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Year 10 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. Patterns and Solving Equations

2.1

2.2

Combining like terms

2.3

Evaluating algebraic expressions

2.4

Solving one-step equations: x + a = b

2.5

Graphing linear relations

3. Linear Equations (Basic)

3.1

Model and solve one-step linear equations: ax = b, x/a = b

3.2

Solving two-step linear equations using addition and subtraction: ax + b = c

3.3

Solving two-step linear equations using multiplication and division: x/a + b = c

3.4

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

4. Solving Linear Equations

4.1

Solving linear equations using multiplication and division

4.2

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

4.3

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

4.4

Solving linear equations with variables on both sides

4.5

Solving literal equations

5. Solving Linear Inequalities

5.1

Express linear inequalities graphically and algebraically

5.2

Solving one-step linear inequalities

5.3

Solving multi-step linear inequalities

5.4

Compound 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 Relations

7.1

Representing patterns in linear relations

7.2

Reading linear relation graphs

7.3

Solving linear equations by graphing

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 gradient-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

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. Transformations of Functions

10.1

Transformations of functions: Horizontal translations

10.2

Transformations of functions: Vertical translations

10.3

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

10.4

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

10.5

Transformations of functions: Horizontal stretches

10.6

Transformations of functions: Vertical stretches

10.7

Combining transformations of functions

10.8

Even and odd functions

11. Exponents

11.1

Product rule of exponents

11.2

Quotient rule of exponents

11.3

Power of a product rule

11.4

Power of a quotient rule

11.5

Power of a power rule

11.6

Negative exponent rule

11.7

Combining the exponent rules

11.8

Scientific notation

11.9

Convert between radicals and rational exponents

11.10

Solving for exponents

12. Exponential Functions

12.1

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

12.2

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

12.3

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

12.4

Exponents: Negative exponents

12.5

Exponents: Zero exponent: a^0 = 1

12.6

Exponents: Rational exponents

12.7

Graphing exponential functions

12.8

Graphing transformations of exponential functions

12.9

Finding an exponential function given its graph

12.10

Finance: Compound interest

13. Logarithmic Functions

13.1

What is a logarithm?

13.2

Converting from logarithmic form to exponential form

13.3

Evaluating logarithms without a calculator

13.4

Common logarithms

13.5

Natural log: ln

13.6

Evaluating logarithms using change-of-base formula

13.7

Converting from exponential form to logarithmic form

13.8

Solving exponential equations with logarithms

13.9

Product rule of logarithms

13.10

Quotient rule of logarithms

13.11

Combining product rule and quotient rule in logarithms

13.12

Evaluating logarithms using logarithm rules

13.13

Solving logarithmic equations

13.14

Graphing logarithmic functions

13.15

Finding a logarithmic function given its graph

14. Introduction to Polynomials

14.1

Characteristics of polynomials

14.2

Equivalent expressions of polynomials

14.3

Adding and subtracting polynomials

15. Multiplying and Dividing Polynomials

15.1

Multiplying and dividing monomials

15.2

Multiplying polynomials by monomials

15.3

Dividing polynomials by monomials

16. Operations of Polynomials

16.1

What is a polynomial?

16.2

Polynomial components

16.3

Multiplying monomial by monomial

16.4

Multiplying monomial by binomial

16.5

Multiplying binomial by binomial

16.6

Multiplying polynomial by polynomial

16.7

Applications of polynomials

17. Factorising Polynomial Expressions

17.1

Common factors of polynomials

17.2

Factorising polynomials by grouping

17.3

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

17.4

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

17.5

Factorising polynomials: x^2 + bx + c

17.6

Applications of polynomials: x^2 + bx + c

17.7

Solving polynomials with the unknown "b" from

ax^2 + bx + c

17.8

Factorising polynomials:

