Welcome to our Maths National Exam! (Seniors)

What is our Maths National Exam? (Seniors)

Description

The NextGen Olympiad Mathematics National Exam is designed to challenge and inspire advanced mathematical minds through our prestigious international competition. Built on Australian curriculum standards, this exam offers senior students worldwide the opportunity to demonstrate their mathematical excellence and compete with peers globally at the highest academic level.

Our Mathematics National Exam features 25 carefully crafted multiple-choice questions designed to test advanced problem-solving skills, mathematical reasoning, and sophisticated curriculum knowledge appropriate for senior students. Students have 50 minutes to complete the exam, with questions covering complex mathematical concepts including algebra, calculus, statistics, and advanced applications that encourage critical thinking and analytical prowess.

Exam Format:

25 multiple-choice questions
50 minute duration
Australian curriculum-aligned Content
Multi-language support available
Secure National proctoring

Scoring System:

4 points for each correct answer
Maximum score: 100 points+-
-1 for every wrong answer

Global Round Qualification:

Anyone who scores 50% or above on the exam will qualify for our prestigious Global Round in Sydney, Australia (April 2026), featuring enhanced prizes, international recognition, and an unforgettable educational experience.

Important Information:

Exam Date: 24th October 2026
Registration Fee: $15 USD per student

Challenge yourself against the most talented mathematical students worldwide and showcase your advanced problem-solving abilities on the international stage!

The Levels it’s broken into

There are three categories of participation for our Senior Mathematics National Exam:

Category 4 – Ages 12-13 (Year 7-8)
Category 5 – Ages 14-15 (Year 9-10)
Category 6 – Ages 16-17 (Year 11-12)

Each category is specifically designed with increasingly sophisticated mathematical concepts, covering advanced topics such as functions, trigonometry, calculus, and statistical analysis while maintaining the intellectual rigor that prepares students for higher education and professional mathematical applications.

Senior Level 1 – Exam Topics

Year 7-8 (Senior Level 1)

Addition, Subtraction, Multiplication, and Division in Periodic Sequences
Algebraic Expressions and Solving Linear Equations
Solving Systems of Equations (2 Variables) using Substitution or Elimination
Function Tables, Value of Functions, and Simple Function Graphs
Number Patterns and Recursive Sequences
Clock and Calendar Problems Involving Time Gaps and Day Counting
Area, Perimeter of 2D Shapes and Surface Area & Volume of 3D Shapes
Applying Pythagorean Theorem to Solve Geometric Problems
Transformations and Coordinate Geometry (Reflections, Rotations, Translations)
Understanding and Applying Basic Trapezium and Triangle Area Properties
Magic Squares and Number Placement Logic
Representing and Interpreting Data Using Tables, Bar Graphs, Line Graphs
Probability Basics (Simple Events, Compound Events, Likelihood, Venn Diagrams)
Statistical Measures (Mean, Median, Mode, Range)

Senior Level 2 – Exam Topics

Year 9-10 (Senior Level 2)

Algebraic Expressions (including Algebraic Fractions, Absolute Value, and Radicals)
Solving Linear and Quadratic Equations, Inequalities, and Systems of Equations
Formulating and Solving Word Problems Using Equations
Time, Distance, and Speed Word Problems Involving Multi-Step Reasoning
Analysing and Continuing Number Patterns, Figure Patterns, and Algebraic Sequences
Evaluating the Value of Functions and Exploring Arithmetic & Geometric Sequences
Counting Principles: Rule of Product, Rule of Sum, and Simple Permutations/Combinations
Magic Squares and Numerical Arrangement Logic Problems
Angle Properties, and Area of Triangles, Quadrilaterals, Polygons, and Circles
Solving Problems Involving Congruent and Similar Triangles (Using Side/Angle Properties)
Coordinate Geometry Applications (Distance, Midpoint, Gradient, and Linear Graphs)
Representing Data Using Tables, Bar Graphs, Pie Charts, and Line Graphs
Analysing and Interpreting Data for Comparison and Decision Making
Probability with Simple and Compound Events (Including Venn Diagrams and Tree Diagrams)
Statistical Measures (Mean, Median, Mode, Range, and Outlier Identification)
Functional Reasoning and Graph Interpretation (Linear and Non-linear)
Challenging Logic and Elimination Problems with Multiple Constraints

Senior Level 3 – Exam Topics

Year 11-12 (Senior Level 3)

Exponents and Logarithms (Laws, Simplification, Equations, and Applications)
Solving Equations and Inequalities (Linear, Quadratic, Rational, Irrational, and Logarithmic)
Systems of Linear Equations (2 or 3 Variables – Substitution, Elimination, Matrix Methods)
Sequences and Series (Arithmetic, Geometric, Recursive, and Summation Problems)
Mathematical Induction and Proof by Contradiction (Introductory Level)
Word Problems Involving Equations, Age, Mixture, Investment, and Geometry
Rate Problems Involving Time, Distance, Speed with Multiple Constraints
Counting Principles and Combinatorics (Permutations, Combinations, Pascal’s Triangle)
Binomial Theorem and Coefficient Extraction
Vectors (2D/3D, Magnitude, Direction, Scalar Product, Application in Geometry)
Coordinate Geometry (Distance, Midpoint, Gradient, Intersection, Locus)
Trigonometry (Identities, Equations, Graphs, Sine and Cosine Rules, Circular Functions)
Applications of Trigonometry (Heights, Distances, Bearings, Area of Triangles)
Calculus – Differentiation and Integration (Basics, Applications to Rates and Area)
Congruence and Similarity Proofs (Triangles, Quadrilaterals, Circles)
Probability – Independent/Dependent Events, Conditional Probability, Tree/Venn Diagrams
Statistics – Mean, Median, Mode, Range, Standard Deviation, Boxplots, Normal Distribution
Advanced Logic Problems and Argument Structures (e.g., If–Then, Contrapositive, Logical Connectives)