Maths

**Functions**

**A.1**Domain and range

**A.2**Identify functions

**A.3**Find the slope of a linear function

**A.4**Graph a linear function

**A.5**Write the equation of a linear function

**A.6**Evaluate functions

**A.7**Find values using function graphs

**A.8**Complete a table for a function graph

**A.9**Add, subtract, multiply and divide functions

**A.10**Composition of functions

**A.11**Identify inverse functions

**A.12**Find values of inverse functions from tables

**A.13**Find values of inverse functions from graphs

**A.14**Find inverse functions and relations

**Families of functions**

**B.1**Translations of functions

**B.2**Reflections of functions

**B.3**Dilations of functions

**B.4**Transformations of functions

**B.5**Function transformation rules

**B.6**Describe function transformations

**Polynomials**

**C.1**Divide polynomials using long division

**C.2**Divide polynomials using synthetic division

**C.3**Evaluate polynomials using synthetic division

**C.4**Write a polynomial from its roots

**C.5**Find the roots of factorised polynomials

**C.6**Rational root theorem

**C.7**Complex conjugate theorem

**C.8**Conjugate root theorems

**C.9**Descartes' Rule of Signs

**C.10**Fundamental Theorem of Algebra

**C.11**Match polynomials and graphs

**C.12**Factorise sums and differences of cubes

**C.13**Solve equations with sums and differences of cubes

**C.14**Factorise using a quadratic pattern

**C.15**Solve equations using a quadratic pattern

**C.16**Pascal's triangle

**C.17**Pascal's triangle and the Binomial Theorem

**C.18**Binomial Theorem I

**C.19**Binomial Theorem II

**Systems of inequalities**

**D.1**Solve systems of linear inequalities by graphing

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

**D.3**Find the vertices of a solution set

**D.4**Linear programming

**Nonlinear inequalities**

**E.1**Graph solutions to quadratic inequalities

**E.2**Solve quadratic inequalities

**E.3**Graph solutions to higher-degree inequalities

**E.4**Solve higher-degree inequalities

**Matrices**

**F.1**Matrix vocabulary

**F.2**Matrix operation rules

**F.3**Add and subtract matrices

**F.4**Multiply a matrix by a scalar

**F.5**Linear combinations of matrices

**F.6**Multiply two matrices

**F.7**Simplify matrix expressions

**F.8**Solve matrix equations

**F.9**Determinant of a matrix

**F.10**Is a matrix invertible?

**F.11**Inverse of a 2 x 2 matrix

**F.12**Inverse of a 3 x 3 matrix

**F.13**Identify inverse matrices

**F.14**Solve matrix equations using inverses

**Trigonometry**

**G.1**Convert between radians and degrees

**G.2**Radians and arc length

**G.3**Quadrants

**G.4**Coterminal and reference angles

**G.5**Find trigonometric ratios using right triangles

**G.6**Find trigonometric ratios using the unit circle

**G.7**Find trigonometric ratios using reference angles

**G.8**Inverses of trigonometric functions

**G.9**Solve trigonometric equations

**G.10**Trigonometric ratios: find a side length

**G.11**Trigonometric ratios: find an angle measure

**G.12**Solve a right triangle

**G.13**Law of Sines

**G.14**Law of Cosines

**G.15**Solve a triangle

**G.16**Area of a triangle: sine formula

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

**Trigonometric functions**

**H.1**Find properties of sine functions

**H.2**Write equations of sine functions from graphs

**H.3**Write equations of sine functions using properties

**H.4**Graph sine functions

**H.5**Find properties of cosine functions

**H.6**Write equations of cosine functions from graphs

**H.7**Write equations of cosine functions using properties

**H.8**Graph cosine functions

**H.9**Graph sine and cosine functions

**Trigonometric identities**

**I.1**Complementary angle identities

**I.2**Symmetry and periodicity of trigonometric functions

**I.3**Trigonometric identities I

**I.4**Trigonometric identities II

**Conic sections**

**J.1**Find properties of parabolas

**J.2**Write equations of parabolas in vertex form

**J.3**Graph parabolas

**J.4**Find properties of circles

**J.5**Write equations of circles in standard form

**J.6**Graph circles

**J.7**Find properties of ellipses

**J.8**Find the eccentricity of an ellipse

**J.9**Write equations of ellipses in standard form

**J.10**Find properties of hyperbolas

**J.11**Find the eccentricity of a hyperbola

**J.12**Write equations of hyperbolas in standard form

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

**Complex numbers**

**K.1**Add and subtract complex numbers

**K.2**Complex conjugates

**K.3**Multiply and divide complex numbers

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

**K.5**Absolute values of complex numbers

**K.6**Powers of i

**Argand plane**

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

**L.2**Graph complex numbers

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

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

**L.5**Graph complex conjugates

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

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

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

**Polar form**

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

**M.2**Convert complex numbers from rectangular to polar form

**M.3**Convert complex numbers from polar to rectangular form

**M.4**Convert complex numbers between rectangular and polar form

**M.5**Match polar equations and graphs

**Two-dimensional vectors**

**N.1**Find the magnitude of a vector

**N.2**Find the direction angle of a vector

**N.3**Find the component form of a vector

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

