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Secondary 3 Maths topics

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1Number System and Radicals

1.1Understanding the number systems (free lessons)
1.2Prime factorization
1.3Greatest Common Factors (GCF)
1.4Least Common Multiple (LCM) (free lessons)
1.5Rational vs. Irrational numbers
1.6Converting repeating decimals to fractions

2Rational Numbers

2.1Comparing and ordering rational numbers (free lessons)
2.2Solving problems with rational numbers in decimal form
2.3Solving problems with rational numbers in fraction form
2.4Determine square roots of rational numbers

3Ratios, Rates, and Proportions

3.1Ratios (free lessons)
3.2Rates
3.3Proportions

4Percents

4.1Representing percents (free lessons)
4.2Percents, fractions, and decimals
4.3Percent of a number
4.4Adding and multiplying percents
4.5Taxes, discounts, tips and more
4.6Simple interest

5Coordinates, Quadrants, and Transformations

5.1Cartesian plane
5.2Draw on coordinate planes
5.3Introduction to transformations
5.4Horizontal and vertical distances

6Angles, Lines and Transversals

6.1Pairs of lines and angles
6.2Parallel lines and transversals
6.3Parallel line proofs
6.4Perpendicular line proofs (free lessons)
6.5Parallel and perpendicular line segments
6.6Perpendicular bisectors
6.7Angle Bisectors

7Properties of Triangles

7.1Classifying Triangles
7.2Isosceles and Equilateral Triangles

8Congruent Triangles

8.1Congruence and Congruent Triangles
8.2Triangles Congruent by SSS Proofs
8.3Triangles Congruent by SAS and HL Proofs
8.4Triangles Congruent by ASA and AAS Proofs

9Symmetry and Surface Area

9.1Line symmetry (free lessons)
9.2Rotational symmetry and transformations
9.3Surface area of 3-dimensional shapes (free lessons)

10Pythagorean Theorem

10.1Squares and square roots (free lessons)
10.2Pythagorean theorem (free lessons)
10.3Estimating square roots (free lessons)
10.4Using the pythagorean relationship
10.5Applications of pythagorean theorem

11Surface Area of 3D Shapes

11.1Introduction to surface area of 3-dimensional shapes (free lessons)
11.2Nets of 3-dimensional shapes
11.3Surface area of prisms
11.4Surface area of cylinders

12Circle Geometry

12.1Angles in a circle (free lessons)
12.2Chord properties
12.3Tangent properties
12.4Circles and circumference
12.5Arcs of a circle
12.6Areas and sectors of circles
12.7Inscribed Angles and Proofs
12.8Central and inscribed angles in circles

13Volume of 3D Shapes

13.1Introduction to volume
13.2Volume of prisms
13.3Volume of cylinders
13.4Word problems relating volume of prisms and cylinders

14Scale Factors and Similarity

14.1Enlargements and reductions with scale factors (free lessons)
14.2Scale diagrams
14.3Similar triangles
14.4Similar polygons

15Trigonometry

15.1Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h} ) (free lessons)
15.2Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
15.3Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a} )
15.4Combination of SohCahToa questions (free lessons)
15.5Solving expressions using 45-45-90 special right triangles (free lessons)
15.6Solving expressions using 30-60-90 special right triangles
15.7Word problems relating ladder in trigonometry
15.8Word problems relating guy wire in trigonometry
15.9Other word problems relating angles in trigonometry

16Solving Linear Equations

16.1Solving linear equations using multiplication and division (free lessons)
16.2Solving two-step linear equations: ax+b=cax + b = c, xa+b=c{x \over a} + b = c
16.3Solving linear equations using distributive property: a(x+b)=ca(x + b) = c (free lessons)
16.4Solving linear equations with variables on both sides
16.5Solving literal equations

17Linear Inequalities

17.1Express linear inequalities graphically and algebraically (free lessons)
17.2Solving one-step linear inequalities (free lessons)
17.3Solving multi-step linear inequalities (free lessons)
17.4Compound inequalities

18Introduction to Relations and Functions

18.1Relationship between two variables (free lessons)
18.2Understand relations between x- and y-intercepts
18.3Domain and range of a function (free lessons)
18.4Identifying functions
18.5Function notation (free lessons)

19Linear Functions

19.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} (free lessons)
19.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2) (free lessons)
19.3Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
19.4Gradient intercept form: y = mx + b (free lessons)
19.5General form: Ax + By + C = 0 (free lessons)
19.6Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1) (free lessons)
19.7Rate of change
19.8Graphing linear functions using table of values
19.9Graphing linear functions using x- and y-intercepts (free lessons)
19.10Graphing from gradient-intercept form y=mx+b
19.11Graphing linear functions using a single point and gradient
19.12Word problems of graphing linear functions
19.13Parallel and perpendicular lines in linear functions (free lessons)
19.14Applications of linear relations

