May 2026 Contest — Grade 5

The May 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

May 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 — Advanced Mathematics

When the following puzzle pieces are arranged correctly from left to right, they form a rectangle with a complete calculation. What is the result of this calculation?

• A.4
• B.7
• C.9
• D.37
• E.None of these

Show the worked solution

Step 1 — Read the image By carefully examining the edges of each of the five puzzle pieces, we can identify their shapes: Piece 'X': Left side is convex (tab), Right side is concave (indentation). Piece '3': Left side is convex (tab), Right side is convex (tab). Piece '5': Left side is flat, Right side is concave (indentation). Piece '8': Left side is concave (indentation), Right side is flat. Piece '-': Left side is concave (indentation), Right side is convex (tab). Step 2 — Solve To form a complete rectangle, the leftmost piece must have a flat left edge, and the rightmost piece must have a flat right edge. The only piece with a flat left edge is '5', so it must be the first piece. The only piece with a flat right edge is '8', so it must be the last piece. Now we arrange the remaining pieces from left to right: 1. First piece: '5' (flat left, concave right). 2. Second piece: Since the right side of '5' is concave, the next piece must have a convex left side. This can be 'X' or '3'. Let's place 'X' (convex left, concave right). 3. Third piece: Since the right side of 'X' is concave, the next piece must have a convex left side, which is '3' (convex left, convex right). 4. Fourth piece: Since the right side of '3' is convex, the next piece must have a concave left side, which is '-' (concave left, convex right). 5. Fifth piece: Since the right side of '-' is convex, it fits perfectly with the concave left side of '8' (concave left, flat right). This gives the complete sequence of pieces from left to right: 5, X, 3, -, 8 Now, we perform the calculation using the order of operations (multiplication before subtraction): 5 x 3 - 8 = 15 - 8 = 7 Step 3 — Select The result of the calculation is 7, which corresponds to option B. The answer is B

Question 12 — Advanced Mathematics

This diagram shows three small squares inside a larger one, with a few key measurements provided. Find the total side length of the outermost square.

• A.31
• B.32
• C.30
• D.33
• E.None of these

Show the worked solution

To find the total side length of the outermost square, we can analyze the vertical dimensions of the squares from the bottom to the top: 1. Identify the given measurements from the image: The top-left square has a side length of 9. The middle square has a side length of 19. The bottom-right square has a side length of 7. The vertical distance from the bottom of the outer square to the bottom of the middle square is 4. 2. Calculate the vertical positions (heights) from the bottom up: Let the bottom edge of the outer square be at height 0. The bottom edge of the middle square is at height 4. Since the middle square has a side length of 19, its top edge is at height: 4 + 19 = 23 The top-left square sits directly on the top edge of the middle square, so its bottom edge is at height 23. Since the top-left square has a side length of 9, its top edge is at height: 23 + 9 = 32 The top edge of this top-left square aligns with the top edge of the outer square. Therefore, the total side length of the outermost square is 32. The answer is B

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