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Fifth Year Maths Topics

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1. Number System and Radicals

1.1

Understanding the number systems

1.2

Prime factorisation

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. Exponents

2.1

Product rule of exponents

2.2

Quotient rule of exponents

2.3

Power of a product rule

2.4

Power of a quotient rule

2.5

Power of a power rule

2.6

Negative exponent rule

2.7

Combining the exponent rules

2.8

Scientific notation

2.9

Convert between radicals and rational exponents

2.10

Solving for exponents

3. Linear Inequalities

3.1

Express linear inequalities graphically and algebraically

3.2

Solving one-step linear inequalities

3.3

Solving multi-step linear inequalities

3.4

Compound inequalities

4. Quadratic Equations and Inequalities

4.1

Solving quadratic equations by factorising

4.2

Solving quadratic equations by completing the square

4.3

Using quadratic formula to solve quadratic equations

4.4

Nature of roots of quadratic equations: The discriminant

4.5

Applications of quadratic equations

4.6

Solving quadratic inequalities

5. Introduction to Relations and Functions

5.1

Relationship between two variables

5.2

Understand relations between x- and y-intercepts

5.3

Domain and range of a function

5.4

Identifying functions

5.5

Function notation

6. Solving Simultaneous Equations

6.1

Determining number of solutions to linear equations

6.2

Solving simultaneous equations by graphing

6.3

Solving simultaneous equations by elimination

6.4

Solving simultaneous equations by substitution

6.5

Money related questions in linear equations

6.6

Unknown number related questions in linear equations

6.7

Distance and time related questions in linear equations

6.8

Rectangular shape related questions in linear equations

7. Inequalities in two variables

7.1

Graphing linear inequalities in two variables

7.2

Graphing simultaneous linear inequalities

7.3

Graphing quadratic inequalities in two variables

7.4

Graphing simultaneous quadratic inequalities

7.5

Applications of inequalities

7.6

What is linear programming?

7.7

Linear programming word problems

8. Imaginary and Complex Numbers

8.1

Introduction to imaginary numbers

8.2

Complex numbers and complex planes

8.3

Adding and subtracting complex numbers

8.4

Complex conjugates

8.5

Multiplying and dividing complex numbers

8.6

Distance and midpoint of complex numbers

8.7

Angle and absolute value of complex numbers

8.8

Polar form of complex numbers

8.9

Operations on complex numbers in polar form

9. Factorising Quadratic Functions

9.1

Factorise by taking out the greatest common factor

9.2

Factorise by grouping

9.3

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

9.4

Factorising trinomials

9.5

Factoring difference of cubes

9.6

Factoring sum of cubes

10. Quadratic Functions

10.1

Characteristics of quadratic functions

10.2

Transformations of quadratic functions

10.3

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

10.4

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

10.5

Completing the square

10.6

Converting from general to vertex form by completing the square

10.7

Shortcut: Vertex formula

10.8

Graphing parabolas for given quadratic functions

10.9

Finding the quadratic functions for given parabolas

10.10

Applications of quadratic functions

11. Operations of Polynomials

11.1

What is a polynomial?

11.2

Using algebra tiles to factorise polynomials

12. Polynomial Functions

12.1

What is a polynomial function?

12.2

Polynomial long division

12.3

Polynomial synthetic division

12.4

Remainder theorem

12.5

12.6

Rational zero theorem

12.7

Characteristics of polynomial graphs

12.8

Multiplicities of polynomials

12.9

Imaginary zeros of polynomials

12.10

Determining the equation of a polynomial function

12.11

Applications of polynomial functions

12.12

Solving polynomial inequalities

12.13

Fundamental theorem of algebra

12.14

Descartes' rule of signs

13. Radicals

13.1

Operations with radicals

13.2

Conversion between entire radicals and mixed radicals

13.3

Adding and subtracting radicals

13.4

Multiplying radicals

13.5

Solving radical equations

14. Radical Functions

14.1

Basic radical functions

14.2

Transformations of radical functions

14.3

Square root of a function

15. Exponential Functions

15.1

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

15.2

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

15.3

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

15.4

Exponents: Negative exponents

15.5

Exponents: Zero exponent: a^0 = 1

15.6

Exponents: Rational exponents

15.7

Graphing exponential functions

15.8

Graphing transformations of exponential functions

15.9

Finding an exponential function given its graph

16. Rational Expressions

16.1

Simplifying rational expressions and restrictions

16.2

Adding and subtracting rational expressions

16.3

Multiplying rational expressions

16.4

Dividing rational expressions

16.5

Solving rational equations

16.6

Applications of rational equations

16.7

Simplifying complex fractions

16.8

Partial fraction decomposition

17. Reciprocal Functions

17.1

Graphing reciprocals of linear functions

17.2

Graphing reciprocals of quadratic functions

18. Function Operations

18.1

Function notation

18.2

Operations with functions

18.3

Adding functions

18.4

Subtracting functions

18.5

Multiplying functions

18.6

Dividing functions

18.7

Composite functions

18.8

Inequalities of combined functions

18.9

Inverse functions

18.10

One to one functions

18.11

Difference quotient: applications of functions

19. Logarithmic Functions

19.1

What is a logarithm?

