Grades 1–8 · Free + paid
Math Kangaroo Practice: Questions, Tests & Problems
The best way to get ready for Math Kangaroo is to practice with problems that look and feel like the real test. Start with our free practice questions by grade, learn exactly how the test works, then take a full practice test when your child is ready.
Next contest: Math Kangaroo 2027 date & registration →
Free Math Kangaroo practice questions by grade
Twelve original problems written at real Math Kangaroo difficulty, three per grade band, in the same 3–4–5 point structure the contest uses. Let your child try each one before opening the solution.
Grades 1–2
24 questions in 75 minutes.Mia has 3 toy ladybugs. Each ladybug has 4 spots on its back. How many spots are there altogether?
- (A) 7
- (B) 10
- (C) 12
- (D) 14
- (E) 16
Show the solution +
Answer: (C) 12
Three groups of 4 spots: 4 + 4 + 4 = 12. A child who has not met multiplication yet can draw three ladybugs and count the spots one at a time.
A necklace repeats the same four beads over and over: red, red, blue, yellow, red, red, blue, yellow, and so on. What color is the 10th bead?
- (A) Red
- (B) Blue
- (C) Yellow
- (D) Green
- (E) White
Show the solution +
Answer: (A) Red
The pattern repeats every 4 beads, so beads 1 to 4 and beads 5 to 8 look the same. Bead 9 starts the pattern over again with red, which makes bead 10 the second red.
On a balance scale, 3 cats and 1 dog weigh exactly the same as 5 cats. Every cat weighs the same, and every dog weighs the same. One dog weighs as much as how many cats?
- (A) 1
- (B) 2
- (C) 3
- (D) 4
- (E) 5
Show the solution +
Answer: (B) 2
Take 3 cats off both sides of the scale. That leaves 1 dog on one side and 2 cats on the other, so the dog weighs as much as 2 cats.
Grades 3–4
24 questions in 75 minutes.A box holds 6 crayons. Sam buys 4 boxes, then gives 7 crayons to his sister. How many crayons does Sam have left?
- (A) 15
- (B) 16
- (C) 17
- (D) 18
- (E) 21
Show the solution +
Answer: (C) 17
Four boxes of 6 crayons is 24 crayons. After giving away 7, Sam has 24 − 7 = 17 left.
Ben writes out every whole number from 1 to 20. How many times does he write the digit 1?
- (A) 10
- (B) 11
- (C) 12
- (D) 13
- (E) 20
Show the solution +
Answer: (C) 12
The numbers 1 and 10 each use the digit once, which is 2. The number 11 uses it twice, bringing the count to 4. Then 12, 13, 14, 15, 16, 17, 18 and 19 use it once each, which is 8 more, for a total of 12. Counting 11 only once is the slip most children make here.
Four friends ran a race and nobody tied. Ana finished ahead of Ben. Carla finished behind Ben but ahead of Dan. Who finished last?
- (A) Ana
- (B) Ben
- (C) Carla
- (D) Dan
- (E) It cannot be decided
Show the solution +
Answer: (D) Dan
Ana beat Ben, Ben beat Carla, and Carla beat Dan. Writing the finishing order out in a line gives Ana, Ben, Carla, Dan, so Dan came last.
Grades 5–6
30 questions in 75 minutes.A shirt costs $24. During a sale it is marked 25% off. What is the sale price?
- (A) $6
- (B) $16
- (C) $18
- (D) $20
- (E) $22
Show the solution +
Answer: (C) $18
25% of $24 is $6, so the sale price is $24 − $6 = $18. Another way to see it: a quarter off means paying three quarters of the price.
The average of five numbers is 12. Four of the numbers are 8, 10, 14 and 16. What is the fifth number?
- (A) 10
- (B) 11
- (C) 12
- (D) 13
- (E) 14
Show the solution +
Answer: (C) 12
If five numbers average 12, they add up to 5 × 12 = 60. The four given numbers add to 48, so the missing number is 60 − 48 = 12.
A rectangular garden measures 12 m by 8 m. A path 1 m wide runs all the way around the inside edge. What is the area of the path?
- (A) 30 m²
- (B) 32 m²
- (C) 34 m²
- (D) 36 m²
- (E) 40 m²
Show the solution +
Answer: (D) 36 m²
The whole garden is 12 × 8 = 96 m². The path takes 1 m off both sides of each dimension, so the space left inside it is 10 m by 6 m, or 60 m². The path is 96 − 60 = 36 m². Taking off only 1 m instead of 2 m is the usual mistake.
Grades 7–8
30 questions in 75 minutes.If 3x + 7 = 28, what is the value of 6x + 1?
- (A) 36
- (B) 41
- (C) 43
- (D) 45
- (E) 49
Show the solution +
Answer: (C) 43
From 3x + 7 = 28 we get 3x = 21, so x = 7 and 6x + 1 = 42 + 1 = 43. The quicker route skips x entirely: 6x is double 3x, which is 42, then add 1.
What is the smallest whole number greater than 2 that leaves a remainder of 2 when divided by 3, by 4 and by 5?
- (A) 22
- (B) 32
- (C) 47
- (D) 62
- (E) 122
Show the solution +
Answer: (D) 62
A number that leaves remainder 2 for all three divisors sits exactly 2 above a common multiple of 3, 4 and 5. The smallest common multiple is 60, which gives 62. Choice (E) also leaves remainder 2, but 122 is not the smallest.
A square has the same perimeter as a rectangle measuring 18 cm by 6 cm. How much larger is the area of the square than the area of the rectangle?
- (A) 24 cm²
- (B) 30 cm²
- (C) 36 cm²
- (D) 42 cm²
- (E) 48 cm²
Show the solution +
Answer: (C) 36 cm²
The rectangle’s perimeter is 2 × (18 + 6) = 48 cm, so the square has sides of 48 ÷ 4 = 12 cm. The square covers 144 cm² and the rectangle covers 18 × 6 = 108 cm², a difference of 36 cm².
Every problem above 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.
Go deeper: full free problem sets
Want more than three problems? These free sets go further, each with a full, kid-friendly worked solution. No cost and no sign-up to read them.
Grades 3–4 practice problems
5 original Math Kangaroo–style problems with step-by-step solutions.
Start practicing →Grades 5–6 practice problems
5 original problems at grade-5–6 difficulty, each fully worked out.
Start practicing →Problem of the Week (free)
One original challenge in your inbox every week — a no-pressure practice habit.
Start practicing →Know the format before you practice
Practice feels far less stressful when the format isn't a surprise. Here's the shape of the test:
Time limit, every grade level
Questions (24 for Grades 1–4, 30 for 5–12)
Answer choices per question
Wrong answers never lose points
Full practice tests by grade
When your child is ready for a complete, timed run-through, each grade-band guide includes original strategies, dozens of practice problems, and a full practice test with step-by-step solutions. Every guide has a free sample to try first.
Grades 1–2
Math Kangaroo Practice Guide
$5.00Grades 3–4
Math Kangaroo Practice Guide
$5.00Grades 5–6
Math Kangaroo Practice Guide
$5.00Grades 7–8
Math Kangaroo Practice Guide
$5.00See all Math Kangaroo guides →
Math Kangaroo practice: common questions
Are there free Math Kangaroo practice questions? +
Yes. Our Grades 3–4 and Grades 5–6 practice problem sets are completely free, each with full step-by-step solutions, and the weekly Problem of the Week is free too. Each grade-band guide also includes a free sample you can download.
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; Grades 5–12 answer 30. 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.