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Essential Maths Topics

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1. Adding and Subtracting Fractions

1.1

Using models to add and subtract fractions

1.2

Adding fractions with like denominators

1.3

Subtracting fractions with like denominators

1.4

Adding and subtracting fractions with unlike denominators

1.5

Adding and subtracting mixed numbers

2. Multiplying and Dividing Fractions

2.1

Multiplying fractions and whole numbers

2.2

Dividing fractions with whole numbers

2.3

Multiplying proper fractions

2.4

Multiplying improper fractions and mixed numbers

2.5

Dividing fractions and mixed numbers

2.6

Applications of fraction operations

3. Pythagorean Theorem

3.1

Squares and square roots

3.2

Pythagorean theorem

3.3

Estimating square roots

3.4

Using the pythagorean relationship

3.5

Applications of pythagorean theorem

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. Surds

5.1

Square and square roots

5.2

Cubic and cube roots

5.3

Evaluating and simplifying surds

5.4

Converting radicals to mixed radicals

5.5

Converting radicals to entire radicals

5.6

Adding and subtracting surds

5.7

Multiplying and dividing surds

5.8

Rationalize the denominator

6. Algebraic Expressions

6.1

Equivalent algebraic expressions

6.2

Adding and subtracting algebraic expressions

6.3

Multiplying monomial by monomial

6.4

Multiplying monomial by binomial

6.5

Multiplying binomial by binomial

6.6

Multiplying polynomial by polynomial

6.7

Applications of polynomials

7. Introduction to Relations and Functions

7.1

Relationship between two variables

7.2

Understand relations between x- and y-intercepts

7.3

Domain and range of a function

7.4

Identifying functions

7.5

Function notation

8. Linear Functions

8.1

Distance formula:

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

8.2

Midpoint formula:

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

8.3

Gradient equation:

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

8.4

Gradient intercept form: y = mx + b

8.5

General form: Ax + By + C = 0

8.6

Gradient-point form:

y - y_1 = m (x - x_1)

