Mathematical Kangaroo

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Math Kangaroo is an international mathematical competition for students in grades 1 through 12. The competition consists of a single round that is taken on the same date (third Thursday of March) at a registered center. Awards are given to the top scoring students per grade at the national level. High scoring students in the US that are ranked high within their state will also be awarded as a state winner.


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Registration and Eligibility

Any student that is currently enrolled in grades 1 through 12 (or homeschooled equivalent) is eligible to participate. They must register to a center several months prior to the testing date and pay a small participation fee. After the registration deadline students may still compete, but the fee increases and does not guarantee a spot. Students must take the contest at the registered center. The center they register does not have to be in their home state or country, so competitors often register for a testing site that is the closest or most convenient for them despite being outside of the state.

Competitors will automatically be placed in a specific level according to their grades. For example, someone in grade 5 will be placed in level 5.

Problem Format, Scoring, and Rules


The test is 75 minutes long and consists of a series of multiple choice questions. Level 1 and 2 competitors will take the same test, level 3 and 4 students will take their test (which is distinct from levels 1 and 2’s test), and similarly, up to levels 11 and 12. Levels 1 through 4 tests is made up of 24 problems, each multiple choice with 5 possible answer choices. The remaining levels have tests with 30 problems, each multiple choice with 5 possible answer choices.


Not all problems are worth the same number of points. Each question within first third of the problems is worth 3 points, each problem within the second one-third of the test is worth 4 points, and the remaining problems are worth 5 points. No penalty or partial credit is given to unanswered or incorrectly answered questions, so it will be to the student’s advantage to guess questions he or she cannot solve. Thus, the maximum score a student can score is $8\times3+8\times4+8\times5=96$ points for levels 1 through 4, and $10\times3+10\times4+10\times5=120$ points for levels 5 through 12.


There are 75 minutes is given to solve all problems, each with exactly 5 answer choices. No problems require the use of a calculator, and calculators of all types are prohibited. Calculations may be done on scratch paper, which is provided by the testing center. However, only one sheet of scratch paper is given, so it is important for competitors to ask for more as they are used up. Some testing centers may allow students to use their own scratch paper, as long as they do not contain any markings (so graph paper and lined papers are not allowed). Other aids may not be used, particularly a ruler, compass, or protractor.

Incorrect Problems

Occasionally a problem may be incorrect. Under such circumstances, the problem is voided and all competitors receive credit.

Problem Content and Difficulty

A variety of problems are used in levels 7 through 12. The majority of the problems are algebra or geometry. Math Kangaroo puts a special emphasis on three-dimensional geometry, which are usually not seen on many other competitions. Problems in discrete mathematics (number theory and counting and probability) are occasionally used, but in a lower proportion when compared to other mathematical competitions. A few logic and physics questions may also appear. None of the problems require the use of precalculus concepts (logs, summations, complex numbers) or trigonometry. Similarly, there are no calculus problems.

The tests are divided into three parts. The first third are easy, one-step problems involving little thinking. These are the routine, standard problems that are commonly seen in the mainstream mathematical curriculum offered in most schools. The second third of the problems are more difficult. The require moderate thinking and creativity in problem solving outside of standard math classes. The final third are the most difficult problems. These are typically multi-step problems at a much higher level than the school curriculum.

While most problems in the first section are roughly identical in terms of difficulty, and similarly, the problems in the second section are about the same difficulty, problems in the third section are arranged in order, with the last few problems especially challenging.


Past sets may be ordered from the US Math Kangaroo website. The Canadian and International (primarily used in Europe) websites have released their problems from past years. The various versions differ from each other in terms of names and grammar usage. Most problems remain identical, though there are usually a few problems that are different.

Another way to prepare is to use past AMC problems, especially for levels 9-12, since the AMC 10/12 and level 9-12 Math Kangaroo both are 75 minutes, multiple choice with 5 answer choices each, no calculator, and contains roughly the same number of problems. However, the last few problems on the AMC are comparatively much more challenging than 5 point Math Kangaroo problems. Level 11/12 Math Kangaroo does not have precalculus concepts (logs, complex numbers, trigonometry, set notation, or summation/product notation) whereas AMC 12 does.


The tests are usually graded by late May. The individual's result may be accessed on Math Kangaroo's website via testing code. Results of high scoring students (state and national winners) are posted in roughly a year.

See Also