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Third Year Maths Topics

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video
Number System and Radicals
Understanding the number systems
Prime factorisation
Greatest Common Factors (GCF)
Least Common Multiple (LCM)
Rational vs. Irrational numbers
Converting repeating decimals to fractions
video
Ratios, Rates, and Proportions
Ratios
Rates
Proportions
video
Percents
Representing percents
Percents, fractions, and decimals
Percent of a number
Adding and multiplying percents
Taxes, discounts, tips and more
Simple interest
video
Measuring Systems
Metric systems
Imperial systems
Conversions between metric and imperial systems
Conversions involve squares and cubic
video
Coordinates, Quadrants, and Transformations
Cartesian plane
Draw on coordinate planes
Introduction to transformations
Horizontal and vertical distances
video
Angles, Lines, and Transversals
Pairs of lines and angles
Parallel lines and transversals
Parallel line proofs
Perpendicular line proofs
video
Properties of Triangles
Classifying triangles
Isosceles and equilateral triangles
video
Circles
Circles and circumference
Angles in a circle
Arcs of a circle
Areas and sectors of circles
video
Congruent Triangles
Congruence and congruent triangles
Triangles congruent by SSS proofs
Triangles congruent by SAS and HL proofs
Triangles congruent by ASA and AAS proofs
video
Symmetry and Surface Area
Line symmetry
Rotational symmetry and transformations
Surface area of 3-dimensional shapes
video
Scale Factors and Similarity
Enlargements and reductions with scale factors
Scale diagrams
Similar triangles
Similar polygons
video
Pythagorean Theorem
Squares and square roots
Pythagorean theorem
Estimating square roots
Using the pythagorean relationship
Applications of pythagorean theorem
video
Introduction to 3-Dimensional Figures
Introduction to surface area of 3-dimensional shapes
Nets of 3-dimensional shapes
Surface area of prisms
Surface area of cylinders
video
Volume
Introduction to volume
Volume of prisms
Volume of cylinders
Word problems relating volume of prisms and cylinders
video
Introduction to Trigonometry
Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h}ho​ )
Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h}ha​ )
Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a}ao​ )
Combination of SohCahToa questions
Solving expressions using 45-45-90 special right triangles
Solving expressions using 30-60-90 special right triangles
Word problems relating ladder in trigonometry
Word problems relating guy wire in trigonometry
Other word problems relating angles in trigonometry
video
Patterns and Solving Equations
Patterns
Evaluating algebraic expressions
Solving one - step equations: x + a = b
Graphing linear relations
video
Introduction to Linear Relations
Representing patterns in linear relations
Reading linear relation graphs
Solving linear equations by graphing
video
Linear Inequalities
Express linear inequalities graphically and algebraically
Solving one-step linear inequalities
Solving multi-step linear inequalities
Compound inequalities
video
Introduction to Relations and Functions
Relationship between two variables
Understand relations between x- and y-intercepts
Domain and range of a function
Identifying functions
Function notation
video
Data and Graphs
Reading and drawing bar graphs
Reading and drawing histograms
Reading and drawing line graphs
Box-and-whisker plots and scatter plots
Stem-and-leaf plots
Circle graphs
Reading and drawing Venn diagrams
Frequency tables and dot plots
video
Linear Functions
Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}d=(x2​−x1​)2+(y2​−y1​)2​
Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)M=(2x1​+x2​​,2y1​+y2​​)
Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}m=x2​−x1​y2​−y1​​
Gradient intercept form: y = mx + b
General form: Ax + By + C = 0
Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)y−y1​=m(x−x1​)
Rate of change
Graphing linear functions using table of values
Graphing linear functions using x- and y-intercepts
Graphing from gradient-intercept form y=mx+b
Graphing linear functions using a single point and gradient
Word problems of graphing linear functions
Parallel and perpendicular lines in linear functions
Applications of linear relations
video
Linear Equations
Introduction to linear equations
Introduction to nonlinear equations
Special case of linear equations: Horizontal lines
Special case of linear equations: Vertical lines
Parallel line equation
Perpendicular line equation
Combination of both parallel and perpendicular line equations
Applications of linear equations
video
Solving Simultaneous Equations
Determining number of solutions to linear equations
Solving simultaneous equations by graphing
Solving simultaneous equations by elimination
Solving simultaneous equations by substitution
Money related questions in linear equations
Unknown number related questions in linear equations
Distance and time related questions in linear equations
Rectangular shape related questions in linear equations
video
Exponents
Product rule of exponents
Quotient rule of exponents
Power of a product rule
Power of a quotient rule
Power of a power rule
Negative exponent rule
Combining the exponent rules
Scientific notation
Convert between radicals and rational exponents
Solving for exponents
video
Quadratic Functions
Characteristics of quadratic functions
Transformations of quadratic functions
Quadratic function in general form: y = ax^2 + bx + c
Quadratic function in vertex form: y = a(x-p)^2 + q
Completing the square
Converting from general to vertex form by completing the square
Shortcut: Vertex formula
Graphing parabolas for given quadratic functions
Finding the quadratic functions for given parabolas
Applications of quadratic functions
video
Polynomials
Characteristics of polynomials
Equivalent expressions of polynomials
Adding and subtracting polynomials
video
Operations of Polynomials
What is a polynomial?
Using algebra tiles to factorise polynomials
video
Factorising Polynomial expressions
Common factors of polynomials
Factorising polynomials by grouping
Solving polynomials with the unknown "b" from x^2 + bx + c
Solving polynomials with the unknown "c" from x^2 + bx + c
Factorising polynomials: x^2 + bx + c
Applications of polynomials: x^2 + bx + c
Solving polynomials with the unknown "b" from ax2+bx+cax^2 + bx + cax2+bx+c
Factorising polynomials: ax2+bx+cax^2 + bx + cax2+bx+c
Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2
Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)
Evaluating polynomials
Solving polynomial equations
Word problems of polynomials
video
Radicals
Square and square roots
Cubic and cube roots
Evaluating and simplifying radicals
Converting radicals to mixed radicals
Converting radicals to entire radicals
Adding and subtracting radicals
Multiplying and dividing radicals
Rationalize the denominator
video
Rational Expressions
Simplifying rational expressions and restrictions
Adding and subtracting rational expressions
Multiplying rational expressions
Dividing rational expressions
Solving rational equations
Applications of rational equations
Simplifying complex fractions
Partial fraction decomposition
video
Reciprocal Functions
Graphing reciprocals of linear functions
Graphing reciprocals of quadratic functions
video
Probability
Determining probabilities using tree diagrams and tables
Probability of independent events
Probability with Venn diagrams

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