April 2026 Contest — Grade 8
The April 2026 North Star contest paper for Grade 8 has 12 questions and a 60-minute limit. Two sample questions with worked solutions are below, and you can take the whole paper online for free — no account, no sign-up.
- Grade
- Grade 8
- Questions
- 12
- Time limit
- 60 minutes
- Contest
- April 2026
- Subject
- Mathematics
- School year
- 2025-26
Before you start
- The timer starts when you press Start and runs for 60 minutes.
- Answer the 12 questions in any order; each is multiple choice.
- Your answers are marked as you go. Nothing is saved to an account, so finish in one sitting.
Sample questions
The first and last questions from this paper, with their worked solutions.
Question 1 — Advanced Mathematics
The product of 2026 positive integers is 5. Which of the following could be their sum?
- A.2024
- B.2025
- C.2026
- D.2027
- E.2030
Show the worked solution
To find the possible sum of the 2026 positive integers, we first analyze their product.
We are given that the product of 2026 positive integers is 5. Since 5 is a prime number, its only positive integer factors are 1 and 5.
Therefore, the only way to write 5 as a product of 2026 positive integers is to have one of the integers be 5, and the remaining 2026 - 1 = 2025 integers be 1.
Now, we calculate the sum of these 2026 integers:
Sum = 5 + underbrace{1 + 1 + dots + 1}\_2025 times
Sum = 5 + 2025 x 1 = 5 + 2025 = 2030
Thus, the sum of the integers must be 2030, which corresponds to option E.
Question 12 — Data & Statistics
Fifteen students attended a gaming tournament. On average, each student scored 1.5 goals in a mini-soccer game. None of them scored more than 2 goals, and three students didn't score at all. No goals were shared between players. How many students scored exactly 2 goals?
- A.4
- B.5
- C.6
- D.7
- E.9
Show the worked solution
To find the number of students who scored exactly 2 goals, we can analyze the information step-by-step:
1. Identify the number of students who scored goals:
There are 15 students in total. We are told that 3 students did not score any goals. Therefore, the number of students who scored at least one goal is:
15 - 3 = 12 students
2. Determine the total number of goals:
Since goals must be whole numbers, the total number of goals scored in the tournament must also be an integer.
If the average of 1.5 goals applied to all 15 students, the total goals would be 15 x 1.5 = 22.5, which is impossible because you cannot score half a goal.
Therefore, the average of 1.5 goals must refer to the 12 students who actually scored.
The total number of goals scored by these 12 students is:
12 x 1.5 = 18 goals
3. Set up the equations:
Let x be the number of students who scored exactly 2 goals.
Since no student scored more than 2 goals, and we are only considering the 12 students who scored, the remaining students must have scored exactly 1 goal.
The number of students who scored exactly 1 goal is:
12 - x
Now, we can write an equation for the total number of goals:
2(x) + 1(12 - x) = 18
2x + 12 - x = 18
x + 12 = 18
x = 6
Thus, exactly 6 students scored 2 goals.
The answer is C
Take the whole paper
All 12 questions, 60 minutes, marked as you go. No account needed.