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Secondary 3 Maths Topics

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1.Number System and Radicals

1.1Understanding the number systems (free lessons)

1.2Prime factorization

1.3Greatest Common Factors (GCF)

1.4Least Common Multiple (LCM) (free lessons)

1.5Rational vs. Irrational numbers

1.6Converting repeating decimals to fractions

2.Rational Numbers

2.1Comparing and ordering rational numbers (free lessons)

2.2Solving problems with rational numbers in decimal form

2.3Solving problems with rational numbers in fraction form

2.4Determine square roots of rational numbers

3.Ratios, Rates, and Proportions

3.1Ratios (free lessons)

4.Percents

4.1Representing percents (free lessons)

4.2Percents, fractions, and decimals

4.3Percent of a number

4.4Adding and multiplying percents

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)

6.5Parallel and perpendicular line segments

6.6Perpendicular bisectors

6.7Angle Bisectors

7.Properties of Triangles

7.1Classifying Triangles

7.2Isosceles and Equilateral Triangles

8.Congruent Triangles

8.1Congruence and Congruent Triangles

8.2Triangles Congruent by SSS Proofs

8.3Triangles Congruent by SAS and HL Proofs

8.4Triangles Congruent by ASA and AAS Proofs

9.Symmetry and Surface Area

9.1Line symmetry (free lessons)

9.2Rotational symmetry and transformations

9.3Surface area of 3-dimensional shapes (free lessons)

10.Pythagorean Theorem

10.1Squares and square roots (free lessons)

10.2Pythagorean theorem (free lessons)

10.3Estimating square roots (free lessons)

10.4Using the pythagorean relationship

10.5Applications of pythagorean theorem

11.Surface Area of 3D Shapes

11.1Introduction to surface area of 3-dimensional shapes (free lessons)

11.2Nets of 3-dimensional shapes

11.3Surface area of prisms

11.4Surface area of cylinders

12.Circle Geometry

12.1Angles in a circle (free lessons)

12.2Chord properties

12.3Tangent properties

12.4Circles and circumference

12.5Arcs of a circle

12.6Areas and sectors of circles

12.7Inscribed Angles and Proofs

12.8Central and inscribed angles in circles

13.Volume of 3D Shapes

13.1Introduction to volume

13.2Volume of prisms

13.3Volume of cylinders

13.4Word problems relating volume of prisms and cylinders

14.Scale Factors and Similarity

14.1Enlargements and reductions with scale factors (free lessons)

14.2Scale diagrams

14.3Similar triangles

14.4Similar polygons

15.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.Solving Linear Equations

16.1Solving linear equations using multiplication and division (free lessons)

16.2Solving two-step linear equations:

ax + b = c

{x \over a} + b = c

16.3Solving linear equations using distributive property:

a(x + b) = c

(free lessons)

16.4Solving linear equations with variables on both sides

16.5Solving literal equations

17.Linear Inequalities

17.1Express linear inequalities graphically and algebraically (free lessons)

17.2Solving one-step linear inequalities

17.3Solving multi-step linear inequalities

18.Introduction to Relations and Functions

18.1Relationship between two variables (free lessons)

18.2Understand relations between x- and y-intercepts

18.3Domain and range of a function (free lessons)

18.4Identifying functions

18.5Function notation (free lessons)

19.Linear Functions

19.1Distance formula:

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

(free lessons)

19.2Midpoint formula:

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

(free lessons)

19.3Gradient equation:

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

19.4Gradient intercept form: y = mx + b (free lessons)

19.5General form: Ax + By + C = 0 (free lessons)

19.6Gradient-point form:

y - y_1 = m (x - x_1)

(free lessons)

19.7Rate of change

19.8Graphing linear functions using table of values

19.9Graphing linear functions using x- and y-intercepts (free lessons)

19.10Graphing from gradient-intercept form y=mx+b

19.11Graphing linear functions using a single point and gradient

19.12Word problems of graphing linear functions

19.13Parallel and perpendicular lines in linear functions (free lessons)

19.14Applications of linear relations

20.Linear equations (Advanced)

20.1Introduction to linear equations (free lessons)

