Master Year 13 Maths Online
Practice calculus, algebra, and statistics with step-by-step video lessons and worked examples
Photo Search
Snap any maths problem to find matching video lessons
Expert Video Solutions
Master calculus, algebra, and stats step-by-step
Adaptive Practice
Complete NCEA Level 3 topic practice
Try It Now
Test your knowledge
Our approach aligns with the evidence
+13-25%
Exam Scores
2x
Better Recall
25%
Less Anxiety
Year 13 Maths Topics
Topic includes:
Practice
Video
Quiz
950+ students practicing now
1. Functions
1.1 Function notation
1.2 Operations with functions
1.3 Adding functions
1.4 Subtracting functions
1.5 Multiplying functions
1.6 Dividing functions
1.7 Composite functions
1.8 Inequalities of combined functions
1.9 Inverse functions
1.10 One to one functions
1.11 Difference quotient: applications of functions
2. Transformations of Functions
2.1 Transformations of functions: Horizontal translations
2.2 Transformations of functions: Vertical translations
2.3 Reflection across the y-axis: y = f(-x)
2.4 Reflection across the x-axis: y = -f(x)
2.5 Transformations of functions: Horizontal stretches
2.6 Transformations of functions: Vertical stretches
2.7 Combining transformations of functions
2.8 Even and odd functions
3. Quadratic Functions
3.1 Characteristics of quadratic functions
3.2 Transformations of quadratic functions
3.3 Quadratic function in general form: y = ax^2 + bx + c
3.4 Quadratic function in vertex form: y = a(x-p)^2 + q
3.5 Completing the square
3.6 Converting from general to vertex form by completing the square
3.7 Shortcut: Vertex formula
3.8 Graphing parabolas for given quadratic functions
3.9 Finding the quadratic functions for given parabolas
3.10 Applications of quadratic functions
4. Polynomial Functions
4.1 What is a polynomial function?
4.2 Polynomial long division
4.3 Polynomial synthetic division
4.4 Remainder theorem
4.5 Factor theorem
4.6 Rational zero theorem
4.7 Characteristics of polynomial graphs
4.8 Multiplicities of polynomials
4.9 Imaginary zeros of polynomials
4.10 Determining the equation of a polynomial function
4.11 Applications of polynomial functions
4.12 Solving polynomial inequalities
4.13 Fundamental theorem of algebra
4.14 Descartes' rule of signs
5. Rational Functions
6. Exponential Functions
6.1 Exponents: Product rule (a^x)(a^y) = a^(x+y)
6.2 Exponents: Division rule (a^x / a^y) = a^(x-y)
6.3 Exponents: Power rule (a^x)^y = a^(x * y)
6.4 Exponents: Negative exponents
6.5 Exponents: Zero exponent: a^0 = 1
6.6 Exponents: Rational exponents
6.7 Graphing exponential functions
6.8 Graphing transformations of exponential functions
6.9 Finding an exponential function given its graph
7. Logarithmic Functions
7.1 What is a logarithm?
7.2 Converting from logarithmic form to exponential form
7.3 Evaluating logarithms without a calculator
7.4 Common logarithms
7.5 Natural log: ln
7.6 Evaluating logarithms using change-of-base formula
7.7 Converting from exponential form to logarithmic form
7.8 Solving exponential equations with logarithms
7.9 Product rule of logarithms
7.10 Quotient rule of logarithms
7.11 Combining product rule and quotient rule in logarithms
7.12 Evaluating logarithms using logarithm rules
7.13 Solving logarithmic equations
7.14 Graphing logarithmic functions
7.15 Finding a logarithmic function given its graph
8. Applications of Exponential and Logarithmic Functions
8.1 Exponential growth and decay by a factor
8.2 Exponential decay: Half-life
8.3 Exponential growth and decay by percentage
8.4 Finance: Compound interest
8.5 Continuous growth and decay
8.6 Logarithmic scale: Richter scale (earthquake)
8.7 Logarithmic scale: pH scale
8.8 Logarithmic scale: dB scale
8.9 Finance: Future value and present value
9. Quadratic Equations and Inequalities
10. Solving Simultaneous Equations
10.1 Determining number of solutions to linear equations
10.2 Solving simultaneous equations by graphing
