#### Maths Year 13

studyif offers hundreds of year 13 maths skills to explore and learn! Not sure where to start? Go to your personalised Recommendations wall and choose a skill that looks interesting!

Functions
1.1 Write the equation of a linear function Quiz
1.2 Evaluate functions Quiz
1.3 Add, subtract, multiply and divide functions Quiz
1.4 Composition of functions Quiz
1.5 Identify inverse functions Quiz
1.6 Find values using function graphs Quiz
1.7 Complete a table for a function graph Quiz
1.8 Find values of inverse functions from graphs Quiz

Families of functions
2.1 Reflections of functions Quiz
2.2 Dilations of functions Quiz
2.3 Transformations of functions Quiz
2.4 Function transformation rules Quiz
2.5 Translations of functions Quiz

Polynomials
3.1 Write a polynomial from its roots Quiz
3.2 Find the roots of factorised polynomials Quiz
3.3 Conjugate root theorems Quiz
3.4 Descartes’ Rule of Signs Quiz
3.5 Fundamental Theorem of Algebra Quiz
3.6 Factorise using a quadratic pattern Quiz
3.7 Complex conjugate theorem Quiz

Exponential and logarithmic functions
4.1 Convert between exponential and logarithmic form Quiz
4.2 Evaluate logarithms Quiz
4.3 Product property of logarithms Quiz
4.4 Quotient property of logarithms Quiz
4.5 Power property of logarithms Quiz
4.6 Evaluate logarithms using properties Quiz
4.7 Solve logarithmic equations with one logarithm Quiz
4.8 Exponential growth and decay: word problems Quiz

5.2 Domain and range of radical functions Quiz

Roots and rational exponents
6.1 Roots of integers Quiz
6.2 Roots of rational numbers Quiz
6.3 Find roots using a calculator Quiz
6.4 Evaluate rational exponents Quiz
6.5 Nth roots Quiz
6.6 Simplify radical expressions with variables Quiz

Trigonometric functions and identities
7.1 Complementary angle identities Quiz
7.2 Symmetry and periodicity of trigonometric functions Quiz
7.3 Find properties of sine functions Quiz
7.4 Find properties of cosine functions Quiz
7.5 Find trigonometric functions using a calculator Quiz

Sequences and series
8.1 Find terms of a sequence Quiz
8.2 Identify a sequence as explicit or recursive Quiz
8.3 Introduction to partial sums Quiz
8.4 Partial sums of arithmetic series Quiz
8.5 Partial sums of geometric series Quiz
8.6 Partial sums: mixed review Quiz
8.7 Find terms of a recursive sequence Quiz

Probability
9.1 Introduction to probability Quiz
9.2 Calculate probabilities of events Quiz
9.3 Combinations and permutations Quiz
9.4 Find probabilities using combinations and permutations Quiz
9.5 Independence and conditional probability Quiz
9.6 Find probabilities using the addition rule Quiz

Probability distributions
10.1 Identify discrete and continuous random variables Quiz

Statistics
11.1 Identify biased samples Quiz
11.2 Variance and standard deviation Quiz
11.3 Identify an outlier Quiz
11.4 Identify an outlier and describe the effect of removing it Quiz
11.5 Calculate correlation coefficients Quiz
11.6 Find the equation of a regression line Quiz
11.7 Interpret regression lines Quiz
11.8 Analyse a regression line of a data set Quiz

Introduction to derivatives
12.1 Average rate of change I Quiz
12.2 Average rate of change II Quiz
12.3 Velocity as a rate of change Quiz

Derivative rules
13.1 Sum and difference rules Quiz
13.2 Product rule Quiz
13.3 Power rule I Quiz
13.4 Inverse function rule Quiz
13.5 Power rule II Quiz

Derivative strategies
14.1 Find derivatives using implicit differentiation Quiz
14.2 Find tangent lines using implicit differentiation Quiz

Calculate derivatives
15.1 Find derivatives of polynomials Quiz
15.2 Find derivatives of trigonometric functions I Quiz
15.3 Find derivatives of trigonometric functions II Quiz
15.4 Find derivatives of exponential functions Quiz
15.5 Find derivatives of logarithmic functions Quiz
15.6 Find derivatives using the product rule Quiz
15.7 Find derivatives using the chain rule Quiz

Rational functions
16.1 Rational functions: asymptotes and excluded values Quiz
16.2 Solve rational equations Quiz

Calculate higher derivatives
17.1 Find higher derivatives of polynomials Quiz
17.2 Find higher derivatives of rational and radical functions Quiz
17.3 Find second derivatives of trigonometric, exponential and logarithmic functions Quiz
17.4 Find higher derivatives using patterns Quiz

18.1 Solve a quadratic equation using square roots Quiz
18.2 Solve a quadratic equation by factorising Quiz
18.3 Solve a quadratic equation by completing the square Quiz
18.5 Using the discriminant Quiz

#### English Year 13

studyif offers more than 100 year 13 English skills to explore and learn! Not sure where to start? Hover your mouse over any skill name to preview it, then click to practise!