ax^2 + bx + c

17.9

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

17.10

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

17.11

Evaluating polynomials

17.12

Using algebra tiles to factorise polynomials

17.13

Solving polynomial equations

17.14

Word problems of polynomials

18. Factorising Polynomial (Advanced)

18.1

Factorise by taking out the greatest common factor

18.2

Factorise by grouping

18.3

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

18.4

Factorising trinomials

18.5

Factoring difference of cubes

18.6

Factoring sum of cubes

19. Quadratic Functions

19.1

Characteristics of quadratic functions

19.2

Transformations of quadratic functions

19.3

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

19.4

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

19.5

Completing the square

19.6

Converting from general to vertex form by completing the square

19.7

Shortcut: Vertex formula

19.8

Graphing parabolas for given quadratic functions

19.9

Finding the quadratic functions for given parabolas

19.10

Applications of quadratic functions

20. Conics

20.1

Conics - Parabola

20.2

Conics - Ellipse

20.3

Conics - Circle

20.4

Conics - Hyperbola

21. Radicals

21.1

Square and square roots

21.2

Cubic and cube roots

21.3

Evaluating and simplifying radicals

21.4

Converting radicals to mixed radicals

21.5

Converting radicals to entire radicals

21.6

Adding and subtracting radicals

21.7

Multiplying and dividing radicals

21.8

Rationalize the denominator

22. Algebraic Fractions

22.1

Simplifying algebraic fractions and restrictions

22.2

Adding and subtracting algebraic fractions

22.3

Multiplying algebraic fractions

22.4

Dividing algebraic fractions

22.5

Solving equations with algebraic fractions

22.6

Applications of equations with algebraic fractions

22.7

Simplifying complex fractions

22.8

Partial fraction decomposition

23. Reciprocal Functions

23.1

Graphing reciprocals of linear functions

23.2

Graphing reciprocals of quadratic functions

24. Scale Factors and Similarity

24.1

Enlargements and reductions with scale factors

24.2

24.3

Similar triangles

24.4

Similar polygons

25. Properties of Triangles

25.1

Classifying Triangles

25.2

Isosceles and Equilateral Triangles

26. Congruent Triangles

26.1

Congruence and congruent triangles

26.2

Triangles congruent by SSS proofs

26.3

Triangles congruent by SAS and HL proofs

26.4

Triangles congruent by ASA and AAS proofs

27. Pythagorean Theorem

27.1

Squares and square roots

27.2

Pythagorean theorem

27.3

Estimating square roots

27.4

Using the pythagorean relationship

27.5

Applications of pythagorean theorem

28. Introduction to Surface Area of 3D Shapes

28.1

Introduction to surface area of 3-dimensional shapes

28.2

Nets of 3-dimensional shapes

28.3

Surface area of prisms

28.4

Surface area of cylinders

29. Introduction to Volume

29.1

Introduction to volume

29.2

Volume of prisms

29.3

Volume of cylinders

29.4

Word problems relating volume of prisms and cylinders

30. Surface Area and Volume

30.1

Surface area and volume of prisms

30.2

Surface area and volume of pyramids

30.3

Surface area and volume of cylinders

30.4

Surface area and volume of cones

30.5

Surface area and volume of spheres

31. Circles

31.1

Circles and circumference

31.2

Angles in a circle

31.3

Arcs of a circle

31.4

Areas and sectors of circles

32. Introduction to Trigonometry

32.1

Use sine ratio to calculate angles and sides (Sin =

\frac{o}{h}

32.2

Use cosine ratio to calculate angles and sides (Cos =

\frac{a}{h}

32.3

Use tangent ratio to calculate angles and sides (Tan =

\frac{o}{a}

32.4

Combination of SohCahToa questions

32.5

Solving expressions using 45-45-90 special right triangles

32.6

Solving expressions using 30-60-90 special right triangles

32.7

Word problems relating ladder in trigonometry

32.8

Word problems relating guy wire in trigonometry

32.9

Other word problems relating angles in trigonometry

33. Trigonometric Ratios and Angle Measure

33.1

33.2

Coterminal angles

33.3

Reference angles

33.4

Find the exact value of trigonometric ratios

33.5

ASTC rule in trigonometry (All Students Take Calculus)

33.6

33.7

33.8

33.9

Applications of the sine rule and cosine rule

34. Bearings

34.1

Introduction to bearings

34.2

Bearings and direction word problems

34.3

Angle of elevation and depression

35. Graphing Trigonometric Functions

35.1

Sine graph: y = sin x

35.2

Cosine graph: y = cos x

35.3

Tangent graph: y = tan x

35.4

Cotangent graph: y = cot x

35.5

Secant graph: y = sec x

35.6

Cosecant graph: y = csc x

35.7

Graphing transformations of trigonometric functions

35.8

Determining trigonometric functions given their graphs

36. Introduction to Probability

36.1

Introduction to probability

36.2

Organizing outcomes

36.3

Probability of independent events

36.4

Comparing experimental and theoretical probability

37. Statistics

37.1

Median and mode

37.2

37.3

Range and outliers

37.4

Application of averages

38. Data and Graphs

38.1

Reading and drawing bar graphs

38.2

Reading and drawing histograms

38.3

Reading and drawing line graphs

38.4

Box-and-whisker plots and scatter plots

38.5

38.6

Reading and drawing Venn diagrams

38.7

Stem-and-leaf plots

38.8

Frequency tables and dot plots

39. Introduction to Matrices

39.1

Notation of matrices

39.2

Adding and subtracting matrices

39.3

Scalar multiplication

39.4

Matrix multiplication

39.5

The three types of matrix row operations

39.6

Representing a linear system as a matrix

39.7

Solving a linear system with matrices using Gaussian elimination

40. Determinants and Inverses of Matrices

40.1

The determinant of a 2 x 2 matrix

40.2

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

40.3

The inverse of a 2 x 2 matrix

40.4

The inverse of 3 x 3 matrices with matrix row operations

40.5

The inverse of 3 x 3 matrix with determinants and adjugate

40.6

2 x 2 invertible matrix

40.7

Solving linear systems using Cramer's Rule

40.8

Solving linear systems using 2 x 2 inverse matrices

40Chapters

254Topics

1709Videos

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