20Linear equations (Advanced)

20.1Introduction to linear equations (free lessons)
20.2Introduction to nonlinear equations
20.3Special case of linear equations: Horizontal lines
20.4Special case of linear equations: Vertical lines
20.5Parallel line equation (free lessons)
20.6Perpendicular line equation
20.7Combination of both parallel and perpendicular line equations
20.8Applications of linear equations

21Solving Simultaneous Equations

21.1Determining number of solutions to linear equations (free lessons)
21.2Solving simultaneous equations by graphing
21.3Solving simultaneous equations by elimination
21.4Solving simultaneous equations by substitution
21.5Money related questions in linear equations (free lessons)
21.6Unknown number related questions in linear equations
21.7Distance and time related questions in linear equations
21.8Rectangular shape related questions in linear equations

22Exponents

22.1Product rule of exponents (free lessons)
22.2Quotient rule of exponents
22.3Power of a product rule
22.4Power of a quotient rule
22.5Power of a power rule (free lessons)
22.6Negative exponent rule
22.7Combining the exponent rules
22.8Scientific notation
22.9Convert between radicals and rational exponents (free lessons)
22.10Solving for exponents

23Operations of Polynomials

23.1What is a polynomial? (free lessons)
23.2Polynomial components
23.3Multiplying monomial by monomial
23.4Multiplying monomial by binomial
23.5Multiplying binomial by binomial (free lessons)
23.6Multiplying polynomial by polynomial
23.7Applications of polynomials

24Exponential Functions

24.1Exponents: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
24.2Exponents: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
24.3Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
24.4Exponents: Negative exponents
24.5Exponents: Zero exponent: a0=1 a^0 = 1
24.6Exponents: Rational exponents
24.7Graphing exponential functions
24.8Graphing transformations of exponential functions
24.9Finding an exponential function given its graph

25Factorising Polynomial Functions

25.1Common factors of polynomials (free lessons)
25.2Factorising polynomials by grouping
25.3Solving polynomials with the unknown "b" from x2+bx+cx^2 + bx + c
25.4Solving polynomials with the unknown "c" from x2+bx+cx^2 + bx + c
25.5Factorising polynomials: x2+bx+cx^2 + bx + c (free lessons)
25.6Applications of polynomials: x2+bx+cx^2 + bx + c
25.7Solving polynomials with the unknown "b" from ax2+bx+cax^2 + bx + c
25.8Factorising polynomials: ax2+bx+cax^2 + bx + c
25.9Factorising perfect square trinomials: (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2 or (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2 (free lessons)
25.10Find the difference of squares: (a−b)(a+b)=(a2−b2)(a - b)(a + b) = (a^2 - b^2)
25.11Evaluating polynomials
25.12Using algebra tiles to factorise polynomials
25.13Solving polynomial equations (free lessons)
25.14Word problems of polynomials

26Quadratic Functions

26.1Characteristics of quadratic functions (free lessons)
26.2Transformations of quadratic functions
26.3Quadratic function in general form: y=ax2+bx+cy = ax^2 + bx+c
26.4Quadratic function in vertex form: y = a(x−p)2+qa(x-p)^2 + q
26.5Completing the square (free lessons)
26.6Converting from general to vertex form by completing the square
26.7Shortcut: Vertex formula (free lessons)
26.8Graphing parabolas for given quadratic functions
26.9Finding the quadratic functions for given parabolas (free lessons)
26.10Applications of quadratic functions

27Algebraic Fractions

27.1Simplifying algebraic fractions and restrictions
27.2Adding and subtracting algebraic fractions (free lessons)
27.3Multiplying algebraic fractions
27.4Dividing algebraic fractions
27.5Solving equations with algebraic fractions
27.6Applications of equations with algebraic fractions
27.7Simplifying complex fractions
27.8Partial fraction decomposition

28Reciprocal Functions

28.1Graphing reciprocals of linear functions
28.2Graphing reciprocals of quadratic functions

29Direct and Inverse Variation

29.1Direct variation

30Probability

30.1Determining probabilities using tree diagrams and tables (free lessons)
30.2Probability of independent events
30.3Probability with Venn diagrams

31Statistics

31.1Median and mode
31.2Mean
31.3Range and outliers
31.4Application of averages
31.5Circle graphs

32Introduction to Matrices

32.1Notation of matrices
32.2Adding and subtracting matrices
32.3Scalar multiplication
32.4Matrix multiplication
32.5The three types of matrix row operations
32.6Representing a linear system as a matrix
32.7Solving a linear system with matrices using Gaussian elimination
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