Midterm | Mathematics in the Modern World

Complete the analogy by choosing the word that best completes the relationship. A false observation disproving a general statement is to counterexample as a specific observation confirming a general rule is to ___________________.

• Observation

• Hypothesis

• Deductive reasoning

• Conjecture

Complete the analogy by choosing the word that best completes the relationship. The step one in Polya’s steps in problem-solving is to understand the problem while step two in Polya’s steps in problem-solving is to ___________________.

• Look Back

• Understand the Problem

• Carry out the Plan

• Devise a Plan

Complete the analogy by choosing the word that best completes the relationship. Intuition is to a _____________ as a proof is to a ___________________.

• Assumption, Conclusion

• Guess, Fact

• Theory, Experiment

• Hypothesis, Theorem

Complete the analogy by choosing the word that best completes the relationship. Devise a Plan in the Money Exchange Example is to Working Backwards from Final Amounts as Devise a Plan in the Algebra Example is to ___________________.

• Calculating Probability

• Estimating the Sum

• Drawing a Diagram

• Setting Up an Equation

Complete the analogy by choosing the word that best completes the relationship. An infinite sequence whose domain is the set of positive integers is to finite sequence whose domain of the function contains __________________________.

• negative integers

• rational numbers

• natural numbers

• n positive integers only

Complete the analogy by choosing the word that best completes the relationship. Constructing a Difference Table for a Sequence is to Predicting the Next Term as Using a Formula for a Polygonal Number is to _____________________________.

• Determining the Number of Sides

• Calculating the Angles

• Drawing the Shape

• Finding the nth Term

Complete the analogy by choosing the word that best completes the relationship. Peak Primes: 123494321 * Valley Primes: ___________________

• 120343021

• 765404567

• 323232323

• 199999991

Complete the analogy by choosing the word that best completes the relationship. Recall an example. Given in example 3, step 1 in weighing the coins on the left side include 1, 2, 3, 4, 5, 6 as the right side includes ___________________.

• 2, 8, 10, 12

• 7, 9, 10, 11

• 7, 10, 11, 12

• 7, 8, 9, 10, 11, 12

Complete the analogy by choosing the word that best completes the relationship. Inductive reasoning is to generalization as deductive reasoning is to ________________________.

• Hypothesis

• Observation

• Counterexample

• Specific conclusion

Complete the analogy by choosing the word that best completes the relationship. Look for a formula/formulas: Step 2 * Modify the plan or try a new plan: ___________

• Step 4

• Step 1

• Step 3

• Step 5