What does Prep cover for Math Kangaroo?

Levels 1–2, Levels 3–4, Levels 5–6, Levels 7–8, Levels 9–10, Levels 11–12. Each Level has its own chapter map, practice rounds, sealed practice exams with every answer and worked solution at the end, and a published gate to the next Level.

When is the next Math Kangaroo date?

The next official date has not been announced yet. We update the page as soon as the organizer publishes it.

How much does it cost?

Each child's first round and its summary are free, with no card needed. After that, a Series pass is $14.99 a month for the whole family (up to 5 people) and covers every Level of the Series, so moving up never meets a new paywall.

Does Prep guarantee a score?

No. Prep shows exactly what your child has mastered, what comes next and when they are ready for the next Level. Nobody can promise a contest result.

Math Kangaroo — Levels 11–12

Grades 11–12. Original annual papers, answer keys and available worked solutions, organized by year. Timed paper practice and printable originals.

Grades:: Grades 11–12

Let my child try (free)

Series pass $14.99/month for the whole family · the first round and its summary are free, no card needed

Next official date

Date to be announced

Dates and formats come from the organizer (mathkangaroo.org). Prep is not affiliated with it; the contest name is used to describe what we help with.

What Levels 11–12 covers

Math Kangaroo Student (grades 11–12) is the hardest Kangaroo paper: short, clever multiple-choice problems in three point bands, leaning on algebra and functions, number theory, geometry in two and three dimensions, probability and logic. This map groups the skills those papers actually test.

Unit questions open after sign-in with a Series pass. Each child's first round is free, with its summary.

