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Third Year Maths Topics

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1.Number System and Radicals

1.1Understanding the number systems (free lessons)

1.2Prime factorisation

1.3Greatest Common Factors (GCF)

1.4Least Common Multiple (LCM) (free lessons)

1.5Rational vs. Irrational numbers

1.6Converting repeating decimals to fractions

2.Ratios, Rates, and Proportions

2.1Ratios (free lessons)

3.Percents

3.1Squares and square roots (free lessons)

3.2Pythagorean theorem (free lessons)

3.3Estimating square roots (free lessons)

3.4Using the pythagorean relationship

3.5Applications of pythagorean theorem

4.Measuring Systems

4.1Metric systems (free lessons)

4.2Imperial systems

4.3Conversions between metric and imperial systems

4.4Conversions involve squares and cubic

5.Coordinates, Quadrants, and Transformations

5.1Cartesian plane

5.2Draw on coordinate planes

5.3Introduction to transformations

5.4Horizontal and vertical distances

6.Angles, Lines, and Transversals

6.1Pairs of lines and angles

6.2Parallel lines and transversals

6.3Parallel line proofs

6.4Perpendicular line proofs (free lessons)

7.Properties of Triangles

7.1Classifying triangles

7.2Isosceles and equilateral triangles

8.Circles

8.1Circles and circumference

8.2Angles in a circle (free lessons)

8.3Arcs of a circle

8.4Areas and sectors of circles

9.Congruent Triangles

9.1Congruence and congruent triangles

9.2Triangles congruent by SSS proofs

9.3Triangles congruent by SAS and HL proofs

9.4Triangles congruent by ASA and AAS proofs

10.Symmetry and Surface Area

10.1Line symmetry (free lessons)

10.2Rotational symmetry and transformations

10.3Surface area of 3-dimensional shapes (free lessons)

11.Scale Factors and Similarity

11.1Enlargements and reductions with scale factors (free lessons)

11.2Scale diagrams

11.3Similar triangles

11.4Similar polygons

12.Pythagorean Theorem

12.1Squares and square roots (free lessons)

12.2Pythagorean theorem (free lessons)

12.3Estimating square roots (free lessons)

12.4Using the pythagorean relationship

12.5Applications of pythagorean theorem

13.Introduction to 3-Dimensional Figures

13.1Introduction to surface area of 3-dimensional shapes (free lessons)

13.2Nets of 3-dimensional shapes

13.3Surface area of prisms

13.4Surface area of cylinders

14.Volume

14.1Introduction to volume

14.2Volume of prisms

14.3Volume of cylinders

14.4Word problems relating volume of prisms and cylinders

15.Introduction to Trigonometry

15.1Use sine ratio to calculate angles and side (Sin =

\frac{o}{h}

) (free lessons)

15.2Use cosine ratio to calculate angles and side (Cos =

\frac{a}{h}

15.3Use tangent ratio to calculate angles and side (Tan =

\frac{o}{a}

15.4Combination of SohCahToa questions (free lessons)

15.5Solving expressions using 45-45-90 special right triangles (free lessons)

15.6Solving expressions using 30-60-90 special right triangles

15.7Word problems relating ladder in trigonometry

15.8Word problems relating guy wire in trigonometry

15.9Other word problems relating angles in trigonometry

16.Patterns and Solving Equations

16.2Evaluating algebraic expressions

17.Introduction to Linear Relations

17.1Representing patterns in linear relations

17.2Reading linear relation graphs

17.3Solving linear equations by graphing

18.Linear Inequalities

18.1Express linear inequalities graphically and algebraically (free lessons)

18.2Solving one-step linear inequalities

18.3Solving multi-step linear inequalities

19.Introduction to Relations and Functions

19.1Relationship between two variables (free lessons)

19.2Understand relations between x- and y-intercepts

19.3Domain and range of a function (free lessons)

19.4Identifying functions

19.5Function notation (free lessons)

20.Data and Graphs

20.1Reading and drawing histograms

20.2Reading and drawing line graphs

20.3Box-and-whisker plots and scatter plots

20.4Stem-and-leaf plots

20.5Reading and drawing Venn diagrams

21.Linear Functions

21.1Distance formula:

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

(free lessons)

21.2Midpoint formula:

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

(free lessons)

21.3Gradient equation:

