Maths

Consumer maths

A.1Simple interest

A.2Compound interest

A.3Continuously compounded interest

A.4Percent of a number: VAT, discount and more

A.5Find the percent: discount and mark-up

A.6Multi-step problems with percents

Single-variable inequalities

B.1Graph inequalities

B.2Write inequalities from graphs

B.3Identify solutions to inequalities

B.4Solve one-step linear inequalities: addition and subtraction

B.5Solve one-step linear inequalities: multiplication and division

B.6Solve one-step linear inequalities

B.7Graph solutions to one-step linear inequalities

B.8Solve two-step linear inequalities

B.9Graph solutions to two-step linear inequalities

B.10Solve advanced linear inequalities

B.11Graph solutions to advanced linear inequalities

B.12Graph compound inequalities

B.13Write compound inequalities from graphs

B.14Solve compound inequalities

B.15Graph solutions to compound inequalities

B.16Graph solutions to quadratic inequalities

B.17Solve quadratic inequalities

Relations and functions

C.1Relations: convert between tables, graphs, mappings and lists of points

C.2Domain and range of relations

C.3Identify independent and dependent variables

C.4Identify functions

C.5Identify functions: vertical line test

C.6Find values using function graphs

C.7Evaluate a function

C.8Evaluate a function: plug in an expression

C.9Complete a function table from a graph

C.10Complete a function table from an equation

C.11Interpret the graph of a function: word problems

Linear functions

D.1Find the slope of a graph

D.2Find the slope from two points

D.3Find a missing coordinate using slope

D.4Slope-intercept form: find the slope and y-intercept

D.5Slope-intercept form: graph an equation

D.6Slope-intercept form: write an equation from a graph

D.7Slope-intercept form: write an equation

D.8Slope-intercept form: write an equation from a table

D.9Slope-intercept form: write an equation from a word problem

D.10Write linear functions to solve word problems

D.11Complete a table and graph a linear function

D.12Write equations in standard form

D.13Standard form: find x- and y-intercepts

D.14Standard form: graph an equation

D.15Equations of horizontal and vertical lines

D.16Graph a horizontal or vertical line

D.17Slopes of parallel and perpendicular lines

D.18Write an equation for a parallel or perpendicular line

D.19Transformations of linear functions

Linear inequalities

E.1Does (x, y) satisfy the inequality?

E.2Linear inequalities: solve for y

E.3Graph a linear inequality in the coordinate plane

E.4Linear inequalities: word problems

E.5Is (x, y) a solution to the system of inequalities?

