1. Which two numbers should come next in the sequence?
a.
41, 46
b.
37, 42
c.
38, 43
d.
37, 34
ANSWER:
c
2. Find the sixth term in the pattern.
, ...
135
23
21
24
d
3. What is the missing number in the sequence below?
, , 1, ? , , ...
4. Use inductive reasoning to predict the most probable next number in the given list.
, ?
256
125
101
625
e.
91
b
5. Use inductive reasoning to predict the most probable next number in the given list.
, ?
33
39
16
7
20
e
6. Use inductive reasoning to decide whether the conclusion for the following argument is correct. Pick any counting number. Multiply the number by 8. Subtract 4 from the product. Divide the difference by the sum of the original number and 10. The resulting number is 8.
The conclusion is correct
The conclusion is incorrect
There is not enough information to determine the validity of the conclusion.
7. Use the data in the table and inductive reasoning to answer the question.
Cube edge length
Weight of water inside cube(water fills entire cube)
1 cm2 cm3 cm4 cm
1 g
8 g27 g64 g
If a cube is filled with water and the weight of the water is 729 grams, what is the edge length of the cube?
243
81
9
8
8. Use inductive reasoning to help complete the table. Round your answer to two decimal places, if necessary.
Number of sides of a regular polygon
4
5
6
7
8
17
Interior angle measure
90
108
120
128.57
140, 158.82
135, 382.5
135, 158.82
140, 382.5
9. Which is a valid conclusion based on the following information? An equilateral triangle has three congruent sides.
Given: is equilateral.
has a measure between and 0 and 90.
and are collinear.
B is the midpoint of
has three congruent sides.
10. Alisa reads in a geometry book that two intersecting lines will lie in the same plane. Which statement is correct about the conclusion Alisa can make?
She can use deductive reasoning to conclude that if she draws two intersecting lines, the lines will not lie in the same plane.
She can use deductive reasoning to conclude that if she draws two intersecting lines, the lines will lie in the same plane.
She can use deductive reasoning to conclude that if she draws three intersecting lines, the lines will lie in the same plane.
She can use deductive reasoning to conclude that if she draws three intersecting lines, the lines will not lie in the same plane
11. Use the pattern to make a conjecture. Then, use the conjecture to find the next product.
The product of a number consisting of and 8 consists of , and . The next product is
12. Find a counterexample to show that is a false statement.
choose
13. Which choice gives an example that supports the conjecture, and a counterexample that shows the conjecture is false?
For any real number , .
, but
14. Find a counterexample to show that is a false statement.
choose
15. Use deductive reasoning to determine the number that will always be produced from the following procedure. Pick a number. Add 6 to the number and multiply the sum by 2. Subtract 7 and then decrease this difference by 2 times the original number.
Let be the original number
(add 6)
(multiply by 2)
(substract 7)
(decrease by 2 times original number)
(final number)
Let be the original number
16. A number is divisible by 6 if the sum of the digits of the number is divisible by 3 and the number is even. Which statement is correct about the conclusion that can be made?
Deductive reasoning can be used to determine that 156084 is divisible by 6.
Inductive reasoning can be used to determine that 156084 is not divisible by 6.
Inductive reasoning can be used to determine that 156084 is divisible by 6.
Deductive reasoning can be used to determine that 156084 is not divisible by 6.
a
17. Three boys are in three different rooms. Ernest always tells the truth. Barry sometimes tells the truth. Mario never tells the truth. Use the statements made by the person in each room to tell who is in each of the rooms.
Room 1
Room 2
Room 3
The guy in Room 2 is Mario.
I’m Barry.
The guy in Room 2 is Ernest.
Room 1 - Mario; Room 2 - Barry; Room 3 - Ernest
Room 1 - Ernest; Room 2 - Mario; Room 3 - Barry
Room 1 - Barry; Room 2 - Ernest; Room 3 - Mario
Room 1 - Mario; Room 2 - Ernest; Room 3 - Barry
18. Use inductive reasoning to predict the most probable next letter in the list. . . . , H, I, M, N, R, S, . . .
W
19. Construct a difference table to predict the next term of the sequence
13, 46, 99, 172, 265,...
