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📘 Year 12 Maths – FULL Curriculum

A. Equations

  1. Solve linear equations

  2. Solve linear equations: word problems

  3. Solve absolute value equations

  4. Graph solutions to absolute value equations

B. Inequalities

  1. Graph a linear inequality in one variable

  2. Graph a linear inequality in the coordinate plane

  3. Write inequalities from graphs

  4. Write a linear inequality: word problems

  5. Solve linear inequalities

  6. Graph solutions to linear inequalities

  7. Solve absolute value inequalities

  8. Graph solutions to absolute value inequalities

  9. Graph solutions to quadratic inequalities

  10. Solve quadratic inequalities

C. Functions

  1. Domain and range

  2. Identify functions

  3. Evaluate functions

  4. Find values using function graphs

  5. Complete a table for a function graph

  6. Find the gradient of a linear function

  7. Gradients of parallel and perpendicular lines

  8. Graph a linear function

  9. Write linear equations in standard form

  10. Write linear equations in point-gradient form

  11. Write an equation for a parallel or perpendicular line

  12. Linear functions over unit intervals

  13. Complete a function table: absolute value functions

  14. Graph an absolute value function

D. Simultaneous Equations

  1. Is (x, y) a solution to the simultaneous equations?

  2. Solve simultaneous equations by graphing

  3. Solve simultaneous equations by graphing: word problems

  4. Find the number of solutions to simultaneous equations

  5. Solve simultaneous equations using substitution

  6. Solve simultaneous equations using substitution: word problems

  7. Solve simultaneous equations using elimination

  8. Solve simultaneous equations using elimination: word problems

  9. Solve simultaneous equations using any method

  10. Solve simultaneous equations using any method: word problems

  11. Solve nonlinear simultaneous equations

E. Factorising

  1. Factorise out a monomial

  2. Factorise quadratics using algebra tiles

  3. Factorise quadratics

  4. Factorise using a quadratic pattern

  5. Factorise by grouping

  6. Factorise sums and differences of cubes

  7. Factorise polynomials

F. Quadratic Functions

  1. Characteristics of quadratic functions

  2. Complete a function table: quadratic functions

  3. Find a quadratic function

  4. Graph a quadratic function

  5. Match quadratic functions and graphs

  6. Solve a quadratic equation using square roots

  7. Solve a quadratic equation using the zero product property

  8. Solve a quadratic equation by factorising

  9. Complete the square

  10. Solve a quadratic equation using the quadratic formula

  11. Modelling projectile motion with quadratic equations

  12. Using the discriminant

G. Complex Numbers

  1. Introduction to complex numbers

  2. Add and subtract complex numbers

  3. Complex conjugates

  4. Multiply and divide complex numbers

  5. Add, subtract, multiply and divide complex numbers

  6. Absolute values of complex numbers

  7. Powers of i

H. Polynomials

  1. Polynomial vocabulary

  2. Add and subtract polynomials

  3. Multiply polynomials

  4. Divide polynomials using long division

  5. Solve polynomial equations

  6. Find the roots of factorised polynomials

  7. Write a polynomial from its roots

  8. Rational root theorem

  9. Descartes’ Rule of Signs

  10. Match polynomials and graphs

  11. Fundamental Theorem of Algebra

  12. Pascal’s triangle

  13. Pascal’s triangle and the Binomial Theorem

  14. Binomial Theorem I

  15. Binomial Theorem II

I. Radical Functions and Expressions

  1. Roots of integers

  2. Roots of rational numbers

  3. Find roots using a calculator

  4. nth roots

  5. Simplify radical expressions with variables I

  6. Simplify radical expressions with variables II

  7. Multiply radical expressions

  8. Divide radical expressions

  9. Add and subtract radical expressions

  10. Simplify radical expressions using the distributive property

  11. Simplify radical expressions using conjugates

  12. Domain and range of radical functions

  13. Solve radical equations

J. Rational Indices

  1. Evaluate rational indices

  2. Multiplication with rational indices

  3. Division with rational indices

  4. Power rule

  5. Simplify expressions involving rational indices I