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

21.4Gradient intercept form: y = mx + b (free lessons)

21.5General form: Ax + By + C = 0 (free lessons)

21.6Gradient-point form:

y - y_1 = m (x - x_1)

(free lessons)

21.7Rate of change

21.8Graphing linear functions using table of values

21.9Graphing linear functions using x- and y-intercepts (free lessons)

21.10Graphing from gradient-intercept form y=mx+b

21.11Graphing linear functions using a single point and gradient

21.12Word problems of graphing linear functions

21.13Parallel and perpendicular lines in linear functions (free lessons)

21.14Applications of linear relations

22.Linear Equations

22.1Introduction to linear equations (free lessons)

22.2Introduction to nonlinear equations

22.3Special case of linear equations: Horizontal lines

22.4Special case of linear equations: Vertical lines

22.5Parallel line equation (free lessons)

22.6Perpendicular line equation

22.7Combination of both parallel and perpendicular line equations

22.8Applications of linear equations

23.Solving Simultaneous Equations

23.1Determining number of solutions to linear equations (free lessons)

23.2Solving simultaneous equations by graphing

23.3Solving simultaneous equations by elimination

23.4Solving simultaneous equations by substitution

23.5Money related questions in linear equations (free lessons)

23.6Unknown number related questions in linear equations

23.7Distance and time related questions in linear equations

23.8Rectangular shape related questions in linear equations

24.Exponents

24.1Product rule of exponents (free lessons)

24.2Quotient rule of exponents

24.3Power of a product rule

24.4Power of a quotient rule

24.5Power of a power rule (free lessons)

24.6Negative exponent rule

24.7Combining the exponent rules

24.8Scientific notation

24.9Convert between radicals and rational exponents (free lessons)

24.10Solving for exponents

25.Quadratic Functions

25.1Characteristics of quadratic functions (free lessons)

25.2Transformations of quadratic functions

25.3Quadratic function in general form:

y = ax^2 + bx+c

25.4Quadratic function in vertex form: y =

a(x-p)^2 + q

25.5Completing the square

25.6Converting from general to vertex form by completing the square

25.7Shortcut: Vertex formula (free lessons)

25.8Finding the quadratic functions for given parabolas (free lessons)

25.9Applications of quadratic functions

26.Polynomials

26.1Characteristics of polynomials (free lessons)

26.2Equivalent expressions of polynomials

26.3Adding and subtracting polynomials

27.Operations of Polynomials

27.1What is a polynomial? (free lessons)

27.2Using algebra tiles to solve polynomials

28.Factorising Polynomial expressions

28.1Common factors of polynomials (free lessons)

28.2Factorising polynomials by grouping

28.3Solving polynomials with the unknown "b" from

x^2 + bx + c

28.4Solving polynomials with the unknown "c" from

x^2 + bx + c

28.5Factorising polynomials:

x^2 + bx + c

(free lessons)

28.6Applications of polynomials:

x^2 + bx + c

28.7Solving polynomials with the unknown "b" from

ax^2 + bx + c

28.8Factorising polynomials:

ax^2 + bx + c

28.9Factorising perfect square trinomials:

(a + b)^2 = a^2 + 2ab + b^2

(a - b)^2 = a^2 - 2ab + b^2

(free lessons)

28.10Find the difference of squares:

(a - b)(a + b) = (a^2 - b^2)

28.11Evaluating polynomials

28.12Using algebra tiles to solve polynomials

28.13Solving polynomial equations (free lessons)

28.14Word problems of polynomials

29.Radicals

29.1Square and square roots (free lessons)

29.2Cubic and cube roots

29.3Evaluating and simplifying radicals

29.4Converting radicals to mixed radicals

29.5Converting radicals to entire radicals (free lessons)

29.6Adding and subtracting radicals

29.7Multiplying and dividing radicals

29.8Rationalize the denominator

30.Rational Expressions

30.1Simplifying rational expressions and restrictions

30.2Adding and subtracting rational expressions (free lessons)

30.3Multiplying rational expressions

30.4Dividing rational expressions

30.5Solving rational equations

30.6Applications of rational equations

30.7Simplifying complex fractions

30.8Partial fraction decomposition

31.Probability

31.1Determining probabilities using tree diagrams and tables (free lessons)

