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Secondary 2 Maths Topics

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1. Number Theory

1.1

Divisibility Rules

1.2

Prime factorization

1.3

Determining Common Factors

1.4

Determining Common Multiples

1.5

Introduction to Exponents

2. Adding and Subtracting Integers

2.1

Introduction to integer addition

2.2

Adding integers

2.3

Introduction to integer subtraction

2.4

Subtracting integers

2.5

Application of integer operations

3. Multiplying and Dividing Integers

3.1

Understanding integer multiplication

3.2

Multiplying integers

3.3

Understanding integer division

3.4

Dividing integers

3.5

Applications of integer operations

4. Rational Numbers

4.1

Comparing and ordering rational numbers

4.2

Solving problems with rational numbers in decimal form

4.3

Solving problems with rational numbers in fraction form

4.4

Determine square roots of rational numbers

5. Radicals

5.1

Square and square roots

5.2

Cubic and cube roots

5.3

Evaluating and simplifying radicals

5.4

Converting radicals to mixed radicals

5.5

Converting radicals to entire radicals

5.6

Adding and subtracting radicals

5.7

Multiplying and dividing radicals

5.8

Rationalize the denominator

6. Exponents

6.1

Product rule of exponents

6.2

Quotient rule of exponents

6.3

Power of a product rule

6.4

Power of a quotient rule

6.5

Power of a power rule

6.6

Negative exponent rule

6.7

Combining the exponent rules

6.8

Scientific notation

6.9

Convert between radicals and rational exponents

6.10

Solving for exponents

7. Ratios, Rates and Proportions

7.1

Ratios

7.2

Rates

7.3

Proportions

8. Proportional Relationships

8.1

Identifying proportional relationships

8.2

Understanding graphs of proportional relationships

8.3

Graphing and writing equations of proportional relationships

8.4

Applications of proportional relationships

9. Percents

9.1

Representing percents

9.2

Percent of a number

9.3

Converting among decimals, fractions, and percents

9.4

Applications of percents

9.5

Taxes, discounts, tips and more

9.6

Simple interest

10. Measuring Systems

10.1

Metric systems

10.2

Imperial systems

10.3

Conversions between metric and imperial systems

10.4

Conversions involve squares and cubic

11. Coordinates, Quadrants, and Transformations

11.1

Cartesian plane

11.2

Draw on coordinate planes

11.3

Introduction to transformations

11.4

Horizontal and vertical distances

12. Angles, Lines and Transversals

12.1

Pairs of lines and angles

12.2

Parallel lines and transversals

12.3

Parallel line proofs

12.4

Perpendicular line proofs

12.5

Parallel and perpendicular line segments

12.6

Perpendicular bisectors

12.7

Angle bisectors

13. Properties of Triangles

13.1

Classifying Triangles

13.2

Isosceles and Equilateral Triangles

14. Congruent Triangles

14.1

Congruence and Congruent Triangles

14.2

Triangles Congruent by SSS Proofs

14.3

Triangles Congruent by SAS and HL Proofs

14.4

Triangles Congruent by ASA and AAS Proofs

15. Symmetry and Surface Area

15.1

Line symmetry

15.2

Rotational symmetry and transformations

15.3

Surface area of 3-dimensional shapes

16. Pythagorean Theorem

16.1

Squares and square roots

16.2

Pythagorean theorem

16.3

Estimating square roots

16.4

Using the pythagorean relationship

16.5

Applications of pythagorean theorem

17. Surface Area of 3D Shapes

17.1

Introduction to surface area of 3-dimensional shapes

17.2

Nets of 3-dimensional shapes

17.3

Surface area of prisms

17.4

Surface area of cylinders

18. Circles

18.1

Circles and circumference

18.2

Angles in a circle

18.3

Arcs of a circle

18.4

Areas and sectors of circles

19. Volume of 3D Shapes

19.1

Introduction to volume

19.2

Volume of prisms

19.3

Volume of cylinders

19.4

Word problems relating volume of prisms and cylinders

20. Scale Factors and Similarity

20.1

Enlargements and reductions with scale factors

20.2

Scale diagrams

20.3

Similar triangles

20.4

Similar polygons

21. Linear Equations (Basic)

21.1

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

21.2

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

21.3

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

21.4

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

22. Solving Linear Equations

22.1

Solving linear equations using multiplication and division

22.2

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

22.3

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

22.4

Solving linear equations with variables on both sides

22.5

Solving literal equations

23. Linear Inequalities

23.1

Express linear inequalities graphically and algebraically

23.2

Solving one-step linear inequalities

23.3

Solving multi-step linear inequalities

23.4

Compound inequalities

24. Introduction to Relations and Functions

24.1

Relationship between two variables

24.2

Understand relations between x- and y-intercepts

24.3

Domain and range of a function

24.4

Identifying functions

24.5

Function notation

25. Linear Functions

25.1

Distance formula:

