Inductive Reasoning Worksheet
A Grade 11 math worksheet focusing on inductive reasoning, pattern recognition, and forming conjectures.
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Inductive Reasoning
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Read each question carefully and use inductive reasoning to determine the pattern, make a conjecture, or find the next term. Show all your work for short answer questions.
1. Identify the pattern and find the next three terms in the sequence: 2, 5, 9, 14, 20, ...
2. Identify the pattern and find the next three terms in the sequence: 1, 4, 9, 16, 25, ...
3. Based on the following observations: 1 + 3 = 4, 3 + 5 = 8, 5 + 7 = 12. Make a conjecture about the sum of two odd numbers: The sum of two odd numbers is always .
4. Observe the products: 9 x 1 = 9, 9 x 2 = 18, 9 x 3 = 27, 9 x 4 = 36. Make a conjecture about the sum of the digits of a multiple of 9: The sum of the digits of any multiple of 9 is always .
5. Inductive reasoning always leads to a true conclusion.
True
False
6. A counterexample is a specific case for which a conjecture is false.
True
False
7. Provide a counterexample to the following conjecture: "All prime numbers are odd."
8. Provide a counterexample to the following conjecture: "If a number is divisible by 3, then it is also divisible by 6."
9. Which of the following is an example of inductive reasoning?
All men are mortal. Socrates is a man. Therefore, Socrates is mortal.
Every time I've observed a raven, it has been black. Therefore, all ravens are black.
If a triangle has three equal sides, then it has three equal angles. Triangle ABC has three equal sides. Therefore, Triangle ABC has three equal angles.
All squares are rectangles. Figure A is a square. Therefore, Figure A is a rectangle.