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YEAR 13
Math
English
Unlock 160+ Year 13 Math topics on Learndigo! Hover over a concept for a preview, then click to begin mastering advanced skills.
Functions
Learn - Functions
1.1 - Write the equation of a linear function
1.2 - Evaluate functions
1.3 - Add, subtract, multiply and divide functions
1.4 - Composition of functions
Learn - Inverse functions
1.5 - Identify inverse functions
1.6 - Find values using function graphs
1.7 - Complete a table for a function graph
1.8 - Find values of inverse functions from graphs
1.9 - Composition and inverse of Functions
Families of functions
Learn - Family of functions
2.1 - Reflections of functions
2.2 - Dilations of functions
2.3 - Transformations of functions
2.4 - Function transformation rules
2.5 - Translations of functions
2.6 - Functions questions
Polynomials
Learn - Polynomials
3.1 - Write a polynomial from its roots
3.2 - Find the roots of factorised polynomials
3.3 - Conjugate root theorems
Learn - Descartes' Rule of Signs
3.4 - Descartes' Rule of Signs
3.5 - Fundamental Theorem of Algebra
3.6 - Factorise using a quadratic pattern
3.7 - Complex conjugate theorem
3.8 - Factoring quadractic polynomials cases
Exponential and logarithmic functions
Learn - Logarithm
4.1 - Convert between exponential and logarithmic form
4.2 - Evaluate logarithms
4.3 - Product property of logarithms
4.4 - Quotient property of logarithms
4.5 - Power property of logarithms
4.6 - Evaluate logarithms using properties
4.7 - Solve logarithmic equations with one logarithm
4.8 - Exponential growth and decay: word problems
4.9 - Exercise on logarithms
4.10 - logarithmic equations
Learn - Logarithm Law
Radical functions
Learn - Radical equation
5.1 - Solve radical equations
Learn - Domain and Range
5.2 - Domain and range of radical functions
Learn - Linear Equation
5.3 - Linear equations
Learn - Method to solve Linear equations
5.4 - System of equations
Roots and rational exponents
Learn - Square roots
6.1 - Roots of integers
6.2 - Roots of rational numbers
6.3 - Find roots using a calculator
6.4 - Evaluate rational exponents
6.5 - Nth roots
6.6 Simplify radical expressions with variables
Learn - Division and Rationalization of Fraction
6.7 - Fractions of division
6.8 - Rationalizing the denominator
Trigonometric functions and identities
Learn - Complementary angles and Trigonometric Identities
7.1 - Complementary angle identities
Learn - Amplitude of Sinusoidal Functions
7.2 - Symmetry and periodicity of trigonometric functions
7.3 - Find properties of sine functions
7.4 - Find properties of cosine functions
7.5 - Find trigonometric functions using a calculator
Learn - Double and Half identities
7.6 - Half and double identities
Sequences and series
Learn - Sequence, Recursive and Explicit
8.1 - Find terms of a sequence
8.2 - Identify a sequence as explicit or recursive
Learn - Partial sum of series
8.3 - Introduction to partial sums
8.4 - Partial sums of arithmetic series
8.5 - Partial sums of geometric series
8.6 - Partial sums: mixed review
8.7 - Find terms of a recursive sequence
Probability
Learn - Sample space and probabilities
9.1 - Introduction to probability
9.2 - Calculate probabilities of events
Learn - Combinations and permutations
9.3 - Combinations and permutations
9.4 - Find probabilities using combinations and permutations
Learn - Addition for Probability
9.5 - Independence and conditional probability
9.6 - Find probabilities using the addition rule
9.7 - Probabilities of sum and difference rule
