Year 12

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Equations

A.1 Solve linear equations

A.2 Solve linear equations: word problems

A.3 Solve absolute value equations

A.4 Graph solutions to absolute value equations
Inequalities

B.1 Graph a linear inequality in one variable

B.2 Graph a linear inequality in the coordinate plane

B.3 https://www.youtube.com/watch?v=64643Op6WJoWrite inequalities from graphs

B.4 Write a linear inequality: word problems

B.5 Solve linear inequalities

B.6 Graph solutions to linear inequalities

B.7 Solve absolute value inequalities

B.8 Graph solutions to absolute value inequalities

B.9 Graph solutions to quadratic inequalities

B.10 Solve quadratic inequalities
Functions

C.1 Domain and range

C.2 Identify functions

C.3 Evaluate functions

C.4 Find values using function graphs

C.5 Complete a table for a function graph

C.6 Find the gradient of a linear function

C.7 Gradients of parallel and perpendicular lines

C.8 Graph a linear function

C.9 Write linear equations in standard form

C.10 Write linear equations in point-gradient form

C.11 Write an equation for a parallel or perpendicular line

C.12 Linear functions over unit intervals

C.13 Complete a function table: absolute value functions

C.14 Graph an absolute value function
Simultaneous equations

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

D.2 Solve simultaneous equations by graphing

D.3 Solve simultaneous equations by graphing: word problems

D.4 Find the number of solutions to simultaneous equations

D.5 Solve simultaneous equations using substitution

D.6 Solve simultaneous equations using substitution: word problems

D.7 Solve simultaneous equations using elimination

D.8 Solve simultaneous equations using elimination: word problems

D.9 Solve simultaneous equations using any method

D.10 Solve simultaneous equations using any method: word problems

D.11 Solve non-linear simultaneous equations
Complex numbers

G.1 Introduction to complex numbers

G.2 Add and subtract complex numbers

G.3 Complex conjugates

G.4 Multiply and divide complex numbers

G.5 Add, subtract, multiply and divide complex numbers

G.6 Absolute values of complex numbers

G.7 Powers of i
Polynomials

H.1 Polynomial vocabulary

H.2 Add and subtract polynomials

H.3 Multiply polynomials

H.4 Divide polynomials using long division

H.5 Solve polynomial equations

H.6 Find the roots of factorised polynomials

H.7 Write a polynomial from its roots

H.8 Rational root theorem

H.9 Descartes’ Rule of Signs

H.10 Match polynomials and graphs

H.11 Fundamental Theorem of Algebra

H.12 Pascal’s triangle

H.13 Pascal’s triangle and the Binomial Theorem

H.14 Binomial Theorem I

H.15 Binomial Theorem II
Radical functions and expressions

I.1 Roots of integers

I.2 Roots of rational numbers

I.3 Find roots using a calculator

I.4 Nth roots

I.5 Simplify radical expressions with variables I

I.6 Simplify radical expressions with variables II

I.7 Multiply radical expressions

I.8 Divide radical expressions

I.9 Add and subtract radical expressions

I.10 Simplify radical expressions using the distributive property

I.11 Simplify radical expressions using conjugates

I.12 Domain and range of radical functions

I.13 Solve radical equations
Rational exponents

J.1 Evaluate rational exponents

J.2 Multiplication with rational exponents

J.3 Division with rational exponents

J.4 Power rule

J.5 Simplify expressions involving rational exponents I

J.6 Simplify expressions involving rational exponents II
Rational functions and expressions