20.2Introduction to nonlinear equations

20.3Special case of linear equations: Horizontal lines

20.4Special case of linear equations: Vertical lines

20.5Parallel line equation (free lessons)

20.6Perpendicular line equation

20.7Combination of both parallel and perpendicular line equations

20.8Applications of linear equations

21.Solving Simultaneous Equations

21.1Determining number of solutions to linear equations (free lessons)

21.2Solving simultaneous equations by graphing

21.3Solving simultaneous equations by elimination

21.4Solving simultaneous equations by substitution

21.5Money related questions in linear equations (free lessons)

21.6Unknown number related questions in linear equations

21.7Distance and time related questions in linear equations

21.8Rectangular shape related questions in linear equations

22.Exponents

22.1Product rule of exponents (free lessons)

22.2Quotient rule of exponents

22.3Power of a product rule

22.4Power of a quotient rule

22.5Power of a power rule (free lessons)

22.6Negative exponent rule

22.7Combining the exponent rules

22.8Scientific notation

22.9Convert between radicals and rational exponents (free lessons)

22.10Solving for exponents

23.Operations of Polynomials

23.1What is a polynomial? (free lessons)

23.2Polynomial components

23.3Multiplying monomial by monomial

23.4Multiplying monomial by binomial

23.5Multiplying binomial by binomial (free lessons)

23.6Multiplying polynomial by polynomial

23.7Applications of polynomials

24.Exponential Functions

24.1Exponents: Product rule

(a^x)(a^y)=a^{(x+y)}

(free lessons)

24.2Exponents: Division rule

{a^x \over a^y}=a^{(x-y)}

24.3Exponents: Power rule

(a^x)^y = a^{(x\cdot y)}

(free lessons)

24.4Exponents: Negative exponents

24.5Exponents: Zero exponent:

a^0 = 1

24.6Exponents: Rational exponents

24.7Graphing exponential functions

24.8Graphing transformations of exponential functions

24.9Finding an exponential function given its graph

25.Factorising Polynomial Functions

25.1Common factors of polynomials (free lessons)

25.2Factorising polynomials by grouping

25.3Solving polynomials with the unknown "b" from

x^2 + bx + c

25.4Solving polynomials with the unknown "c" from

x^2 + bx + c

25.5Factorising polynomials:

x^2 + bx + c

(free lessons)

25.6Applications of polynomials:

x^2 + bx + c

25.7Solving polynomials with the unknown "b" from

ax^2 + bx + c

25.8Factorising polynomials:

ax^2 + bx + c

25.9Factorising perfect square trinomials:

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

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

(free lessons)

25.10Find the difference of squares:

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

25.11Evaluating polynomials

25.12Using algebra tiles to solve polynomials

25.13Solving polynomial equations (free lessons)

25.14Word problems of polynomials

26.Quadratic Functions

26.1Characteristics of quadratic functions (free lessons)

26.2Transformations of quadratic functions

26.3Quadratic function in general form:

y = ax^2 + bx+c

26.4Quadratic function in vertex form: y =

a(x-p)^2 + q

26.5Completing the square

26.6Converting from general to vertex form by completing the square

26.7Shortcut: Vertex formula (free lessons)

26.8Finding the quadratic functions for given parabolas (free lessons)

26.9Applications of quadratic functions

27.Rational Expressions

27.1Simplifying rational expressions and restrictions

27.2Adding and subtracting rational expressions (free lessons)

27.3Multiplying rational expressions

27.4Dividing rational expressions

27.5Solving rational equations

27.6Applications of rational equations

27.7Simplifying complex fractions

27.8Partial fraction decomposition

28.Probability

28.1Determining probabilities using tree diagrams and tables (free lessons)

28.2Probability of independent events

28.3Probability with Venn diagrams

29.Statistics

29.1Median and mode

29.3Range and outliers

29.4Application of averages

30.Introduction to Matrices

30.1Notation of matrices

30.2Adding and subtracting matrices

30.3Multiplying a matrix by a scalar

30.4Multiplying a matrix by another matrix

30.5The three types of matrix row operations

30.6Representing a linear system as a matrix

30.7Solving a linear system with matrices using Gaussian elimination

1.Number System and Radicals

1.1Understanding the number systems (free lessons)

