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Secondary 3 Maths Help for O-Level Success

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Secondary 3 Maths Topics

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1. Number System and Radicals

1.1

Understanding the number systems

1.2

Prime factorization

1.3

Greatest Common Factors (GCF)

1.4

Least Common Multiple (LCM)

1.5

Rational vs. Irrational numbers

1.6

Converting repeating decimals to fractions

2. Rational Numbers

2.1

Comparing and ordering rational numbers

2.2

Solving problems with rational numbers in decimal form

2.3

Solving problems with rational numbers in fraction form

2.4

Determine square roots of rational numbers

3. Ratios, Rates, and Proportions

3.1

Ratios

3.2

Rates

3.3

Proportions

4. Percents

4.1

Representing percents

4.2

Percents, fractions, and decimals

4.3

Percent of a number

4.4

Adding and multiplying percents

4.5

Taxes, discounts, tips and more

4.6

Simple interest

5. Coordinates, Quadrants, and Transformations

5.1

Cartesian plane

5.2

Draw on coordinate planes

5.3

Introduction to transformations

5.4

Horizontal and vertical distances

6. Angles, Lines and Transversals

6.1

Pairs of lines and angles

6.2

Parallel lines and transversals

6.3

Parallel line proofs

6.4

Perpendicular line proofs

6.5

Parallel and perpendicular line segments

6.6

Perpendicular bisectors

6.7

Angle Bisectors

7. Properties of Triangles

7.1

Classifying Triangles

7.2

Isosceles and Equilateral Triangles

8. Congruent Triangles

8.1

Congruence and Congruent Triangles

8.2

Triangles Congruent by SSS Proofs

8.3

Triangles Congruent by SAS and HL Proofs

8.4

Triangles Congruent by ASA and AAS Proofs

9. Symmetry and Surface Area

9.1

Line symmetry

9.2

Rotational symmetry and transformations

9.3

Surface area of 3-dimensional shapes

10. Pythagorean Theorem

10.1

Squares and square roots

10.2

Pythagorean theorem

10.3

Estimating square roots

10.4

Using the pythagorean relationship

10.5

Applications of pythagorean theorem

11. Surface Area of 3D Shapes

11.1

Introduction to surface area of 3-dimensional shapes

11.2

Nets of 3-dimensional shapes

11.3

Surface area of prisms

11.4

Surface area of cylinders

12. Circle Geometry

12.1

Angles in a circle

12.2

Chord properties

12.3

Tangent properties

12.4

Circles and circumference

12.5

Arcs of a circle

12.6

Areas and sectors of circles

12.7

Inscribed Angles and Proofs

12.8

Central and inscribed angles in circles

13. Volume of 3D Shapes

13.1

Introduction to volume

13.2

Volume of prisms

13.3

Volume of cylinders

13.4

Word problems relating volume of prisms and cylinders

14. Scale Factors and Similarity

14.1

Enlargements and reductions with scale factors

14.2

Scale diagrams

14.3

Similar triangles

14.4

Similar polygons

15. Trigonometry

15.1

Use sine ratio to calculate angles and sides (Sin =

\frac{o}{h}

)

15.2

Use cosine ratio to calculate angles and sides (Cos =

\frac{a}{h}

)

15.3

Use tangent ratio to calculate angles and sides (Tan =

\frac{o}{a}

)

15.4

Combination of SohCahToa questions

15.5

Solving expressions using 45-45-90 special right triangles

15.6

Solving expressions using 30-60-90 special right triangles

15.7

Word problems relating ladder in trigonometry

15.8

Word problems relating guy wire in trigonometry

15.9

Other word problems relating angles in trigonometry

16. Solving Linear Equations

16.1

Solving linear equations using multiplication and division

16.2

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

16.3

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

16.4

Solving linear equations with variables on both sides

16.5

Solving literal equations

17. Linear Inequalities

17.1

Express linear inequalities graphically and algebraically

17.2

Solving one-step linear inequalities

17.3

Solving multi-step linear inequalities

17.4

Compound inequalities

18. Introduction to Relations and Functions

18.1

Relationship between two variables

18.2

Understand relations between x- and y-intercepts

18.3

Domain and range of a function

18.4

Identifying functions

18.5

Function notation

19. Linear Functions

19.1

Distance formula:

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

19.2

Midpoint formula:

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

19.3

Gradient equation:

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

19.4

Gradient intercept form: y = mx + b

19.5

General form: Ax + By + C = 0

19.6

Gradient-point form:

y - y_1 = m (x - x_1)

19.7

Rate of change

19.8

Graphing linear functions using table of values

19.9

Graphing linear functions using x- and y-intercepts

19.10

Graphing from gradient-intercept form y=mx+b

19.11

Graphing linear functions using a single point and gradient

19.12

Word problems of graphing linear functions

19.13

Parallel and perpendicular lines in linear functions

19.14

Applications of linear relations

20. Linear equations (Advanced)

20.1

Introduction to linear equations

20.2

Introduction to nonlinear equations

20.3

Special case of linear equations: Horizontal lines

20.4

Special case of linear equations: Vertical lines

20.5

Parallel line equation

20.6

Perpendicular line equation

20.7

Combination of both parallel and perpendicular line equations

20.8

Applications of linear equations

21. Solving Simultaneous Equations

21.1

Determining number of solutions to linear equations

21.2

Solving simultaneous equations by graphing

21.3

Solving simultaneous equations by elimination

21.4

Solving simultaneous equations by substitution

21.5

21.6

Unknown number related questions in linear equations

21.7

Distance and time related questions in linear equations

21.8

Rectangular shape related questions in linear equations

22. Exponents

22.1

Product rule of exponents

22.2

Quotient rule of exponents

22.3

Power of a product rule

22.4

Power of a quotient rule

22.5

Power of a power rule

22.6

Negative exponent rule

22.7

Combining the exponent rules

22.8

Scientific notation

22.9

Convert between radicals and rational exponents

22.10

Solving for exponents

23. Operations of Polynomials

23.1

What is a polynomial?

23.2

Polynomial components

23.3

Multiplying monomial by monomial

23.4

Multiplying monomial by binomial

23.5

Multiplying binomial by binomial

23.6

Multiplying polynomial by polynomial

23.7

Applications of polynomials

24. Exponential Functions

24.1

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

24.2

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

24.3

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

24.4

Exponents: Negative exponents

24.5

Exponents: Zero exponent: a^0 = 1

24.6

Exponents: Rational exponents

24.7

Graphing exponential functions

24.8

Graphing transformations of exponential functions

24.9

Finding an exponential function given its graph

25. Factorising Polynomial Functions

25.1

Common factors of polynomials

25.2

Factorising polynomials by grouping

25.3

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

25.4

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

25.5

Factorising polynomials: x^2 + bx + c

25.6

Applications of polynomials: x^2 + bx + c

25.7

Solving polynomials with the unknown "b" from

ax^2 + bx + c

25.8

Factorising polynomials:

ax^2 + bx + c

25.9

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

25.10

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

25.11

Evaluating polynomials

25.12

Using algebra tiles to factorise polynomials

25.13

Solving polynomial equations

25.14

Word problems of polynomials

26. Quadratic Functions

26.1

Characteristics of quadratic functions

26.2

Transformations of quadratic functions

26.3

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

26.4

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

26.5

Completing the square

26.6

Converting from general to vertex form by completing the square

26.7

Shortcut: Vertex formula

26.8

Graphing parabolas for given quadratic functions

26.9

Finding the quadratic functions for given parabolas

26.10

Applications of quadratic functions

27. Algebraic Fractions

27.1

Simplifying algebraic fractions and restrictions

27.2

Adding and subtracting algebraic fractions

27.3

Multiplying algebraic fractions

27.4

Dividing algebraic fractions

27.5

Solving equations with algebraic fractions

27.6

Applications of equations with algebraic fractions

27.7

Simplifying complex fractions

27.8

Partial fraction decomposition

28. Reciprocal Functions

28.1

Graphing reciprocals of linear functions

28.2

Graphing reciprocals of quadratic functions

29. Direct and Inverse Variation

29.1

Direct variation

30. Probability

30.1

Determining probabilities using tree diagrams and tables

30.2

Probability of independent events

30.3

Probability with Venn diagrams

31. Statistics

31.1

Median and mode

31.2

Mean

31.3

Range and outliers

31.4

Application of averages

31.5

Circle graphs

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

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