June 2026 Contest — Grade 7
The June 2026 North Star contest paper for Grade 7 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 7
- Questions
- 12
- Time limit
- 60 minutes
- Contest
- June 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 — Number Sense & Operations
What is the smallest number Eric can get by multiplying any 4 of the following numbers: -5, 4, 7, -12, 10
- A.-1400
- B.-3360
- C.-1680
- D.-4200
- E.None of these
Show the worked solution
To find the smallest number Eric can get by multiplying any 4 of the given numbers (-5, 4, 7, -12, 10), we need to consider combinations that result in the most negative product. The most negative product will come from multiplying the three largest magnitude negative numbers with the smallest magnitude positive number, or two negative numbers with two positive numbers where the product of the negatives is large and the product of the positives is large. The numbers are -5, 4, 7, -12, 10. The largest magnitude numbers are -12, -5, 10, 7, 4. To get the smallest (most negative) product, we should aim for an odd number of negative factors. The possible combinations of 4 numbers and their products are:
1. -5 4 7 * -12 = 1680
2. -5 4 7 * 10 = -1400
3. -5 4 -12 * 10 = 2400
4. -5 7 -12 * 10 = 4200
5. 4 7 -12 * 10 = -3360
Comparing these products: 1680, -1400, 2400, 4200, -3360. The smallest number is -3360.
Question 12 — Logical Reasoning & Problem Solving
In a robotics tournament, each team consists of four members, and each member competes exactly once against every member from all other teams. For organisational reasons, no more than 300 matches can be held in total. At most, how many teams can enter the tournament?
- A.9
- B.8
- C.7
- D.6
- E.None of these
Show the worked solution
Let T be the number of teams and M be the number of members per team. We are given M = 4. Each member competes against every member from all other teams. The total number of members is 4T. The number of matches is the number of ways to choose 2 members from the total number of members, minus the matches within the same team. However, the problem states each member competes exactly once against every member from all other teams. This means we need to consider pairs of members from different teams. If there are T teams, each with 4 members, the total number of members is 4T. The number of pairs of members from different teams is the total number of pairs of members (4T choose 2) minus the number of pairs of members from the same team. A simpler way to think about it is that each of the 4T members plays against (4T - 4) other members. Since each match involves two members, the total number of matches is (4T (4T - 4)) / 2. However, the problem states 'each member competes exactly once against every member from all other teams'. This implies we are counting pairs of members from different teams. The number of ways to choose 2 teams out of T is T choose 2. For each pair of teams, there are 4 members in the first team and 4 in the second. Each member from the first team plays each member from the second team. So, for a pair of teams, there are 4 4 = 16 matches. The total number of matches is (T choose 2) 16 = (T (T-1) / 2) 16 = 8 T (T-1). We are given that the total number of matches is no more than 300. So, 8 T (T-1) <= 300. Dividing by 8, we get T (T-1) <= 300 / 8 = 37.5. We need to find the largest integer T such that T (T-1) <= 37.5. Let's test values: If T=6, T(T-1) = 65 = 30. If T=7, T(T-1) = 7*6 = 42. Since 42 is greater than 37.5, T cannot be 7. Therefore, the maximum number of teams is 6.
Take the whole paper
All 12 questions, 60 minutes, marked as you go. No account needed.