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**Consumer maths**

**A.1**Simple interest

**A.2**Compound interest

**A.3**Continuously compounded interest

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

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

**A.6**Multi-step problems with percents

**Single-variable inequalities**

**B.1**Graph inequalities

**B.2**Write inequalities from graphs

**B.3**Identify solutions to inequalities

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

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

**B.6**Solve one-step linear inequalities

**B.7**Graph solutions to one-step linear inequalities

**B.8**Solve two-step linear inequalities

**B.9**Graph solutions to two-step linear inequalities

**B.10**Solve advanced linear inequalities

**B.11**Graph solutions to advanced linear inequalities

**B.12**Graph compound inequalities

**B.13**Write compound inequalities from graphs

**B.14**Solve compound inequalities

**B.15**Graph solutions to compound inequalities

**B.16**Graph solutions to quadratic inequalities

**B.17**Solve quadratic inequalities

**Relations and functions**

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

**C.2**Domain and range of relations

**C.3**Identify independent and dependent variables

**C.4**Identify functions

**C.5**Identify functions: vertical line test

**C.6**Find values using function graphs

**C.7**Evaluate a function

**C.8**Evaluate a function: plug in an expression

**C.9**Complete a function table from a graph

**C.10**Complete a function table from an equation

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

**Linear functions**

**D.1**Find the slope of a graph

**D.2**Find the slope from two points

**D.3**Find a missing coordinate using slope

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

**D.5**Slope-intercept form: graph an equation

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

**D.7**Slope-intercept form: write an equation

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

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

**D.10**Write linear functions to solve word problems

**D.11**Complete a table and graph a linear function

**D.12**Write equations in standard form

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

**D.14**Standard form: graph an equation

**D.15**Equations of horizontal and vertical lines

**D.16**Graph a horizontal or vertical line

**D.17**Slopes of parallel and perpendicular lines

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

**D.19**Transformations of linear functions

**Linear inequalities**

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

**E.2**Linear inequalities: solve for y

**E.3**Graph a linear inequality in the coordinate plane

**E.4**Linear inequalities: word problems

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

**E.6**Solve systems of linear inequalities by graphing

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

**Complex numbers**

**F.1**Introduction to complex numbers

**F.2**Add and subtract complex numbers

**F.3**Complex conjugates

**F.4**Multiply complex numbers

**F.5**Divide complex numbers

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

**F.7**Absolute values of complex numbers

**F.8**Powers of i

**Argand plane**

**G.1**Introduction to the Argand plane

**G.2**Graph complex numbers

**G.3**Addition in the Argand plane

**G.4**Subtraction in the Argand plane

**G.5**Graph complex conjugates

**G.6**Absolute value in the Argand plane

**G.7**Midpoints in the Argand plane

**G.8**Distance in the Argand plane

**Factorising**

**H.1**Factorise out a monomial

**H.2**Factorise quadratic polynomials

**H.3**Factorise quadratics using algebra tiles

**H.4**Factorise using a quadratic pattern

**H.5**Factorise by grouping

**H.6**Factorise sums and differences of cubes

**H.7**Factorise polynomials

**Quadratic functions**

**I.1**Characteristics of quadratic functions

**I.2**Complete a function table: quadratic functions

**I.3**Find a quadratic function

**I.4**Graph a quadratic function

**I.5**Match quadratic functions and graphs

**I.6**Solve a quadratic equation using square roots

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

**I.8**Solve a quadratic equation by factorising

**I.9**Complete the square

**I.10**Solve a quadratic equation using the quadratic formula

**I.11**Using the discriminant

**Polynomials**

**J.1**Polynomial vocabulary

**J.2**Add and subtract polynomials

**J.3**Multiply polynomials

**J.4**Divide polynomials using long division

**J.5**Divide polynomials using synthetic division

**J.6**Evaluate polynomials using synthetic division

**J.7**Solve polynomial equations

**J.8**Write a polynomial from its roots

**J.9**Find the roots of factorised polynomials

**J.10**Rational root theorem

**J.11**Complex conjugate theorem

**J.12**Conjugate root theorems

**J.13**Match polynomials and graphs

**J.14**Fundamental Theorem of Algebra

**J.15**Pascal's triangle

**J.16**Pascal's triangle and the Binomial Theorem

**J.17**Binomial Theorem I

**J.18**Binomial Theorem II

**Parabolas**

**K.1**Identify the direction a parabola opens

**K.2**Find the vertex of a parabola

**K.3**Find the focus or directrix of a parabola

**K.4**Find the axis of symmetry of a parabola

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

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

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

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