Sentence structure
1.1 Identify sentence fragments Quiz
1.2 Identify run-on sentences Quiz
1.3 Choose punctuation to avoid fragments and run-ons Quiz
1.4 Form the progressive verb tense Quiz
1.5 Is it a phrase or a clause? Quiz
1.6 Is the sentence simple, compound, complex or compound-complex? Quiz
1.7 Combine sentences using relative clauses Quiz

Pronouns
2.1 Use relative pronouns: who and whom Quiz
2.2 Use relative pronouns: who, whom, whose, which and that Quiz
2.3 Identify vague pronoun references Quiz
2.4 Identify and correct errors with subject and object pronouns Quiz
2.5 Subject and object pronouns review Quiz

Verbs and verbals
3.1 Form the progressive verb tenses Quiz
3.2 Form the perfect verb tenses Quiz
3.3 Identify transitive and intransitive verbs Quiz

4.1 Form and use comparative and superlative adjectives Quiz
4.2 Good, better, best, bad, worse and worst Quiz
4.3 Form and use comparative and superlative adverbs Quiz
4.4 Well, better, best, badly, worse and worst Quiz

Prefixes and suffixes
5.1 Word pattern analogies Quiz
5.2 Word pattern sentences Quiz
5.3 Prefixes Quiz
5.4 Suffixes Quiz

Etymologies and foreign expressions
6.1 Use the correct foreign expression Quiz
6.2 Use context as a clue to the meanings of foreign expressions Quiz
6.3 Use etymologies to determine the meanings of words Quiz
6.4 Determine the meanings of words with Greek and Latin roots Quiz
6.5 Determine the meanings of Greek and Latin roots Quiz
6.6 Use Greek and Latin roots as clues to the meanings of words Quiz

Word choice and usage
7.1 Describe the difference between related words Quiz
7.2 Choose the word whose connotation and denotation best match the sentence Quiz
7.3 Use words accurately and precisely Quiz
7.4 Replace words using a thesaurus Quiz
7.5 Use dictionary entries to determine correct usage Quiz
7.6 Analogies Quiz
7.7 Analogies: challenge Quiz

Context clues
8.1 Determine the meaning of words using synonyms in context Quiz
8.2 Determine the meaning of words using antonyms in contex Quiz
8..3 Domain-specific vocabulary in context: science and technical subjects Quiz

Writing clear and concise sentences
9.1 Are the modifiers used correctly? Quiz
9.2 Use parallel structure Quiz
9.3 Identify sentences with parallel structure Quiz
19.4 Avoid double, illogical and unclear comparisons Quiz
9.5 Transitions with conjunctive adverbs Quiz
9.6 Misplaced modifiers with pictures Quiz

Common errors
10.1 Use the correct homophone Quiz
10.2 Identify and correct errors with homophone Quiz
10.3 Use the correct frequently confused word Quiz
10.4 Identify and correct errors with frequently confused words Quiz
10.5 Identify and correct errors with frequently confused pronouns and contractions Quiz
10.6 Correct errors with commonly misspelled words Quiz

Writing process
11.1 Order topics from broadest to narrowest Quiz
11.2 Choose the topic sentence that best captures the main idea Quiz
11.3 Identify plagiarism Quiz
11.4 Suggest appropriate revisions Quiz

Writing arguements
12.1 Distinguish facts from opinions Quiz
12.2 Choose evidence to support a claim Quiz
12.3 Choose the most appropriate counterclaim for a given claim Quiz
12.4 Choose the analysis that logically connects the evidence to the claim Quiz
12.5 Identify supporting evidence in a text Quiz

Author’s purpose and tone
13.1 Which text is most formal? Quiz
13.2 Identify audience and purpose Quiz
13.3 Use appeals to ethos, pathos and logos in persuasive writing Quiz