K.1 Rational functions: asymptotes and excluded values

K.2 Evaluate rational expressions I

K.3 Evaluate rational expressions II

K.4 Simplify rational expressions

K.5 Multiply and divide rational expressions

K.6 Add and subtract rational expressions

K.7 Solve rational equations
Function operations

L.1 Add and subtract functions

L.2 Multiply functions

L.3 Divide functions

L.4 Composition of linear functions: find a value

L.5 Composition of linear functions: find an equation

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

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

L.8 Identify inverse functions

L.9 Find values of inverse functions from tables

L.10 Find values of inverse functions from graphs

L.11 Find inverse functions and relations
Families of functions

M.1 Translations of functions

M.2 Reflections of functions

M.3 Dilations of functions

M.4 Transformations of functions

M.5 Function transformation rules

M.6 Describe function transformations
Logarithms

N.1 Convert between exponential and logarithmic form: rational bases

N.2 Evaluate logarithms

N.3 Change of base formula

N.4 Identify properties of logarithms

N.5 Product property of logarithms

N.6 Quotient property of logarithms

N.7 Power property of logarithms

N.8 Properties of logarithms: mixed review

N.9 Evaluate logarithms: mixed review
Exponential and logarithmic functions

O.1 Domain and range of exponential and logarithmic functions

O.2 Evaluate exhttps://www.youtube.com/watch?v=64643Op6WJoponential functions

O.3 Match exponential functions and graphs

O.4 Solve exponential equations by factorising

O.5 Solve exponential equations using common logarithms

O.6 Solve logarithmic equations I

O.7 Solve logarithmic equations II

O.8 Identify linear and exponential functions

O.9 Exponential functions over unit intervals

O.10 Describe linear and exponential growth and decay

O.11 Exponential growth and decay: word problems

O.12 Compound interest: word problems

O.13 Continuously compounded interest: word problems
Parabolas

P.1 Identify the direction a parabola opens

P.2 Find the vertex of a parabola

P.3 Find the focus or directrix of a parabola

P.4 Find the axis of symmetry of a parabola

P.5 Write equations of parabolas in vertex form from graphs

P.6 Write equations of parabolas in vertex form using properties

P.7 Convert equations of parabolas from general to vertex form

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

P.9 Graph parabolas
Angle measures

Q.1 Convert between radians and degrees

Q.2 Radians and arc length

Q.3 Quadrants

Q.4 Graphs of angles

Q.5 Coterminal angles

Q.6 Reference angles
Trigonometry

R.1 Pythagoras’ Theorem and its converse

R.2 Special right triangles

R.3 Trigonometric ratios: sin, cos and tan

R.4 Trigonometric ratios: csc, sec and cot

R.5 Trigonometric ratios in similar right triangles

R.6 Find trigonometric ratios using the unit circle

R.7 Sin, cos and tan of special angles

R.8 Csc, sec and cot of special angles

R.9 Find trigonometric functions using a calculator

R.10 Inverses of sin, cos and tan

R.11 Inverses of csc, sec and cot

R.12 Solve trigonometric equations I

R.13 Solve trigonometric equations II

R.14 Trigonometric ratios: find a side length

R.15 Trigonometric ratios: find an angle measure

R.16 Solve a right triangle

R.17 Law of Sines

R.18 Law of Cosines

R.19 Solve a triangle

R.20 Area of a triangle: sine formula

R.21 Area of a triangle: Law of Sines
Trigonometric functions

S.1 Find properties of sine functions

S.2 Write equations of sine functions from graphs

S.3 Write equations of sine functions using properties

S.4 Graph sine functions

S.5 Find properties of cosine functions

S.6 Write equations of cosine functions from graphs

S.7 Write equations of cosine functions using properties

S.8 Graph cosine functions

S.9 Graph sine and cosine functions
Trigonometric identities

T.1 Complementary angle identities

T.2 Symmetry and periodicity of trigonometric functions

T.3 Trigonometric identities I

T.4 Trigonometric identities II
Circles

U.1 Central angles

U.2 Arcs and chords

U.3 Tangent lines

U.4 Inscribed angles

U.5 Angles in inscribed right triangles

U.6 Angles in inscribed quadrilaterals
Circles in the coordinate plane

V.1 Find the centre of a circle

V.2 Find the radius or diameter of a circle

V.3 Write equations of circles in standard form from graphs

V.4 Write equations of circles in standard form using properties