31.2Probability of independent events

31.3Probability with Venn diagrams

1.Number System and Radicals

1.1Understanding the number systems (free lessons)

1.2Prime factorisation

1.3Greatest Common Factors (GCF)

1.4Least Common Multiple (LCM) (free lessons)

1.5Rational vs. Irrational numbers

1.6Converting repeating decimals to fractions

2.Ratios, Rates, and Proportions

2.1Ratios (free lessons)

3.Percents

3.1Squares and square roots (free lessons)

3.2Pythagorean theorem (free lessons)

3.3Estimating square roots (free lessons)

3.4Using the pythagorean relationship

3.5Applications of pythagorean theorem

4.Measuring Systems

4.1Metric systems (free lessons)

4.2Imperial systems

4.3Conversions between metric and imperial systems

4.4Conversions involve squares and cubic

5.Coordinates, Quadrants, and Transformations

5.1Cartesian plane

5.2Draw on coordinate planes

5.3Introduction to transformations

5.4Horizontal and vertical distances

6.Angles, Lines, and Transversals

6.1Pairs of lines and angles

6.2Parallel lines and transversals

6.3Parallel line proofs

6.4Perpendicular line proofs (free lessons)

7.Properties of Triangles

7.1Classifying triangles

7.2Isosceles and equilateral triangles

8.Circles

8.1Circles and circumference

8.2Angles in a circle (free lessons)

8.3Arcs of a circle

8.4Areas and sectors of circles

9.Congruent Triangles

9.1Congruence and congruent triangles

9.2Triangles congruent by SSS proofs

9.3Triangles congruent by SAS and HL proofs

9.4Triangles congruent by ASA and AAS proofs

10.Symmetry and Surface Area

10.1Line symmetry (free lessons)

10.2Rotational symmetry and transformations

10.3Surface area of 3-dimensional shapes (free lessons)

11.Scale Factors and Similarity

11.1Enlargements and reductions with scale factors (free lessons)

11.2Scale diagrams

11.3Similar triangles

11.4Similar polygons

12.Pythagorean Theorem

12.1Squares and square roots (free lessons)

12.2Pythagorean theorem (free lessons)

12.3Estimating square roots (free lessons)

12.4Using the pythagorean relationship

12.5Applications of pythagorean theorem

13.Introduction to 3-Dimensional Figures

13.1Introduction to surface area of 3-dimensional shapes (free lessons)

13.2Nets of 3-dimensional shapes

13.3Surface area of prisms

13.4Surface area of cylinders

14.Volume

14.1Introduction to volume

14.2Volume of prisms

14.3Volume of cylinders

14.4Word problems relating volume of prisms and cylinders

15.Introduction to Trigonometry

15.1Use sine ratio to calculate angles and side (Sin =

\frac{o}{h}

) (free lessons)

15.2Use cosine ratio to calculate angles and side (Cos =

\frac{a}{h}

15.3Use tangent ratio to calculate angles and side (Tan =

\frac{o}{a}

15.4Combination of SohCahToa questions (free lessons)

15.5Solving expressions using 45-45-90 special right triangles (free lessons)

15.6Solving expressions using 30-60-90 special right triangles

15.7Word problems relating ladder in trigonometry

15.8Word problems relating guy wire in trigonometry

15.9Other word problems relating angles in trigonometry

16.Patterns and Solving Equations

16.2Evaluating algebraic expressions

17.Introduction to Linear Relations

17.1Representing patterns in linear relations

17.2Reading linear relation graphs

17.3Solving linear equations by graphing

18.Linear Inequalities

18.1Express linear inequalities graphically and algebraically (free lessons)

18.2Solving one-step linear inequalities

18.3Solving multi-step linear inequalities

19.Introduction to Relations and Functions

19.1Relationship between two variables (free lessons)

19.2Understand relations between x- and y-intercepts

19.3Domain and range of a function (free lessons)

19.4Identifying functions

19.5Function notation (free lessons)

20.Data and Graphs

20.1Reading and drawing histograms

20.2Reading and drawing line graphs

20.3Box-and-whisker plots and scatter plots

20.4Stem-and-leaf plots

20.5Reading and drawing Venn diagrams

21.Linear Functions

21.1Distance formula:

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

(free lessons)

21.2Midpoint formula:

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

(free lessons)

21.3Gradient equation:

