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Year 11 Maths Topics

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1. Solving Linear Equations

1.1

Solving linear equations using multiplication and division

1.2

Solving two-step linear equations: ax + b = c, x/a + b = c

1.3

Solving linear equations using distributive property: a(x + b) = c

1.4

Solving linear equations with variables on both sides

1.5

Solving literal equations

2. Linear Inequalities

2.1

Express linear inequalities graphically and algebraically

2.2

Solving one-step linear inequalities

2.3

Solving multi-step linear inequalities

2.4

Compound inequalities

3. Quadratic Equations and Inequalities

3.1

Solving quadratic equations by factoring

3.2

Solving quadratic equations by completing the square

3.3

Solving quadratic equations using the quadratic formula

3.4

Nature of roots of quadratic equations: The discriminant

3.5

Applications of quadratic equations

3.6

Solving quadratic inequalities

4. Solving Simultaneous Equations

4.1

Determining number of solutions to linear equations

4.2

Solving simultaneous equations by graphing

4.3

Solving simultaneous equations by elimination

4.4

Solving simultaneous equations by substitution

4.5

Money related questions in linear equations

4.6

Unknown number related questions in linear equations

4.7

Distance and time related questions in linear equations

4.8

Rectangular shape related questions in linear equations

5. Linear programming

5.1

What is linear programming?

5.2

Linear programming word problems

6. Introduction to Relations and Functions

6.1

Relationship between two variables

6.2

Understand relations between x- and y-intercepts

6.3

Domain and range of a function

6.4

Identifying functions

6.5

Function notation

7. Direct Variation

7.1

Identifying proportional relationships

7.2

Writing and solving for proportions

7.3

Understanding graphs of proportional relationships

7.4

Graphing and writing equations of proportional relationships

7.5

Applications of proportional relationships

8. Imaginary and Complex Numbers

8.1

Introduction to imaginary numbers

8.2

Complex numbers and complex planes

8.3

Adding and subtracting complex numbers

8.4

Complex conjugates

8.5

Multiplying and dividing complex numbers

8.6

Distance and midpoint of complex numbers

8.7

Angle and absolute value of complex numbers

8.8

Polar form of complex numbers

8.9

Operations on complex numbers in polar form

9. Factorising Polynomial

9.1

Factorise by taking out the greatest common factor

9.2

Factorise by grouping

9.3

Factorising difference of squares: x^2 - y^2

9.4

Factorising trinomials

9.5

Factoring difference of cubes

9.6

Factoring sum of cubes

10. Quadratic Functions

10.1

Characteristics of quadratic functions

10.2

Transformations of quadratic functions

10.3

Quadratic function in general form: y = ax^2 + bx + c

10.4

Quadratic function in vertex form: y = a(x-p)^2 + q

10.5

Completing the square

10.6

Converting from general to vertex form by completing the square

10.7

Shortcut: Vertex formula

10.8

Graphing parabolas for given quadratic functions

10.9

Finding the quadratic functions for given parabolas

10.10

Applications of quadratic functions

11. Polynomial Functions

11.1

What is a polynomial function?

11.2

Polynomial long division

11.3

Polynomial synthetic division

11.4

Remainder theorem

11.5

11.6

Rational zero theorem

11.7

Characteristics of polynomial graphs

11.8

Multiplicities of polynomials

11.9

Imaginary zeros of polynomials

11.10

Determining the equation of a polynomial function

11.11

Applications of polynomial functions

11.12

Solving polynomial inequalities

11.13

Fundamental theorem of algebra

11.14

Descartes' rule of signs

12. Radicals

12.1

Operations with radicals

12.2

Conversion between entire radicals and mixed radicals

12.3

Adding and subtracting radicals

12.4

Multiplying radicals

12.5

Solving radical equations

13. Radical Functions

13.1

Basic radical functions

13.2

Transformations of radical functions

13.3

Square root of a function

14. Exponents

14.1

Product rule of exponents

14.2

Quotient rule of exponents

14.3

Power of a product rule

14.4

Power of a quotient rule

14.5

Power of a power rule

14.6

Negative exponent rule

14.7

Combining the exponent rules

14.8

Scientific notation

14.9

Convert between radicals and rational exponents

14.10

Solving for exponents

15. Exponential Functions

15.1

Exponents: Product rule (a^x)(a^y) = a^(x+y)

15.2

Exponents: Division rule (a^x / a^y) = a^(x-y)

15.3

Exponents: Power rule (a^x)^y = a^(x * y)

15.4

Exponents: Negative exponents

15.5

Exponents: Zero exponent: a^0 = 1

15.6

Exponents: Rational exponents

15.7

Graphing exponential functions

15.8

Graphing transformations of exponential functions

15.9

Finding an exponential function given its graph

16. Logarithmic Functions

16.1

What is a logarithm?