10.3 Solving simultaneous equations by elimination
10.4 Solving simultaneous equations by substitution
10.5 Money related questions in linear equations
10.6 Unknown number related questions in linear equations
10.7 Distance and time related questions in linear equations
10.8 Rectangular shape related questions in linear equations
11. Simultaneous Equations (Advanced)
11.1 Simultaneous linear equations
11.2 Simultaneous linear-quadratic equations
11.3 Simultaneous quadratic-quadratic equations
11.4 Solving 3 variable simultaneous equations by substitution
11.5 Solving 3 variable simultaneous equations by elimination
11.6 Solving 3 variable simultaneous equations with no or infinite solutions
11.7 Word problems relating 3 variable simultaneous equations
12. Introduction to Trigonometry
12.1 Use sine ratio to calculate angles and sides (Sin = )
12.2 Use cosine ratio to calculate angles and sides (Cos = )
12.3 Use tangent ratio to calculate angles and sides (Tan = )
12.4 Combination of SohCahToa questions
12.5 Solving expressions using 45-45-90 special right triangles
12.6 Solving expressions using 30-60-90 special right triangles
12.7 Word problems relating ladder in trigonometry
12.8 Word problems relating guy wire in trigonometry
12.9 Other word problems relating angles in trigonometry
13. Trigonometric Ratios and Angle Measure
14. Bearings
15. Graphing Trigonometric Functions
16. Trigonometric Identities
18. Imaginary and Complex Numbers
18.1 Introduction to imaginary numbers
18.2 Complex numbers and complex planes
18.3 Adding and subtracting complex numbers
18.4 Complex conjugates
18.5 Multiplying and dividing complex numbers
18.6 Distance and midpoint of complex numbers
18.7 Angle and absolute value of complex numbers
18.8 Polar form of complex numbers
18.9 Operations on complex numbers in polar form
19. Sequences and Series
20. Probability
22. Limits
22.1 Finding limits from graphs
22.2 Continuity
22.3 Finding limits algebraically - direct substitution
22.4 Finding limits algebraically - when direct substitution is not possible
22.5 Infinite limits - vertical asymptotes
22.6 Limits at infinity - horizontal asymptotes
22.7 Intermediate value theorem
22.8 Squeeze theorem
23. Derivatives
23.1 Definition of derivative
23.2 Power rule
23.3 Gradient and equation of tangent line
23.4 Chain rule
23.5 Derivative of trigonometric functions
23.6 Derivative of exponential functions
23.7 Product rule
23.8 Quotient rule
23.9 Implicit differentiation
23.10 Derivative of inverse trigonometric functions
23.11 Derivative of logarithmic functions
23.12 Higher order derivatives
Discover Our Learning Areas
Explore key subjects and start learning with interactive content.
Year 13 Maths FAQ
Unsure how StudyPug works? Need help with setting up? Check our frequently asked questions or contact us for help.
Can I sign up free to try it?
Yes — sign up free for sample lessons. Subscribe when you're ready, with a 30-day money-back guarantee.
How much does it cost?
Plans start with one low monthly payment, with annual options for the best value. One plan covers up to 5 children and all subjects. 30-day money-back guarantee. [See all plans →]
What's included in my StudyPug subscription?
Full access to step-by-step video lessons, diagnostic assessments, adaptive practice, Photo Search, and detailed progress tracking across all Year 13 Maths topics.
Can I cancel my subscription anytime?
Yes, you can cancel anytime. There are no contracts or cancellation fees. Your access continues until your billing period ends.
How quickly can I improve in Year 13 Maths?
Most students see better understanding within the first week. With consistent practice, expect significant improvement in NCEA assessments within 2-4 weeks.
Does this cover all NCEA Level 3 Maths standards?
Yes! Our content covers all major NCEA Level 3 Mathematics standards including Calculus, Algebra, Statistics, and Probability topics.
