October 2025 Contest — Grade 5
The October 2025 North Star contest paper for Grade 5 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 5
- 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
Tennis balls are sold in packages of 3, 4 and 5. Jen wants to purchase exactly 9 tennis balls. What is the minimum number of packets that he must purchase?
- A.2
- B.3
- C.4
- D.5
- E.1
Show the worked solution
To find the minimum number of packages Jen must purchase to get exactly 9 tennis balls, we can test the possibilities starting from the smallest number of packages:
1. Can Jen buy exactly 9 tennis balls with 1 package?
No, because the largest package available contains only 5 tennis balls, which is less than 9.
2. Can Jen buy exactly 9 tennis balls with 2 packages?
Let's look at the available package sizes: 3, 4, and 5.
If we choose one package of 4 tennis balls and one package of 5 tennis balls, the total is:
4 + 5 = 9 tennis balls.
This gives us exactly 9 tennis balls.
Since we can achieve exactly 9 tennis balls using 2 packages, and 1 package is not enough, the minimum number of packages Jen must purchase is 2.
Question 12 — General Math
The following structure is made up of 50 cubes. Sam painted the entire structure including the bottom. How many faces were painted?
- A.32
- B.64
- C.144
- D.48
- E.96
Show the worked solution
To find the number of painted faces, we can analyze the surface area of the structure by looking at it from six different directions: top, bottom, and the four lateral sides (front-left, front-right, back-left, and back-right).
Step 1 — Read the image and identify the structure:
The structure is built on a 4 x 4 grid of columns.
The columns have different heights, forming a staircase-like shape that decreases from the back corner to the front corner.
Let's count the columns of each height to verify the total of 50 cubes:
There are 7 columns of height 4 along the back-left and back-right outer walls.
There are 4 columns of height 3 in the middle.
There are 5 columns of height 2 at the front.
Total cubes = (7 x 4) + (4 x 3) + (5 x 2) = 28 + 12 + 10 = 50 cubes.
Step 2 — Calculate the painted faces:
Since the steps are monotonic (they only go down and never go up to create hidden pockets), we can find the total surface area by projecting the structure in the six primary directions:
1. Top view: Looking from directly above, we see the top faces of all 16 columns, which equals 16 faces.
2. Bottom view: The bottom is flat and consists of a 4 x 4 grid, which equals 16 faces.
3. Back-Left view: This is a flat outer wall of size 4 x 4, which equals 16 faces.
4. Back-Right view: This is another flat outer wall of size 4 x 4, which equals 16 faces.
5. Front-Left view: Looking from this direction, the stepped vertical faces project perfectly to a flat 4 x 4 grid, which equals 16 faces.
6. Front-Right view: Similarly, the stepped vertical faces in this direction project to a flat 4 x 4 grid, which equals 16 faces.
Adding the faces from all six directions together:
Total painted faces = 16 + 16 + 16 + 16 + 16 + 16 = 96
Step 3 — Select the correct option:
The total number of painted faces is 96, which corresponds to option E.
The answer is E
Take the whole paper
All 12 questions, 60 minutes, marked as you go. No account needed.