Inductive Reasoning and Conjectures Explained

What is inductive reasoning?

• Reasoning based on specific examples to make a general prediction.

• Reasoning that guarantees logical certainty.

• Reasoning based on mathematical proofs.

• Reasoning that uses only one example to make a prediction.

What is a conjecture?

• A random guess without any basis.

• A statement that is always true.

• An educated guess based on known information.

• A proven mathematical theorem.

What is the next number in the sequence 2, 4, 12, 48, 240?

• 720

• 1440

• 960

• 1200

What is the pattern in the sequence 3 sides, 9 sides, 18 sides?

• Multiplying by 2 each time

• Adding 6 each time

• Adding 3 each time

• Multiplying by 3 each time

What is the next item in the sequence if the pattern is adding 12 each time and the last item is 18?

• 36

• 30

• 42

• 24

What is the sum of an odd and an even number?

• Always a fraction

• Always a whole number

• Always odd

• Always even

If LM = 20, MN = 6, and LN = 14, what can be inferred about the points L, M, and N?

• They form a right angle.

• They are equidistant.

• They form a triangle.

• They are collinear.

What is the predicted sales for the fourth month if the sales for the first three months are $500, $1500, and $4500?

• $6000

• $13500

• $18000

• $9000

What is a counterexample?

• An example that supports a conjecture.

• An example that shows a statement is not always true.

• An example that proves a statement is always true.

• An example that is irrelevant to the conjecture.

Which city serves as a counterexample to the statement 'The unemployment rate is highest in cities with the most people'?

• Houston

• El Paso

• Cameron

• Maverick