esat.fyi

Mathematics 2 for the ESAT

Advanced mathematics: functions, coordinate geometry, sequences, trigonometry, and calculus.

39 topics across 8 areas, each a full lesson with worked examples.

Algebra and functions

7 topics
  1. Laws Of Indices Rational ExponentsMM1.1
  2. Manipulation Of Surds And Rationalising DenominatorsMM1.2
  3. Quadratic Functions And GraphsMM1.3
  4. Simultaneous Equations Substitution And Analytical SolutionsMM1.4
  5. Linear And Quadratic InequalitiesMM1.5
  6. Algebraic Manipulation Polynomials Factor Remainder TheoremsMM1.6
  7. Function Mappings Modulus And Square RootsMM1.7

Coordinate geometry in the (x,y)-plane

3 topics
  1. Straight Line Equations And PropertiesMM3.1
  2. Coordinate Geometry Of The CircleMM3.2
  3. Circle Properties Coordinate GeometryMM3.3

Differentiation

3 topics
  1. Derivative As Gradient And Rate Of ChangeMM6.1
  2. Differentiation Of Power Functions And Rational IndicesMM6.2
  3. Applications Of Differentiation Stationary PointsMM6.3

Exponentials and logarithms

3 topics
  1. Laws Of Logarithms And Exponential EquationsMM5.1
  2. Laws Of Logarithms And Their PropertiesMM5.2
  3. Solving Exponential And Logarithmic EquationsMM5.3

Graphs of functions

7 topics
  1. Transformations Of FunctionsMM8.1
  2. Graph Transformations And Composite FunctionsMM8.2
  3. Transformations Linear Graphs M And CMM8.3
  4. Transformations Of Quadratic FunctionsMM8.4
  5. Differentiation Graph Shapes Stationary PointsMM8.5
  6. Function Graph Intersections And TransformationsMM8.6
  7. Function Transformations And Geometric SolutionsMM8.7

Integration

6 topics
  1. Definite Integration And Area Between Curve And AxisMM7.1
  2. Integration Powers Areas Trapezium RuleMM7.2
  3. Fundamental Theorem Of Calculus IntegrationMM7.3
  4. Combining Integrals Equal Contiguous RangesMM7.4
  5. Trapezium Rule Approximation Overestimates UnderestimatesMM7.5
  6. Solving Differential Equations Dy Dx FxMM7.6

Sequences and series

4 topics
  1. Sequences Series Recurrence RelationsMM2.1
  2. Arithmetic Series And SequencesMM2.2
  3. Geometric Series Finite Infinite SumsMM2.3
  4. Binomial Expansion Positive IntegersMM2.4

Trigonometry

6 topics
  1. Sine And Cosine Rules And Triangle AreaMM4.1
  2. Radian Measure Arc Length And Sector AreaMM4.2
  3. Exact Trigonometric Values For Standard AnglesMM4.3
  4. Trigonometric Functions Graphs Symmetries PeriodicityMM4.4
  5. Trigonometric Identities And EquationsMM4.5
  6. Solving Trigonometric Equations In IntervalsMM4.6