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Year 12 Maths Topics

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Solving Linear Equations
Solving linear equations using multiplication and division
Solving two-step linear equations: ax + b = c, x/a + b = c
Solving linear equations using distributive property: a(x + b) = c
Solving linear equations with variables on both sides
Solving literal equations
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Linear Inequalities
Express linear inequalities graphically and algebraically
Solving one-step linear inequalities
Solving multi-step linear inequalities
Compound inequalities
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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
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Factorising
Factorise by taking out the greatest common factor
Factorise by grouping
Factorising difference of squares: x^2 - y^2
Factorising trinomials: ax2+bx+cax^2 + bx + cax2+bx+c
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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
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Quadratic Equations and Inequalities
Solving quadratic equations by factorising
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
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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
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Simultaneous Equations (Advanced)
Simultaneous linear equations
Simultaneous linear-quadratic equations
Simultaneous quadratic-quadratic equations
Solving 3 variable simultaneous equations by substitution
Solving 3 variable simultaneous equations by elimination
Solving 3 variable simultaneous equations with no or infinite solutions
Word problems relating 3 variable simultaneous equations
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Inequalities in two variables (Advanced)
Graphing linear inequalities in two variables
Graphing simultaneous linear inequalities
Graphing quadratic inequalities in two variables
Graphing simultaneous quadratic inequalities
Applications of inequalities
What is linear programming?
Linear programming word problems
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Imaginary and Complex Numbers
Introduction to imaginary numbers
Complex numbers and complex planes
Adding and subtracting complex numbers
Complex conjugates
Multiplying and dividing complex numbers
Distance and midpoint of complex numbers
Angle and absolute value of complex numbers
Polar form of complex numbers
Operations on complex numbers in polar form
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Polynomial Functions
What is a polynomial function?
Polynomial long division
Polynomial synthetic division
Remainder theorem
Factor theorem
Rational zero theorem
Characteristics of polynomial graphs
Multiplicities of polynomials
Imaginary zeros of polynomials
Determining the equation of a polynomial function
Applications of polynomial functions
Solving polynomial inequalities
Fundamental theorem of algebra
Descartes' rule of signs
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Radicals
Operations with radicals
Conversion between entire radicals and mixed radicals
Adding and subtracting radicals
Multiplying radicals
Solving radical equations
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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
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Algebraic Fractions
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
Partial fraction decomposition
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Reciprocal Functions
Graphing reciprocals of linear functions
Graphing reciprocals of quadratic functions
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Rational Functions
What is a rational function?
Point of discontinuity
Vertical asymptote
Horizontal asymptote
Slant asymptote
Graphs of rational functions
Solving rational inequalities
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Operations of Functions
Function notation
Operations with functions
Adding functions
Subtracting functions
Multiplying functions
Dividing functions
Composite functions
Inequalities of combined functions
Inverse functions
One to one functions
Difference quotient: applications of functions
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Transformations of Functions
Transformations of functions: Horizontal translations
Transformations of functions: Vertical translations
Reflection across the y-axis: y = f(-x)
Reflection across the x-axis: y = -f(x)
Transformations of functions: Horizontal stretches
Transformations of functions: Vertical stretches
Combining transformations of functions
Even and odd functions
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Exponential Functions
Exponents: Product rule (a^x)(a^y) = a^(x+y)
Exponents: Division rule (a^x / a^y) = a^(x-y)
Exponents: Power rule (a^x)^y = a^(x * y)
Exponents: Negative exponents
Exponents: Zero exponent: a^0 = 1
Exponents: Rational exponents
Graphing exponential functions
Graphing transformations of exponential functions
Finding an exponential function given its graph
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Logarithmic Functions
What is a logarithm?
Converting from logarithmic form to exponential form
Evaluating logarithms without a calculator
Common logarithms
Natural log: ln
Evaluating logarithms using change-of-base formula
Converting from exponential form to logarithmic form
Solving exponential equations with logarithms
Product rule of logarithms
Quotient rule of logarithms
Combining product rule and quotient rule in logarithms
Evaluating logarithms using logarithm rules
Solving logarithmic equations
Graphing logarithmic functions
Finding a logarithmic function given its graph
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Applications of Exponential and Logarithmic Functions
Exponential growth and decay by a factor
Exponential decay: Half-life
Exponential growth and decay by percentage
Finance: Compound interest
Continuous growth and decay
Logarithmic scale: Richter scale (earthquake)
Logarithmic scale: pH scale
Logarithmic scale: dB scale
Finance: Future value and present value
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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
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Trigonometric Ratios and Angle Measure
Standard angle
Coterminal angles
Reference angles
Find the exact value of trigonometric ratios
ASTC rule in trigonometry (All Students Take Calculus)
Unit circle
Law of sines
Law of cosines
Applications of the sine law and cosine law
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Bearings
Introduction to bearings
Bearings and direction word problems
Angle of elevation and depression
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Graphing Trigonometric Functions
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
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Trigonometric Identities
Quotient identities and reciprocal identities
Pythagorean identities
Sum and difference identities
Cofunction identities
Double-angle identities
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Conics
Conics - Parabola
Conics - Ellipse
Conics - Circle
Conics - Hyperbola
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Surface Area and Volume
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
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Sequences and Series
Arithmetic sequences
Arithmetic series
Geometric sequences
Geometric series
Infinite geometric series
Sigma notation
Arithmetic mean vs. Geometric mean
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Probability
Determining probabilities using tree diagrams and tables
Probability of independent events
Probability with Venn diagrams
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Permutations and Combinations
Fundamental counting principle
Factorial notation
Path counting problems
Permutation vs. Combination
Permutations
Combinations
Problems involving both permutations and combinations
Pascal's triangle
Binomial theorem
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Statistics
Median and mode
Mean
Range and outliers
Application of averages
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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
Reading and drawing Venn diagrams
Frequency tables and dot plots

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