M115

Which of the following best describes a non-routine problem?

• A problem with a single known solution

• A problem requiring creative strategies and exploration

• A problem solved by memorized formulas

• A problem with clearly defined steps

What is the most appropriate first step in solving a complex mathematical problem?

• Guess the answer based on intuition

• Identify known and unknown information

• Apply a standard algorithm immediately

• Look for a similar problem in a textbook

Which statement best defines a mathematical investigation?

• A process of solving equations using formulas

• A method of exploring patterns and testing conjectures

• A way to memorize mathematical facts

• A routine procedure for solving word problems

What makes a conjecture different from a hypothesis?

• A conjecture is based on data; a hypothesis is not

• A conjecture is a guess based on observed patterns

• A hypothesis is always proven true

• A hypothesis is used only in science

Which of the following is the most appropriate strategy when testing a mathematical hypothesis?

• Accept it without proof

• Use examples and counterexamples to evaluate it

• Assume it is false until proven

• Avoid using data to support it

What is the best reason to use a diagram when solving a word problem?

• It makes the solution look more creative

• It helps visualize relationships and structure

• It replaces the need for calculations

• It guarantees a correct answer

Which of the following is an example of a pattern?

• A random list of numbers

• A sequence increasing by 3 each time

• A single number repeated

• A list of unrelated shapes

What is the most effective way to verify a conjecture?

• Assume it is true for all cases

• Test it with multiple examples and counterexamples

• Use only one example to prove it

• Ask someone else to confirm it

Which of the following best describes a mathematical model?

• A physical object used in experiments

• A simplified representation of a real-world situation using math

• A drawing used to decorate a solution

• A list of unrelated equations

What is the purpose of making a hypothesis in a mathematical investigation?

• To guess the final answer

• To propose a testable idea based on patterns

• To avoid doing calculations

• To memorize a formula