Probability distributions
Probability distributions
10.1 - Identify discrete and continuous random variables
Learn - Power Rule and derivation
10.2 - Power rule variables
Learn - Derivation by limit
10.3 - Derevatives using limits
Statistics
Learn - Biased Sample
11.1 - Identify biased samples
Learn - Variance and Standard Deviation
11.2 - Variance and standard deviation
Learn - Outlier
11.3 - Identify an outlier
11.4 - Identify an outlier and describe the effect of removing it
Learn - Correlation coefficient
11.5 - Calculate correlation coefficients
Learn - Regression
11.6 - Find the equation of a regression line
11.7 - Interpret regression lines
11.8 - Analyze a regression line of a data set
Learn - Remainder theorem
11.9 - Remainder theorem
Introduction to derivatives
Learn - Average rate of change
12.1 - Average rate of change I
12.2 - Average rate of change II
12.3 - Velocity as a rate of change
Derivative rules
Learn - Sum and difference rule
13.1 - Sum and difference rules
Learn - Product Rule
13.2 - Product rule
Learn - Power rule
13.3 - Power rule I
Learn - Inverse function
13.4 - Inverse function rule
13.5 - Power rule II
13.6 - Power rule problems
Derivative strategies
Learn - Implicit and Explicit
14.1 - Find derivatives using implicit differentiation
14.2 - Find tangent lines using implicit differentiation
Calculate derivatives
Learn - Derivation of polynomial
15.1 - Find derivatives of polynomials
Learn - Derivation of trigonometry
15.2 - Find derivatives of trigonometric functions I
15.3 - Find derivatives of trigonometric functions II
Learn - Derivation of exponential function
15.4 - Find derivatives of exponential functions
Learn - Derivation of Logarithmic Functions
15.5 - Find derivatives of logarithmic functions
15.6 - Find derivatives using the product rule
Learn - Derivation using product rule
15.7 - Find derivatives using the chain rule
Learn - Trigonometry
15.8 - Fundamental and Pythagorean identities
Rational functions
16.1 - Rational functions: asymptotes and excluded values
Learn - Rational equation
16.2 - Solve rational equations
Learn - Rationalizing the denominator
16.3 - Rationalizing the denominator
16.4 - Difference rule
Calculate higher derivatives
Learn - Second Derivation
17.1 - Find higher derivatives of polynomials
17.2 - Find higher derivatives of rational and radical functions
17.3 - Find second derivatives of trigonometric, exponential and logarithmic functions
17.4 - Find higher derivatives using patterns
17.5 - Multiplication and divison of polynomials
Quadratic functions
Learn - Quadratic equation
18.1 - Solve a quadratic equation using square roots
18.2 - Solve a quadratic equation by factorizing
18.3 - Solve a quadratic equation by completing the square
18.4 - Solve a quadratic equation using the quadratic formula
Learn - Discriminant formula
18.5 - Using the discriminant
Learn - Quadratic inequalities
18.6 - Quadratic inequalities
Volume and Area
Learn - Prism
19.1 - Volume and area of prism
Learn - Pyramid
19.2 - Area and volume of pyramid
Explore over 120, Year 13 English topics with Learndigo! Hover over each concept to preview, then click to begin mastering advanced lessons.
Sentence, Verb and Clause
Learn - Sentences
1.1 - Recognize sentence fragments
1.2 - Recognize run-on sentences
1.3 - Recognize type of sentence
1.4 - To avoid fragments and run-ons, use punctuation
Learn - Tenses
1.5 - Create progressive verb tense
1.6 - Create perfect verb tenses
Learn - Phrases and Clauses
1.7 - Phrase or clause?
