Maths

Functions

A.1Domain and range

A.2Identify functions

A.3Find the slope of a linear function

A.4Graph a linear function

A.5Write the equation of a linear function

A.6Evaluate functions

A.7Find values using function graphs

A.8Complete a table for a function graph

A.9Add, subtract, multiply and divide functions

A.10Composition of functions

A.11Identify inverse functions

A.12Find values of inverse functions from tables

A.13Find values of inverse functions from graphs

A.14Find inverse functions and relations

Families of functions

B.1Translations of functions

B.2Reflections of functions

B.3Dilations of functions

B.4Transformations of functions

B.5Function transformation rules

B.6Describe function transformations

Polynomials

C.1Divide polynomials using long division

C.2Divide polynomials using synthetic division

C.3Evaluate polynomials using synthetic division

C.4Write a polynomial from its roots

C.5Find the roots of factorised polynomials

C.6Rational root theorem

C.7Complex conjugate theorem

C.8Conjugate root theorems

C.9Descartes' Rule of Signs

C.10Fundamental Theorem of Algebra

C.11Match polynomials and graphs

C.12Factorise sums and differences of cubes

C.13Solve equations with sums and differences of cubes

C.14Factorise using a quadratic pattern

C.15Solve equations using a quadratic pattern

C.16Pascal's triangle

C.17Pascal's triangle and the Binomial Theorem

C.18Binomial Theorem I

C.19Binomial Theorem II

Systems of inequalities

D.1Solve systems of linear inequalities by graphing

D.2Solve systems of linear and absolute value inequalities by graphing

D.3Find the vertices of a solution set

D.4Linear programming

Nonlinear inequalities

E.1Graph solutions to quadratic inequalities

E.2Solve quadratic inequalities

E.3Graph solutions to higher-degree inequalities

E.4Solve higher-degree inequalities

Matrices

F.1Matrix vocabulary

F.2Matrix operation rules

F.3Add and subtract matrices

F.4Multiply a matrix by a scalar

F.5Linear combinations of matrices

F.6Multiply two matrices

F.7Simplify matrix expressions

F.8Solve matrix equations

F.9Determinant of a matrix

F.10Is a matrix invertible?

