Algebra and Trigonometry, Blitzer - Exam Preparation Test Bank (Downloadable Doc)

Ch. 0 Chapter P: Prerequisites: Fundamental Concepts of Algebra
0.1 Algebraic Expressions, Mathematical Models, and Real Numbers
1 Evaluate Algebraic Expressions
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Evaluate the algebraic expression for the given value or values of the variable(s).
1) 9x + 8; x=7
A) 71 B) 126 C) 17 D) 55

2) 8x + 3; x = -2
A) -13 B) 19 C) -19 D) 13

3) 2(x + 1) + 21; x = -4
A) 15 B) -15 C) 35 D) 7

4) 6x2 + 8y; x = 7 and y = 5
A) 334 B) 1804 C) 1710 D) 206

5) (x + 4y)2; x = 4 and y = 2
A) 144 B) 12 C) 24 D) 64

6) 2 + 6(x - 6)3; x=8
A) 50 B) 14 C) 64 D) -46

7) x2 - 4(x - y); x = 6 and y = 2
A) 20 B) 10 C) 14 D) -52

6(x + 3)
8) ; x=5
2x + 2
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A) 4 B) 1 C) 8 D)
2

y - 4x
9) ; x = -1 and y = 3
7x + xy
7 1 1 9
A) - B) C) D) -
10 10 4 10

2 Use Mathematical Models
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve.
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1) The formula C = (F - 32) expresses the relationship between Fahrenheit temperature, F, and Celsius
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temperature, C. Use the formula to convert 68°F to its equivalent temperature on the Celsius scale.
A) 20°C B) 4°C C) 56°C D) 65°C




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, 2) A stone is dropped from a tower that is 770 feet high. The formula h = 770 - 16t2 describes the stone's
height above the ground, h, in feet, t seconds after it was dropped. What is the stone's height 4 seconds
after it is released?
A) 514 ft B) 524 ft C) 489 ft D) 539 ft

3) If a rock falls from a height of 50 meters above the ground, the height H (in meters) after x seconds can be
approximated using the formula H = 50 - 4.9x2. What is the height of the rock after 3 seconds?
A) 5.9 m B) 405.9 m C) -166.09 m D) 35.3 m

4) As the relative humidity increases, the temperature seems higher than it is. The formula T = 0.113x + 77.98
approximates the apparent temperature for an actual temperature of 85°F, where x is the relative
humidity. What is the apparent temperature (to the nearest degree) for a relative humidity of 40%?
A) 83°F B) 352°F C) 118°F D) 78°F

5) The winning times (in seconds) in a speed-skating event for men can be represented by the formula
T = 46.18 - 0.095x, where x represents the year, with x = 0 corresponding to 1920. (For example in 1992, x
would be 1992 - 1920 = 72.) According to the formula, what was the winning time in 1998? Round to the
nearest hundredth.
A) 38.77 sec B) 3594.63 sec C) 39.72 sec D) 40.67 sec

6) It is estimated that y, the number of items of a particular commodity (in millions) sold in the United States
in year x, where x represents the number of years since 1990, is given by the formula y = 1.3x + 3.07. That
is, x = 0 represents 1990, x = 1 represents 1991, and so on. According to the formula, how many items sold
in 1995?
A) 9.57 millions B) 3.07 millions C) 21.85 millions D) 10.87 millions

3 Find the Intersection of Two Sets
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the intersection of the two sets.
1) {1, 3, 5, 8} ∩ {5, 11, 1}
A) {1, 5} B) {1} C) {1, 5, 8, 3, 11} D) ∅

2) {2, 10, 8} ∩ {4, 6}
A) ∅ B) {10, 8} C) {2, 4, 8, 10, 6} D) {2, 8}

3) {6, 8, 9, 11} ∩ ∅
A) ∅ B) {6, 8, 9, 11} C) {6, 8} D) {9, 11}

4 Find the Union of Two Sets
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the union of the two sets.
1) {2, 5, 8, 10} ∪ {2, 5, 12}
A) {2, 5, 8, 10, 12} B) {2, 5} C) {8, 10, 12} D) ∅

2) {2, 10} ∪ {2, 4, 8}
A) {2, 4, 8, 10} B) {2} C) {4, 8, 10} D) ∅

3) {1, 3, 4, 6} ∪ ∅
A) {1, 3, 4, 6} B) {1, 3} C) {4, 6} D) ∅


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,5 Recognize Subsets of the Real Numbers
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

List all numbers from the given set B that are members of the given Real Number subset.
1) B = {17, 5, -22, 0, 0.6, 25} Integers
A) 17, -22, 0, 25 B) 17, 0 C) 17, -22, 0 D) 17, 0, 25

2) B = {11, 6, -16, 0, 0.1, 4} Whole numbers
A) 11, 0, 4 B) 11, -16, 0 C) 11, -16, 0, 4 D) 11, 0

3) B = {10, 6, -9, 0, 0.6, 9} Natural numbers

A) 10, 9 B) 10, 0, 9 C) 10, 0 D) 10

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4) B = {16, 5, -2, 0, , 25, 0.3, 0.73} Rational numbers
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8
A) 16, -2, 0, , 25, 0.73, 0.3 B) 16, 0, 25
9
8
C) 5, 25 D) 5, , 0.73
9

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5) B = {11, 7, -11, 0, , 4, 0.7, 0.35} Irrational numbers
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A) 7 B) 7, 0.7 C) 7, 4, 0.7 D) 7, 4, 0.35

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6) B = {4, 8, 0, , 9, -0.9, 0.53, -23} Real numbers
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5 5
A) 4, 8, 0, , 9, -0.9, 0.53, -23 B) 4, 8, 0, , 9, 0.53
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5 5
C) 4, 8, , 9, -0.9, 0.53, -23 D) 4, 0, , -0.9, 0.53, -23
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6 Use Inequality Symbols
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine whether the statement is true or false.
1) 21 > 24
A) False B) True

2) 17 ≥ 4
A) True B) False

3) -81 < 0
A) True B) False

4) 24 < -6
A) False B) True

5) 12 ≤ 11
A) False B) True


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, 6) -5 ≤ 8
A) True B) False

7) 15 > 13
A) True B) False

8) -8 ≥ 15
A) False B) True

9) -π ≥ -π
A) True B) False

10) π < 3
A) False B) True

7 Evaluate Absolute Value

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Rewrite the expression without absolute value bars.
1) |13|
A) 13 B) -13 C) 26 D) 0

2) |-2|
A) 2 B) -2 C) 4 D) 0

19
3)
-1
A) 19 B) -1 C) 1 D) -19

4) 10 - 13
A) 13 - 10 B) 10 - 13 C) -3 D) 3

5) |5 + (-10)|
A) 5 B) 15 C) -5 D) -15

6) -4 - -9
A) 5 B) 13 C) -5 D) -13

7) -6 + -8
A) 14 B) 2 C) -2 D) -14

Evaluate the expression for the given values of x and y.
|x| |y|
8) + ; x = 6 and y = -3
x y
A) 0 B) 2 C) 1 D) -1




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