**K.9**Graph parabolas

**Circles**

**L.1**Find the centre of a circle

**L.2**Find the radius or diameter of a circle

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

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

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

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

**L.7**Graph circles

**Ellipses**

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

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

**M.3**Find the foci of an ellipse

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

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

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

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

**Hyperbolas**

**N.1**Find the center of a hyperbola

**N.2**Find the vertices of a hyperbola

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

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

**N.5**Find the foci of a hyperbola

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

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

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

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

**Rational functions and expressions**

**O.1**Rational functions: asymptotes and excluded values

**O.2**Evaluate rational expressions I

**O.3**Evaluate rational expressions II

**O.4**Simplify rational expressions

**O.5**Multiply and divide rational expressions

**O.6**Add and subtract rational expressions

**O.7**Solve rational equations

**Function operations**

**P.1**Add and subtract functions

**P.2**Multiply functions

**P.3**Divide functions

**P.4**Composition of linear functions: find a value

**P.5**Composition of linear functions: find an equation

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

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

**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

**Problem solving**

**U.1**Word problems: mixed review

**U.2**Word problems with money

**U.3**Consecutive integer problems

**U.4**Rate of travel: word problems

**U.5**Weighted averages: word problems

**Logic**

**V.1**Identify hypotheses and conclusions

**V.2**Counterexamples

**V.3**Truth tables

**V.4**Truth values

**V.5**Conditionals

**V.6**Negations

**V.7**Converses, inverses and contrapositives

**V.8**Biconditionals

**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

**Introduction to limits**

**X.1**Find limits using graphs

**X.2**Find one-sided limits using graphs

**X.3**Determine if a limit exists

**Calculate limits**

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

**Y.2**Find limits using the division law

**Y.3**Find limits using power and root laws

**Y.4**Find limits using limit laws

**Y.5**Find limits of polynomials and rational functions

**Y.6**Find limits involving factorisation and rationalisation

**Limits involving infinity**

**Z.1**Find limits at vertical asymptotes using graphs

**Z.2**Determine end behaviour using graphs

**Z.3**Determine end behaviour of polynomial and rational functions

**Limits and rational functions**

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

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

**Continuity**

**BB.1**Identify graphs of continuous functions

**BB.2**Determine continuity using graphs

**BB.3**Determine one-sided continuity using graphs

**BB.4**Find and analyse points of discontinuity using graphs

**BB.5**Determine continuity on an interval using graphs

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

**BB.7**Make a piecewise function continuous

**BB.8**Intermediate Value Theorem

**Introduction to derivatives**

**CC.1**Average rate of change I

**CC.2**Average rate of change II

**CC.3**Find instantaneous rates of change

**CC.4**Velocity as a rate of change

**CC.5**Find values of derivatives using limits

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

**CC.7**Find equations of tangent lines using limits

**Calculate derivatives**

**DD.1**Sum and difference rules

**DD.2**Product rule

**DD.3**Quotient rule

**DD.4**Power rule I

**DD.5**Power rule II

**DD.6**Find derivatives of polynomials

**DD.7**Find derivatives of rational functions

**DD.8**Find derivatives of trigonometric functions I

**DD.9**Find derivatives of trigonometric functions II

**DD.10**Chain rule

**DD.11**Find derivatives of radical functions

**DD.12**Find derivatives using the product rule

**DD.13**Find derivatives using the quotient rule I

**DD.14**Find derivatives using the quotient rule II

**DD.15**Find derivatives using the chain rule I

**DD.16**Find derivatives using the chain rule II

**Probability**

**EE.1**Introduction to probability

**EE.2**Theoretical and experimental probability

**EE.3**Compound events: find the number of outcomes

**EE.4**Calculate probabilities of events

**EE.5**Permutations

**EE.6**Counting principle

**EE.7**Permutation and combination notation

**EE.8**Find probabilities using permutations and combinations

**EE.9**Find probabilities using two-way frequency tables

**EE.10**Identify independent events

**EE.11**Probability of independent and dependent events

**EE.12**Geometric probability

**EE.13**Find conditional probabilities

**EE.14**Independence and conditional probability

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

