Precalculus, 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) 8x + 3; x=2
A) 19 B) 32 C) 11 D) 13

2) 3x + 6; x = -3
A) -3 B) 15 C) -15 D) 3

3) 2(x + 3) + 17; x = -11
A) 1 B) -1 C) 55 D) -21

4) 4x2 + 8y; x = 7 and y = 9
A) 268 B) 856 C) 2052 D) 380

5) (x + 4y) 2 ; x = 2 and y = 2
A) 100 B) 10 C) 20 D) 36

6) 6 + 5(x - 2)3 ; x=4
A) 46 B) 16 C) 88 D) -34

7) x2 - 3(x - y); x = 8 and y = 2
A) 46 B) 38 C) 42 D) -82

7(x + 1)
8) ; x=5
2x + 4
7
A) 3 B) 2 C) 6 D)
2

y - 2x
9) ; x = -4 and y = 1
3x + xy
9 7 7 1
A) - B) C) D) -
16 16 8 16

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 86°F to its equivalent temperature on the Celsius scale.
A) 30°C B) 6°C C) 66°C D) 97°C




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, 2) A stone is dropped from a tower that is 740 feet high. The formula h = 740 - 16t2 describes the stoneʹs height
above the ground, h, in feet, t seconds after it was dropped. What is the stoneʹs height 5 seconds after it is
released?
A) 340 ft B) 350 ft C) 315 ft D) 365 ft

3) If a rock falls from a height of 70 meters above the ground, the height H (in meters) after x seconds can be
approximated using the formula H = 70 - 4.9x2 . What is the height of the rock after 3 seconds?
A) 25.9 m B) 585.9 m C) -146.09 m D) 55.3 m

4) As the relative humidity increases, the temperature seems higher than it is. The formula T = 0.101x + 82.57
approximates the apparent temperature for an actual temperature of 90°F, where x is the relative humidity.
What is the apparent temperature (to the nearest degree) for a relative humidity of 80%?
A) 91°F B) 667°F C) 163°F D) 83°F

5) The winning times (in seconds) in a speed-skating event for men can be represented by the formula
T = 46.97 - 0.099x, 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 1997? Round to the nearest
hundredth.
A) 39.35 sec B) 3609.07 sec C) 40.34 sec D) 41.33 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 = 1.23x + 4.5. That is, x = 0
represents 1990, x = 1 represents 1991, and so on. According to the formula, how many items sold in 1996?
A) 11.88 millions B) 4.5 millions C) 34.38 millions D) 13.11 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, 7, 4, 9} ∩ {4, 6, 1}
A) {1, 4} B) {1} C) {1, 4, 9, 7, 6} D) ∅

2) {1, 3, 9} ∩ {5, 6}
A) ∅ B) {3, 9} C) {1, 5, 9, 3, 6} D) {1, 9}

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) {1, 4, 8, 11} ∪ {1, 4, 13}
A) {1, 4, 8, 11, 13} B) {1, 4} C) {8, 11, 13} D) ∅

2) {1, 11} ∪ {1, 4, 9}
A) {1, 4, 9, 11} B) {1} C) {4, 9, 11} D) ∅

3) {4, 6, 7, 9} ∪ ∅
A) {4, 6, 7, 9} B) {4, 6} C) {7, 9} 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 = {6, 7, -11, 0, 0.9, 9} Integers
A) 6, -11, 0, 9 B) 6, 0 C) 6, -11, 0 D) 6, 0, 9

2) B = {17, 7, -15, 0, 0.7, 9} Whole numbers
A) 17, 0, 9 B) 17, -15, 0 C) 17, -15, 0, 9 D) 17, 0

3) B = {17, 5, -18, 0, 0.8, 4} Natural numbers

A) 17, 4 B) 17, 0, 4 C) 17, 0 D) 17

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4) B = {14, 6, -19, 0, , 16, 0.8, 0.62} Rational numbers
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5
A) 14, -19, 0, , 16, 0.62, 0.8 B) 14, 0, 16
6
5
C) 6, 16 D) 6, , 0.62
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5) B = {3, 8, -15, 0, , 4, 0.6, 0.7} Irrational numbers
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A) 8 B) 8, 0.6 C) 8, 4, 0.6 D) 8, 4, 0.7

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6) B = {5, 8, 0, , 16, -0.9, 0.17, -11} Real numbers
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5 5
A) 5, 8, 0, , 16, -0.9, 0.17, -11 B) 5, 8, 0, , 16, 0.17
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5 5
C) 5, 8, , 16, -0.9, 0.17, -11 D) 5, 0, , -0.9, 0.17, -11
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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) 12 > 21
A) False B) True

2) 14 ≥ 4
A) True B) False

3) -26 < 0
A) True B) False

4) 19 < -8
A) False B) True

5) 16 ≤ 11
A) False B) True


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, 6) -7 ≤ 7
A) True B) False

7) 12 > 2
A) True B) False

8) -2 ≥ 6
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) |9|
A) 9 B) -9 C) 18 D) 0

2) |-7|
A) 7 B) -7 C) 14 D) 0

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3)
1
A) 10 B) -1 C) 1 D) -10

4) 6 - 17
A) 17 - 6 B) 6 - 17 C) -11 D) 11

5) |3 + (-8)|
A) 5 B) 11 C) -5 D) -11

6) -4 - -8
A) 4 B) 12 C) -4 D) -12

7) -1 + -4
A) 5 B) 3 C) -3 D) -5

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

8 Use Absolute Value to Express Distance

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

Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute
value expression.
1) 38 and 96
A) |38 - 96| = 58 B) -|96 - 38| = -58 C) |38 + 96| = 134 D) -|38 + 96| = -134

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