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Study Notes

TMUA

Applying mathematical knowledge and mathematical reasoning for the Test of Mathematics for University Admission.

16 sections · 18 notes

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Section 1A5 notes
Section 1B7 notes
Section 1C6 notes2 locked
Section 2A0 notesLocked

Function Notation Domain and Range

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Composite Functions

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Inverse Functions

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Graph Transformations

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Interpreting and Sketching Graphs

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Functions and Graph Transformations Review

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Section 2B0 notesLocked

Arithmetic Sequences and Series

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Geometric Sequences and Series

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Recurrence Relations

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Binomial Expansion

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Sequences and Binomial Expansion Review

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Exponential Functions

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Laws of Logarithms

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Exponential and Logarithmic Equations

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Exponential Models

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Exponentials and Logarithms Review

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Section 3A0 notesLocked

Coordinates Distance and Midpoint

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Straight Lines and Gradients

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Parallel and Perpendicular Lines

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Equations of Circles

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Line and Circle Intersections

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Coordinate Geometry Review

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Angles Polygons and Geometric Reasoning

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Congruence and Similarity

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Circle Theorems

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Perimeter Area and Volume

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Bearings and Spatial Problems

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Vectors and Geometric Proofs

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Geometry Measures and Vectors Review

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Section 3C0 notesLocked

Right Triangle Trigonometry

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Radians Arcs and Sectors

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Trigonometric Functions and Graphs

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Trigonometric Identities and Equations

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Sine and Cosine Rules

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Trigonometry Review

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Section 4A0 notesLocked

Gradients and Rates of Change

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Differentiating Powers and Sums

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Tangents and Normals

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Stationary Points and Curve Sketching

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Optimisation and Motion

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Differentiation and Applications Review

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Section 4B0 notesLocked

Integration as Reverse Differentiation

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Constants of Integration and Initial Conditions

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Definite Integrals and Signed Area

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Areas Between Curves

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Trapezium Estimates

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Integration and Applications Review

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Section 5A0 notesLocked

Data Types and Statistical Diagrams

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Averages and Measures of Spread

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Histograms and Frequency Density

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Cumulative Frequency and Box Plots

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Scatter Diagrams and Data Interpretation

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Statistics and Data Interpretation Review

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Sample Spaces and Counting

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Probability Rules and Combined Events

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Tree Diagrams and Independent Events

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Conditional Probability

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Probability and Counting Review

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Section 6A0 notesLocked

Mathematical Statements and Negations

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Implication and Equivalence

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Necessary and Sufficient Conditions

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Quantifiers and Logical Reasoning

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Logic and Mathematical Language Review

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Section 6B0 notesLocked

Direct Proof and Deduction

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Proof by Exhaustion and Cases

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Proof by Contradiction

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Disproof by Counterexample

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Identifying Errors in Arguments

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Proof and Errors in Reasoning Review

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Section 7A0 notesLocked

Mixed Algebra and Functions

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Mixed Geometry and Trigonometry

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Mixed Calculus and Graphs

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Mixed Data and Probability

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Mathematical Reasoning Review

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Full Course Review

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