October 2025 Contest — Grade 7
The October 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
- October 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 — General Math
Ten kids Anna, Bevan, Cena, Doris, Eva, Fema, Geromy, Huan, Isa and Jon are sitting on a merry-go-round in that order clockwise. In the beginning Anna was at point X. If the merry-go-round turns by y 180 degrees, which kid is at point X.
- A.Geromy
- B.Fema
- C.Huan
- D.Isa
- E.Jon
Show the worked solution
To find which kid is at point X after the merry-go-round turns by 180 degrees, we can follow these steps:
1. Identify the positions of the kids:
There are 10 kids sitting on the merry-go-round in clockwise order:
1. Anna (at point X)
2. Bevan
3. Cena
4. Doris
5. Eva
6. Fema
7. Geromy
8. Huan
9. Isa
10. Jon
2. Determine the effect of a 180-degree turn:
A full circle is 360 degrees. A turn of 180 degrees is exactly half of a full circle (180^circ / 360^circ = 1/2).
Since there are 10 equally spaced positions on the merry-go-round, half of a full turn corresponds to moving by exactly 5 positions (10 / 2 = 5).
3. Find the kid opposite to Anna:
Since Anna starts at point X (position 1), the kid who is directly opposite to her (5 positions away) will end up at point X after a 180-degree turn.
Counting 5 positions clockwise from Anna:
1 position away: Bevan
2 positions away: Cena
3 positions away: Doris
4 positions away: Eva
5 positions away: Fema
Thus, Fema is directly opposite to Anna and will be at point X after the 180-degree turn.
The answer is B
Question 12 — General Math
Let’s assume that the earth’s equator is 40,075 kilometers long and a cyclist can travel the earth along its equator. What is the approximate distance that the cyclist’s head will travel extra, than the length of the equator, if the head is 1.5 meters above the ground?
- A.5 meters
- B.10 meters
- C.12 meters
- D.15 meters
- E.18 meters
Show the worked solution
To find the extra distance the cyclist's head travels compared to the equator, we can model the Earth as a perfect sphere at the equator with radius R.
The length of the equator (the path of the cyclist's feet/wheels) is the circumference of a circle of radius R:
C\_1 = 2pi R
The cyclist's head is at a height of h = 1.5 meters above the ground. Therefore, the path of the head is a concentric circle with radius R + h. The length of this path is:
C\_2 = 2pi(R + h)
The extra distance traveled by the head is the difference between these two circumferences:
Extra distance = C\_2 - C\_1 = 2pi(R + h) - 2pi R = 2pi h
Notice that the radius of the Earth, R, cancels out completely. This means the extra distance depends only on the height h and not on the size of the Earth.
Substituting h = 1.5 meters into the formula:
Extra distance = 2 x pi x 1.5 = 3pi meters
Using the approximation pi approx 3.14:
Extra distance approx 3 x 3.14 = 9.42 meters
Among the given options, 10 meters is the closest approximation to 9.42 meters.
The answer is B
Take the whole paper
All 12 questions, 60 minutes, marked as you go. No account needed.