**EE.16**Find probabilities using the addition rule

**EE.17**Find probabilities using the normal distribution

**Statistics**

**FF.1**Mean, median, mode and range

**FF.2**Quartiles

**FF.3**Identify biased samples

**FF.4**Mean absolute deviation

**FF.5**Variance and standard deviation

**Sentence structure**

**A.1**Identify sentence fragments

**A.2**Identify run-on sentences

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

**A.4**Is it a phrase or a clause?

**A.5**Identify prepositional phrases

**A.6**Identify appositives and appositive phrases

**A.7**Identify dependent and independent clauses

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

**A.9**Combine sentences using relative clauses

**Pronouns**

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

**B.2**Subject and object pronouns review

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

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

**B.5**Use relative pronouns: who and whom

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

**B.7**Identify vague pronoun references

**B.8**Identify all of the possible antecedents

**Verbs and verbals**

**C.1**Identify transitive and intransitive verbs

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

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

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

**C.5**Identify and correct verb agreement with compound subjects

**C.6**Identify and correct inappropriate shifts in verb tense

**C.7**Form the progressive verb tenses

**C.8**Form the perfect verb tenses

**C.9**Identify participles and what they modify

**C.10**Identify gerunds and their functions

**C.11**Identify infinitives and infinitive phrases

**Adjectives and adverbs**

**D.1**Form and use comparative and superlative adjectives

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

**D.3**Form and use comparative and superlative adverbs

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

**Punctuation and capitalisation**

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

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

**E.3**Commas with coordinate adjectives

**E.4**Commas: review

**E.5**Commas with non-restrictive elements

**E.6**Join sentences with semicolons, colons and commas

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

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

**E.9**Semicolons, colons and commas review

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

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

**E.12**Use dashes

**E.13**Use hyphens in compound adjectives

**E.14**Decide whether ellipses are used appropriately

**E.15**Correct capitalisation errors

**Prefixes and suffixes**

**F.1**Word pattern analogies

**F.2**Word pattern sentences

**F.3**Prefixes

**F.4**Suffixes

**Etymologies and foreign expressions**

**G.1**Sort words by shared Greek or Latin roots

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

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

**G.4**Determine the meanings of Greek and Latin roots

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

**G.6**Use etymologies to determine the meanings of words

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

**G.8**Use the correct foreign expression

**Word choice and usage**

**H.1**Describe the difference between related words

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

**H.3**Use words accurately and precisely

**H.4**Replace words using a thesaurus

**H.5**Use dictionary entries to determine correct usage

**H.6**Analogies

**H.7**Analogies: challenge

**Context clues**

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

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

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

**Writing clear and concise sentences**

**J.1**Transitions with conjunctive adverbs

**J.2**Avoid double, illogical and unclear comparisons

**J.3**Identify sentences with parallel structure

**J.4**Use parallel structure

**J.5**Remove redundant words or phrases

**J.6**Misplaced modifiers with pictures

**J.7**Select the misplaced or dangling modifier

**J.8**Are the modifiers used correctly?

**Common errors**

**K.1**Use the correct homophone

**K.2**Identify and correct errors with homophones

**K.3**Use the correct frequently confused word

**K.4**Identify and correct errors with frequently confused words

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

**K.6**Correct errors with commonly misspelled words

**K.7**Correct errors in everyday use

**Writing process**

**L.1**Order topics from broadest to narrowest

**L.2**Organise information by main idea

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

**L.4**Identify plagiarism

**L.5**Suggest appropriate revisions

**Writing arguments**

**M.1**Distinguish facts from opinions

**M.2**Choose evidence to support a claim

**M.3**Identify supporting evidence in a text

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

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

**Author's purpose and tone**

**N.1**Which text is most formal?

**N.2**Compare passages for tone

**N.3**Identify audience and purpose

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

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

**Literary devices**

**O.1**Identify the narrative point of view

**O.2**Interpret the figure of speech

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

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

**O.5**Classify the figure of speech: review

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

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