1.2Prime factorization

1.3Greatest Common Factors (GCF)

1.4Least Common Multiple (LCM) (free lessons)

1.5Rational vs. Irrational numbers

1.6Converting repeating decimals to fractions

2.Rational Numbers

2.1Comparing and ordering rational numbers (free lessons)

2.2Solving problems with rational numbers in decimal form

2.3Solving problems with rational numbers in fraction form

2.4Determine square roots of rational numbers

3.Ratios, Rates, and Proportions

3.1Ratios (free lessons)

4.Percents

4.1Representing percents (free lessons)

4.2Percents, fractions, and decimals

4.3Percent of a number

4.4Adding and multiplying percents

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)

6.5Parallel and perpendicular line segments

6.6Perpendicular bisectors

6.7Angle Bisectors

7.Properties of Triangles

7.1Classifying Triangles

7.2Isosceles and Equilateral Triangles

8.Congruent Triangles

8.1Congruence and Congruent Triangles

8.2Triangles Congruent by SSS Proofs

8.3Triangles Congruent by SAS and HL Proofs

8.4Triangles Congruent by ASA and AAS Proofs

9.Symmetry and Surface Area

9.1Line symmetry (free lessons)

9.2Rotational symmetry and transformations

9.3Surface area of 3-dimensional shapes (free lessons)

10.Pythagorean Theorem

10.1Squares and square roots (free lessons)

10.2Pythagorean theorem (free lessons)

10.3Estimating square roots (free lessons)

10.4Using the pythagorean relationship

10.5Applications of pythagorean theorem

11.Surface Area of 3D Shapes

11.1Introduction to surface area of 3-dimensional shapes (free lessons)

11.2Nets of 3-dimensional shapes

11.3Surface area of prisms

11.4Surface area of cylinders

12.Circle Geometry

12.1Angles in a circle (free lessons)

12.2Chord properties

12.3Tangent properties

12.4Circles and circumference

12.5Arcs of a circle

12.6Areas and sectors of circles

12.7Inscribed Angles and Proofs

12.8Central and inscribed angles in circles

13.Volume of 3D Shapes

13.1Introduction to volume

13.2Volume of prisms

13.3Volume of cylinders

13.4Word problems relating volume of prisms and cylinders

14.Scale Factors and Similarity

14.1Enlargements and reductions with scale factors (free lessons)

14.2Scale diagrams

14.3Similar triangles

14.4Similar polygons

15.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.Solving Linear Equations

16.1Solving linear equations using multiplication and division (free lessons)

16.2Solving two-step linear equations:

ax + b = c

{x \over a} + b = c

16.3Solving linear equations using distributive property:

a(x + b) = c

(free lessons)

16.4Solving linear equations with variables on both sides

16.5Solving literal equations

17.Linear Inequalities

17.1Express linear inequalities graphically and algebraically (free lessons)

17.2Solving one-step linear inequalities

17.3Solving multi-step linear inequalities

18.Introduction to Relations and Functions

18.1Relationship between two variables (free lessons)

18.2Understand relations between x- and y-intercepts

18.3Domain and range of a function (free lessons)

18.4Identifying functions

18.5Function notation (free lessons)

19.Linear Functions

19.1Distance formula:

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

(free lessons)

19.2Midpoint formula:

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

(free lessons)

19.3Gradient equation:

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

19.4Gradient intercept form: y = mx + b (free lessons)

19.5General form: Ax + By + C = 0 (free lessons)

19.6Gradient-point form:

y - y_1 = m (x - x_1)

(free lessons)

19.7Rate of change

19.8Graphing linear functions using table of values

19.9Graphing linear functions using x- and y-intercepts (free lessons)

19.10Graphing from gradient-intercept form y=mx+b

19.11Graphing linear functions using a single point and gradient

19.12Word problems of graphing linear functions

19.13Parallel and perpendicular lines in linear functions (free lessons)

19.14Applications of linear relations

20.Linear equations (Advanced)

20.1Introduction to linear equations (free lessons)

