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Higher 1 Maths Topics

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1. Solving Linear Equations

1.1

Solving linear equations using multiplication and division

1.2

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

1.3

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

1.4

Solving linear equations with variables on both sides

1.5

Solving literal equations

2. Linear Inequalities

2.1

Express linear inequalities graphically and algebraically

2.2

Solving one-step linear inequalities

2.3

Solving multi-step linear inequalities

2.4

Compound inequalities

3. Factorising Quadratic Equations

3.1

Factorise by taking out the greatest common factor

3.2

Factorise by grouping

3.3

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

3.4

Factorising trinomials

3.5

Factoring difference of cubes

3.6

Factoring sum of cubes

4. Quadratic Functions

4.1

Characteristics of quadratic functions

4.2

Transformations of quadratic functions

4.3

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

4.4

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

4.5

Completing the square

4.6

Converting from general to vertex form by completing the square

4.7

Shortcut: Vertex formula

4.8

Graphing parabolas for given quadratic functions

4.9

Finding the quadratic functions for given parabolas

4.10

Applications of quadratic functions

5. Quadratic Equations and Inequalities

5.1

Solving quadratic equations by factorising

5.2

Solving quadratic equations by completing the square

5.3

Using quadratic formula to solve quadratic equations

5.4

Nature of roots of quadratic equations: The discriminant

5.5

Applications of quadratic equations

5.6

Solving quadratic inequalities

6. Introduction to Relations and Functions

6.1

Relationship between two variables

6.2

Understand relations between x- and y-intercepts

6.3

Domain and range of a function

6.4

Identifying functions

6.5

Function notation

7. Linear Functions

7.1

Distance formula:

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

7.2

Midpoint formula:

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

7.3

Gradient equation:

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

7.4

Gradient intercept form: y = mx + b

7.5

General form: Ax + By + C = 0

7.6

Gradient-point form:

y - y_1 = m (x - x_1)

7.7

7.8

Graphing linear functions using table of values

7.9

Graphing linear functions using x- and y-intercepts

7.10

Graphing from gradient-intercept form y=mx+b

7.11

Graphing linear functions using a single point and gradient

7.12

Word problems of graphing linear functions

7.13

Parallel and perpendicular lines in linear functions

7.14

Applications of linear relations

8. Linear equations (Advanced)

8.1

Introduction to linear equations

8.2

Introduction to nonlinear equations

8.3

Special case of linear equations: Horizontal lines

8.4

Special case of linear equations: Vertical lines

8.5

Parallel line equation

8.6

Perpendicular line equation

8.7

Combination of both parallel and perpendicular line equations

8.8

Applications of linear equations

9. Solving Simultaneous Equations

9.1

Determining number of solutions to linear equations

9.2

Solving simultaneous equations by graphing

9.3

Solving simultaneous equations by elimination

9.4

Solving simultaneous 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

10. Imaginary and Complex Numbers

10.1

Introduction to imaginary numbers

10.2

Complex numbers and complex planes

10.3

Adding and subtracting complex numbers

10.4

Complex conjugates

10.5

Multiplying and dividing complex numbers

10.6

Distance and midpoint of complex numbers

10.7

Angle and absolute value of complex numbers

10.8

Polar form of complex numbers

10.9

Operations on complex numbers in polar form

11. Operations of polynomials

11.1

What is a polynomial?

11.2

Polynomial components

11.3

Multiplying monomial by monomial

11.4

Multiplying monomial by binomial

11.5

Multiplying binomial by binomial

11.6

Multiplying polynomial by polynomial

11.7

Applications of polynomials

11.8

Fundamental theorem of algebra

11.9

Pascal's triangle

11.10

Binomial theorem

12. Radicals

12.1

Operations with radicals

12.2

Conversion between entire radicals and mixed radicals

12.3

Adding and subtracting radicals

12.4

Multiplying radicals

12.5

Solving radical equations

13. Radical Functions

13.1

Basic radical functions

13.2

Transformations of radical functions

13.3

Square root of a function

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. Rational Functions

16.1

What is a rational function?

