GCSE Mathematics (Higher) Edexcel
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217 topics in 19 modules
āļø 3D Trigonometry and Pythagoras 10 topics
- Understanding coordinate system and the space
- Introduction to 3D Trigonometry
- Understanding Pythagoras' Theorem in 3D
- Application of Pythagoras' Theorem in 3D problems
- Introduction to the sine rule and cosine rule
- Application of the sine rule and cosine rule in 3D problems
- Calculation of angles and distances in 3D figures
- 3D problem solving involving spheres and cylinders
- Application of Trigonometric ratios in 3D Trigonometry
- Real world applications and problem solving with 3D Trigonometry and Pythagoras
āļø Circle theorems 12 topics
- Understanding Parts of a Circle
- The Angle at the Centre Theorem
- The Angles in the Same Segment Theorem
- The Angle in a Semi-Circle Theorem
- Opposite Angles of a Cyclic Quadrilateral Theorem
- The Alternate Segment Theorem
- Tangents to a Circle Theorem
- Perpendicularity in Circles
- Chord Properties in Circles
- Cyclic Quadrilaterals and Circles
- Solving Problems Using Circle Theorems
- Application of Circle Theorems in Real-life Scenarios
āļø Inequalities 15 topics
- Understanding the Concept of Inequalities
- Legal Moves in Inequalities
- Solving Linear Inequalities
- Solving Quadratic Inequalities
- Inequalities with Absolute Values
- Compound Inequalities
- Inequalities Involving Surds
- Inequalities on Number Lines
- Solving Inequalities Graphically
- Region Graphs for Linear Inequalities
- Introduction to Quadratic Inequalities
- Real-World Applications of Inequalities
- Using Inequalities to Solve Problems
- Inequalities in Two Variables
- Writing and Using Your Own Inequalities
āļø Iteration 11 topics
- Introduction to Iteration
- Defining Iterative Processes
- Embedding Equations into Iterative Processes
- Convergence and Divergence in Iteration
- Rate of Convergence
- Understanding Decimals in the Context of Iteration
- Bisection Method in Iteration
- Newton-Raphson Method in Iteration
- Fixed Points and their Stability in Iteration
- Usage of Iterative Methods in Problem Solving
- Real-World Applications of Iteration
āļø Number 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
āļø Quadratic Sequences 10 topics
- Understanding Quadratic Sequences
- Recognizing Patterns in Quadratic Sequences
- Using the Difference Method for Quadratic Sequences
- Synthesizing Quadratic Sequences From Their nth Terms
- Expressing Quadratic Sequences in nth Term Format
- Problem Solving with Quadratic Sequences
- Summing Quadratic Sequences
- Practical Applications of Quadratic Sequences
- Interpreting Quadratic Sequences in Graphs
- Using Quadratic Sequences in Algebraic Functions
āļø Simultaneous Equations 11 topics
- Understanding the concept of simultaneous equations
- Graphical Solutions to Simultaneous Equations
- Solving linear simultaneous equations algebraically
- Solving linear simultaneous equations through substitution
- Solving linear simultaneous equations through elimination
- Forming simultaneous equations from worded problems
- Solving simultaneous equations with one linear and one quadratic equation
- Using simultaneous equations in real-life context
- Checking solutions of simultaneous equations
- Solving simultaneous equations with three unknowns
- Presenting and interpreting solutions to simultaneous equations
āļø Surds 10 topics
- Introduction to Surds
- Simplifying Surds
- Rationalising the Denominator
- Addition and Subtraction of Surds
- Multiplication and Division of Surds
- Solving Equations Involving Surds
- The Difference of Squares Method
- Conjugate Surds
- Expansion and Simplifications involving Surds
- Real-World Applications of Surds.
āļø Transformations 11 topics
- Introduction to Transformations
- Understanding and Identifying Transformations
- Translation: Understanding and Application
- Reflection: Across Axes and Specific Lines
- Rotation: Center and Angle of Rotation
- Enlargement: Center, Scale Factors, and Negative Scale Factors
- Combination of Transformations
- Transformations of Graphs
- Transformation Matrices
- Invariant Points and Lines
- Real-World Applications of Transformations
āļø Vectors 0 topics
āļø 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
āļø 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
āļø Ratio, Proportions and Rates of Change 6 topics
- Ratios
- Direct and Inverse Proportion
- Percentages
- Compound Growth and Decay
- Unit Conversions
- Speed, Pressure and Density
āļø 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
āļø 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
āļø 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
āļø Representing data 16 topics
- Types of Data (qualitative, quantitative, continuous, and discrete)
- Designing Surveys and Questionnaires
- Sampling Methods (random, stratified, and systematic)
- Frequency Tables and Tally Charts
- Bar Charts (including vertical and horizontal)
- Pie Charts
- Line Graphs
- Dual and Compound Bar Charts
- Pictograms
- Time Series Graphs
- Comparing Data Sets Using Graphs
- Stem and Leaf Diagrams
- Two-Way Tables
- Misleading Graphs
- Constructing and Interpreting Graphs
- Choosing Suitable Graphs for Data Presentation
āļø Laws of indices 12 topics
- Introduction to Indices and Powers
- The Law of Multiplication for Indices (am Ć an = am+n)
- The Law of Division for Indices (am Ć· an = am-n)
- Power of a Power Rule ((am)n = amn)
- Understanding Zero Exponents (a^0 = 1)
- Working with Negative Indices (a^(-n) = 1/an)
- Fractional Indices (a^(1/n) = nāa)
- Simplifying Expressions with Indices
- Combining Different Laws of Indices in Expressions
- Solving Equations Involving Indices
- Real World Applications of Indices
- Misconceptions and Common Errors with Indices
āļø Circle Theorems 11 topics
- Parts of a Circle: Understanding key components like the radius, diameter, chord, tangent, and arc.
- The Angle at the Centre Theorem: Investigating how the angle at the centre is twice the angle at the circle's circumference.
- Angles in the Same Segment: Exploring how angles in the same segment are equal.
- Angle in a Semi-Circle: Recognizing that the angle in a semi-circle is 90 degrees.
- Opposite Angles of a Cyclic Quadrilateral: Understanding that opposite angles of a cyclic quadrilateral sum to 180 degrees.
- The Alternate Segment Theorem: Learning how the angle between a tangent and a chord is equal to the angle in the opposite segment.
- Tangent and Radius Perpendicularity: Demonstrating that a tangent to a circle is perpendicular to the radius at the point of contact.
- Chord Properties: Investigating the properties and relations of chords within a circle.
- Cyclic Quadrilaterals: Identifying and solving problems involving quadrilaterals inscribed in circles.
- Solving Application Problems: Using circle theorems to solve practical and theoretical problems.
- Circle Theorems in Context: Applying theorems to interpret and solve real-world scenarios.
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GCSE Mathematics (Higher) Edexcel Revision Content
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GCSE Mathematics (Higher) Edexcel - Number - BODMAS and types of number Content Preview
Number
BODMAS and types of number
It's important to know about different types of numbers for the exam.
- Integers are whole numbers, either positive or negative. 0 is also an integer
- Rational numbers can be written as fractions, but irrational numbers can't - instead, they're never-ending, non-repeating decimals
- Surds are numbers / expressions containing irrational roots
BODMAS is an important acroynym to learn. It tells you the order in which to perform operations within an equation. It stands for:
- Brackets
- Other
- Division
- Multiplication
- Addition
- Subtraction
Question: Using the BODMAS rule, calculate the value of this expression: (5 + 3)Ā² Ć· 4 - 2 + 6 * Ā³ā2. If your answer is a surd, provide it in its simplest form.
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