E.6Solve systems of linear inequalities by graphing

E.7Solve systems of linear and absolute value inequalities by graphing

Complex numbers

F.1Introduction to complex numbers

F.2Add and subtract complex numbers

F.3Complex conjugates

F.4Multiply complex numbers

F.5Divide complex numbers

F.6Add, subtract, multiply and divide complex numbers

F.7Absolute values of complex numbers

F.8Powers of i

Argand plane

G.1Introduction to the Argand plane

G.2Graph complex numbers

G.3Addition in the Argand plane

G.4Subtraction in the Argand plane

G.5Graph complex conjugates

G.6Absolute value in the Argand plane

G.7Midpoints in the Argand plane

G.8Distance in the Argand plane

Factorising

H.1Factorise out a monomial

H.2Factorise quadratic polynomials

H.3Factorise quadratics using algebra tiles

H.4Factorise using a quadratic pattern

H.5Factorise by grouping

H.6Factorise sums and differences of cubes

H.7Factorise polynomials

Quadratic functions

I.1Characteristics of quadratic functions

I.2Complete a function table: quadratic functions

I.3Find a quadratic function

I.4Graph a quadratic function

I.5Match quadratic functions and graphs

I.6Solve a quadratic equation using square roots

I.7Solve a quadratic equation using the zero product property

I.8Solve a quadratic equation by factorising

I.9Complete the square

I.10Solve a quadratic equation using the quadratic formula

I.11Using the discriminant

Polynomials

J.1Polynomial vocabulary

J.2Add and subtract polynomials

J.3Multiply polynomials

J.4Divide polynomials using long division

J.5Divide polynomials using synthetic division

J.6Evaluate polynomials using synthetic division

J.7Solve polynomial equations

J.8Write a polynomial from its roots

J.9Find the roots of factorised polynomials

J.10Rational root theorem

J.11Complex conjugate theorem

J.12Conjugate root theorems

J.13Match polynomials and graphs

J.14Fundamental Theorem of Algebra

J.15Pascal's triangle

J.16Pascal's triangle and the Binomial Theorem

J.17Binomial Theorem I

J.18Binomial Theorem II

Parabolas

K.1Identify the direction a parabola opens

K.2Find the vertex of a parabola

K.3Find the focus or directrix of a parabola

K.4Find the axis of symmetry of a parabola

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

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

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

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

K.9Graph parabolas

Circles

L.1Find the centre of a circle

L.2Find the radius or diameter of a circle

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

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

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

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

L.7Graph circles

Ellipses

M.1Find the center, vertices, or co-vertices of an ellipse

M.2Find the length of the major or minor axes of an ellipse

M.3Find the foci of an ellipse

M.4Write equations of ellipses in standard form from graphs

M.5Write equations of ellipses in standard form using properties

M.6Convert equations of ellipses from general to standard form

M.7Find properties of ellipses from equations in general form

Hyperbolas

N.1Find the center of a hyperbola

N.2Find the vertices of a hyperbola

N.3Find the length of the transverse or conjugate axes of a hyperbola

N.4Find the equations for the asymptotes of a hyperbola

N.5Find the foci of a hyperbola

N.6Write equations of hyperbolas in standard form from graphs

N.7Write equations of hyperbolas in standard form using properties

N.8Convert equations of hyperbolas from general to standard form

N.9Find properties of hyperbolas from equations in general form

Rational functions and expressions

O.1Rational functions: asymptotes and excluded values

O.2Evaluate rational expressions I

O.3Evaluate rational expressions II

O.4Simplify rational expressions

O.5Multiply and divide rational expressions

O.6Add and subtract rational expressions

O.7Solve rational equations

Function operations

P.1Add and subtract functions

P.2Multiply functions

P.3Divide functions

P.4Composition of linear functions: find a value

P.5Composition of linear functions: find an equation

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

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

Angle measures

Q.1Convert between radians and degrees

Q.2Radians and arc length

Q.3Quadrants

Q.4Graphs of angles

Q.5Coterminal angles

Q.6Reference angles

Trigonometry

R.1Pythagoras' Theorem and its converse

R.2Special right triangles

R.3Trigonometric ratios: sin, cos and tan

R.4Trigonometric ratios: csc, sec and cot

R.5Trigonometric ratios in similar right triangles

R.6Find trigonometric ratios using the unit circle

R.7Sin, cos and tan of special angles

R.8Csc, sec and cot of special angles

R.9Find trigonometric functions using a calculator

R.10Inverses of sin, cos and tan

R.11Inverses of csc, sec and cot

R.12Solve trigonometric equations I

R.13Solve trigonometric equations II

