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Year 11 Maths Topics

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1. Rational Numbers

1.1

Comparing and ordering rational numbers

1.2

Solving problems with rational numbers in decimal form

1.3

Solving problems with rational numbers in fraction form

1.4

Determine square roots of rational numbers

2. Ratios, Rates, and Proportions

2.1

2.2

2.3

3. Direct variation

3.1

Identifying proportional relationships

3.2

Understanding graphs of proportional relationships

3.3

Graphing and writing equations of proportional relationships

3.4

Applications of proportional relationships

4. Introduction to Relations and Functions

4.1

Relationship between two variables

4.2

Understand relations between x- and y-intercepts

4.3

Domain and range of a function

4.4

Identifying functions

4.5

Function notation

5. Linear Functions

5.1

Distance formula:

d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

5.2

Midpoint formula:

M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)

5.3

Gradient equation:

m = \frac{y_2-y_1}{x_2- x_1}

5.4

Gradient intercept form: y = mx + b

5.5

General form: Ax + By + C = 0

5.6

Gradient-point form:

y - y_1 = m (x - x_1)

5.7

5.8

Graphing linear functions using table of values

5.9

Graphing linear functions using x- and y-intercepts

5.10

Graphing from gradient-intercept form y=mx+b

5.11

Graphing linear functions using a single point and gradient

5.12

Word problems of graphing linear functions

5.13

Parallel and perpendicular lines in linear functions

5.14

Applications of linear relations

6. Linear Inequalities

6.1

Express linear inequalities graphically and algebraically

6.2

Solving one-step linear inequalities

6.3

Solving multi-step linear inequalities

6.4

Compound inequalities

7. Solving Simultaneous Equations

7.1

Determining number of solutions to linear equations

7.2

Solving simultaneous equations by graphing

7.3

Solving simultaneous equations by elimination

7.4

Solving simultaneous equations by substitution

7.5

Money related questions in linear equations

7.6

Unknown number related questions in linear equations

7.7

Distance and time related questions in linear equations

7.8

Rectangular shape related questions in linear equations

8. Exponents

8.1

Product rule of exponents

8.2

Quotient rule of exponents

8.3

Power of a product rule

8.4

Power of a quotient rule

8.5

Power of a power rule

8.6

Negative exponent rule

8.7

Combining the exponent rules

8.8

Scientific notation

8.9

Convert between radicals and rational exponents

8.10

Solving for exponents

9. Exponential Functions

9.1

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

9.2

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

9.3

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

9.4

Exponents: Negative exponents

9.5

Exponents: Zero exponent: a^0 = 1

9.6

Exponents: Rational exponents

9.7

Graphing exponential functions

9.8

Graphing transformations of exponential functions

9.9

Finding an exponential function given its graph

10. Logarithmic Functions

10.1

What is a logarithm?

10.2

Converting from logarithmic form to exponential form

10.3

Evaluating logarithms without a calculator

10.4

Common logarithms

10.5

Natural log: ln

10.6

Evaluating logarithms using change-of-base formula

10.7

Converting from exponential form to logarithmic form

10.8

Solving exponential equations with logarithms

10.9

Product rule of logarithms

10.10

Quotient rule of logarithms

10.11

Combining product rule and quotient rule in logarithms

10.12

Evaluating logarithms using logarithm rules

10.13

Solving logarithmic equations

10.14

Graphing logarithmic functions

10.15

Finding a logarithmic function given its graph

11. Introduction to Polynomials

11.1

Characteristics of polynomials

11.2

Equivalent expressions of polynomials

11.3

Adding and subtracting polynomials

12. Operations of Polynomials

12.1

What is a polynomial?

12.2

Polynomial components

12.3

Multiplying monomial by monomial

12.4

Multiplying monomial by binomial

12.5

Multiplying binomial by binomial

12.6

Multiplying polynomial by polynomial

12.7

Applications of polynomials

13. Factorising Polynomial Expressions

13.1

Common factors of polynomials

13.2

Factorising polynomials by grouping

13.3

Solving polynomials with the unknown "b" from x^2 + bx + c

13.4

Solving polynomials with the unknown "c" from x^2 + bx + c

13.5

Factorising polynomials: x^2 + bx + c

13.6

Applications of polynomials: x^2 + bx + c

13.7

Solving polynomials with the unknown "b" from

ax^2 + bx + c

13.8

Factorising polynomials:

ax^2 + bx + c

13.9

Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

13.10

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

13.11

Evaluating polynomials

13.12

Using algebra tiles to factorise polynomials

13.13

Solving polynomial equations

13.14

Word problems of polynomials

14. Quadratic Functions

14.1

Characteristics of quadratic functions

14.2

Transformations of quadratic functions

14.3

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

14.4

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

14.5

Completing the square

14.6

Converting from general to vertex form by completing the square

14.7

Shortcut: Vertex formula

14.8

Graphing parabolas for given quadratic functions

14.9

Finding the quadratic functions for given parabolas

14.10

Applications of quadratic functions

15. Conics

15.1

Conics - Parabola

15.2

Conics - Ellipse

15.3

Conics - Circle

15.4

Conics - Hyperbola

16. Radicals

16.1

Operations with radicals

16.2

Conversion between entire radicals and mixed radicals

16.3

Adding and subtracting radicals

16.4

Multiplying radicals

16.5

Solving radical equations

17. Algebraic Fractions

17.1

Simplifying algebraic fractions and restrictions

17.2

Adding and subtracting algebraic fractions

17.3

Multiplying algebraic fractions

17.4

Dividing algebraic fractions

17.5

Solving equations with algebraic fractions

17.6

Applications of equations with algebraic fractions

17.7

Simplifying complex fractions

17.8

Partial fraction decomposition

18. Reciprocal Functions

18.1

Graphing reciprocals of linear functions

18.2

Graphing reciprocals of quadratic functions

19. Rational Functions

19.1

What is a rational function?

19.2

Point of discontinuity

19.3

Vertical asymptote

19.4

Horizontal asymptote

19.5

Slant asymptote

19.6

Graphs of rational functions

19.7

Solving rational inequalities

20. Sequences and Series

20.1

Arithmetic sequences

20.2

Arithmetic series

20.3

Geometric sequences

20.4

Geometric series

20.5

Infinite geometric series

20.6

20.7

Arithmetic mean vs. Geometric mean

21. Angles, Lines and Transversals

21.1

Pairs of lines and angles

21.2

Parallel lines and transversals

21.3

Parallel line proofs

21.4

Perpendicular line proofs

22. Symmetry and Surface Area

22.1

22.2

Rotational symmetry and transformations

22.3

Surface area of 3-dimensional shapes

23. Properties of triangles

23.1

Classifying Triangles

23.2

Isosceles and Equilateral Triangles

24. Pythagorean Theorem

24.1

Squares and square roots

24.2

Pythagorean theorem

24.3

Estimating square roots

24.4

Using the pythagorean relationship

24.5

Applications of pythagorean theorem

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

26. Scale Factors and Similarity

26.1

Enlargements and reductions with scale factors

26.2

26.3

Similar triangles

26.4

Similar polygons

27. Congruent Triangles

27.1

Congruence and Congruent Triangles

27.2

Triangles Congruent by SSS Proofs

27.3

Triangles Congruent by SAS and HL Proofs

27.4

Triangles Congruent by ASA and AAS Proofs

28. Introduction to volume

28.1

Introduction to volume

28.2

Volume of prisms

28.3

Volume of cylinders

28.4

Word problems relating volume of prisms and cylinders

29. Surface Area and Volume

29.1

Surface area and volume of prisms

29.2

Surface area and volume of pyramids

29.3

Surface area and volume of cylinders

29.4

Surface area and volume of cones

29.5

Surface area and volume of spheres

30. Introduction to Trigonometry

30.1

Use sine ratio to calculate angles and sides (Sin =

\frac{o}{h}

30.2

Use cosine ratio to calculate angles and sides (Cos =

\frac{a}{h}

30.3

Use tangent ratio to calculate angles and sides (Tan =

\frac{o}{a}

30.4

Combination of SohCahToa questions

30.5

Solving expressions using 45-45-90 special right triangles

30.6

Solving expressions using 30-60-90 special right triangles

30.7

Word problems relating ladder in trigonometry

30.8

Word problems relating guy wire in trigonometry

30.9

Other word problems relating angles in trigonometry

31. Trigonometric Ratios and Angle Measure

31.1

31.2

Coterminal angles

31.3

Reference angles

31.4

Find the exact value of trigonometric ratios

31.5

ASTC rule in trigonometry (All Students Take Calculus)

31.6

31.7

31.8

31.9

Applications of the sine law and cosine law

32. Bearings

32.1

Introduction to bearings

32.2

Bearings and direction word problems

32.3

Angle of elevation and depression

33. Statistics

33.1

Median and mode

33.2

33.3

Range and outliers

33.4

Application of averages

34. Probability

34.1

Determining probabilities using tree diagrams and tables

34.2

Probability of independent events

34.3

Probability with Venn diagrams

35. Data and Graphs

35.1

Reading and drawing bar graphs

35.2

Reading and drawing histograms

35.3

Reading and drawing line graphs

35.4

Box-and-whisker plots and scatter plots

35.5

Stem-and-leaf plots

35.6

Reading and drawing Venn diagrams

35.7

Frequency tables and dot plots

35Chapters

215Topics

1504Videos

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