V.5 Convert equations of circles from general to standard form

V.6 Find properties of circles from equations in general form

V.7 Graph circles
Sequences and series

W.1 Classify formulas and sequences

W.2 Find terms of an arithmetic sequence

W.3 Find terms of a geometric sequence

W.4 Find terms of a recursive sequence

W.5 Evaluate formulas for sequences

W.6 Write a formula for an arithmetic sequence

W.7 Write a formula for a geometric sequence

W.8 Write a formula for a recursive sequence

W.9 Sequences: mixed review

W.10 Introduction to sigma notation

W.11 Identify arithmetic and geometric series

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

W.13 Introduction to partial sums

W.14 Partial sums of arithmetic series

W.15 Partial sums of geometric series

W.16 Partial sums: mixed review

W.17 Convergent and divergent geometric series

W.18 Find the value of an infinite geometric series

W.19 Write a repeating decimal as a fraction
Probability

X.1 Introduction to probability

X.2 Theoretical and experimental probability

X.3 Compound events: find the number of outcomes

X.4 Factorials

X.5 Calculate probabilities of events

X.6 Counting principle

X.7 Permutations

X.8 Permutation and combination notation

X.9 Find probabilities using permutations and combinations

X.10 Find probabilities using two-way frequency tables

X.11 Identify independent events

X.12 Probability of independent and dependent events

X.13 Geometric probability

X.14 Find conditional probabilities

X.15 Independence and conditional probability

X.16 Find conditional probabilities using two-way frequency tables

X.17 Find probabilities using the addition rule
Statistics

Y.1 Mean, median, mode and range

Y.2 Quartiles

Y.3 Identify biased samples

Y.4 Mean absolute deviation

Y.5 Variance and standard deviation
Data and graphs

Z.1 Interpret bar graphs for continuous data

Z.2 Create bar graphs for continuous data

Z.3 Interpret stem-and-leaf plots

Z.4 Interpret box-and-whisker plots

Z.5 Interpret a scatter plot

Z.6 Scatter plots: line of best fit
Introduction to limits

AA.1 Find limits using graphs

AA.2 Find one-sided limits using graphs

AA.3 Determine if a limit exists
Calculate limits

BB.1 Find limits using addition, subtraction and multiplication laws

BB.2 Find limits using the division law

BB.3 Find limits using power and root laws

BB.4 Find limits using limit laws

BB.5 Find limits of polynomials and rational functions

BB.6 Find limits involving factorisation and rationalisation

BB.7 Find limits involving absolute value functions

BB.8 Find limits involving trigonometric functions
Limits and rational functions

CC.1 Find limits at vertical asymptotes using graphs

CC.2 Determine end behaviour using graphs

CC.3 Determine end behaviour of polynomial and rational functions

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

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

DD.1 Identify graphs of continuous functions

DD.2 Determine continuity using graphs

DD.3 Determine one-sided continuity using graphs

DD.4 Find and analyse points of discontinuity using graphs

DD.5 Determine continuity on an interval using graphs

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

DD.7 Make a piecewise function continuous

DD.8 Intermediate Value Theorem
Introduction to derivatives

EE.1 Average rate of change I

EE.2 Average rate of change II

EE.3 Find instantaneous rates of change

EE.4 Velocity as a rate of change

EE.5 Find values of derivatives using limits

EE.6 Find the gradient of a tangent line using limits

EE.7 Find equations of tangent lines using limits

EE.8 Power rule I

EE.9 Power rule II

EE.10 Find derivatives of polynomials

EE.11 Find second derivatives of polynomials

Taha Naguib is an experience instructor devoted to make math more intuitive and fun for students.

Year 12

Year 12

Equations

Inequalities

Functions

Simultaneous equations

Complex numbers

Polynomials

Radical functions and expressions

Rational exponents

Rational functions and expressions

Function operations

Families of functions

Logarithms

Exponential and logarithmic functions

Parabolas

Angle measures

Trigonometry

Trigonometric functions

Trigonometric identities

Circles

Circles in the coordinate plane

Sequences and series

Probability

Statistics

Data and graphs

Introduction to limits

Calculate limits

Limits and rational functions

Continuity

Introduction to derivatives

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