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

21.4Gradient intercept form: y = mx + b (free lessons)

21.5General form: Ax + By + C = 0 (free lessons)

21.6Gradient-point form:

y - y_1 = m (x - x_1)

(free lessons)

21.7Rate of change

21.8Graphing linear functions using table of values

21.9Graphing linear functions using x- and y-intercepts (free lessons)

21.10Graphing from gradient-intercept form y=mx+b

21.11Graphing linear functions using a single point and gradient

21.12Word problems of graphing linear functions

21.13Parallel and perpendicular lines in linear functions (free lessons)

21.14Applications of linear relations

22.Linear Equations

22.1Introduction to linear equations (free lessons)

22.2Introduction to nonlinear equations

22.3Special case of linear equations: Horizontal lines

22.4Special case of linear equations: Vertical lines

22.5Parallel line equation (free lessons)

22.6Perpendicular line equation

22.7Combination of both parallel and perpendicular line equations

22.8Applications of linear equations

23.Solving Simultaneous Equations

23.1Determining number of solutions to linear equations (free lessons)

23.2Solving simultaneous equations by graphing

23.3Solving simultaneous equations by elimination

23.4Solving simultaneous equations by substitution

23.5Money related questions in linear equations (free lessons)

23.6Unknown number related questions in linear equations

23.7Distance and time related questions in linear equations

23.8Rectangular shape related questions in linear equations

24.Exponents

24.1Product rule of exponents (free lessons)

24.2Quotient rule of exponents

24.3Power of a product rule

24.4Power of a quotient rule

24.5Power of a power rule (free lessons)

24.6Negative exponent rule

24.7Combining the exponent rules

24.8Scientific notation

24.9Convert between radicals and rational exponents (free lessons)

24.10Solving for exponents

25.Quadratic Functions

25.1Characteristics of quadratic functions (free lessons)

25.2Transformations of quadratic functions

25.3Quadratic function in general form:

y = ax^2 + bx+c

25.4Quadratic function in vertex form: y =

a(x-p)^2 + q

25.5Completing the square

25.6Converting from general to vertex form by completing the square

25.7Shortcut: Vertex formula (free lessons)

25.8Finding the quadratic functions for given parabolas (free lessons)

25.9Applications of quadratic functions

26.Polynomials

26.1Characteristics of polynomials (free lessons)

26.2Equivalent expressions of polynomials

26.3Adding and subtracting polynomials

27.Operations of Polynomials

27.1What is a polynomial? (free lessons)

27.2Using algebra tiles to solve polynomials

28.Factorising Polynomial expressions

28.1Common factors of polynomials (free lessons)

28.2Factorising polynomials by grouping

28.3Solving polynomials with the unknown "b" from

x^2 + bx + c

28.4Solving polynomials with the unknown "c" from

x^2 + bx + c

28.5Factorising polynomials:

x^2 + bx + c

(free lessons)

28.6Applications of polynomials:

x^2 + bx + c

28.7Solving polynomials with the unknown "b" from

ax^2 + bx + c

28.8Factorising polynomials:

ax^2 + bx + c

28.9Factorising perfect square trinomials:

(a + b)^2 = a^2 + 2ab + b^2

(a - b)^2 = a^2 - 2ab + b^2

(free lessons)

28.10Find the difference of squares:

(a - b)(a + b) = (a^2 - b^2)

28.11Evaluating polynomials

28.12Using algebra tiles to solve polynomials

28.13Solving polynomial equations (free lessons)

28.14Word problems of polynomials

29.Radicals

29.1Square and square roots (free lessons)

29.2Cubic and cube roots

29.3Evaluating and simplifying radicals

29.4Converting radicals to mixed radicals

29.5Converting radicals to entire radicals (free lessons)

29.6Adding and subtracting radicals

29.7Multiplying and dividing radicals

29.8Rationalize the denominator

30.Rational Expressions

30.1Simplifying rational expressions and restrictions

30.2Adding and subtracting rational expressions (free lessons)

30.3Multiplying rational expressions

30.4Dividing rational expressions

30.5Solving rational equations

30.6Applications of rational equations

30.7Simplifying complex fractions

30.8Partial fraction decomposition

31.Probability

31.1Determining probabilities using tree diagrams and tables (free lessons)

31.2Probability of independent events

31.3Probability with Venn diagrams

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