Free practice
Math Kangaroo Practice: Questions, Tests & Problems
Free Math Kangaroo practice questions for every grade band with full solutions, one sample question per level to try right here, the test format by grade, and where to find the official past papers.
Math Kangaroo full prep and practice guides: 1–2 3–4 5–6 7–8
Free practice by grade: 1–2 3–4 5–6 7–8
Next contest: Math Kangaroo 2027 date & registration →
Printable PDF: a free 10-problem set for each grade band, with every answer explained.
On this page · 6 sections
Free Math Kangaroo practice questions by grade
Each grade band has its own free page: ten original problems at real Math Kangaroo difficulty, with pictures, then every answer explained, including the most common wrong answer. No sign-up to read them, and each set also comes as a printable PDF.
Grades 1–2
10 picture problems for 1st and 2nd graders, with solutions any parent can walk through.
10 practice problems →
Grades 3–4
10 problems from warm-ups to the hardest 5-point kind, with step-by-step solutions.
10 practice problems →
Grades 5–6
10 problems at the Levels 5–6 paper's difficulty, each fully worked out.
10 practice problems →
Grades 7–8
10 problems for the Levels 7–8 paper, from warm-ups to the hardest kind.
10 practice problems →
Every problem is original, written by us in the style of the contest. Math Kangaroo does not release its real problems for reuse, so practicing on original material is the honest way to prepare. For one new problem every week, try our free Problem of the Week.
Try one Math Kangaroo sample question per grade
One problem from each free set, at contest difficulty. Try it first, then open the answer.
Grades 1–2
The clocks show when Mia goes to bed and when she wakes up the next morning. Leo goes to bed 2 hours later than Mia and wakes up 1 hour earlier. How many hours does Leo sleep?
Show the answer
8 hours. Mia goes to bed at 8, so Leo goes at 10. Mia wakes at 7, so Leo wakes at 6. From 10 to 12 is 2 hours, from 12 to 6 is 6 more: 2 + 6 = 8.
Grades 3–4
Each pet was weighed together with one other pet, as the scales show. How much does the dog weigh?
Show the answer
10 kg. 13 + 7 + 14 = 34 kg weighs every pet twice, so the three pets together weigh 17 kg. Take away the turtle and the rabbit (7 kg): the dog is 10 kg.
Grades 5–6
Leo lies on Tuesdays, Wednesdays and Thursdays and tells the truth on all other days. Mia lies on Saturdays, Sundays and Mondays and tells the truth on all other days. One day Leo says, "I lied yesterday," and Mia says, "I will lie tomorrow." What day of the week is it?
Show the answer
Friday. Leo's sentence fits only on Tuesday and Friday. Mia's fits only on Monday and Friday. So it is Friday.
Grades 7–8
Each scale shows the total weight of the things on it. All the packages weigh the same, and all the gifts weigh the same. How heavy is one package?
Show the answer
7 kg. Add the scales: 4 packages + 4 gifts = 48 kg, so one of each is 12 kg. Compare them: 2 extra packages for 2 gifts add 4 kg, so a package is 2 kg heavier than a gift. The package is 7 kg.
The Math Kangaroo format by grade
Every level has a 75-minute time limit and 5 answer choices per question, and a wrong answer never loses points.
| Level | Questions | Points by question number | Top score |
|---|---|---|---|
| Grades 1–2 | 24 | 1–8: 3 points9–16: 4 points17–24: 5 points | 96 |
| Grades 3–4 | 24 | 1–8: 3 points9–16: 4 points17–24: 5 points | 96 |
| Grades 5–6 | 30 | 1–10: 3 points11–20: 4 points21–30: 5 points | 120 |
| Grades 7–8 | 30 | 1–10: 3 points11–20: 4 points21–30: 5 points | 120 |
Read the full format guide: levels, scoring and time limit →
Math Kangaroo past papers and official sample questions
- Free official samples: Math Kangaroo USA's Free Sample Questions page has a PDF for every year since 2006. Each gives three real questions per grade band (one for 3 points, one for 4, one for 5) followed by the answers.
- Past tests: the complete paper tests from previous years are sold as printed booklets, one set per grade band, through the Math Kangaroo store.
A plan that combines them: work through our free ten-problem set for your child's grade, add the official samples from the last few years to see real questions, then finish with a full-length practice test under the 75-minute limit a few weeks before the contest.
Full practice tests by grade
The free sets above have ten problems each. For a complete, timed run-through, each grade-band guide has 120 original practice problems and two full-length practice tests in the real 75-minute format, with every answer explained. Every guide has a free sample to try first.
- Math Kangaroo Grades 1–2: $20.00
- Math Kangaroo Grades 3–4: $20.00
- Math Kangaroo Grades 5–6: $20.00
- Math Kangaroo Grades 7–8: $20.00
See all Math Kangaroo guides →
Math Kangaroo practice: common questions
Are there free Math Kangaroo practice questions?
Yes. Every grade band, 1–2 through 7–8, has a free page of ten original practice problems with step-by-step solutions, also available as a printable PDF, and the weekly Problem of the Week is free too. Math Kangaroo USA also posts free sample questions for every year since 2006: three per grade band, with answers.
Where can I find Math Kangaroo past papers?
Math Kangaroo USA sells the original paper tests from previous years as printed booklets, one set per grade band, through its online store. For free, its Free Sample Questions page has a PDF for each year since 2006 with three real questions per grade band (one each for 3, 4 and 5 points) and their answers.
Is there a free Math Kangaroo practice test?
The official free samples have three questions per level, and complete past tests are sold as booklets. Our free practice pages give ten original problems per grade band, and each of our grade-band guides includes two full-length practice tests in the real 75-minute format, with every answer explained.
How many questions are on Math Kangaroo, and what is the time limit?
Every level has a 75-minute time limit. Grades 1–4 answer 24 multiple-choice questions (top score 96); Grades 5–12 answer 30 (top score 120). There are five answer choices per question and no points are deducted for a wrong answer, so a guess never hurts.
What is the best way to practice for Math Kangaroo?
Short and steady beats cramming: a couple of problems a few times a week, always reviewing the full solution. Once your child is comfortable, do one full practice test under the real 75-minute limit so the timing feels familiar on contest day.
When is the next Math Kangaroo competition?
Math Kangaroo is held on the third Thursday in March each year. The next contest is March 18, 2027; see our Math Kangaroo 2027 page for the registration timeline and fees.
Build a steady practice habit, free
Get one original math challenge in your inbox every week with our free Problem of the Week. The easiest way to keep Math Kangaroo skills sharp all year.
Get the free Problem of the WeekThis guide is not affiliated with or endorsed by Math Kangaroo USA or Kangourou sans Frontières. “Math Kangaroo” is a trademark of its respective owners.