8.7

8.8

Graphing linear functions using table of values

8.9

Graphing linear functions using x- and y-intercepts

8.10

Graphing from slope-intercept form y=mx+b

8.11

Graphing linear functions using a single point and gradient

8.12

Word problems of graphing linear functions

8.13

Parallel and perpendicular lines in linear functions

8.14

Applications of linear relations

8.15

Perpendicular line equation

9. Simultaneous Equations

9.1

Determining number of solutions to linear equations

9.2

Solving simultaneous linear equations by graphing

9.3

Solving simultaneous linear equations by elimination

9.4

Solving simultaneous linear equations by substitution

9.5

Money related questions in linear equations

9.6

Unknown number related questions in linear equations

9.7

Distance and time related questions in linear equations

9.8

Rectangular shape related questions in linear equations

9.9

Simultaneous linear-quadratic equations

9.10

Simultaneous quadratic-quadratic equations

9.11

Solving 3 variable simultaneous equations by substitution

9.12

Solving 3 variable simultaneous equations by elimination

9.13

Solving 3 variable simultaneous equations with no solution, infinite solutions

9.14

Word problems relating 3 variable simultaneous equations

10. Factorisation

10.1

Factorise by taking out the greatest common factor

10.2

Factorise by grouping

10.3

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

10.4

Factorising trinomials

10.5

Factoring difference of cubes

10.6

Factoring sum of cubes

11. Quadratic Functions

11.1

Introduction to quadratic functions

11.2

Transformations of quadratic functions

11.3

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

11.4

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

11.5

Completing the square

11.6

Converting from general to vertex form by completing the square

11.7

Shortcut: Vertex formula

11.8

Graphing quadratic functions: General form VS. Vertex form

11.9

Finding the quadratic functions for given parabolas

11.10

Applications of quadratic functions

12. Solving Quadratic Equations

12.1

Solving quadratic equations by factorising

12.2

Solving quadratic equations by completing the square

12.3

Using quadratic formula to solve quadratic equations

12.4

Nature of roots of quadratic equations: The discriminant

12.5

Applications of quadratic equations

13. Inequalities

13.1

Express linear inequalities graphically and algebraically

13.2

Solving one-step linear inequalities

13.3

Solving multi-step linear inequalities

13.4

Compound inequalities

13.5

Solving absolute value inequalities

13.6

Graphing linear inequalities in two variables

13.7

Graphing simultaneous inequalities

13.8

Solving quadratic inequalities in one variable

14. Algebraic Fractions

14.1

Simplifying algebraic fractions and restrictions

14.2

Adding and subtracting algebraic fractions

14.3

Multiplying algebraic fractions

14.4

Dividing algebraic fractions

14.5

Solving equations with algebraic fractions

14.6

Applications of equations with algebraic fractions

14.7

Simplifying complex fractions

14.8

Partial fraction decomposition

15. Reciprocal Functions

15.1

Graphing reciprocals of linear functions

15.2

Graphing reciprocals of quadratic functions

16. Angles, Lines, and Transversals

16.1

Pairs of lines and angles

16.2

Parallel lines and transversals

16.3

Parallel line proofs

16.4

Perpendicular line proofs

17. Scale Factors and Similarity

17.1

Enlargements and reductions with scale factors

17.2

17.3

Similar triangles

17.4

Similar polygons

18. Properties of Triangles

18.1

Classifying Triangles

18.2

Isosceles and Equilateral Triangles

19. Congruent Triangles

19.1

Congruence and Congruent Triangles

19.2

Triangles Congruent by SSS Proofs

19.3

Triangles Congruent by SAS and HL Proofs

19.4

Triangles Congruent by ASA and AAS Proofs

20. Functions

20.1

Function notation

20.2

Operations with functions

20.3

Adding functions

20.4

Subtracting functions

20.5

Multiplying functions

20.6

Dividing functions

20.7

Composite functions

20.8

Even and odd functions

21. Rational Functions

21.1

What is a rational function?

21.2

Point of discontinuity

21.3

Vertical asymptote

21.4

Horizontal asymptote

21.5

Slant asymptote

21.6

Graphs of rational functions

22. Indices

22.1

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

22.2

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

22.3

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

22.4

Indices: Negative exponents

22.5

Indices: Zero exponent: a^0 = 1

22.6

Indices: Rational exponents

22.7

Combining laws of indices

22.8

Scientific notation

22.9

Convert between radicals and rational exponents

22.10

Solving for indices

23. Exponential Functions

23.1

Solving exponential equations using exponent rules

23.2

Graphing exponential functions

23.3

Graphing transformations of exponential functions

23.4

Finding an exponential function given its graph

24. Logarithmic Functions

24.1

What is a logarithm?

24.2

Converting from logarithmic form to exponential form

24.3

Evaluating logarithms without a calculator

24.4

Common logarithms

24.5

Natural log: ln

24.6

Evaluating logarithms using change-of-base formula

24.7

Converting from exponential form to logarithmic form

24.8

Solving exponential equations with logarithms

24.9

Product rule of logarithms

24.10

Quotient rule of logarithms

24.11

Combining product rule and quotient rule in logarithms

24.12

Evaluating logarithms using logarithm rules

24.13

Solving logarithmic equations

24.14

Graphing logarithmic functions

24.15

Finding a logarithmic function given its graph

25. Trigonometric Ratios and Angle Measure

25.1

Angle in standard position

25.2

Coterminal angles

25.3

Reference angle

25.4

Find the exact value of trigonometric ratios

25.5

ASTC rule in trigonometry (All Students Take Calculus)

25.6

25.7

Converting between degrees and radians

25.8

Trigonometric ratios of angles in radians

25.9

Radian measure and arc length

26. Sine Rule and Cosine Rule

26.1

26.2

26.3

Sine rule and cosine rule word problems

27. Trigonometric Graphs

27.1

Sine graph: y = sin x

27.2

Cosine graph: y = cos x

27.3

Tangent graph: y = tan x

28. Inverse Trigonometric Functions

28.1

Finding inverse trigonometric function from its graph

28.2

Evaluating inverse trigonometric functions

28.3

Finding inverse reciprocal trigonometric function from its graph

28.4

Finding exact value of inverse reciprocal trig functions

29. Bearings

29.1

Introduction to bearings

29.2

Bearings and direction word problems

29.3

Angle of elevation and depression

30. Series

30.1

Arithmetic series

30.2

Geometric series

30.3

Convergence and divergence of normal infinite series

30.4

Convergence & divergence of geometric series

31. Growth and Decay

31.1

Exponential growth and decay by a factor

31.2

Exponential growth and decay by percentage

31.3

Finance: Compound interest

31.4

Finance: Future value and present value

32. Conics

32.1

Conics - Parabola

32.2

Conics - Ellipse

32.3

Conics - Circle

32.4

Conics - Hyperbola

33. Probability

33.1

Addition rule for "OR"

33.2

Multiplication rule for "AND"

34. Limits

34.1

Finding limits from graphs

34.2

34.3

Finding limits algebraically - direct substitution

34.4

Finding limits algebraically - when direct substitution is not possible

34.5

35. Derivatives

35.1

Definition of derivative

35.2

35.3

Slope and equation of tangent line

35.4

35.5

Derivative of trigonometric functions

35.6

Derivative of exponential functions

35.7

35.8

35.9

Derivative of logarithmic functions

35.10

Higher order derivatives

36. Derivative Applications

36.1

Rectilinear Motion: Derivative

36.2

Critical number & maximum and minimum values

36.3

Curve sketching

37. Integrals

37.1

Antiderivatives

37.2

37.3

Definite integral

37.4

Fundamental theorem of calculus

38. Integral Applications

38.1

Areas between curves

38.2

Volumes of solids of revolution - Disc method

38.3

Volumes of solids of revolution - Shell method

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