Mathematical Ideas, 14th Edition by
Charles D. Miller
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are included (Ch 1 to 15)
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,Chapter 1: The Art of Problem Solving
Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Decide whether the argument is an example of inductive or deductive reasoning.
1) |-p| = p, therefore |-73| = 73 1)
A) Inductive B) Deductive
2) 17 + 11 = 28, 41 + 23 = 64, 11 + 13 = 24. Therefore, the sum of two prime numbers is even. 2)
A) Inductive B) Deductive
Determine the most probable next term in the sequence.
3) 6, -12, 24, -48, 96 3)
A) 144 B) -192 C) 192 D) -144
3 5 7 9 11
4) , , , , 4)
2 4 6 8 10
12 12 13 13
A) B) C) D)
11 13 11 12
Use inductive reasoning to predict the next equation.
5) 3 × 3 = 9 5)
33 × 33 = 1089
333 × 333 = 110,889
A) 333 × 3333 = 11,108,889 B) 3333 × 3333 = 112,889
C) 3333 × 3333 = 11,108,889 D) 3333 × 3333 = 111,889
6) 36 - 34 + 32 - 30 = 37 - 35 + 33 - 31 6)
46 - 44 + 42 - 40 = 47 - 45 + 43 - 41
A) 56 + 54 - 52 - 50 = 57 + 55 - 53 + 51 B) 56 + 54 - 52 + 50 = 57 + 55 - 53 + 51
C) 56 - 54 - 52 + 50 = 57 - 55 + 53 - 51 D) 56 - 54 + 52 - 50 = 57 - 55 + 53 - 51
Use the method of Gauss to find the sum.
7) 4 + 8 + 12 + . . . + 300 7)
A) 1406.25 B) 90,000 C) 11,250 D) 11,400
8) 2 + 4 + 6 + . . . + 600 8)
A) 90,000 B) 362,404 C) 90,300 D) 22,500
1
, Find a pattern and use it to solve the problem.
9) Draw the next figure in the pattern. 9)
A) B)
C) D)
10) Find the next term: 6, 12, 18, 30 10)
A) 36 B) 66 C) 60 D) 42
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem using inductive reasoning.
11) How many rectangles are there in the last two figures? 11)
→1 rectangle
→3 rectangles
→ ? rectangles
→ ? rectangles
12) How many line segments are determined by joining dots on the last two circles? 12)
3 segments 6 segments segments segments
2