20.2Introduction to nonlinear equations

20.3Special case of linear equations: Horizontal lines

20.4Special case of linear equations: Vertical lines

20.5Parallel line equation (free lessons)

20.6Perpendicular line equation

20.7Combination of both parallel and perpendicular line equations

20.8Applications of linear equations

21.Solving Simultaneous Equations

21.1Determining number of solutions to linear equations (free lessons)

21.2Solving simultaneous equations by graphing

21.3Solving simultaneous equations by elimination

21.4Solving simultaneous equations by substitution

21.5Money related questions in linear equations (free lessons)

21.6Unknown number related questions in linear equations

21.7Distance and time related questions in linear equations

21.8Rectangular shape related questions in linear equations

22.Exponents

22.1Product rule of exponents (free lessons)

22.2Quotient rule of exponents

22.3Power of a product rule

22.4Power of a quotient rule

22.5Power of a power rule (free lessons)

22.6Negative exponent rule

22.7Combining the exponent rules

22.8Scientific notation

22.9Convert between radicals and rational exponents (free lessons)

22.10Solving for exponents

23.Operations of Polynomials

23.1What is a polynomial? (free lessons)

23.2Polynomial components

23.3Multiplying monomial by monomial

23.4Multiplying monomial by binomial

23.5Multiplying binomial by binomial (free lessons)

23.6Multiplying polynomial by polynomial

23.7Applications of polynomials

24.Exponential Functions

24.1Exponents: Product rule

(a^x)(a^y)=a^{(x+y)}

(free lessons)

24.2Exponents: Division rule

{a^x \over a^y}=a^{(x-y)}

24.3Exponents: Power rule

(a^x)^y = a^{(x\cdot y)}

(free lessons)

24.4Exponents: Negative exponents

24.5Exponents: Zero exponent:

a^0 = 1

24.6Exponents: Rational exponents

24.7Graphing exponential functions

24.8Graphing transformations of exponential functions

24.9Finding an exponential function given its graph

25.Factorising Polynomial Functions

25.1Common factors of polynomials (free lessons)

25.2Factorising polynomials by grouping

25.3Solving polynomials with the unknown "b" from

x^2 + bx + c

25.4Solving polynomials with the unknown "c" from

x^2 + bx + c

25.5Factorising polynomials:

x^2 + bx + c

(free lessons)

25.6Applications of polynomials:

x^2 + bx + c

25.7Solving polynomials with the unknown "b" from

ax^2 + bx + c

25.8Factorising polynomials:

ax^2 + bx + c

25.9Factorising perfect square trinomials:

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

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

(free lessons)

25.10Find the difference of squares:

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

25.11Evaluating polynomials

25.12Using algebra tiles to solve polynomials

25.13Solving polynomial equations (free lessons)

25.14Word problems of polynomials

26.Quadratic Functions

26.1Characteristics of quadratic functions (free lessons)

26.2Transformations of quadratic functions

26.3Quadratic function in general form:

y = ax^2 + bx+c

26.4Quadratic function in vertex form: y =

a(x-p)^2 + q

26.5Completing the square

26.6Converting from general to vertex form by completing the square

26.7Shortcut: Vertex formula (free lessons)

26.8Finding the quadratic functions for given parabolas (free lessons)

26.9Applications of quadratic functions

27.Rational Expressions

27.1Simplifying rational expressions and restrictions

27.2Adding and subtracting rational expressions (free lessons)

27.3Multiplying rational expressions

27.4Dividing rational expressions

27.5Solving rational equations

27.6Applications of rational equations

27.7Simplifying complex fractions

27.8Partial fraction decomposition

28.Probability

28.1Determining probabilities using tree diagrams and tables (free lessons)

28.2Probability of independent events

28.3Probability with Venn diagrams

29.Statistics

29.1Median and mode

29.3Range and outliers

29.4Application of averages

30.Introduction to Matrices

30.1Notation of matrices

30.2Adding and subtracting matrices

30.3Multiplying a matrix by a scalar

30.4Multiplying a matrix by another matrix

30.5The three types of matrix row operations

30.6Representing a linear system as a matrix

30.7Solving a linear system with matrices using Gaussian elimination

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