16.2

Converting from logarithmic form to exponential form

16.3

Evaluating logarithms without a calculator

16.4

Common logarithms

16.5

Natural log: ln

16.6

Evaluating logarithms using change-of-base formula

16.7

Converting from exponential form to logarithmic form

16.8

Solving exponential equations with logarithms

16.9

Product rule of logarithms

16.10

Quotient rule of logarithms

16.11

Combining product rule and quotient rule in logarithms

16.12

Evaluating logarithms using logarithm rules

16.13

Solving logarithmic equations

16.14

Graphing logarithmic functions

16.15

Finding a logarithmic function given its graph

17. Applications of Exponential and Logarithmic Functions

17.1

Exponential growth and decay by a factor

17.2

Exponential decay: Half-life

17.3

Exponential growth and decay by percentage

17.4

Finance: Compound interest

17.5

Continuous growth and decay

17.6

Logarithmic scale: Richter scale (earthquake)

17.7

Logarithmic scale: pH scale

17.8

Logarithmic scale: dB scale

17.9

Finance: Future value and present value

18. Conics

18.1

Conics - Parabola

18.2

Conics - Ellipse

18.3

Conics - Circle

18.4

Conics - Hyperbola

19. Introduction to Trigonometry

19.1

Use sine ratio to calculate angles and sides (Sin =

\frac{o}{h}

19.2

Use cosine ratio to calculate angles and sides (Cos =

\frac{a}{h}

19.3

Use tangent ratio to calculate angles and side (Tan =

\frac{o}{a}

19.4

Combination of SohCahToa questions

19.5

Solving expressions using 45-45-90 special right triangles

19.6

Solving expressions using 30-60-90 special right triangles

19.7

Word problems relating ladder in trigonometry

19.8

Word problems relating guy wire in trigonometry

19.9

Other word problems relating angles in trigonometry

20. Trigonometric Ratios and Angle Measure

20.1

20.2

Coterminal angles

20.3

Reference angles

20.4

Find the exact value of trigonometric ratios

20.5

ASTC rule in trigonometry (All Students Take Calculus)

20.6

20.7

20.8

20.9

Applications of the sine rule and cosine rule

21. Bearings

21.1

Introduction to bearings

21.2

Bearings and direction word problems

21.3

Angle of elevation and depression

22. Graphing Trigonometric Functions

22.1

Sine graph: y = sin x

22.2

Cosine graph: y = cos x

22.3

Tangent graph: y = tan x

22.4

Cotangent graph: y = cot x

22.5

Secant graph: y = sec x

22.6

Cosecant graph: y = csc x

22.7

Graphing transformations of trigonometric functions

22.8

Determining trigonometric functions given their graphs

23. Applications of Trigonometric Functions

23.1

Ferris wheel trig problems

23.2

Tides and water depth trig problems

23.3

Spring (simple harmonic motion) trig problems

24. Trigonometric Identities

24.1

Quotient identities and reciprocal identities

24.2

Pythagorean identities

24.3

Sum and difference identities

24.4

Cofunction identities

24.5

Double-angle identities

25. Circle Geometry

25.1

Angles in a circle

25.2

Chord properties

25.3

Tangent properties

25.4

Circles and circumference

25.5

Arcs of a circle

25.6

Areas and sectors of circles

25.7

Inscribed Angles and Proofs

25.8

Central and inscribed angles in circles

26. Sequences and Series

26.1

Arithmetic sequences

26.2

Arithmetic series

26.3

Geometric sequences

26.4

Geometric series

26.5

Infinite geometric series

26.6

26.7

Arithmetic mean vs. Geometric mean

27. Introduction to Probability

27.1

Introduction to probability

27.2

Organizing outcomes

27.3

Probability of independent events

27.4

Comparing experimental and theoretical probability

28. Probability

28.1

Determining probabilities using tree diagrams and tables

28.2

Probability of independent events

28.3

Probability with Venn diagrams

29. Statistics

29.1

Median and mode

29.2

29.3

Range and outliers

29.4

Application of averages

30. Limits

30.1

Finding limits from graphs

30.2

30.3

Finding limits algebraically - direct substitution

30.4

Finding limits algebraically - when direct substitution is not possible

30.5

Infinite limits - vertical asymptotes

30.6

Limits at infinity - horizontal asymptotes

30.7

Intermediate value theorem

30.8

Squeeze theorem

31. Derivatives

31.1

Definition of derivative

31.2

31.3

Gradient and equation of tangent line

31.4

31.5

Derivative of trigonometric functions

31.6

Derivative of exponential functions

31.7

31.8

31.9

Implicit differentiation

31.10

Derivative of inverse trigonometric functions

31.11

Derivative of logarithmic functions

31.12

Higher order derivatives

31.13

Position velocity acceleration

32. Introduction to Matrices

32.1

Notation of matrices

32.2

Adding and subtracting matrices

32.3

Scalar multiplication

32.4

Matrix multiplication

32.5

The three types of matrix row operations

32.6

Representing a linear system as a matrix

32.7

Solving a linear system with matrices using Gaussian elimination

33. Determinants and Inverses of Matrices

33.1

The determinant of a 2 x 2 matrix

33.2

The determinant of a 3 x 3 matrix (General & Shortcut Method)

33.3

The inverse of a 2 x 2 matrix

33.4

The inverse of 3 x 3 matrices with matrix row operations

33.5

The inverse of 3 x 3 matrix with determinants and adjugate

33.6

2 x 2 invertible matrix

33.7

Solving linear systems using Cramer's Rule

33.8

Solving linear systems using 2 x 2 inverse matrices

33Chapters

228Topics

1422Videos

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