19.2

Converting from logarithmic form to exponential form

19.3

Evaluating logarithms without a calculator

19.4

Common logarithms

19.5

Natural log: ln

19.6

Evaluating logarithms using change-of-base formula

19.7

Converting from exponential form to logarithmic form

19.8

Solving exponential equations with logarithms

19.9

Product rule of logarithms

19.10

Quotient rule of logarithms

19.11

Combining product rule and quotient rule in logarithms

19.12

Evaluating logarithms using logarithm rules

19.13

Solving logarithmic equations

19.14

Graphing logarithmic functions

19.15

Finding a logarithmic function given its graph

20. Exponential Growth and Decay

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

Continuous growth and decay

21. Trigonometry

21.1

Angle in standard position

21.2

Coterminal angles

21.3

Reference angle

21.4

Find the exact value of trigonometric ratios

21.5

ASTC rule in trigonometry (All Students Take Calculus)

21.6

21.7

Converting between degrees and radians

21.8

Trigonometric ratios of angles in radians

21.9

Radian measure and arc length

21.10

21.11

21.12

Applications of the sine law and cosine law

22. Bearings

22.1

Introduction to bearings

22.2

Bearings and direction word problems

22.3

Angle of elevation and depression

23. Graphing Trigonometric Functions

23.1

Sine graph: y = sin x

23.2

Cosine graph: y = cos x

23.3

Tangent graph: y = tan x

23.4

Cotangent graph: y = cot x

23.5

Secant graph: y = sec x

23.6

Cosecant graph: y = csc x

23.7

Graphing transformations of trigonometric functions

23.8

Determining trigonometric functions given their graphs

24. Applications of Trigonometric Functions

24.1

Ferris wheel trig problems

24.2

Tides and water depth trig problems

24.3

Spring (simple harmonic motion) trig problems

25. Trigonometric Identities

25.1

Quotient identities and reciprocal identities

25.2

Pythagorean identities

25.3

Sum and difference identities

25.4

Cofunction identities

25.5

Double-angle identities

26. Scale Factors and Similarity

26.1

Enlargements and reductions with scale factors

26.2

26.3

Similar triangles

26.4

Similar polygons

27. Circle Geometry

27.1

Angles in a circle

27.2

Chord properties

27.3

Tangent properties

27.4

Circles and circumference

27.5

Arcs of a circle

27.6

Areas and sectors of circles

27.7

Inscribed Angles and Proofs

27.8

Central and inscribed angles in circles

28. Conics

28.1

Conics - Parabola

28.2

Conics - Ellipse

28.3

Conics - Circle

28.4

Conics - Hyperbola

29. Surface Area and Volume

29.1

Surface area and volume of prisms

29.2

Surface area and volume of pyramids

29.3

Surface area and volume of cylinders

29.4

Surface area and volume of cones

29.5

Surface area and volume of spheres

30. Sequences and series

30.1

Arithmetic sequences

30.2

Arithmetic series

30.3

Geometric sequences

30.4

Geometric series

30.5

Infinite geometric series

30.6

30.7

Arithmetic mean vs. Geometric mean

31. Probability

31.1

Determining probabilities using tree diagrams and tables

31.2

Probability of independent events

31.3

Probability with Venn diagrams

32. Permutations and Combinations

32.1

Fundamental counting principle

32.2

Factorial notation

32.3

Path counting problems

32.4

Permutation vs. Combination

32.5

32.6

32.7

Problems involving both permutations and combinations

32.8

Pascal's triangle

32.9

Binomial theorem

33. Statistics

33.1

Median and mode

33.2

33.3

Range and outliers

33.4

Application of averages

34. Data and Graphs

34.1

Reading and drawing bar graphs

34.2

Reading and drawing histograms

34.3

Reading and drawing line graphs

34.4

Box-and-whisker plots and scatter plots

34.5

Stem-and-leaf plots

34.6

34.7

Reading and drawing Venn diagrams

34.8

Frequency tables and dot plots

34Chapters

227Topics

1406Videos

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