  6. Simplify expressions involving rational indices II

K. Rational Functions and Expressions

  1. Rational functions: asymptotes and excluded values

  2. Evaluate rational expressions I

  3. Evaluate rational expressions II

  4. Simplify rational expressions

  5. Multiply and divide rational expressions

  6. Add and subtract rational expressions

  7. Solve rational equations

L. Function Operations

  1. Add and subtract functions

  2. Multiply functions

  3. Divide functions

  4. Composition of linear functions: find a value

  5. Composition of linear functions: find an equation

  6. Composition of linear and quadratic functions: find a value

  7. Composition of linear and quadratic functions: find an equation

  8. Identify inverse functions

  9. Find values of inverse functions from tables

  10. Find values of inverse functions from graphs

  11. Find inverse functions and relations

M. Families of Functions

  1. Translations of functions

  2. Reflections of functions

  3. Dilations of functions

  4. Transformations of functions

  5. Function transformation rules

  6. Describe function transformations

N. Logarithms

  1. Convert between exponential and logarithmic form: rational bases

  2. Evaluate logarithms

  3. Change of base formula

  4. Identify properties of logarithms

  5. Product property of logarithms

  6. Quotient property of logarithms

  7. Power property of logarithms

  8. Properties of logarithms: mixed review

  9. Evaluate logarithms: mixed review

O. Exponential and Logarithmic Functions

  1. Domain and range of exponential and logarithmic functions

  2. Evaluate exponential functions

  3. Match exponential functions and graphs

  4. Solve exponential equations by rewriting the base

  5. Solve exponential equations using common logarithms

  6. Solve logarithmic equations I

  7. Solve logarithmic equations II

  8. Identify linear and exponential functions

  9. Exponential functions over unit intervals

  10. Describe linear and exponential growth and decay

  11. Exponential growth and decay: word problems

  12. Compound interest: word problems

  13. Continuously compounded interest: word problems

P. Parabolas

  1. Identify the direction a parabola opens

  2. Find the vertex of a parabola

  3. Find the focus or directrix of a parabola

  4. Find the axis of symmetry of a parabola

  5. Write equations of parabolas in vertex form from graphs

  6. Write equations of parabolas in vertex form using properties

  7. Convert equations of parabolas from general to vertex form

  8. Find properties of a parabola from equations in general form

  9. Graph parabolas

Q. Angle Measures

  1. Convert between radians and degrees

  2. Radians and arc length

  3. Quadrants

  4. Graphs of angles

  5. Coterminal angles

  6. Reference angles

R. Trigonometry

  1. Pythagoras’ Theorem and its converse

  2. Special right triangles

  3. Trigonometric ratios: sin, cos and tan

  4. Trigonometric ratios: csc, sec and cot

  5. Trigonometric ratios in similar right triangles

  6. Find trigonometric ratios using the unit circle

  7. Sin, cos and tan of special angles

  8. Csc, sec and cot of special angles

  9. Find trigonometric functions using a calculator

  10. Inverses of sin, cos and tan

  11. Inverses of csc, sec and cot

  12. Solve trigonometric equations I

  13. Solve trigonometric equations II

  14. Trigonometric ratios: find a side length

  15. Trigonometric ratios: find an angle measure

  16. Solve a right triangle

  17. Law of Sines

  18. Law of Cosines

  19. Solve a triangle

  20. Area of a triangle: sine formula

  21. Area of a triangle: Law of Sines

S. Trigonometric Functions

  1. Find properties of sine functions

  2. Write equations of sine functions from graphs

  3. Write equations of sine functions using properties

  4. Graph sine functions

  5. Find properties of cosine functions

  6. Write equations of cosine functions from graphs

  7. Write equations of cosine functions using properties

  8. Graph cosine functions

  9. Graph sine and cosine functions

T. Trigonometric Identities

  1. Complementary angle identities

  2. Symmetry and periodicity of trigonometric functions

  3. Find trigonometric ratios using a Pythagorean or reciprocal identity

  4. Find trigonometric ratios using multiple identities

