GCSE Mathematics (Higher) AQA
Full course content, a smart revision plan and instant past paper feedback for GCSE Mathematics (Higher) AQA.
Start revising this course →Content Overview
158 topics in 13 modules
☑️ Angles, lines and polygons 15 topics
- Basics of Angles - Acute, Obtuse, Right, Straight, Reflex
- Types of Lines - Parallel, Perpendicular, Intersecting and Collinear
- Interior and Exterior Angles in Polygons
- Understanding Basic Polygons - Triangle, Quadrilateral, Pentagon, and Hexagon
- Further Study of Polygons - Heptagon, Octagon, Nonagon, and Decagon
- Concepts of Regular and Irregular Polygons
- Angle Relationships - Complementary, Supplementary and Vertically Opposite
- Properties of Parallelograms, Rhombuses, Rectangles and Squares
- Understanding Tessellations and Regular Tilings
- Concepts of Symmetry - Line Symmetry and Rotation Symmetry
- Investigations on Angle-Angle Phenomena
- Application of Angles, Lines and Polygons in Real Life Scenarios
- Solving Complex Problems Involving Angles, Lines and Polygons
- Understanding Geometric Proofs and Their Applications
- Angle Properties of Circles and Tangents
☑️ Bounds 15 topics
- Understanding the Concept of Bounds
- Lower and Upper Bounds
- Establishing Bounds from Given Information
- Working with Decimal Approximations and Bounds
- Calculating with Bounds
- Bounds in Practical Contexts and Measurements
- Estimating Calculation Errors Using Bounds
- Handling Errors Analysis and Bounds in Measurements
- Application of Bounds in Real Life Scenarios
- Appreciation of the Inequalities Arising from Bounds
- Dealing with Multiple Bounds in Calculations
- Exploration of the Range of Possible Exact Values
- Bounds and Significant Figures
- Rounding Numbers and Its Effects on Bounds
- Complex Bounds Scenarios and Problem Solving
☑️ Circle theorems 12 topics
- Understanding Circle Terminology
- Theorem: Angles Subtended by the Same Arc
- Theorem: The Angle at the Centre is Twice the Angle at the Circumference
- Theorem: Angles in a Semi-Circle
- Theorem: Angles in the Same Segment are Equal
- Theorem: The Alternate Segment
- Theorem: The Angle Between the Tangent and Chord
- Theorem: Cyclic Quadrilaterals
- Summary and Applications of Circle Theorems
- Proof of Theorems
- Solving Problems Using Circle Theorems
- Extended Practice: Complex Scenarios Involving Multiple Theorems
☑️ Higher 10 topics
- BODMAS and types of number
- Multiples, prime factors and factors
- HCF and LCM
- Fractions
- Fractions, percentages and decimals
- Fractions and recurring decimals
- Rounding numbers
- Estimating
- Bounds
- Standard form
☑️ Percentages 16 topics
- Understanding of Percentages
- Converting Fractions, Decimals and Percentages
- Percentage Increase and Decrease
- Finding the Original Amount After a Percentage Change
- Expressing One Quantity as a Percentage of Another
- Percentage Multipliers
- Calculating Simple Interest
- Compound Interest and Depreciation
- Problem Solving Using Percentages in Real-Life Contexts
- Reverse Percentage Calculations
- Percentages and Proportional Division
- Calculating Percentage Profit and Loss
- Working with Simple and Compound Percentage Growth
- Using Percentages to Compare Proportions
- Tax and Interest Rates
- Using Percentages in Data Interpretation
☑️ Surds 12 topics
- Introduction to Surds
- Simplifying Surds
- Rationalising the Denominator
- Operations with Surds (Addition, Subtraction, Multiplication, Division)
- Conjugate of Surds
- Surds in the Real world
- Expansion Using Surds
- Representing Surds on a Number Line
- Solving Equations with Surds
- Surds and Exponents
- Complex Numbers Involving Surds
- Surds in Geometry (Pythagoras and Quadratics)
☑️ Algebra 18 topics