Arithmetic
Number sense, place value, fractions, ratios and percents used with care.
9 units
- Digits & Place Value — Place value, Digit sums & digit counting, Digit puzzles (reversals, rearrangements).
- Percent Change — Percent increase & decrease, Successive percent changes, Discounts & markups.
- Negative Numbers & Absolute Value — Operations with negatives, Absolute value, Number line & ordering.
- Percents — Percent of a number, Finding the whole from a percent, Percents ↔ fractions.
- Smart Calculation — Regrouping & friendly numbers, Distributive shortcuts, Estimation & rounding.
- Order of Operations & Powers — Order of operations, Powers with whole-number exponents, Nested brackets.
- Arithmetic in Context — Multi-step arithmetic word problems, Comparisons & differences, Working backwards.
- Fractions — Fraction of an amount, Adding & subtracting fractions, Multiplying & dividing fractions, Comparing & ordering fractions.
- Roots & Powers — Square roots, Perfect squares & cubes, Estimating roots.
Number Theory
Primes, divisibility, factors and remainders — the integer reasoning Kangaroo loves.
6 units
- Primes & Prime Factorization — Recognizing primes, Prime factorization, Prime puzzles.
- Divisibility & Digit Arguments — Divisibility rules, Digit arguments for divisibility, Parity & last digits.
- Counting Divisors — Counting divisors, Sums & products of divisors.
- Factors & Multiples — Factors & multiples, Factor pairs & products, Multiples in a range.
- Remainders & Modular Arithmetic — Remainders of a division, Common remainders (simultaneous conditions), Remainders of powers & cycles, Modular reasoning.
- GCD & LCM — Greatest common divisor, Least common multiple, GCD & LCM word problems.
Algebra
Expressions, equations, functions and sequences, set up from the situation.
13 units
- Exponents & Radicals — Exponent rules, Radicals & rational exponents, Exponential equations.
- Polynomials & Vieta — Polynomial arithmetic, Remainder & factor theorems, Vieta's formulas.
- Quadratic Equations — Factoring quadratics, Quadratic formula & discriminant, Quadratics in context, Sum & product of roots.
- Functions & Their Features — Evaluating functions, Domain & range, Composition & inverses.
- Systems of Equations — Two-variable systems, Substitution & elimination, Systems from word problems.
- Simplifying & Evaluating — Evaluating expressions, Simplifying & combining terms, Translating words to expressions.
- Inequalities — Solving inequalities, Inequalities in context.
- Word Problems with Algebra — Age problems, Work & rate problems, Mixture problems, Number relation problems.
- Trigonometry — Trig ratios, Identities & equations, Laws of sines & cosines.
- Linear Equations — One- and two-step equations, Multi-step equations, Equations from word problems.
- Function Transformations — Shifts & stretches, Even, odd & symmetry.
- Linear Functions & Lines — Slope & rate of change, Equation of a line, Reading graphs.
- Sequences & Series — Arithmetic sequences, Geometric sequences, Recursive sequences.
Geometry
Angles, triangles, circles, areas and solids, plus coordinates and transformations.
10 units
- Circles — Circumference & area, Arcs, sectors & central angles, Inscribed angles & chords, Tangents & power of a point.
- Solids & Spatial Reasoning — Recognizing & visualising solids, Painted cube & unit cubes, Views & cross-sections.
- Nets, Surface Area & Volume — Nets, Surface area, Volume.
- The Pythagorean Theorem — Pythagorean theorem, Pythagorean triples, Distances & diagonals.
- Coordinate Geometry — Coordinates & distance, Midpoint & slope, Area from coordinates.
- Triangles — Triangle inequality, Isosceles, equilateral & right triangles, Similar triangles, Area ratios in triangles.
- Angles & Polygons — Complementary, supplementary & vertical angles, Angles with parallel lines, Interior & exterior angles of polygons, Angle sum of a triangle.
- Geometric Transformations — Reflections & rotations, Translations & symmetry, Dilations.
- Composite Figures — Area of composite figures, Shaded regions, Figures on a grid.
- Perimeter & Area — Perimeter, Area of rectangles & squares, Area of triangles, Parallelograms & trapezoids.
Counting & Probability
Systematic counting, arrangements, probability and averages.
3 units
- Probability — Single-event probability, Compound events, Conditional probability, Expected value.
- Counting Integers in Ranges — Counting integers in a range, Counting with conditions.
- Combinations & Binomial Coefficients — Combinations, Binomial identities.
Logic & Patterns
Logic puzzles, cycles, patterns and clock problems that reward a clear head.
2 units
- Logic Puzzles — Truth-tellers & liars, Grid & elimination deduction, Ordering & ranking puzzles.
- Cycles & Repetition — Position in a repeating cycle, Last-digit cycles, Weekday & calendar cycles.
More topics
Further topics from the exam's official scope.
8 units

This is the top Level of the Series.

A sample question from Levels 11–12

Marbles numbered 1 to 2015 are coloured so that marbles with the same digit sum share a colour and different digit sums get different colours. How many colours are used on exactly one marble?

Answer: 1

Worked solution

Digit sums run from 1 to 28.
Digit sum 28 needs 1999 only (the other digits must be 9, 9, 9 after a leading 1): one marble.
Any sum s from 1 to 27 appears at least twice: once on a number below 1000 with digit sum s, and once on 1abc where abc has digit sum s − 1.
So exactly one colour appears on a single marble.

Read-only. Every other question opens after sign-in; each child's first round is free.

Questions families ask

What does Prep cover for Math Kangaroo?: Levels 1–2, Levels 3–4, Levels 5–6, Levels 7–8, Levels 9–10, Levels 11–12. Each Level has its own chapter map, practice rounds, sealed practice exams with every answer and worked solution at the end, and a published gate to the next Level.
When is the next Math Kangaroo date?: The next official date has not been announced yet. We update the page as soon as the organizer publishes it.
How much does it cost?: Each child's first round and its summary are free, with no card needed. After that, a Series pass is $14.99 a month for the whole family (up to 5 people) and covers every Level of the Series, so moving up never meets a new paywall.
Does Prep guarantee a score?: No. Prep shows exactly what your child has mastered, what comes next and when they are ready for the next Level. Nobody can promise a contest result.