U. Circles

  1. Central angles

  2. Arcs and chords

  3. Tangent lines

  4. Inscribed angles

  5. Angles in inscribed right triangles

  6. Angles in inscribed quadrilaterals

V. Circles in the Coordinate Plane

  1. Find the centre of a circle

  2. Find the radius or diameter of a circle

  3. Write equations of circles in standard form from graphs

  4. Write equations of circles in standard form using properties

  5. Convert equations of circles from general to standard form

  6. Find properties of circles from equations in general form

  7. Graph circles

W. Sequences and Series

  1. Classify formulas and sequences

  2. Find terms of an arithmetic sequence

  3. Find terms of a geometric sequence

  4. Find terms of a recursive sequence

  5. Evaluate formulas for sequences

  6. Write a formula for an arithmetic sequence

  7. Write a formula for a geometric sequence

  8. Write a formula for a recursive sequence

  9. Sequences: mixed review

  10. Introduction to sigma notation

  11. Identify arithmetic and geometric series

  12. Find the sum of a finite arithmetic or geometric series

  13. Introduction to partial sums

  14. Partial sums of arithmetic series

  15. Partial sums of geometric series

  16. Partial sums: mixed review

  17. Convergent and divergent geometric series

  18. Find the value of an infinite geometric series

  19. Write a repeating decimal as a fraction

X. Probability

  1. Introduction to probability

  2. Theoretical and experimental probability

  3. Compound events: find the number of outcomes

  4. Factorials

  5. Calculate probabilities of events

  6. Counting principle

  7. Permutations

  8. Permutation and combination notation

  9. Find probabilities using permutations and combinations

  10. Find probabilities using two-way frequency tables

  11. Identify independent events

  12. Probability of independent and dependent events

  13. Geometric probability

  14. Find conditional probabilities

  15. Independence and conditional probability

  16. Find conditional probabilities using two-way frequency tables

  17. Find probabilities using the addition rule

Y. Statistics

  1. Mean, median, mode and range

  2. Quartiles

  3. Identify biased samples

  4. Mean absolute deviation

  5. Variance and standard deviation

Z. Data and Graphs

  1. Interpret bar graphs for continuous data

  2. Create bar graphs for continuous data

  3. Interpret stem-and-leaf plots

  4. Interpret box-and-whisker plots

  5. Interpret a scatter plot

  6. Scatter plots: line of best fit

AA. Introduction to Limits

  1. Find limits using graphs

  2. Find one-sided limits using graphs

  3. Determine if a limit exists

BB. Calculate Limits

  1. Find limits using addition, subtraction and multiplication laws

  2. Find limits using the division law

  3. Find limits using power and root laws

  4. Find limits using limit laws

  5. Find limits of polynomials and rational functions

  6. Find limits involving factorisation and rationalisation

  7. Find limits involving absolute value functions

  8. Find limits involving trigonometric functions

CC. Limits and Rational Functions

  1. Find limits at vertical asymptotes using graphs

  2. Determine end behaviour using graphs

  3. Determine end behaviour of polynomial and rational functions

  4. Find the limit at a vertical asymptote of a rational function I

  5. Find the limit at a vertical asymptote of a rational function II

DD. Continuity

  1. Identify graphs of continuous functions

  2. Determine continuity using graphs

  3. Determine one-sided continuity using graphs

  4. Find and analyse points of discontinuity using graphs

  5. Determine continuity on an interval using graphs

  6. Determine the continuity of a piecewise function at a point

  7. Make a piecewise function continuous

  8. Intermediate Value Theorem

EE. Introduction to Derivatives

  1. Average rate of change I

  2. Average rate of change II

  3. Find instantaneous rates of change

  4. Velocity as a rate of change

  5. Find values of derivatives using limits

  6. Find the gradient of a tangent line using limits

  7. Find equations of tangent lines using limits

  8. Power rule I

  9. Power rule II

  10. Find derivatives of polynomials

  11. Find second derivatives of polynomials

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