esat.fyi

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, each a full lesson with worked examples.

Algebra

19 topics
  1. Algebraic Notation And ConventionsM4.1
  2. Index Laws Algebraic Multiplication DivisionM4.2
  3. Substitution And Algebraic VocabularyM4.3
  4. Algebraic Manipulation Collecting Terms Expanding BracketsM4.4
  5. Factorising Quadratic ExpressionsM4.5
  6. Simplifying Algebraic And Rational ExpressionsM4.6
  7. Changing The Subject Of A FormulaM4.7
  8. Equations Identities Algebraic EquivalenceM4.8
  9. Coordinates In Four QuadrantsM4.9
  10. Linear Equations Gradients And InterceptsM4.10
  11. Roots Intercepts And Turning Points Of QuadraticsM4.11
  12. Sketching And Interpreting GraphsM4.12
  13. Interpreting Graphs And Non Standard FunctionsM4.13
  14. Calculating Gradients And Areas Under GraphsM4.14
  15. Algebraic Manipulation Solving Equations SequencesM4.15
  16. Solving Quadratic EquationsM4.16
  17. Solving Linear InequalitiesM4.17
  18. Generating Sequence Terms RulesM4.18
  19. Deducing Linear And Quadratic SequencesM4.19

Geometry

19 topics
  1. Geometry Terms Notation And SymmetryM5.1
  2. Angle Properties Parallel Lines PolygonsM5.2
  3. Properties Of Quadrilaterals And TrianglesM5.3
  4. Congruence Criteria For TrianglesM5.4
  5. Geometry Triangles Quadrilaterals Angles SidesM5.5
  6. Geometry Transformations Congruence SimilarityM5.6
  7. Pythagoras Theorem 2d 3dM5.7
  8. Circle Geometry Definitions And TheoremsM5.8
  9. Circle Theorems Geometric ResultsM5.9
  10. Coordinate Geometry Problem SolvingM5.10
  11. Geometry Terminology Faces Edges VerticesM5.11
  12. Interpreting Plans And Elevations 3d ShapesM5.12
  13. Maps Scale Drawings And Three Figure BearingsM5.13
  14. Area And Volume Of Polygons And Right PrismsM5.14
  15. Geometry Of Circles And SolidsM5.15
  16. Arc Lengths Sector Areas And SimilarityM5.16
  17. Congruence Similarity And Geometric PropertiesM5.17
  18. Trigonometric Ratios Right Angled TrianglesM5.18
  19. Vector Operations And Geometric ProofsM5.19

Number

14 topics
  1. Ordering Integers Decimals And FractionsM2.1
  2. Four Operations Integers Decimals FractionsM2.2
  3. Prime Factorisation Hcf And LcmM2.3
  4. Relationships Between Operations And PriorityM2.4
  5. Systematic Listing StrategiesM2.5
  6. Squares Cubes And Index LawsM2.6
  7. Index Laws And PowersM2.7
  8. Standard Index Form NumbersM2.8
  9. Converting Decimals Percentages FractionsM2.9
  10. Fractions Decimals And Percentages In CalculationsM2.10
  11. Exact Calculations Fractions Surds PiM2.11
  12. Upper And Lower Bounds RoundingM2.12
  13. Rounding To Accuracy And Error IntervalsM2.13
  14. Approximation And Estimation CalculationsM2.14

Probability

7 topics
  1. Frequency Tables And Frequency TreesM7.1
  2. Probability Expected Outcomes And RandomnessM7.2
  3. Theoretical Probability Expected Frequency ScaleM7.3
  4. Exhaustive And Mutually Exclusive ProbabilitiesM7.4
  5. Enumerating Sets And CombinationsM7.5
  6. Theoretical Possibility Spaces And ProbabilityM7.6
  7. Probability Addition Multiplication And Conditional EventsM7.7

Ratio and proportion

11 topics
  1. Scale Factors Diagrams And MapsM3.1
  2. Expressing One Quantity As A Fraction Of AnotherM3.2
  3. Understanding Ratio NotationM3.3
  4. Dividing Quantities In RatiosM3.4
  5. Ratio And Proportion ApplicationsM3.5
  6. Ratio And Proportion Linear FunctionsM3.6
  7. Fractions In Ratio ProblemsM3.7
  8. Percentage Calculations And ChangeM3.8
  9. Direct And Inverse ProportionM3.9
  10. Ratio Proportion Similarity Lengths Areas VolumesM3.10
  11. Growth Decay And Iterative ProcessesM3.11

Statistics

4 topics
  1. Statistical Tables Charts And DiagramsM6.1
  2. Histograms And Cumulative Frequency GraphsM6.2
  3. Statistics Averages And SpreadM6.3
  4. Scatter Graphs Bivariate Data CorrelationM6.4

Units

2 topics
  1. Standard And Compound Units Conversion M1 1M1.1
  2. Standard And Compound UnitsM1.2