16.2

Point of discontinuity

16.3

Vertical asymptote

16.4

Horizontal asymptote

16.5

Slant asymptote

16.6

Graphs of rational functions

16.7

Solving rational inequalities

17. Operations of Functions

17.1

Function notation

17.2

Operations with functions

17.3

Adding functions

17.4

Subtracting functions

17.5

Multiplying functions

17.6

Dividing functions

17.7

Composite functions

17.8

Inequalities of combined functions

17.9

Inverse functions

17.10

One to one functions

17.11

Difference quotient: applications of functions

18. Transformations of Functions

18.1

Transformations of functions: Horizontal translations

18.2

Transformations of functions: Vertical translations

18.3

Reflection across the y-axis: y = f(-x)

18.4

Reflection across the x-axis: y = -f(x)

18.5

Transformations of functions: Horizontal stretches

18.6

Transformations of functions: Vertical stretches

18.7

Combining transformations of functions

18.8

Even and odd functions

19. Exponential Functions

19.1

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

19.2

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

19.3

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

19.4

Exponents: Negative exponents

19.5

Exponents: Zero exponent: a^0 = 1

19.6

Exponents: Rational exponents

19.7

Graphing exponential functions

19.8

Graphing transformations of exponential functions

19.9

Finding an exponential function given its graph

20. Applications of Exponential Functions

20.1

Exponential growth and decay by a factor

20.2

Exponential decay: Half-life

20.3

Exponential growth and decay by percentage

20.4

Finance: Compound interest

20.5

Continuous growth and decay

21. Logarithmic Functions

21.1

What is a logarithm?

21.2

Converting from logarithmic form to exponential form

21.3

Evaluating logarithms without a calculator

21.4

Common logarithms

21.5

Natural log: ln

21.6

Evaluating logarithms using change-of-base formula

21.7

Converting from exponential form to logarithmic form

21.8

Solving exponential equations with logarithms

21.9

Product rule of logarithms

21.10

Quotient rule of logarithms

21.11

Combining product rule and quotient rule in logarithms

21.12

Evaluating logarithms using logarithm rules

21.13

Solving logarithmic equations

21.14

Graphing logarithmic functions

21.15

Finding a logarithmic function given its graph

22. Conics

22.1

Conics - Parabola

22.2

Conics - Ellipse

22.3

Conics - Circle

22.4

Conics - Hyperbola

23. Introduction to Trigonometry

23.1

Use sine ratio to calculate angles and sides (Sin =

\frac{o}{h}

23.2

Use cosine ratio to calculate angles and sides (Cos =

\frac{a}{h}

23.3

Use tangent ratio to calculate angles and sides (Tan =

\frac{o}{a}

23.4

Combination of SohCahToa questions

23.5

Solving expressions using 45-45-90 special right triangles

23.6

Solving expressions using 30-60-90 special right triangles

23.7

Word problems relating ladder in trigonometry

23.8

Word problems relating guy wire in trigonometry

23.9

Other word problems relating angles in trigonometry

24. Trigonometry

24.1

Angle in standard position

24.2

Coterminal angles

24.3

Reference angle

24.4

Find the exact value of trigonometric ratios

24.5

ASTC rule in trigonometry (All Students Take Calculus)

24.6

24.7

Converting between degrees and radians

24.8

Trigonometric ratios of angles in radians

24.9

Radian measure and arc length

24.10

24.11

24.12

Applications of the sine law and cosine law

25. Bearings

25.1

Introduction to bearings

25.2

Bearings and direction word problems

25.3

Angle of elevation and depression

26. Graphing Trigonometric Functions

26.1

Sine graph: y = sin x

26.2

Cosine graph: y = cos x

26.3

Tangent graph: y = tan x

26.4

Cotangent graph: y = cot x

26.5

Secant graph: y = sec x

26.6

Cosecant graph: y = csc x

26.7

Graphing transformations of trigonometric functions

26.8

Determining trigonometric functions given their graphs

27. Trigonometric Identities

27.1

Quotient identities and reciprocal identities

27.2

Pythagorean identities

27.3

Sum and difference identities

27.4

Cofunction identities

27.5

Double-angle identities

28. Sequences

28.1

Arithmetic sequences

28.2

Geometric sequences

28.3

29. Derivatives

29.1

Definition of derivative

29.2

29.3

29.4

Derivative of exponential functions

29.5

29.6

29.7

Derivative of logarithmic functions

30. Probability

30.1

Determining probabilities using tree diagrams and tables

30.2

Probability of independent events

30.3

Probability with Venn diagrams

30.4

Addition rule for "OR"

30.5

Multiplication rule for "AND"

30.6

Conditional probability

31. Statistics

31.1

Median and mode

31.2

31.3

Range and outliers

31.4

Application of averages

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

33. Determinants and Inverses of Matrices

33.1

The determinant of a 2 x 2 matrix

33.2

The determinant of a 3 x 3 matrix (General & Shortcut Method)

33.3

The inverse of a 2 x 2 matrix

33.4

The inverse of 3 x 3 matrices with matrix row operations

33.5

The inverse of 3 x 3 matrix with determinants and adjugate

33.6

2 x 2 invertible matrix

33.7

Solving linear systems using Cramer's Rule

33.8

Solving linear systems using 2 x 2 inverse matrices

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