra: Equations & Graphs
Linear Equations Quadratics
Form and solve equations by balancing both sides. To find Expand brackets using FOIL, factorise by finding two
the nth term of a sequence, identify the common difference numbers that multiply to give c and add to give b in
and use an + b where a is the difference. x2 + bx + c.
Example: Find nth term of 5, 8, 11, 14... Example: Factorise x2 + 7x + 12
Common difference = 3, so 3n + b. First term: 3(1) + b = 5, so Need two numbers: multiply to 12, add to 7. 3 and 4 work.
b=2
Answer: (x + 3)(x + 4)
Answer: 3n + 2
01 02
Expanding & Simplifying Factorising
Expand brackets first, then collect like terms Find HCF or use double brackets for quadratics
03 04
Solving Equations Changing Subject
Balance both sides, isolate the variable Treat like solving, but isolate the required variable
, Geometry: Shapes & Measures
Pythagoras Circles Volume
a2 + b2 = c2 where c is hypotenuse Circumference: 2πr, Area: πr2 Prism: cross-sectional area × length
For surface area, find the area of each face and add them together. With cylinders, remember there are two circles and a
rectangle (the curved surface). For sectors and arcs, use fractions of the full circle: θ
360 × πr2 for area, θ
360 × 2πr for arc length.
Angles in Parallel Lines Angles in Polygons
Corresponding angles (F-shape), alternate angles (Z- Sum of interior angles: (n − 2) × 180°. For regular
shape), and co-interior angles (C-shape) help find polygons, divide by n to find each angle
missing angles