F.11Inverse of a 2 x 2 matrix

F.12Inverse of a 3 x 3 matrix

F.13Identify inverse matrices

F.14Solve matrix equations using inverses

Trigonometry

G.1Convert between radians and degrees

G.2Radians and arc length

G.3Quadrants

G.4Coterminal and reference angles

G.5Find trigonometric ratios using right triangles

G.6Find trigonometric ratios using the unit circle

G.7Find trigonometric ratios using reference angles

G.8Inverses of trigonometric functions

G.9Solve trigonometric equations

G.10Trigonometric ratios: find a side length

G.11Trigonometric ratios: find an angle measure

G.12Solve a right triangle

G.13Law of Sines

G.14Law of Cosines

G.15Solve a triangle

G.16Area of a triangle: sine formula

G.17Area of a triangle: Heron's formula

Trigonometric functions

H.1Find properties of sine functions

H.2Write equations of sine functions from graphs

H.3Write equations of sine functions using properties

H.4Graph sine functions

H.5Find properties of cosine functions

H.6Write equations of cosine functions from graphs

H.7Write equations of cosine functions using properties

H.8Graph cosine functions

H.9Graph sine and cosine functions

Trigonometric identities

I.1Complementary angle identities

I.2Symmetry and periodicity of trigonometric functions

I.3Trigonometric identities I

I.4Trigonometric identities II

Conic sections

J.1Find properties of parabolas

J.2Write equations of parabolas in vertex form

J.3Graph parabolas

J.4Find properties of circles

J.5Write equations of circles in standard form

J.6Graph circles

J.7Find properties of ellipses

J.8Find the eccentricity of an ellipse

J.9Write equations of ellipses in standard form

J.10Find properties of hyperbolas

J.11Find the eccentricity of a hyperbola

J.12Write equations of hyperbolas in standard form

J.13Convert equations of conic sections from general to standard form

Complex numbers

K.1Add and subtract complex numbers

K.2Complex conjugates

K.3Multiply and divide complex numbers

K.4Add, subtract, multiply and divide complex numbers

K.5Absolute values of complex numbers

K.6Powers of i

Argand plane

L.1Introduction to the Argand plane

L.2Graph complex numbers

L.3Addition in the Argand plane

L.4Subtraction in the Argand plane

L.5Graph complex conjugates

L.6Absolute value in the Argand plane

L.7Midpoints in the Argand plane

L.8Distance in the Argand plane

Polar form

M.1Find the modulus and argument of a complex number

M.2Convert complex numbers from rectangular to polar form

M.3Convert complex numbers from polar to rectangular form

M.4Convert complex numbers between rectangular and polar form

M.5Match polar equations and graphs

Two-dimensional vectors

N.1Find the magnitude of a vector

N.2Find the direction angle of a vector

N.3Find the component form of a vector

N.4Find the component form of a vector from its magnitude and direction angle

N.5Find a unit vector

N.6Add and subtract vectors

N.7Multiply a vector by a scalar

N.8Find the magnitude or direction of a vector scalar multiple

N.9Find the magnitude and direction of a vector sum

N.10Linear combinations of vectors

N.11Graph a resultant vector using the triangle method

N.12Graph a resultant vector using the parallelogram method

Three-dimensional vectors

O.1Find the magnitude of a three-dimensional vector

O.2Find the component form of a three-dimensional vector

O.3Find a three-dimensional unit vector

O.4Add and subtract three-dimensional vectors

O.5Scalar multiples of three-dimensional vectors

O.6Linear combinations of three-dimensional vectors

Sequences and series

P.1Find terms of a sequence

P.2Find terms of a recursive sequence

P.3Identify a sequence as explicit or recursive

P.4Find a recursive formula

P.5Find recursive and explicit formulas

P.6Convert a recursive formula to an explicit formula

P.7Convert an explicit formula to a recursive formula

P.8Convert between explicit and recursive formulas

P.9Introduction to sigma notation

P.10Identify arithmetic and geometric series

P.11Find the sum of a finite arithmetic or geometric series

P.12Introduction to partial sums

P.13Partial sums of arithmetic series

P.14Partial sums of geometric series

P.15Partial sums: mixed review

P.16Convergent and divergent geometric series

P.17Find the value of an infinite geometric series

P.18Write a repeating decimal as a fraction

Continuity

Q.1Identify graphs of continuous functions

Q.2Determine continuity using graphs

Q.3Determine one-sided continuity using graphs

Q.4Find and analyse points of discontinuity using graphs

Q.5Determine continuity on an interval using graphs

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

Q.7Make a piecewise function continuous

Q.8Intermediate Value Theorem

Introduction to derivatives

R.1Average rate of change I

R.2Average rate of change II

R.3Find instantaneous rates of change

R.4Velocity as a rate of change

R.5Find values of derivatives using limits

R.6Find the slope of a tangent line using limits

R.7Find equations of tangent lines using limits

Derivative rules

S.1Sum and difference rules

S.2Product rule

S.3Quotient rule

S.4Power rule I

S.5Power rule II

S.6Chain rule

S.7Inverse function rule

Calculate derivatives

T.1Find derivatives of polynomials

T.2Find derivatives of rational functions

T.3Find derivatives of trigonometric functions I

T.4Find derivatives of trigonometric functions II

T.5Find derivatives of exponential functions

T.6Find derivatives of logarithmic functions

T.7Find derivatives of inverse trigonometric functions

T.8Find derivatives of radical functions

T.9Find derivatives using the product rule I

T.10Find derivatives using the product rule II

T.11Find derivatives using the quotient rule I

T.12Find derivatives using the quotient rule II

T.13Find derivatives using the chain rule I

T.14Find derivatives using the chain rule II

Derivative strategies

U.1Find derivatives using implicit differentiation

U.2Find tangent lines using implicit differentiation

U.3Find derivatives using logarithmic differentiation

Calculate higher derivatives

V.1Find higher derivatives of polynomials

V.2Find higher derivatives of rational and radical functions

V.3Find second derivatives of trigonometric, exponential and logarithmic functions

V.4Find higher derivatives using patterns

Probability

W.1Introduction to probability

W.2Calculate probabilities of events

W.3Combinations and permutations

W.4Find probabilities using combinations and permutations

W.5Find probabilities using two-way frequency tables

W.6Identify independent events

W.7Find conditional probabilities

W.8Independence and conditional probability

W.9Find conditional probabilities using two-way frequency tables

W.10Find probabilities using the addition rule

Probability distributions

X.1Identify discrete and continuous random variables

X.2Write a discrete probability distribution

X.3Graph a discrete probability distribution

X.4Expected values of random variables

X.5Variance of random variables

X.6Standard deviation of random variables

X.7Write the probability distribution for a game of chance

X.8Expected values for a game of chance

X.9Choose the better bet

X.10Find probabilities using the binomial distribution

X.11Mean, variance and standard deviation of binomial distributions

X.12Find probabilities using the normal distribution I

X.13Find probabilities using the normal distribution II

X.14Find z-values

X.15Find values of normal variables

X.16Distributions of sample means

X.17The Central Limit Theorem

X.18Use normal distributions to approximate binomial distributions

Statistics

Y.1Match correlation coefficients to scatter plots

Y.2Calculate correlation coefficients

Y.3Find the equation of a regression line

Y.4Interpret regression lines

Y.5Analyse a regression line of a data set

Y.6Analyse a regression line using statistics of a data set

Sentence structure

A.1Identify sentence fragments

A.2Identify run-on sentences

A.3Choose punctuation to avoid fragments and run-ons

A.4Is it a phrase or a clause?

