Mathematics 1 for the ESAT
Core mathematics: number, algebra, ratio, and the foundations you are expected to be fluent in.
76 topics across 7 areas. Every topic below is a full lesson with worked examples.
Algebra
- Algebraic Notation And Conventions
- Index Laws Algebraic Multiplication Division
- Substitution And Algebraic Vocabulary
- Algebraic Manipulation Collecting Terms Expanding Brackets
- Factorising Quadratic Expressions
- Simplifying Algebraic And Rational Expressions
- Changing The Subject Of A Formula
- Equations Identities Algebraic Equivalence
- Coordinates In Four Quadrants
- Linear Equations Gradients And Intercepts
- Roots Intercepts And Turning Points Of Quadratics
- Sketching And Interpreting Graphs
- Interpreting Graphs And Non Standard Functions
- Calculating Gradients And Areas Under Graphs
- Algebraic Manipulation Solving Equations Sequences
- Solving Quadratic Equations
- Solving Linear Inequalities
- Generating Sequence Terms Rules
- Deducing Linear And Quadratic Sequences
Geometry
- Geometry Terms Notation And Symmetry
- Angle Properties Parallel Lines Polygons
- Properties Of Quadrilaterals And Triangles
- Congruence Criteria For Triangles
- Geometry Triangles Quadrilaterals Angles Sides
- Geometry Transformations Congruence Similarity
- Pythagoras Theorem 2d 3d
- Circle Geometry Definitions And Theorems
- Circle Theorems Geometric Results
- Coordinate Geometry Problem Solving
- Geometry Terminology Faces Edges Vertices
- Interpreting Plans And Elevations 3d Shapes
- Maps Scale Drawings And Three Figure Bearings
- Area And Volume Of Polygons And Right Prisms
- Geometry Of Circles And Solids
- Arc Lengths Sector Areas And Similarity
- Congruence Similarity And Geometric Properties
- Trigonometric Ratios Right Angled Triangles
- Vector Operations And Geometric Proofs
Number
- Ordering Integers Decimals And Fractions
- Four Operations Integers Decimals Fractions
- Prime Factorisation Hcf And Lcm
- Relationships Between Operations And Priority
- Systematic Listing Strategies
- Squares Cubes And Index Laws
- Index Laws And Powers
- Standard Index Form Numbers
- Converting Decimals Percentages Fractions
- Fractions Decimals And Percentages In Calculations
- Exact Calculations Fractions Surds Pi
- Upper And Lower Bounds Rounding
- Rounding To Accuracy And Error Intervals
- Approximation And Estimation Calculations
Probability
- Frequency Tables And Frequency Trees
- Probability Expected Outcomes And Randomness
- Theoretical Probability Expected Frequency Scale
- Exhaustive And Mutually Exclusive Probabilities
- Enumerating Sets And Combinations
- Theoretical Possibility Spaces And Probability
- Probability Addition Multiplication And Conditional Events
Ratio and proportion
- Scale Factors Diagrams And Maps
- Expressing One Quantity As A Fraction Of Another
- Understanding Ratio Notation
- Dividing Quantities In Ratios
- Ratio And Proportion Applications
- Ratio And Proportion Linear Functions
- Fractions In Ratio Problems
- Percentage Calculations And Change
- Direct And Inverse Proportion
- Ratio Proportion Similarity Lengths Areas Volumes
- Growth Decay And Iterative Processes