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Express linear inequalities graphically and algebraically
Solving one-step linear inequalities
Solving multi-step linear inequalities
Equivalent algebraic expressions
Adding and subtracting algebraic expressions
Multiplying monomial by monomial
Multiplying monomial by binomial
Multiplying binomial by binomial
Multiplying polynomial by polynomial
Applications of algebraic expressions
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−x1y2−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 slope-intercept form y=mx+b
Graphing linear functions using a single point and gradient
Word problems of graphing linear functions
Applications of linear relations
Determining number of solutions to linear equations
Solving simultaneous linear equations by graphing
Solving simultaneous linear equations by elimination
Solving simultaneous linear 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
Factorise by taking out the greatest common factor
Factorise by grouping
Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2
Factorising difference of squares: x^2 - y^2
Factorise trinomials
Solving polynomials with unknown coefficients
Solving polynomials with unknown constant terms
Factorising difference of cubes: a3−b3a^3-b^3a3−b3
Factorising sum of cubes: a3+b3a^3+b^3a3+b3
Introduction to 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 quadratic functions: General form VS. Vertex form
Finding the quadratic functions for given parabolas
Applications of quadratic functions
Solving quadratic equations by factoring
Solving quadratic equations by completing the square
Using quadratic formula to solve quadratic equations
Nature of roots of quadratic equations: The discriminant
Applications of quadratic equations
Solving quadratic inequalities
Square and square roots
Cubic and cube roots
Operations with surds
Conversion between entire radicals and mixed radicals
Adding and subtracting surds
Multiplying surds
Rationalize the denominator
Solving equations with surds
System of linear equations
System of linear-quadratic equations
System of quadratic-quadratic equations
Solving 3 variable systems of equations by substitution
Solving 3 variable systems of equations by elimination
Solving 3 variable systems of equations with no solution, infinite solutions
Word problems relating 3 variable systems of equations
Indices: Product rule (a^x)(a^y) = a^(x+y)
Indices: Division rule (a^x / a^y) = a^(x-y)
Indices: Power rule (a^x)^y = a^(x * y)
Negative indices
Zero index: a^0 = 1
Rational indices
Standard form
Simplifying algebraic fractions and restrictions
Adding and subtracting algebraic fractions
Multiplying algebraic fractions
Dividing algebraic fractions
Solving equations with algebraic fractions
Applications of equations with algebraic fractions
Simplifying complex fractions
Solving exponential equations using laws of indices
Graphing exponential functions
Graphing transformations of exponential functions
Finding an exponential function given its graph
Factorial notation
Binomial theorem
Parallel and perpendicular line segments
Perpendicular bisectors
Angle bisectors
Classifying Triangles
Congruence and Congruent Triangles
Triangles Congruent by SSS Proofs
Triangles Congruent by SAS and HL Proofs
Triangles Congruent by ASA and AAS Proofs
Isosceles and Equilateral Triangles
Pairs of lines and angles
Parallel lines and transversals
Parallel line proofs
Perpendicular line proofs
Angles in a circle
Chord properties
Tangent properties
Circle and circumference
Arcs of a circle
Areas and sectors of circles
Inscribed quadrilaterals in circles
Central and inscribed angles in circles
Surface area and volume of prisms
Surface area and volume of pyramids
Surface area and volume of cylinders
Surface area and volume of cones
Surface area and volume of spheres
Conics - Parabola
Conics - Circle
Angle in standard position
Coterminal angles
Reference angle
Find the exact value of trigonometric ratios
ASTC rule in trigonometry (All Students Take Calculus)
Unit circle
Converting between degrees and radians
Trigonometric ratios of angles in radians
Radian measure and arc length
Sine rule
Cosine rule
Sine rule and cosine rule word problems
Introduction to bearings
Bearings and direction word problems
Angle of elevation and depression
Sine graph: y = sin x
Cosine graph: y = cos x
Tangent graph: y = tan x
Cotangent graph: y = cot x
Secant graph: y = sec x
Cosecant graph: y = csc x
Graphing transformations of trigonometric functions
Determining trigonometric functions given their graphs
Ferris wheel trig problems
Tides and water depth trig problems
Spring (simple harmonic motion) trig problems
Quotient identities and reciprocal identities
Pythagorean identities
Sum and difference identities
Cofunction identities
Double-angle identities
Solving first degree trigonometric equations
Determining non-permissible values for trig expressions
Solving second degree trigonometric equations
Solving trigonometric equations involving multiple angles
Solving trigonometric equations using pythagorean identities
Solving trigonometric equations using sum and difference identities
Solving trigonometric equations using double-angle identities
Finding inverse trigonometric function from its graph
Evaluating inverse trigonometric functions
Finding inverse reciprocal trigonometric function from its graph
Inverse reciprocal trigonometric function: finding the exact value
Reading and drawing bar graphs
Reading and drawing histograms
Reading and drawing line graphs
Box-and-whisker plots and scatter plots
Reading and drawing stem-and-leaf diagrams
Reading and drawing Venn diagrams
Frequency tables and dot diagrams
Pie charts
Advantages and disadvantages of different graphs
Misleading graphs
Critiquing data presentation
Median and mode
Mean
Range and outliers
Application of averages
Standard deviation, and variance
Z-score, quartiles, and percentiles
Determining probabilities using tree diagrams and tables
Probability of independent events
Frequency distribution and histograms
Addition rule for "OR"
Multiplication rule for "AND"
Power rule
Slope and equation of tangent line
Chain rule
Product rule
Quotient rule
Higher order derivatives
Critical number & maximum and minimum values
Antiderivatives
Definite integral
Integration by parts
Integration of rational functions by partial fractions
Areas between curves
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