A.5Identify prepositional phrases

A.6Identify appositives and appositive phrases

A.7Identify dependent and independent clauses

A.8Is the sentence simple, compound, complex or compound-complex?

A.9Combine sentences using relative clauses

Pronouns

B.1Identify and correct errors with subject and object pronouns

B.2Subject and object pronouns review

B.3Pronouns after 'than' and 'as'

B.4Identify and correct pronoun errors with 'who'

B.5Use relative pronouns: who and whom

B.6Use relative pronouns: who, whom, whose, which and that

B.7Identify vague pronoun references

B.8Identify all of the possible antecedents

Verbs and verbals

C.1Identify transitive and intransitive verbs

C.2Identify linking verbs, predicate adjectives and predicate nouns

C.3Identify and correct errors with subject-verb agreement

C.4Identify and correct errors with indefinite pronoun-verb agreement

C.5Identify and correct verb agreement with compound subjects

C.6Identify and correct inappropriate shifts in verb tense

C.7Form the progressive verb tenses

C.8Form the perfect verb tenses

C.9Identify participles and what they modify

C.10Identify gerunds and their functions

C.11Identify infinitives and infinitive phrases

Adjectives and adverbs

D.1Form and use comparative and superlative adjectives

D.2Good, better, best, bad, worse and worst

D.3Form and use comparative and superlative adverbs

D.4Well, better, best, badly, worse and worst

Punctuation and capitalisation

E.1Commas with direct addresses, introductory elements, absolute phrases, interjections, interrupters and antithetical phrases

E.2Commas with compound, complex and compound-complex sentences

E.3Commas with coordinate adjectives

E.4Commas: review

E.5Commas with non-restrictive elements

E.6Join sentences with semicolons, colons and commas

E.7Use colons and commas to introduce lists, quotations and appositives

E.8Use semicolons and commas to separate items in a series

E.9Semicolons, colons and commas review

E.10Identify and correct errors with plural and possessive nouns

E.11Identify and correct errors with compound and joint possession

E.12Use dashes

E.13Use hyphens in compound adjectives

E.14Decide whether ellipses are used appropriately

E.15Correct capitalisation errors

Prefixes and suffixes

F.1Word pattern analogies

F.2Word pattern sentences

F.3Prefixes

F.4Suffixes

Etymologies and foreign expressions

G.1Sort words by shared Greek or Latin roots

G.2Use Greek and Latin roots as clues to the meanings of words

G.3Use words as clues to the meanings of Greek and Latin roots

G.4Determine the meanings of Greek and Latin roots

G.5Determine the meanings of words with Greek and Latin roots

G.6Use etymologies to determine the meanings of words

G.7Use context as a clue to the meanings of foreign expressions

G.8Use the correct foreign expression

Word choice and usage

H.1Describe the difference between related words

H.2Choose the word whose connotation and denotation best match the sentence

H.3Use words accurately and precisely

H.4Replace words using a thesaurus

H.5Use dictionary entries to determine correct usage

H.6Analogies

H.7Analogies: challenge

Context clues

I.1Determine the meaning of words using synonyms in context

I.2Determine the meaning of words using antonyms in context

I.3Domain-specific vocabulary in context: science and technical subjects

Writing clear and concise sentences

J.1Transitions with conjunctive adverbs

J.2Avoid double, illogical and unclear comparisons

J.3Identify sentences with parallel structure

J.4Use parallel structure

J.5Remove redundant words or phrases

J.6Misplaced modifiers with pictures

J.7Select the misplaced or dangling modifier

J.8Are the modifiers used correctly?

Common errors

K.1Use the correct homophone

K.2Identify and correct errors with homophones

K.3Use the correct frequently confused word

K.4Identify and correct errors with frequently confused words

K.5Identify and correct errors with frequently confused pronouns and contractions

K.6Correct errors with commonly misspelled words

K.7Correct errors in everyday use

Writing process

L.1Order topics from broadest to narrowest

L.2Organise information by main idea

L.3Choose the topic sentence that best captures the main idea

L.4Identify plagiarism

L.5Suggest appropriate revisions

Writing arguments

M.1Distinguish facts from opinions

M.2Choose evidence to support a claim

M.3Identify supporting evidence in a text

M.4Choose the most appropriate counterclaim for a given claim

M.5Choose the analysis that logically connects the evidence to the claim

Author's purpose and tone

N.1Which text is most formal?

N.2Compare passages for tone

N.3Identify audience and purpose

N.4Identify appeals to ethos, pathos and logos in advertisements

N.5Use appeals to ethos, pathos and logos in persuasive writing

Literary devices

O.1Identify the narrative point of view

O.2Interpret the figure of speech

O.3Classify the figure of speech: euphemism, hyperbole, oxymoron, paradox

O.4Classify the figure of speech: anaphora, antithesis, apostrophe, assonance, chiasmus, understatement

O.5Classify the figure of speech: review

O.6Analyse the effects of figures of speech on meaning and tone