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Third Year Maths Topics

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1Number System and Radicals

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

2Ratios, Rates, and Proportions

2.1Ratios (free lessons)
2.2Rates
2.3Proportions

3Percents

3.1Representing percents (free lessons)
3.2Percents, fractions, and decimals
3.3Percent of a number
3.4Adding and multiplying percents
3.5Taxes, discounts, tips and more
3.6Simple interest

4Measuring Systems

4.1Metric systems (free lessons)
4.2Imperial systems
4.3Conversions between metric and imperial systems
4.4Conversions involve squares and cubic

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)

7Properties of Triangles

7.1Classifying triangles
7.2Isosceles and equilateral triangles

8Circles

8.1Circles and circumference
8.2Angles in a circle (free lessons)
8.3Arcs of a circle
8.4Areas and sectors of circles

9Congruent Triangles

9.1Congruence and congruent triangles
9.2Triangles congruent by SSS proofs
9.3Triangles congruent by SAS and HL proofs
9.4Triangles congruent by ASA and AAS proofs

10Symmetry and Surface Area

10.1Line symmetry (free lessons)
10.2Rotational symmetry and transformations
10.3Surface area of 3-dimensional shapes (free lessons)

11Scale Factors and Similarity

11.1Enlargements and reductions with scale factors (free lessons)
11.2Scale diagrams
11.3Similar triangles
11.4Similar polygons

12Pythagorean Theorem

12.1Squares and square roots (free lessons)
12.2Pythagorean theorem (free lessons)
12.3Estimating square roots (free lessons)
12.4Using the pythagorean relationship
12.5Applications of pythagorean theorem

13Introduction to 3-Dimensional Figures

13.1Introduction to surface area of 3-dimensional shapes (free lessons)
13.2Nets of 3-dimensional shapes
13.3Surface area of prisms
13.4Surface area of cylinders

14Volume

14.1Introduction to volume
14.2Volume of prisms
14.3Volume of cylinders
14.4Word problems relating volume of prisms and cylinders

15Introduction to Trigonometry

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

16Patterns and Solving Equations

16.1Patterns
16.2Evaluating algebraic expressions
16.3Solving one - step equations: x+a=bx + a = b
16.4Graphing linear relations

17Introduction to Linear Relations

17.1Representing patterns in linear relations
17.2Reading linear relation graphs
17.3Solving linear equations by graphing

18Linear Inequalities

18.1Express linear inequalities graphically and algebraically (free lessons)
18.2Solving one-step linear inequalities (free lessons)
18.3Solving multi-step linear inequalities (free lessons)
18.4Compound inequalities

19Introduction to Relations and Functions

19.1Relationship between two variables (free lessons)
19.2Understand relations between x- and y-intercepts
19.3Domain and range of a function (free lessons)
19.4Identifying functions
19.5Function notation (free lessons)

20Data and Graphs

20.1Reading and drawing bar graphs
20.2Reading and drawing histograms
20.3Reading and drawing line graphs
20.4Box-and-whisker plots and scatter plots
20.5Stem-and-leaf plots
20.6Circle graphs
20.7Reading and drawing Venn diagrams

21Linear Functions

21.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} (free lessons)
21.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2) (free lessons)
21.3Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
21.4Gradient intercept form: y = mx + b (free lessons)
21.5General form: Ax + By + C = 0 (free lessons)
21.6Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1) (free lessons)
21.7Rate of change
21.8Graphing linear functions using table of values
21.9Graphing linear functions using x- and y-intercepts (free lessons)
21.10Graphing from gradient-intercept form y=mx+b
21.11Graphing linear functions using a single point and gradient
21.12Word problems of graphing linear functions
21.13Parallel and perpendicular lines in linear functions (free lessons)
21.14Applications of linear relations

22Linear Equations

22.1Introduction to linear equations (free lessons)
22.2Introduction to nonlinear equations
22.3Special case of linear equations: Horizontal lines
22.4Special case of linear equations: Vertical lines
22.5Parallel line equation (free lessons)
22.6Perpendicular line equation
22.7Combination of both parallel and perpendicular line equations
22.8Applications of linear equations

23Solving Simultaneous Equations

23.1Determining number of solutions to linear equations (free lessons)
23.2Solving simultaneous equations by graphing
23.3Solving simultaneous equations by elimination
23.4Solving simultaneous equations by substitution
23.5Money related questions in linear equations (free lessons)
23.6Unknown number related questions in linear equations
23.7Distance and time related questions in linear equations
23.8Rectangular shape related questions in linear equations

24Exponents

24.1Product rule of exponents (free lessons)
24.2Quotient rule of exponents
24.3Power of a product rule
24.4Power of a quotient rule
24.5Power of a power rule (free lessons)
24.6Negative exponent rule
24.7Combining the exponent rules
24.8Scientific notation
24.9Convert between radicals and rational exponents (free lessons)
24.10Solving for exponents

25Quadratic Functions

25.1Characteristics of quadratic functions (free lessons)
25.2Transformations of quadratic functions
25.3Quadratic function in general form: y=ax2+bx+cy = ax^2 + bx+c
25.4Quadratic function in vertex form: y = a(x−p)2+qa(x-p)^2 + q
25.5Completing the square (free lessons)
25.6Converting from general to vertex form by completing the square
25.7Shortcut: Vertex formula (free lessons)
25.8Graphing parabolas for given quadratic functions
25.9Finding the quadratic functions for given parabolas (free lessons)
25.10Applications of quadratic functions

26Polynomials

26.1Characteristics of polynomials (free lessons)
26.2Equivalent expressions of polynomials
26.3Adding and subtracting polynomials

27Operations of Polynomials

27.1What is a polynomial? (free lessons)
27.2Using algebra tiles to solve polynomials

28Factorising Polynomial expressions

28.1Common factors of polynomials (free lessons)
28.2Factorising polynomials by grouping
28.3Solving polynomials with the unknown "b" from x2+bx+cx^2 + bx + c
28.4Solving polynomials with the unknown "c" from x2+bx+cx^2 + bx + c
28.5Factorising polynomials: x2+bx+cx^2 + bx + c (free lessons)
28.6Applications of polynomials: x2+bx+cx^2 + bx + c
28.7Solving polynomials with the unknown "b" from ax2+bx+cax^2 + bx + c
28.8Factorising polynomials: ax2+bx+cax^2 + bx + c
28.9Factorising 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)
28.10Find the difference of squares: (a−b)(a+b)=(a2−b2)(a - b)(a + b) = (a^2 - b^2)
28.11Evaluating polynomials
28.12Solving polynomial equations (free lessons)
28.13Word problems of polynomials

29Radicals

29.1Square and square roots (free lessons)
29.2Cubic and cube roots
29.3Evaluating and simplifying radicals
29.4Converting radicals to mixed radicals
29.5Converting radicals to entire radicals (free lessons)
29.6Adding and subtracting radicals
29.7Multiplying and dividing radicals
29.8Rationalize the denominator

30Rational Expressions

30.1Simplifying rational expressions and restrictions
30.2Adding and subtracting rational expressions (free lessons)
30.3Multiplying rational expressions
30.4Dividing rational expressions
30.5Solving rational equations
30.6Applications of rational equations
30.7Simplifying complex fractions
30.8Partial fraction decomposition

31Reciprocal Functions

31.1Graphing reciprocals of linear functions
31.2Graphing reciprocals of quadratic functions

32Probability

32.1Determining probabilities using tree diagrams and tables (free lessons)
32.2Probability of independent events
32.3Probability with Venn diagrams
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