YEAR 12

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Equations

Inequalities

Learn - Inequalities
2.1 - Inequalities from graphs
2.2 - Linear inequality: word problems
2.3 - Linear inequalities
2.4 - Absolute value inequalities
2.5 - Quadratic functions
2.6 - Inequalities practical problems
2.7 - Review on Inequalities

Functions

Learn - Function and Graph
3.1 - Identifying functions
3.2 - Evaluating functions
3.3 - Find values using function graphs
3.4 - Complete a table for a function graph
Learn - Linear Functions and Domain
3.5 - Finding the gradient of a linear function
3.6 - Write linear equations in point-gradient form
3.7 - Write linear equations in standard form
3.8 - Domain and range

Simultaneous equations

Learn - Simultaneous equations and Non - linear
4.1 - Is (x, y) a solution to the simultaneous equations?
4.2 - Solving non-linear simultaneous equations
Learn - Types of Simultaneous equations
4.3 - Evaluating simultaneous equations using substitution: word problems
4.4 - Evaluating simultaneous equations using elimination
4.5 - Evaluating simultaneous equations using any method
4.6 - Evaluating simultaneous equations using substitution
4.7 - Word problems
4.8 - Simultaneous equations revision

Factorising

Learn - Factorize of monomial and polynomials
5.1 - Factorizing out a monomial
5.2 - Factorizing polynomials
5.3 - Evaluating polynomials
Learn - Factorization of quadratic equations
5.4 - Factorizing quadratics
5.5 - Factories using a quadratic pattern
5.6 - Factorizing by grouping
5.7 - Factorizing sums and differences of cubes
5.8 - Find the missing values

Polynomials

Learn - Polynomial
6.1 - Polynomial vocabulary
6.2 - Add and subtract polynomials
6.3 - Multiply polynomials
6.4 - Write a polynomial from its roots
6.5 - Find the roots of factorized polynomials
Learn - Fundamental theorem of Algebra and Descartes’s rule of sings
6.6 - Fundamental Theorem of Algebra
6.7 - Descartes' Rule of Signs

Radical functions and expressions

Learn - Roots of integers and Radical expression
7.1 - Roots of integers
7.2 - Find roots using a calculator
7.3 - Nth roots
7.4 - Simplify radical expressions with variables
7.5 - Solve radical equations
7.6 - Add and subtract radical expressions
7.7 - Simplify radical expressions using the distributive property

Sequences and series

Learn - Recursive and Geometric sequence
8.1 - Find terms of a geometric sequence
8.2 - Partial sums of geometric series
8.3 - Find terms of a recursive sequence
Learn - Arithmetic sequence
8.4 - Find terms of an arithmetic sequence
8.5 - Evaluate formulas for sequences
8.6 - Write a formula for an arithmetic sequence
8.7 - Introduction to partial sums
8.8 - Partial sums of arithmetic series

Probability

Learn - Factorials
9.1 - Factorials
Learn - Probability
9.2 - Introduction to probability
9.3 - Theoretical and experimental probability
9.4 - Calculate probabilities of events
9.5 - Permutations
9.6 - Counting principle
9.7 - Probability questions review
9.8 - Correct or incorrect 3 digits

Statistics

Learn - Mean, Mode, Range and Medain
10.1 - Mean, median, mode and range
10.2 - Mean absolute deviation
10.3 - Mean, Median and Mode review
Learn - Quartiles
10.4 - Quartiles
10.5 - Identify biased samples
10.6 - Variance and standard deviation
10.7 - Quartiles practice questions

Introduction to derivatives

Learn - Average rate of change
11.1 - Average rate of change I
11.2 - Average rate of change II
11.3 -Velocity as a rate of change
Learn - Power rule
11.4 - Solving power rule
11.5 - Power rule I
11.6 - Power rule II
Learn - Polynomial
11.7 - Find derivatives of polynomials
11.8 - Find second derivatives of polynomials
11.9 - Substitution and elimination method

Exponential and logarithmic functions

Learn - Exponential function
12.1 -Evaluate exponential functions
12.2 - Solve exponential equations by factorizing
12.3 - Solve exponential equations using common logarithms.
12.4 - Exponential growth and decay: word problems.
Learn - Logarithmic functions
12.5 - Solve logarithmic equations I.
12.6 - Solve logarithmic equations II.
12.7 - Advance logarithm questions
12.8 - Laws of logarithm

Parabolas

Function operations

Learn - Function
14.1 - Add and subtract functions.
14.2 - Multiply functions.
14.3 - Divide functions.
14.4 - Composition of linear functions: find a value.
14.5 - Composition of linear functions: find an equation.
14.6 - Composition of linear and quadratic functions: find a value.
Learn - Inverse
14.7 - Identify inverse functions.
14.8 - Inverse and composition functions

Logarithms

Learn - Logarithm
15.1 - Convert between exponential and logarithmic form: rational bases.
15.2 - Evaluate logarithms.
15.3 - Product property of logarithms.
15.4 - Power property of logarithms.
15.5 - Quotient property of logarithms.
15.6 - Properties of logarithms: mixed review.
15.7 - Evaluate logarithms: mixed review.

