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Excel in NZ Year 10 Mathematics

Build a strong foundation for NCEA with our engaging video lessons. Master key concepts in number theory, algebra, geometry, and statistics to prepare for senior maths.

Start Your math Journey

Start with number systems to strengthen your foundation. This connects directly to working with polynomials and rational expressions. Geometry concepts build on these skills, leading to trigonometry. Probability and statistics tie everything together, showing real-world applications of core maths principles.

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Our proven video lessons are quick and concise, and our practice targets tricky exam questions.

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Maths is my weakest subject and I am always looking for help. One day, I came across StudyPug online and after I tried out the free maths lessons, I really liked it and signed up right away. Your lessons are very easy to understand even on some of the toughest questions. That's the maths help I have been looking for.

Isla Brown - Year 7 maths student, Hamilton, New Zealand

Year 10 Maths Topics

Number System and Radicals

Understanding the number systems

Prime factorisation

Greatest Common Factors (GCF)

Least Common Multiple (LCM)

Rational vs. Irrational numbers

Converting repeating decimals to fractions

Rational Numbers

Comparing and ordering rational numbers

Solving problems with rational numbers in decimal form

Solving problems with rational numbers in fraction form

Determine square roots of rational numbers

Ratios, Rates, and Proportions

Ratios

Rates

Proportions

Percents

Representing percents

Percents, fractions, and decimals

Percent of a number

Adding and multiplying percents

Taxes, discounts, tips and more

Simple interest

Finance: Compound interest

Pythagorean Theorem

Squares and square roots

Pythagorean theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

Volume

Introduction to volume

Volume of prisms

Volume of cylinders

Word problems relating volume of prisms and cylinders

Scale Factors and Similarity

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Solving Linear Equations

Solving linear equations using multiplication and division

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations with variables on both sides

Solving literal equations

Data and Graphs

Reading and drawing bar graphs

Reading and drawing histograms

Reading and drawing line graphs

Box-and-whisker plots and scatter plots

Stem-and-leaf plots

Pie charts

Reading and drawing Venn diagrams

Frequency tables and dot plots

Direct Variation

Identifying proportional relationships

Understanding graphs of proportional relationships

Understanding tables of values of proportional relationships

Applications of linear relationships

Introduction to Relations and Functions

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Linear Functions

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Midpoint formula: \(M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)\)

Gradient equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Gradient intercept form: y = mx + b

General form: Ax + By + C = 0

Gradient-point form: \(y - y_1 = m (x - x_1)\)

Rate of change

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from gradient-intercept form y=mx+b

Graphing linear functions using a single point and gradient

Word problems of graphing linear functions

Parallel and perpendicular lines in linear functions

Applications of linear relations

Linear Inequalities

Express linear inequalities graphically and algebraically

Solving one-step linear inequalities

Solving multi-step linear inequalities

Compound inequalities

Solving Simultaneous Equations

Determining number of solutions to linear equations

Solving simultaneous equations by graphing

Solving simultaneous equations by elimination

Solving simultaneous equations by substitution

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Exponents

Product rule of exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Negative exponent rule

Combining the exponent rules

Scientific notation

Convert between radicals and rational exponents

Solving for exponents

Introduction to Polynomials

Characteristics of polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

Operations of Polynomials

What is a polynomial?

Polynomial components

Multiplying monomial by monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Applications of polynomials

Factorising Polynomial Expressions

Common factors of polynomials

Factorising polynomials by grouping

Solving polynomials with the unknown "b" from x^2 + bx + c

Solving polynomials with the unknown "c" from x^2 + bx + c

Factorising polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

Solving polynomials with the unknown "b" from \(ax^2 + bx + c\)

Factorising polynomials: \(ax^2 + bx + c\)

Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Evaluating polynomials

Using algebra tiles to factorise polynomials

Solving polynomial equations

Word problems of polynomials

Radicals

Square and square roots

Cubic and cube roots

Evaluating and simplifying radicals

Converting radicals to mixed radicals

Converting radicals to entire radicals

Adding and subtracting radicals

Multiplying and dividing radicals

Rationalize the denominator

Algebraic Fractions

Simplifying algebraic fractions and restrictions

Adding and subtracting algebraic fractions

Multiplying algebraic fractions

Dividing algebraic fractions

Solving equations with algebraic fractions

Applications of equations with algebraic fractions

Simplifying complex fractions

Partial fraction decomposition

Statistics

Median and mode

Mean

Range and outliers

Application of averages

Probability

Determining probabilities using tree diagrams and tables

Probability of independent events

Probability with Venn diagrams

Reciprocal Functions

Graphing reciprocals of linear functions

Graphing reciprocals of quadratic functions

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