Grades 7-8 paper · Math Kangaroo 2027
Math Kangaroo
grade 8 practice
Eighth grade is the older year on the Math Kangaroo grades 7-8 paper and the last year before the high school levels. The format is 30 questions in 75 minutes for up to 120 points, and your child is ranked against other eighth graders only.
Math Kangaroo 2027 for a grade 8 student
| What | Grade 8 |
|---|---|
| Competition day | Thursday, March 18, 2027 |
| Paper your child sits | Grades 7-8 (Math Kangaroo USA “Levels 7 & 8”) |
| Ranked against | 8th graders only, nationally and by state |
| Questions and time | 30 multiple-choice questions in 75 minutes, about 2 and a half minutes each |
| Points | 10 questions each worth 3, 4 and 5 points; top score 120; nothing lost for a wrong answer |
| Calculators | Not allowed |
| Level rule | Your child sits the level for their school grade; a lower level is not allowed |
| Regular registration | September 15 to December 31, 2026 ($20 per student) |
| Late registration | January 1 to February 1, 2027 ($35 per student) |
Source: Math Kangaroo USA's scoring rules, registration page, logistics page and 2027 host letter, checked October 21, 2026. Internationally, the Kangourou sans Frontières association's regulations call roughly this age band Cadet, though each country groups its levels its own way.
Where grade 8 sits on the grades 7-8 paper
An eighth grader has usually sat this paper before, so the aim this year is the 5-point questions, a third of the paper, which in our papers mix algebra, number patterns and counting.
Rankings are by single grade, with the top 20 nationally and the top 3 in each state listed at each grade, so an eighth grader is compared with other eighth graders.
Next year the paper changes again, to the grades 9-10 level. Eighth grade is a good time to build the habits that carry on: checking that an answer is reasonable, and using the answer choices to rule options out.
The 7th grade page covers the other year on this paper: Math Kangaroo grade 7 practice.
How scoring works on the grades 7-8 paper
| Question value | How many | Points available |
|---|---|---|
| 3 points each | 10 | 30 |
| 4 points each | 10 | 40 |
| 5 points each | 10 | 50 |
| Whole paper | 30 | 120 |
A grade 8 student who answers every 3- and 4-point question correctly and misses all 10 of the 5-point ones scores 70 out of 120. Each 5-point question is worth about 4.2% of the top score, so the 5-point third of the paper carries the most weight. A wrong answer costs nothing, so a blank is never better than a guess.
Results are ranked among 8th graders only. The top 20 scores nationally and the top 3 in each state are listed, students who tie on the top score all rank first, and the percentile shows the share of 8th graders, in the state and in the country, who scored lower.
Math Kangaroo USA's own practice for this level includes online past exams by year and practice sets sorted by point value (3-point, 4-point and 5-point questions), plus PDF exams and written solutions going back to 1998. Find them on its grades 7-8 practice page.
Two grade 8 practice problems
Written by us in the Kangaroo style, five answer choices each. Try them before opening the answer.
What is the last digit of 7 raised to the power 2027?
- (A) 1
- (B) 3
- (C) 7
- (D) 9
- (E) 0
Show answer
3. The last digits of 7, 7 x 7, 7 x 7 x 7, and so on run 7, 9, 3, 1 and then repeat every 4 powers. 2027 divided by 4 leaves a remainder of 3, so 7 to the 2027 ends like 7 cubed, which is 343. The last digit is 3.
The squares of two consecutive whole numbers differ by 35. What is the larger of the two numbers?
- (A) 6
- (B) 17
- (C) 18
- (D) 35
- (E) 36
Show answer
18. If the numbers are n and n + 1, the difference of their squares is (n + 1) squared minus n squared, which is 2n + 1. So 2n + 1 = 35 and n = 17, which makes the larger number 18. Check: 324 - 289 = 35.
What our grade 8 papers ask
Our five grade 8 papers are our own, hand-written on the SOF olympiad blueprint rather than the Kangaroo format: 50 questions for 60 marks in 60 minutes, ending with 5 Achievers questions worth 3 marks each. The thinking carries across. Across the five papers you will find:
- Sums and counts built from digit rules, such as every two-digit number whose digits differ by exactly 3.
- Straight lines through given points, and where two lines cross.
- Probability with drawing coloured items without replacement.
- Mean, median and range puzzles with whole numbers.
- Triangles: which side lengths give an obtuse triangle.
- Colouring and pairing arguments: dominoes on a chessboard with two corners removed, numbers sorted into pairs.
Every answer is explained, and every wrong option names the mistake that leads to it. For the official grades 7-8 past papers, go to mathkangaroo.org.
A practice plan for grade 8
- Work mostly on the 5-point questions in past papers. With 10 of them on the paper, they decide most of the score.
- Sit our grade 8 papers and the official grades 7-8 past papers on mathkangaroo.org under the full 75 minutes.
- After each paper, sort mistakes into misread, slip and did not know the idea. Only the last kind needs new teaching.
Grade 8 Math Kangaroo questions parents ask
How hard is Math Kangaroo for grade 8?
It is a 30-question, 75-minute paper shared with seventh graders, with no calculators. Ten questions are worth 3 points, ten 4 points and ten 5 points, for a top score of 120, and wrong answers cost nothing.
Is Math Kangaroo ranked by grade?
Yes. The top 20 scores nationally and the top 3 in each state are ranked at each grade, and percentiles are worked out against students in the same grade.
When is Math Kangaroo 2027 and how much does it cost?
Thursday, March 18, 2027. Registration is $20 per student from September 15 to December 31, 2026, and $35 for late registration from January 1 to February 1, 2027.
When are Math Kangaroo winners announced?
In May. Students who rank in the top 20 in the country or the top 3 in their state at their grade are recognized on the Math Kangaroo website and receive gifts. Every participant gets a participation ribbon, a small mathematical gift and an electronic certificate.