- Algebra basics
- Powers and roots
- Multiplying out brackets
- Factorising
- Manipulating surds
- Solving equations
- Rearranging formulas
- Factorising quadratics
- The Quadratic Formula
- Completing the square
- Algebraic fractions
- Sequences
- Inequalities
- Graphical inequalities
- Iterative methods
- Simultaneous Equations
- Proof
- Functions
☑️ Graphs 13 topics
- Straight Lines and Gradients
- y = mx + c
- Drawing straight line graphs
- Coordinates and ratios
- Parallel and Perpendicular Lines
- Quadratic Graphs
- Harder Graphs
- Solving Equations using graphs
- Graph Transformations
- Real-Life Graphs
- Distance-Time Graphs
- Velocity-Time graphs
- Gradients of Real-Life Graphs
☑️ Ratio, Proportions and Rates of Change 6 topics
- Ratios
- Direct and Inverse Proportion
- Percentages
- Compound Growth and Decay
- Unit Conversions
- Speed, Pressure and Density
☑️ Geometry and Measures 17 topics
- Geometry
- Parallel Lines
- Geometry Problems
- Polygons
- Triangles and Quadrilaterals
- Circle Geometry
- Congruent Shapes
- Similar Shapes
- The Four Transformations
- Areas- Triangles and Quadrilaterals
- Areas- Circles
- 3D shapes - Surface Area
- 3D shapes- Volume
- Enlargements and Projections
- Triangle Constructions
- Loci and Constructions
- Bearings
☑️ Pythagoras and Trigonometry 7 topics
- Pythagoras' Theorem
- Trigonometry- Sin, Cos and Tan
- Trigonometry- Common Values
- The Sine and Cosine Rules
- 3D Pythagoras
- 3D Trigonometry
- Vectors
☑️ Probability and Statistics 17 topics
- Probability basics
- Counting Examples
- Probability Experiments
- The AND/OR Rules
- Tree Diagrams
- Conditional Probability
- Sets and Venn Diagrams
- Sampling and Data Collection
- Mean, Median, Mode and Range
- Frequency Tables- Finding Averages
- Grouped Frequency Tables
- Box Plots
- Cumulative Frequency
- Histograms and Frequency Density
- Scatter Graphs
- Other Graphs and Charts
- Comparing Data Sets
☑️ Vectors 0 topics
Other GCSE Mathematics (Higher) exam boards
GCSE Mathematics (Higher) AQA Revision Content
Take a look at the written content available for this course. Practice-question availability may vary.
GCSE Mathematics (Higher) AQA - Angles, lines and polygons - Basics of Angles - Acute, Obtuse, Right, Straight, Reflex Content Preview
Angles, lines and polygons
Basics of Angles - Acute, Obtuse, Right, Straight, Reflex
Basics of Angles
-
An angle is formed by two lines that start from the same point. The space between these lines is measured in degrees.
-
A full angle measures 360 degrees. This represents a total rotation around a point.
Acute Angles
- An acute angle is an angle that measures less than 90 degrees but more than 0 degrees.
Right Angles
- A right angle measures exactly 90 degrees.
- It is often denoted by a small square in the corner at the point of the angle.
Obtuse Angles
- An obtuse angle is larger than 90 degrees but less than 180 degrees.
Straight Angles
- A straight angle measures exactly 180 degrees. .
- This forms a straight line.
Reflex Angles
- A reflex angle measures more than 180 degrees but less than 360 degrees.
Remember that understanding the different types of angles is fundamental to then working with more complex geometrical figures such as triangles, quadrilaterals and polygons. Make sure to practice identifying and working with different types of angles.
Question: What type of angle would you have if it measures significantly more than 90 degrees but does not form a straight line?
Unlock instant, personalised feedback
Sign up to Adapt to practise the exam questions available for this course with instant, personalised feedback.
Start revising this course →Try Adapt now
Add this exact course and build your personalised revision plan.