86
437
358
378
20. Construct a difference table to predict the next term of the sequence
–4
–22
21. Compute the first five terms the sequence with nth term formula given by . (Assume that n begins with 1.)
22. Write the first five terms of the sequence. (Assume that n begins with 1.)
23. Find the indicated term of the sequence whose nth term is given by the formula.
; ?
4
24. ; ?
3
25. Determine the th term formula for the number of square tiles that will be in the th figure.
26. Determine the th term formula for the number of square tiles that will be in the th figure.
27. Determine the th term formula for the number of square tiles that will be in the th figure.
28. Determine the th term formula for the number of square tiles that will be in the th figure.
29. Find the first five terms of the sequence.
1, 4, 17, -46, 192
1, 4, 10, -56, 176
1, 4, 19, -57, 185
30. Find the first 6 terms of a sequence defined by if the 7th and 8th terms are 51 and 81.
2, 6, 7, 13, 19, 32
1, 5, 8, 12, 20, 31
1, 4, 8, 11, 20, 30
31. One method for finding the golden ratio, believed by the ancient Greeks to be the most pleasing to the human eye, is to follow these steps:
Step 1: Write the first 10 terms of a sequence defined by , andStep 2: Divide each term in the sequence by the term before it.
As the terms increase, their ratios approach the golden ratio.Find the 10th term of this sequence and the golden ratio to the nearest thousandth.
38, 1.621
212, 1.618
133, 1.621
133, 1.618
32. The nth term formula generates 2, 4, 6, 8, 15 for .
Make minor changes to the above formula to produce an nth term formula that will generate the sequence 2, 4, 6, 8, 65.
33. If two ladders are placed end to end, their combined height is 38.5 feet.One ladder is 2.5 feet shorter than the other ladder.What are the heights of the two ladders?
20.5 feet and 18 feet
19.25 feet and 21.75 feet
20.5 feet and 23 feet
18 feet and 15.5 feet
38.5 feet and 36 feet
34. What is the 58th decimal digit in the decimal representation of ?
1
2
5
35. Using the map below, determine the number of direct routes (no backtracking) from point A to point B if you want to pass by point F.
6
36. Morris Mouse can easily find his way through the maze from the entrance A to the exit B. However, he only receives food if he finds the exit without going west or south. (North is towards the top of the page.) How many different paths can he take through the maze to receive food? (Note: Different paths have at least one distinct section. See the diagram for an example.)
252
15,120
30,240
none of these
37. Suppose 46 points are placed around a circle. A line segment is drawn between each pair of points. How many line segments are drawn?
2070
2116
1081
46
1035
38. A parking lot contains a total of 48 cars and motorcycles. There are a total of 172 tires (not counting spare tires) in the lot. Assuming each car has 4 tires and each motorcycle has 2 tires, determine how many cars and how many motorcycles are in the parking lot.
38 motorcycles and 10 cars
10 motorcycles and 38 cars
24 motorcycles and 24 cars
4 motorcycles and 44 cars
13 motorcycles and 35 cars
39. Determine the units digit of .
0
40. The UCSB has 8 squads of badminton players. The UCI team has 5 squads. Every squad from UCSB must play every squad from UCI at least once. What is the least number of games that must be played?
13
40
48
41. In a chess tournament, each player played a game in the first round. The losers dropped out. This process continued until a winner was declared. The winner of the tournament played 8 games. How many people were in the tournament?
128
42. Use the graph below, which shows the average number of weekly viewers of a 30-minute television program (in millions of viewers) from 2000 to 2006.
Find the change in the average number of weekly viewers from 2000 to 2004.
–5 million
no change
5 million
–10 million
10 million
43. A baseball team has won more than 97% (but less than 100%) of its games in a season.What is the least possible number of games that the team could have played in the season?
34
35
36
37
44. On three examinations, a student received scores of 77, 85, and 75. What score will the student need on the fourth examination to have an average of 83?
80
79
95
85
84
45. You may find it helpful to list perfect squares or cubes beneath the sequence terms to try to see how they may relate to the sequence.
343
49
341
47
46. How many digits does it take in total to number a book from page 56 to page 896?
395
840
2479
400
401856
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