Download Chap 1/2 Review KEY

Math 11 Foundations
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Chap 1/2 Review
Chapter 1:
1. What is inductive reasoning?
2. What is a conjecture?
3. What is deductive reasoning?
4. Troy works at a ski shop in Whistler, British Columbia, where three types of downhill
skis are available: parabolic, twin tip, and powder. The manager of the store has ordered
100 pairs of each type, in various lengths, for the upcoming ski season. What conjecture
did the manager make?
5. Make a conjecture about the sum of one odd integer and one even integer. Test your
conjecture with at least three examples.
6. Rachelle claims that the sum of a multiple of 3 and a multiple of 6 must be a multiple
of 6. Do you agree or disagree? Justify your decision.
7. Drew created this step-by-step number trick:
• Choose any number.
• Multiply by 4.
• Add 10.
• Divide by 2.
• Subtract 5.
• Divide by 2.
• Add 3.
a) Show inductively, using three examples, that the result is always 3 more than the
chosen number.
b) Prove deductively that the result is always 3 more than the chosen number.
8. Ali created a math trick in which she always ended with 4. When Ali tried to prove
her trick, however, it did not work.
Ali’s Proof:
n
I used n to represent any number.
2n
Multiply by 2.
2n + 8
Add 8.
2n + 4
Divide by 2.
n+4
Subtract your starting number.
Identify the error in Ali’s proof, and explain why her reasoning is incorrect.
9. Determine the unknown term in this pattern: 17, 22, ___, 35, 43.
Explain your reasoning.
10. a) Draw a diagram like the one to the right. Place the numbers 1 through 9 in the
circles so that the sum of the numbers on each side of the triangle is 17.
Chapter 2:
1. In each diagram, is AB parallel to CD? Explain how you know.
2. Determine the measures of the indicated angles.
3. Determine the measures of all the unknown angles in this diagram, given PQ | RS.
4. Solve for x.
5. Prove: ∆A = 30°
6. Determine the measures of the interior angles of ∆FUN.
7. LMNOP is a regular pentagon.
a) Determine the measure of <OLN.
b) What kind of triangle is ∆LON ?
Explain how you know.
8. a) Determine the sum of the measures
of the interior angles of a 15-sided
regular polygon.
b) Find the value of each interior angle.