Mathematics Problem Solving Quiz

What is the main difference between inductive and deductive reasoning?

• Deductive reasoning is based on repeated observations.

• Inductive reasoning starts with a general statement.

• Deductive reasoning draws a general conclusion from specific examples.

• Inductive reasoning draws a general conclusion from specific observations.

What is the first step in Polya's Four-Steps in Problem Solving?

• Understand the problem.

• Look back.

• Carry out the plan.

• Devise a plan.

Which of the following is an example of deductive reasoning?

• All birds can fly. A penguin is a bird. Therefore, a penguin can fly.

• All humans are mortal. Socrates is a human. Therefore, Socrates is mortal.

• The sun rises in the east. Today is a sunny day. Therefore, the sun will rise.

• Every even number is divisible by 2. 4 is an even number. Therefore, 4 is divisible by 2.

What does a conjecture represent in mathematics?

• A false statement.

• A proven statement.

• A general principle.

• A statement believed to be true but not yet proven.

What is the Goldbach Conjecture?

• Every odd integer greater than 1 can be expressed as the sum of two primes.

• Every even integer greater than 2 can be expressed as the sum of two primes.

• No three positive integers can satisfy the equation an + bn = cn.

• Every prime number is odd.

Which of the following is NOT a step in Polya's problem-solving process?

• Understand the problem.

• Devise a plan.

• Look back.

• Analyze the data.

What is the purpose of a mathematical proof?

• To show that a statement is sometimes true.

• To create a hypothesis.

• To demonstrate that a statement is always true.

• To provide a conjecture.

What is the significance of mathematical intuition?

• It replaces the need for proofs.

• It is always correct.

• It is a reliable belief without formal proof.

• It is a formal proof.

Which of the following is an example of inductive reasoning?

• If it rains, the ground gets wet. It is raining. Therefore, the ground is wet.

• All squares are rectangles. A square has four sides. Therefore, all four-sided shapes are rectangles.

• The sun has risen every day. Therefore, the sun will rise tomorrow.

• All cats are mammals. Felix is a cat. Therefore, Felix is a mammal.

What is the formula for the nth triangular number?

• Tn = n^2

• Tn = n^2 + n

• Tn = n(n - 1)/2

• Tn = n(n + 1)/2