November 2025 Contest — Grade 7
The November 2025 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
- November 2025
- 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 — Algebra & Expressions
Samulen is a sport played by aliens in Galaxy Zeta. If each team A, B, C and D consists of an equal number of players and the total players in all the teams is 12 more than the players in team A, how many players are there in team A?
- A.3
- B.4
- C.6
- D.8
- E.10
Show the worked solution
To find the number of players in team A, let's represent the number of players in team A as P.
Since there are four teams (A, B, C, and D) and each team has an equal number of players, each of the other three teams also has P players.
The total number of players in all four teams combined is:
Total players = P + P + P + P = 4P
According to the problem, the total number of players is 12 more than the number of players in team A. We can write this as:
Total players = P + 12
Now, we can set these two expressions for the total number of players equal to each other:
4P = P + 12
Subtract P from both sides of the equation to group the P terms together:
3P = 12
Divide both sides by 3 to find the value of P:
P = 4
Thus, there are 4 players in team A.
The answer is B
Question 12 — Algebra & Expressions
The average score in an examination of 10 students of a class is 70 where the maximum possible score was 100. If the scores of the top five students are not considered, the average score of the remaining students falls by 10. If it is known that each of the top five students had a distinct integer score and the lowest score among them was 75, what is the maximum possible score of the topper?
- A.100
- B.98
- C.96
- D.94
- E.92
Show the worked solution
To find the maximum possible score of the topper, we can break down the information step-by-step:
1. Find the total sum of all 10 students' scores:
The average score of the 10 students is 70.
Total sum = 10 x 70 = 700
2. Find the sum of the bottom 5 students' scores:
If the top 5 scores are removed, the average of the remaining 5 students falls by 10, making their average 70 - 10 = 60.
Sum of bottom 5 = 5 x 60 = 300
3. Find the sum of the top 5 students' scores:
Sum of top 5 = Total sum - Sum of bottom 5 = 700 - 300 = 400
4. Maximize the topper's score:
Let the top 5 scores, from lowest to highest, be S\_1, S\_2, S\_3, S\_4, S\_5.
We are given that:
The lowest score among them is 75, so S\_1 = 75.
Each of the top 5 scores is a distinct integer.
To make the topper's score (S\_5) as large as possible, we must make the other scores (S\_2, S\_3, S\_4) as small as possible. Since they must be distinct integers greater than 75, their minimum possible values are:
S\_2 = 76
S\_3 = 77
S\_4 = 78
5. Calculate the maximum score of the topper (S\_5):
S\_1 + S\_2 + S\_3 + S\_4 + S\_5 = 400
75 + 76 + 77 + 78 + S\_5 = 400
306 + S\_5 = 400
S\_5 = 400 - 306 = 94
Since 94 is less than the maximum possible score of 100, and the bottom 5 scores can easily be chosen to sum to 300 while remaining less than 75 (for example, five scores of 60), this is a valid and achievable score.
Therefore, the maximum possible score of the topper is 94.
Take the whole paper
All 12 questions, 60 minutes, marked as you go. No account needed.