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2-1 Patterns and Inductive Reasoning
2-1 Patterns and Inductive Reasoning
2-1 Quiz
• The following questions are designed to help
you determine if you understood today’s
lesson.
• Be sure to come and talk to me if you missed
more than you got right and you do not
understand why the answers you had were
wrong.
• Record the number you get right on your
portfolio sheet!
1. Find a counterexample to show that the conjecture is false.
Conjecture: The product of two positive numbers is greater than the
sum of the two numbers.
A.
B.
C.
D.
3 and 5
2 and 2
A counterexample exists, but it is not shown above.
There is no counterexample. The conjecture is true.
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2. Based on the pattern, what are the next two terms of the
sequence?
9, 15, 21, 27, . . .
A.
B.
C.
D.
33, 972
39, 45
162, 972
33, 39
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3. Based on the pattern, what is the next figure
in the sequence?
A.
C.
B.
D.
C.
D.
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4. Based on the pattern, make a conjecture about the
sum of the first 20 positive even numbers.
2
= 2 = 1*2
2+4
= 6 = 2*3
2+4+6
= 12 = 3*4
2+4+6+8
= 20 = 4*5
A.
B.
C.
D.
The sum is 20*21
The sum is 19*20
The sum is 21*22
The sum is 20*20
2 + 4 + 6 + 8 + 10 = 30 = 5*6
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5. Alfred is practicing typing. The first time he tested himself, he could
type 23 words per minute. After practicing for a week, he could type
26 words per minute. After two weeks he could type 29 words per
minute. Based on this pattern, predict how fast Alfred will be able to
type after 4 weeks of practice.
A.
B.
C.
D.
39 words per minute
29 words per minute
35 words per minute
32 words per minute
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Assignment
2-1 p.85 #6-36 even