January 2026 Contest — Grade 5
The January 2026 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
- January 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 — Geometry & Measurement
A modern art sculpture consists of a cylinder, and two cuboids. If a drone takes a photo from directly overhead, which set of 2D shapes will appear in the photo?
- A.A
- B.B
- C.C
- D.D
- E.E
Show the worked solution
To find the correct 2D overhead view (top view) of the sculpture, let's analyze each component step by step:
1. The Front Cuboid:
From directly overhead, the top face of this cuboid appears as a simple rectangle.
Although there is a horizontal line near the top of its vertical side faces in the 3D drawing, these vertical faces are not visible from directly overhead. Therefore, the top view of this cuboid is a simple rectangle with a single border, which rules out options C and E (which show a double border).
2. The Taller Cuboid:
This cuboid is located at the back-right of the front cuboid.
From directly overhead, its top face appears as a smaller rectangle attached to the top-right edge of the larger rectangle. This rules out options B and E (where the smaller rectangle is in the middle).
3. The Cylinder:
Since the cylinder is standing vertically, its top view is a circle.
In the 3D drawing, the cylinder is positioned near the middle of the front cuboid's top face. Therefore, the circle must be located in the middle of the larger rectangle. This rules out options B and D (where the circle is on the right side).
Combining all these observations, the correct overhead view must have a single-bordered main rectangle, a smaller rectangle on the top-right, and a circle in the middle. This matches option A.
The answer is A
Question 12 — Logical Reasoning & Problem Solving
A stained glass window is divided into 4 adjacent sections. You have paints of 4 different colors. Any two sections that share a border must be painted with different colors. How many distinct ways can you paint the window?
- A.6
- B.12
- C.24
- D.48
- E.96
Show the worked solution
To find the number of distinct ways to paint the stained glass window, let's first identify the 4 sections and how they share borders:
1. Top-Left Section
2. Top-Right Section
3. Bottom-Left Section
4. Bottom-Right Section
By looking at the lines in the image:
The Top-Left Section shares a border with all three other sections: the Top-Right Section, the Bottom-Left Section, and the Bottom-Right Section.
The Bottom-Right Section also shares a border with all three other sections: the Top-Left Section, the Top-Right Section, and the Bottom-Left Section.
The Top-Right Section only shares a border with the Top-Left and Bottom-Right sections.
The Bottom-Left Section only shares a border with the Top-Left and Bottom-Right sections.
Now, let's count the number of ways to paint each section step-by-step using the 4 available colors:
Step 1: Choose a color for the Top-Left Section. There are 4 choices.
Step 2: Choose a color for the Bottom-Right Section. Since it shares a border with the Top-Left Section, it must be a different color. There are 3 choices remaining.
Step 3: Choose a color for the Top-Right Section. Since it shares a border with both the Top-Left and Bottom-Right sections (which have 2 different colors), it must be different from both of them. There are 2 choices remaining.
Step 4: Choose a color for the Bottom-Left Section. Since it also shares a border with both the Top-Left and Bottom-Right sections, it must be different from both of them. There are 2 choices remaining.
To find the total number of distinct ways to paint the window, we multiply the number of choices for each step:
Total ways = 4 x 3 x 2 x 2 = 48
The answer is D
Take the whole paper
All 12 questions, 60 minutes, marked as you go. No account needed.