1.8 - Use relative clauses to join sentences
1.9 - Recognize prepositional phrase
Pronouns
Learn - Relative Pronouns
2.1 - Put relative pronouns to use: who and whom
2.2 - Relative pronouns
Learn - Subject and Object Pronoun
2.3 - Review of subject and object pronouns
2.4 - Find and fix subject- and object-pronoun mistakes
Learn - Vague Pronoun Refrence and Antecedent
2.5 - Recognize vague pronoun references
2.6 - Determine every possible antecedent
2.7 - Correct inappropriate pronoun shifts
Verbs and verbals
Learn - Verbs
3.1 - Create progressive verb tenses
3.2 - Create perfect verb tenses
3.3 - Recognize transitive and intransitive verbs
Learn - Verbal
3.4 - Recognize gerunds
3.5 – Participles
Content Features
Learn - Adjectives and Adverbs
4.1 - Form and use comparative and superlative adjectives
4.2 - Good, better, best, bad, worse and worst
4.3 - Form and use comparative and superlative adverbs
4.4 - Well, better, best, badly, worse and worst
4.5 - Adjective vs Adverb I
4.6 - Adjective vs adverb II
Prefixes and suffixes
Learn - Analogy and Affixation
5.1 - Word pattern analogies
5.2 - Word pattern sentences
5.3 - Prefixes
5.4 - Suffixes
5.5 - Prefix vs Suffix
Etymologies and foreign expressions
Learn - Foreign Expression and Context Clues
6.1 - Use the correct foreign expression
6.2 - Use context as a clue to the meanings of foreign expressions
Learn - Etymology
6.3 - Use etymologies to determine the meanings of words
6.4 - Determine the meanings of words with Greek and Latin roots
6.5 - Determine the meanings of Greek and Latin roots
6.6 - Use Greek and Latin roots as clues to the meanings of words
6.7 - Sort words by sharing Greek or Latin roots
Word choice and usage
Learn - Usage of Word
7.1 - Distinction between related words
7.5 - Use words accurately and precisely
7.6 - Replace words using a thesaurus
7.7 - Use dictionary entries to determine correct usage
Learn - Connotation, Denotation, and Analogy
7.2 - Connotation
7.3 - Denotation
7.4 - Connotation and Denotation
7.8 - Analogies
7.9 - Analogies: challenge
Context clues
Learn - Context Clues
8.1 - Determine the meaning of words using synonyms in context
8.2 - Determine the meaning of words using antonyms in context
8.3 - Domain-specific vocabulary in context: science and technical subjects
8.4 - Use context to determine a word's meaning
8.5 - Use sentences to determine a word's meaning
Concise writing and modifiers
Learn - Modifiers and Parallel Structures
9.1 - Are the modifiers used correctly?
9.7 - Dangling modifier
9.2 - Use parallel structure
9.6 - Misplaced modifiers with pictures
9.3 - Identify sentences with parallel structure
Learn - Writing Concisely
9.4 - Avoid double, illogical and unclear comparisons
9.5 - Transitions with conjunctive adverbs
9.8 - Redundant words or phrases
Homophones and common errors
Learn - Homophones and How to Avoid Common Errors
10.1 - Use the correct homophone
10.2 - Identify and correct errors with homophone
10.3 - Use the correct frequently confused word
10.4 - Identify and correct errors with frequently confused words
10.5 - Identify and correct errors with frequently confused pronouns and contractions
10.6 - Correct errors with commonly misspelled words
10.7 - Misspelled words
10.8 - Misspelled phrases
Writing process
Learn - Writing Process
11.1 - Order topics from broadest to narrowest
11.2 - Choose the topic sentence that best captures the main idea
11.3 - Identify plagiarism
11.4 - Suggest appropriate revisions
Writing arguements
Learn - How to Avoid Writing Arguments
12.1 - Distinguish facts from opinions
12.2 - Choose evidence to support a claim
12.3 - Choose the most appropriate counterclaim for a given claim
12.4 - Choose the analysis that logically connects the evidence to the claim
12.5 - Identify supporting evidence in a text
12.6 - Stronger and weaker evidence to support a claim
Author's purpose and tone
Learn - Formal Text and Tone
13.1 - Which text is most formal?
13.5 - Subjective and Objective tone
Learn - Ethos, Logos, and Pathos
13.2 - Identify audience and purpose
13.3 - Use appeals to ethos, pathos and logos in persuasive writing
13.4 - Identify appeals to ethos, pathos and logos in advertisements
Literary devices
Learn - Allusion and Narrative Point of Veiw
14.2 - Interpret the meaning of an allusion from its source
14.3 - Recall the source of an allusion
14.1 - Identify the narrative point of view
Learn - Figure of Speech
14.4 - Interpret the figure of speech
14.5 - Classify the figure of speech: euphemism, hyperbole, oxymoron, paradox
14.6 - Classify the figure of speech: anaphora, antithesis, apostrophe, assonance, chiasmus, understatement
14.7 - Classify the figure of speech: review
Literature and informational text analysis
Learn - Analysis
15.1 - Short stories
15.2 - Poetry
15.3 - Non-fiction passages
15.4 - Main ideas or Themes
15.5 - Topic sentence