R.14Trigonometric ratios: find a side length

R.15Trigonometric ratios: find an angle measure

R.16Solve a right triangle

R.17Law of Sines

R.18Law of Cosines

R.19Solve a triangle

R.20Area of a triangle: sine formula

R.21Area of a triangle: Law of Sines

Trigonometric functions

S.1Find properties of sine functions

S.2Write equations of sine functions from graphs

S.3Write equations of sine functions using properties

S.4Graph sine functions

S.5Find properties of cosine functions

S.6Write equations of cosine functions from graphs

S.7Write equations of cosine functions using properties

S.8Graph cosine functions

S.9Graph sine and cosine functions

Trigonometric identities

T.1Complementary angle identities

T.2Symmetry and periodicity of trigonometric functions

T.3Trigonometric identities I

T.4Trigonometric identities II

Problem solving

U.1Word problems: mixed review

U.2Word problems with money

U.3Consecutive integer problems

U.4Rate of travel: word problems

U.5Weighted averages: word problems

Logic

V.1Identify hypotheses and conclusions

V.2Counterexamples

V.3Truth tables

V.4Truth values

V.5Conditionals

V.6Negations

V.7Converses, inverses and contrapositives

V.8Biconditionals

Sequences and series

W.1Classify formulas and sequences

W.2Find terms of an arithmetic sequence

W.3Find terms of a geometric sequence

W.4Find terms of a recursive sequence

W.5Evaluate formulas for sequences

W.6Write a formula for an arithmetic sequence

W.7Write a formula for a geometric sequence

W.8Write a formula for a recursive sequence

W.9Sequences: mixed review

W.10Introduction to sigma notation

W.11Identify arithmetic and geometric series

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

W.13Introduction to partial sums

W.14Partial sums of arithmetic series

W.15Partial sums of geometric series

W.16Partial sums: mixed review

W.17Convergent and divergent geometric series

W.18Find the value of an infinite geometric series

W.19Write a repeating decimal as a fraction

Introduction to limits

X.1Find limits using graphs

X.2Find one-sided limits using graphs

X.3Determine if a limit exists

Calculate limits

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

Y.2Find limits using the division law

Y.3Find limits using power and root laws

Y.4Find limits using limit laws

Y.5Find limits of polynomials and rational functions

Y.6Find limits involving factorisation and rationalisation

Limits involving infinity

Z.1Find limits at vertical asymptotes using graphs

Z.2Determine end behaviour using graphs

Z.3Determine end behaviour of polynomial and rational functions

Limits and rational functions

AA.1Find the limit at a vertical asymptote of a rational function I

AA.2Find the limit at a vertical asymptote of a rational function II

Continuity

BB.1Identify graphs of continuous functions

BB.2Determine continuity using graphs

BB.3Determine one-sided continuity using graphs

BB.4Find and analyse points of discontinuity using graphs

BB.5Determine continuity on an interval using graphs

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

BB.7Make a piecewise function continuous

BB.8Intermediate Value Theorem

Introduction to derivatives

CC.1Average rate of change I

CC.2Average rate of change II

CC.3Find instantaneous rates of change

CC.4Velocity as a rate of change

CC.5Find values of derivatives using limits

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

CC.7Find equations of tangent lines using limits

Calculate derivatives

DD.1Sum and difference rules

DD.2Product rule

DD.3Quotient rule

DD.4Power rule I

DD.5Power rule II

DD.6Find derivatives of polynomials

DD.7Find derivatives of rational functions

DD.8Find derivatives of trigonometric functions I

DD.9Find derivatives of trigonometric functions II

DD.10Chain rule

DD.11Find derivatives of radical functions

DD.12Find derivatives using the product rule

DD.13Find derivatives using the quotient rule I

DD.14Find derivatives using the quotient rule II

DD.15Find derivatives using the chain rule I

DD.16Find derivatives using the chain rule II

Probability

EE.1Introduction to probability

EE.2Theoretical and experimental probability

EE.3Compound events: find the number of outcomes

EE.4Calculate probabilities of events

EE.5Permutations

EE.6Counting principle

EE.7Permutation and combination notation

EE.8Find probabilities using permutations and combinations

EE.9Find probabilities using two-way frequency tables

EE.10Identify independent events

EE.11Probability of independent and dependent events

EE.12Geometric probability

EE.13Find conditional probabilities

EE.14Independence and conditional probability

EE.15Find conditional probabilities using two-way frequency tables

EE.16Find probabilities using the addition rule

EE.17Find probabilities using the normal distribution

Statistics

FF.1Mean, median, mode and range

FF.2Quartiles

FF.3Identify biased samples

FF.4Mean absolute deviation

FF.5Variance and standard deviation

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