MATH QUIZ

Which of these is the first step in mathematical induction?

• Prove the statement is true for the first element in the set.

• Show that if the statement is true for the first k elements, then it is true for the (k+1)st case.

• Prove that the problem you are working on is the base to all proofs.

• None of these are correct.

Which of the following is the induction step in mathematical induction?

• Show that if the statement is true for the first k elements, then it is true for the (k+1)st element in the set.

• Show that the statement is true for the first few elements in the set.

• Show that your math problem is different from all other math problems.

• None of these are correct.

1 + 3 + 5 + 7 + . . . + (2n − 1) = n²
On the basis of this assumption,
[The statement is true for n = k:
1 + 3 + 5 + 7 + . . . + (2k − 1) = k²]
What must we show?

• The statement is true for n = 1:
  2x1 − 1 = 1²
• The statement is true for n = k:
  1 + 3 + 5 + 7 + . . . + (2k − 1) = k²
• The statement is true for n = k + 1:
  1 + 3 + 5 + 7 + . . . + (2k − 1) + (2k + 1) = (k + 1)²

The sum of the first n odd numbers is equal to the n^th square. 
1 + 3 + 5 + 7 + . . . + (2n − 1) = n²

To prove this by mathematical induction, what will be the induction assumption?

• The statement is true for n = k:
  1 + 3 + 5 + 7 + . . . + (2k − 1) = k²
• The statement is true for n = 1:
  2x1 − 1 = 1²
• The statement is true for n = k + 1:
  1 + 3 + 5 + 7 + . . . + (2k − 1) + (2k + 1) = (k + 1)²

According to the principle of mathematical induction, to prove a statement that is asserted about every natural number n, there are two things to prove. What is the second?

• The statement is true for n = k+1.
• If the statement is true for n = k, then it will be true for its successor, k + 1.
• The statement is true for n = 1.
• The statement is true for n = k.

A regular 6-sided die is to be rolled one time. What is the probability that the number 5 is rolled?

• 1/5

• 5/6

• 1/6

• 6/5

You draw a marble from a bag that has 4 red, 2 blue, and 3 green, you also flip a fair coin. What is the probability you will draw a blue marble and flip a heads?

• 1/9

• 3/9

• 3/6

• 5/6

If you choose 1 scoop of ice cream from 12 flavors and any 1 topping from a choice of 8, how many different ice-cream sundaes can you make?

• 58
• 96
• 20
• 192

A box contains 5 purple marbles, 3 green marbles and 2 orange marbles. Draws are made without replacement. P(orange,green)

• 1/15
• 2/15
• 3/31
• 1/5