Year 13 Mathematics

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STRAND 13.1 COMPLEX NUMBERS

M13.1.1 Introduction to Complex Numbers 5 Lessons | 1 Quiz

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The number i

Solving Quadratic Equations

Parts of complex numbers

Equality rule

M13.1.1 Practice Exercise

M13.1.1 Practice Quiz

M13.1.2 Manipulation of Complex Numbers 5 Lessons | 1 Quiz

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Working with i

Addition and Subtraction

Multiplication

Division

M13.1.2 Practice Exercise

M13.1.2 Practice Quiz

M13.1.3 Geometrical Representation and Properties 6 Lessons | 1 Quiz

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Geometric Representation of z = a + bi

Polar or Trigonometric Form

Converting Polar to rectangular & vice versa

Argand diagram of polar form

Multiplication and Division in polar form

M13.1.3 Practice Exercise

M13.1.3 Practice Quiz

M13.1.4 Powers and Roots of Complex Numbers 3 Lessons | 1 Quiz

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Raising Complex Numbers to Powers

Finding nth roots

M13.1.4 Practice Exercise

M13.1.4 Practice Quiz

M13.1.5 Curves and Regions 5 Lessons | 1 Quiz

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M13.1.5 Lesson Exercise

M13.1.5 Practice Quiz

STRAND 13.2 VECTORS

M13.2.1 Arithmetic operations on vectors 3 Lessons | 1 Quiz

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Arithmetic Operations on Vectors

Scalar Multiplication

M13.2.1 Practice Exercise

M13.2.1 Practice Quiz

M13.2.2 Norm of a vector and unit vectors 2 Lessons | 1 Quiz

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Norm and Unit Vectors

M13.2.2 Practice Exercise

M13.2.2 Practice Quiz

M13.2.3 Dot product and its applications 4 Lessons | 1 Quiz

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Dot Product

Angle between the vectors

Angle Properties

13.2.3 Practice Exercise

M13.2.3 Practice Quiz

M13.2.4 Equation of lines 2 Lessons | 1 Quiz

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Equation of a line

M13.2.4 Practice Exercise

M13.2.4 Practice Quiz

M13.2.5 Ratio Formula 2 Lessons | 1 Quiz

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Ratio Formula

M13.2.5 Practice Excercise

M13.2.5 Practice Quiz

STRAND M13.3 FUNCTIONS

M13.3.1 Operations on Functions 3 Lessons | 1 Quiz

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New Functions from Old Functions

Domain and Range

M13.3.1 Practice Exercise

M13.3.1 Practice Quiz

M13.3.2 Graphs of Functions 3 Lessons | 1 Quiz

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Graphs of Polynomials

Graphs of Rational functions

M13.3.2 Practice Exercise

M13.3.2 Practice Quiz

STRAND M13.4 TRIGONOMETRY

M13.4.1 Identities and Exact Values of Trigonometric Ratios 3 Lessons | 1 Quiz

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Trigonometric Identities

Exact Values

M13.4.1 Practice Exercise

M13.4.1 Practice Quiz

M13.4.2 Trigonometric Graphs 2 Lessons | 1 Quiz

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Trigonometric Graphs

M13.4.2 Practice Exercise

M13.4.2 Practice Quiz

M13.4.3 Trigonometric Equations 2 Lessons | 1 Quiz

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Solving Trigonometric Equations

M13.4.3 Practice Exercise

M13.4.3 Practice Quiz

M13.4.4 Application of Addition Formulae 2 Lessons | 1 Quiz

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Transformation of A CosB Sin

M13.4.4 Practice Exercise

M13.4.4 Practice Quiz

M13.4.5 Inverse Trigonometric Functions 4 Lessons | 1 Quiz

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Graphs

Identities

Inverse of Reciprocal

M13.4.5 Practice Exercise

M13.4.5 Practice Quiz

STRAND M13.5 LIMITS ,CONTINUITY AND DIFFERENTIABILITY

M13.5.1 Limits 4 Lessons | 1 Quiz

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Computing Limits

Limits of Trigonometric Function

Limits at infinity

M13.5.1 Practice Exercise

M13.5.1 Practice Quiz

M13.5.2 Piecewise Functions 2 Lessons | 1 Quiz

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Graphs

M13.5.2 Practice Exercise

M13.5.2 Practice Quiz

M13.5.3 Limits, Continuity and Differentiability 2 Lessons | 1 Quiz

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Interpretation of graphs

M13.5.3 Practice Exercise

M13.5.3 Practice Quiz

STRAND M13.6 ALGEBRA

M13.6.1 Sequences 2 Lessons | 1 Quiz

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Sequences

M13.6.1 Practice Exercise

M13.6.1 Practice Quiz

M13.6.2 Mathematical Induction 2 Lessons | 1 Quiz

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Prove by Mathematical Induction

M13.6.2 Practice Exercise

M13.6.2 Practice Quiz

M13.6.3 Binomial Theorem 3 Lessons | 1 Quiz

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Binomial Theorem

Finding particular terms, coefficients and the independent term

M13.6.3 Practice Exercise

M13.6.3 Practice Quiz

M13.6.4 Partial fractions 4 Lessons | 1 Quiz

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Denominator with distinct linear factors

Repeated linear factors

Quadratics which cannot be factorised

M13.6.4 Practice Exercise

M13.6.4 Practice Quiz

STRAND M13.7 PROBABILITY AND INFERENTIAL STATISTICS

M13.7.1 Probability of Events 3 Lessons | 1 Quiz

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Types of events

Addition rule

M13.7.1 Practice Exercise

M13.7.1 Practice Quiz

M13.7.2 Inverse Normal Problems 2 Lessons | 1 Quiz

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Inverse Normal Distribution

M13.7.2 Practice Exercise

M13.7.2 Practice Quiz

M13.7.3 Binomial Distribution 4 Lessons | 1 Quiz

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Binomial Probabilities

Table of Binomial Probabilities

Table of Cumulative Binomial Distribution

M13.7.3 Practice Exercise

M13.7.3 Practice Quiz

M13.7.4. Estimation 4 Lessons | 1 Quiz

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Estimation

Confidence Interval

Sample Size for estimation

M13.7.4 Practice Exercise

M13.7.4 Practice Quiz

M13.7.5 Test of Hypothesis 4 Lessons | 1 Quiz

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Hypothesis Testing

One & Two – tailed test

Steps in hypothesis testing

M13.7.5 Practice Exercise

M13.7.5 Practice Quiz

STRAND M13.8 DIFFERENTIATION

M13.8.1 Derivatives of functions 6 Lessons | 1 Quiz

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Common derivatives

Product and Quotient rules

Chain rule

Logarithmic differentiation

Implicit differentiation

M13.8.1 Practice Exercise

M13.8.1 Practice Quiz

M13.8.2 Applications of Differentiation 5 Lessons | 1 Quiz

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Concavity, inflections and turning points

Maxima and Minima

Related rates

Kinematics using differentiation

M13.8.2 Practice Exercise

M13.8.2 Practice Quiz

STRAND M13.9 INTEGRATION

M13.9.1 Integration 4 Lessons | 1 Quiz

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Algebraic Substitution

Use of partial fractions

Use of trigonometric identities

M13.9.1 Practice Exercise

M13.9.1 Practice Quiz

M13.9.2 Applications of Integration 3 Lessons | 1 Quiz

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Area between two graphs

Kinematics using integration

M13.9.2 Practice Exercise

M13.9.2 Practice Quiz

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Course Includes

33 Tutorials
110 Lessons
33 Quizzes