**N.5**Find a unit vector

**N.6**Add and subtract vectors

**N.7**Multiply a vector by a scalar

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

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

**N.10**Linear combinations of vectors

**N.11**Graph a resultant vector using the triangle method

**N.12**Graph a resultant vector using the parallelogram method

**Three-dimensional vectors**

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

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

**O.3**Find a three-dimensional unit vector

**O.4**Add and subtract three-dimensional vectors

**O.5**Scalar multiples of three-dimensional vectors

**O.6**Linear combinations of three-dimensional vectors

**Sequences and series**

**P.1**Find terms of a sequence

**P.2**Find terms of a recursive sequence

**P.3**Identify a sequence as explicit or recursive

**P.4**Find a recursive formula

**P.5**Find recursive and explicit formulas

**P.6**Convert a recursive formula to an explicit formula

**P.7**Convert an explicit formula to a recursive formula

**P.8**Convert between explicit and recursive formulas

**P.9**Introduction to sigma notation

**P.10**Identify arithmetic and geometric series

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

**P.12**Introduction to partial sums

**P.13**Partial sums of arithmetic series

**P.14**Partial sums of geometric series

**P.15**Partial sums: mixed review

**P.16**Convergent and divergent geometric series

**P.17**Find the value of an infinite geometric series

**P.18**Write a repeating decimal as a fraction

**Continuity**

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

**Q.2**Determine continuity using graphs

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

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

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

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

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

**Q.8**Intermediate Value Theorem

**Introduction to derivatives**

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

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

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

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

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

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

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

**Derivative rules**

**S.1**Sum and difference rules

**S.2**Product rule

**S.3**Quotient rule

**S.4**Power rule I

**S.5**Power rule II

**S.6**Chain rule

**S.7**Inverse function rule

**Calculate derivatives**

**T.1**Find derivatives of polynomials

**T.2**Find derivatives of rational functions

**T.3**Find derivatives of trigonometric functions I

**T.4**Find derivatives of trigonometric functions II

**T.5**Find derivatives of exponential functions

**T.6**Find derivatives of logarithmic functions

**T.7**Find derivatives of inverse trigonometric functions

**T.8**Find derivatives of radical functions

**T.9**Find derivatives using the product rule I

**T.10**Find derivatives using the product rule II

**T.11**Find derivatives using the quotient rule I

**T.12**Find derivatives using the quotient rule II

**T.13**Find derivatives using the chain rule I

**T.14**Find derivatives using the chain rule II

**Derivative strategies**

**U.1**Find derivatives using implicit differentiation

**U.2**Find tangent lines using implicit differentiation

**U.3**Find derivatives using logarithmic differentiation

**Calculate higher derivatives**

**V.1**Find higher derivatives of polynomials

**V.2**Find higher derivatives of rational and radical functions

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

**V.4**Find higher derivatives using patterns

**Probability**

**W.1**Introduction to probability

**W.2**Calculate probabilities of events

**W.3**Combinations and permutations

**W.4**Find probabilities using combinations and permutations

**W.5**Find probabilities using two-way frequency tables

**W.6**Identify independent events

**W.7**Find conditional probabilities

**W.8**Independence and conditional probability

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

**W.10**Find probabilities using the addition rule

**Probability distributions**

**X.1**Identify discrete and continuous random variables

**X.2**Write a discrete probability distribution

**X.3**Graph a discrete probability distribution

**X.4**Expected values of random variables

**X.5**Variance of random variables

**X.6**Standard deviation of random variables

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

**X.8**Expected values for a game of chance

**X.9**Choose the better bet

**X.10**Find probabilities using the binomial distribution

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

**X.12**Find probabilities using the normal distribution I

**X.13**Find probabilities using the normal distribution II

**X.14**Find z-values

**X.15**Find values of normal variables

**X.16**Distributions of sample means

**X.17**The Central Limit Theorem

**X.18**Use normal distributions to approximate binomial distributions

**Statistics**

**Y.1**Match correlation coefficients to scatter plots

**Y.2**Calculate correlation coefficients

**Y.3**Find the equation of a regression line

**Y.4**Interpret regression lines

**Y.5**Analyse a regression line of a data set

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

English

**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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