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

25.2

Midpoint formula:

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

25.3

Gradient equation:

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

25.4

Gradient intercept form: y = mx + b

25.5

General form: Ax + By + C = 0

25.6

Gradient-point form:

y - y_1 = m (x - x_1)

25.7

Rate of change

25.8

Graphing linear functions using table of values

25.9

Graphing linear functions using x- and y-intercepts

25.10

Graphing from gradient-intercept form y=mx+b

25.11

Graphing linear functions using a single point and gradient

25.12

Word problems of graphing linear functions

25.13

Parallel and perpendicular lines in linear functions

25.14

Applications of linear relations

26. Linear equations (Advanced)

26.1

Introduction to linear equations

26.2

Introduction to nonlinear equations

26.3

Special case of linear equations: Horizontal lines

26.4

Special case of linear equations: Vertical lines

26.5

Parallel line equation

26.6

Perpendicular line equation

26.7

Combination of both parallel and perpendicular line equations

26.8

Applications of linear equations

27. Solving Simultaneous Equations

27.1

Determining number of solutions to linear equations

27.2

Solving simultaneous equations by graphing

27.3

Solving simultaneous equations by elimination

27.4

Solving simultaneous equations by substitution

27.5

27.6

Unknown number related questions in linear equations

27.7

Distance and time related questions in linear equations

27.8

Rectangular shape related questions in linear equations

28. Adding and Subtracting Polynomials

28.1

Multiplying and dividing monomials

28.2

Multiplying polynomials by monomials

28.3

Dividing polynomials by monomials

29. Multiplying and Dividing Polynomials

29.1

What is a polynomial?

29.2

Polynomial components

29.3

Multiplying monomial by monomial

29.4

Multiplying monomial by binomial

29.5

Multiplying binomial by binomial

29.6

Multiplying polynomial by polynomial

29.7

Applications of polynomials

30. Factorising Polynomial Functions

30.1

Common factors of polynomials

30.2

Factorising polynomials by grouping

30.3

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

30.4

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

30.5

Factorising polynomials: x^2 + bx + c

30.6

Applications of polynomials: x^2 + bx + c

30.7

Solving polynomials with the unknown "b" from

ax^2 + bx + c

30.8

Factorising polynomials:

ax^2 + bx + c

30.9

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

30.10

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

30.11

Evaluating polynomials

30.12

Using algebra tiles to factorise polynomials

30.13

Solving polynomial equations

30.14

Word problems of polynomials

31. Quadratic Functions

31.1

Characteristics of quadratic functions

31.2

Transformations of quadratic functions

31.3

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

31.4

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

31.5

Completing the square

31.6

Converting from general to vertex form by completing the square

31.7

Shortcut: Vertex formula

31.8

Graphing parabolas for given quadratic functions

31.9

Finding the quadratic functions for given parabolas

31.10

Applications of quadratic functions

32. Algebraic Fractions

32.1

Simplifying algebraic fractions and restrictions

32.2

Adding and subtracting algebraic fractions

32.3

Multiplying algebraic fractions

32.4

Dividing algebraic fractions

32.5

Solving equations with algebraic fractions

32.6

Applications of equations with algebraic fractions

32.7

Simplifying complex fractions

32.8

Partial fraction decomposition

33. Reciprocal Functions

33.1

Graphing reciprocals of linear functions

33.2

Graphing reciprocals of quadratic functions

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

Pie charts

34.6

Reading and drawing Venn diagrams

34.7

Stem-and-leaf plots

35. Probability

35.1

Determining probabilities using tree diagrams and tables

35.2

Probability of independent events

35.3

Probability with Venn diagrams

36. Statistics

36.1

Median and mode

36.2

Mean

36.3

Range and outliers

36.4

Application of averages

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