Trigonometry

Learn - Inverse trigonometric functions
16.1 - Inverses of sin, cos and tan.
16.2 - Inverses of csc, sec and cot.
16.3 - Find trigonometric functions using a calculator.
16.4 - Solve a triangle.
16.5 - Trigonometric ratios: sin, cos and tan
16.6 - Trigonometric ratios: csc, sec and cot.
Learn - Pythagoras theorem
16.7 - Pythagoras' Theorem and its converse.
16.8 - Pythagoras theorem problems

Trigonometric functions and identities

Learn - Trigonometric functions
17.1 - Find properties of sine functions
17.2 - Find properties of cosine functions
17.3 - Complementary angle identities
17.4 - Symmetry and periodicity of trigonometric functions
17.5 - Trigonometric problems
17.6 - Half, double, quotient identities

Circles

Learn - Central and Inscribed angle
18.1 - Central angles
18.2 - Inscribed angles
18.3 - Angles in inscribed quadrilaterals
18.4 - Angles in inscribed right triangles
18.5 - Find the center of a circle
18.6 - Find the radius or diameter of a circle
18.7 - Convert equations of circles from general to standard form
18.8 - Find properties of circles from equations in general form
Learn - Area sector of a circle
18.9 - Area of a circular sector
18.10 - Circumference and diameter of circle

Continuity

Learn - Continuity
19.1 - Identify graphs of continuous functions
19.2 - Determine continuity using graphs
19.3 - Determine continuity on an interval using graphs
19.4 - Find and analyses points of discontinuity using graphs
19.5 - Determine one-sided continuity using graphs
19.6 - Continuous Function

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Sentence, Phrase and Clause

Learn - Formation of Sentences
1.1 - Sentence, fragments and run-on sentences
1.2 - To avoid fragments and run-ons, use punctuation
1.3 - Types of sentences
Learn - Phrases and Clauses
1.4 - Phrase or clause
1.5 - Prepositional phrases
1.6 - Appositives and appositive phrases
Learn - Formation of Clauses
1.7 - Dependent and independent clauses
1.8 - Relative Clauses
1.9 - Use relative clauses to join sentences

Pronouns and Verbs

Learn - Identification of Pronouns
2.1 - Subject and object pronouns
2.2 - Pronouns following "Than and As"
2.3 - Antecedent pronouns
2.4 - Pronoun reference
2.5 - Relative pronouns
2.6 - Use relative pronouns: who, whom, whose, which and that
Learn - Verb Tenses
2.7 - Perfect Verb Tense
2.8 - Create progressive verb tense
2.9 - Recognize and correct verb tense changes

Verbs and verbals

Learn - Verbs, Predicate Adjectives, and Nouns
3.1 - Transitive and intransitive verbs
3.2 - Linking verbs, predicate adjectives and predicate nouns
Learn - Types of Verb and Phrases
3.6 - Progressive Tense
3.9 - Create perfect verb tenses
3.7 - Infinitive phrases
Learn - Subject-Verb Agreement
3.3 - Recognize and correct errors in subject-verb agreement
3.4 - Verb agreement with compound subjects
3.5 - Inappropriate shifts in verb tense
3.8 - Indefinite pronoun-verb agreement
Learn - Active and Passive Voice
3.10 - Passive voice
3.11 - Active voice

Adjectives and adverbs

Learn - Adjectives
4.1 - Comparative and superlative adjectives
4.2 - Good, better, best, bad, worse and worst
Learn - Adverbs
4.3 - Comparative and superlative adverbs
4.4 - Well, better, best, badly, worse and worst
4.5 - Adverbial forms
4.6 - Adjective order

Punctuation and Interjection

Learn - Punctuation
5.1 - Commas in direct address
5.7 - Parentheses, quotation and question marks
Learn - Interjection
5.3 - Interjection
5.5 - Interjection types
Learn - Introductory Elements and Absolute Phrase
5.2 - Introductory Elements
5.4 - Absolute Phrase

Affixation and Analogy

Etymology and Foreign expressions

Learn - Etymology
7.1 - Etymology
7.2 - Greek roots
7.3 - Latin roots
7.4 - Meaning of words with Greek and Latin roots
7.5 - Greek and Latin Roots
7.6 - Use words as clues to the meanings of Greek and Latin roots
Learn - Foreign Expression
7.7 - Foreign Policy
7.8 - Meaning of foreign expressions
7.9 - Use context as a clue to the meanings of foreign expressions

Word usage, analogy and homophones

Learn - Usage of Dictionary and Literary Devices
8.2 - Denotation and Connotation
8.4 - Using a Dictionary/Thesaurus
8.3 - Accurately and precisely
Learn - Analogies and Homophones
8.5 - Analogies
8.6 - Analogies: challenge
8.7 - Homophones I
8.8 - Homophones II
8.1 - Distinction between related words

Context clues

Writing clear and concise sentences

Learn - Writing Clearly and Concisely
10.1 - Conjunctive Adverbs
10.7 - Correlative Conjunctions
10.2 - Transitions
10.8 - Concise sentence
Learn - Comparisons and Modifiers
10.3 - Double comparison
10.4 - Unclear comparisons
10.5 - Misplaced modifiers
10.6 - Dangling Modifiers

Common errors

Writing process

Writing arguments

Author's purpose and tone

Learn - Author's tone
14.1 - Formal text
14.2 - Tone
14.3 - Audience
14.5 - Subjective and Objective tone
Learn - Ethos, Logos, and Pathos
14.4 - Ethos, Logos, Pathos
Learn - Figure of Speech
14.6 - Figure of speech