Question 1

Solve the inequality. $\frac { x - 2 } { x ^ { 2 } - 5 x - 14 } \geq 0$

Accepted Answer

A)  $[ - 2,2 ] \cup ( 7 , \infty )$ 
B)  $( - 2 , \infty )$ 
C)  $( - \infty , 2 ] \cup ( 7 , \infty )$ 
D)  $( - 2,2 ] \cup ( 7 , \infty )$ 
E)  $( - 2,7 )$ 
A)  $[ - 2,2 ] \cup ( 7 , \infty )$ 
B)  $( - 2 , \infty )$ 
C)  $( - \infty , 2 ] \cup ( 7 , \infty )$ 
D)  $( - 2,2 ] \cup ( 7 , \infty )$ 
E)  $( - 2,7 )$ D

Question 2

The braking distance d (in feet) of a certain car traveling v mi/hr is given by the equation $d = v + \left( v ^ { 2 } / 40 \right)$ Determine the velocities that result in braking distances of less than 30 feet.

Accepted Answer

A)  $( 0,60 )$ 
B)  $( 0,20 )$ 
C)  $( 20,60 )$ 
D)  $( 20 , \infty )$ 
E)  $( 60 , \infty )$ 
A)  $( 0,60 )$ 
B)  $( 0,20 )$ 
C)  $( 20,60 )$ 
D)  $( 20 , \infty )$ 
E)  $( 60 , \infty )$ B

Question 3

Express as a sum of terms of the form $a x ^ { \gamma }$, where r is a rational number. $\frac { \left( x ^ { 2 } + 6 \right) ^ { 2 } } { x ^ { 5 } }$

Accepted Answer

A)  $x ^ { - 1 } + 6 x ^ { - 3 } + 12 x ^ { - 5 }$ 
B)  $x ^ { - 4 } + 12 x ^ { - 2 } + 36$ 
C)  $x ^ { - 1 } + 12 x ^ { - 3 } + 36 x ^ { - 5 }$ 
D)  $x + 12 x ^ { 3 } + 36 x ^ { 5 }$ 
E)  $x ^ { 4 } + 12 x ^ { 2 } + 36$ 
A)  $x ^ { - 1 } + 6 x ^ { - 3 } + 12 x ^ { - 5 }$ 
B)  $x ^ { - 4 } + 12 x ^ { - 2 } + 36$ 
C)  $x ^ { - 1 } + 12 x ^ { - 3 } + 36 x ^ { - 5 }$ 
D)  $x + 12 x ^ { 3 } + 36 x ^ { 5 }$ 
E)  $x ^ { 4 } + 12 x ^ { 2 } + 36$ C

Question 4

Express the interval (2, 11) as an inequality in the variable x.

Accepted Answer

A)  $11 < x < 2$ 
B)  $2 < x \leq 11$ 
C)  $2 \leq x < 11$ 
D)  $2 \leq x \leq 11$ 
E)  $2 < x < 11$ 
A)  $11 < x < 2$ 
B)  $2 < x \leq 11$ 
C)  $2 \leq x < 11$ 
D)  $2 \leq x \leq 11$ 
E)  $2 < x < 11$

Question 5

The two given numbers are coordinates of points $A$ and $\mathcal { B }$ , respectively, on a coordinate line. Express the indicated statement as an inequality involving the absolute value symbol. $\chi$ , $- 3 ; d ( A , B )$ is at least $6$

Accepted Answer

A) $| - 3 - x | \geq 6$ B) $| - 3 + x | > 6$ C) $| - 3 + x | \geq 6$ D) $| - 3 - x | < 6$ E) $| - 3 - x | \leq 6$ A) $| - 3 - x | \geq 6$ B) $| - 3 + x | > 6$ C) $| - 3 + x | \geq 6$ D) $| - 3 - x | < 6$ E) $| - 3 - x | \leq 6$

Question 6

Express as a quotient. $x ^ { - 1 / 5 } - x ^ { 9 / 5 }$

Accepted Answer

A)  $\frac { 1 - x ^ { 5 } } { x ^ { 1 / 5 } }$ 
B)  $\frac { 1 - x ^ { 2 } } { x ^ { 1 / 5 } }$ 
C)  $\frac { 1 - x ^ { 2 } } { x ^ { 1 / 9 } }$ 
D)  $\frac { 1 - x ^ { 9 } } { x ^ { 1 / 5 } }$ 
E)  $\frac { 1 - x ^ { 2 } } { x ^ { 5 / 9 } }$ 
A)  $\frac { 1 - x ^ { 5 } } { x ^ { 1 / 5 } }$ 
B)  $\frac { 1 - x ^ { 2 } } { x ^ { 1 / 5 } }$ 
C)  $\frac { 1 - x ^ { 2 } } { x ^ { 1 / 9 } }$ 
D)  $\frac { 1 - x ^ { 9 } } { x ^ { 1 / 5 } }$ 
E)  $\frac { 1 - x ^ { 2 } } { x ^ { 5 / 9 } }$

Question 7

Solve the inequality. $| 2 x + 13 | \leq - 13$

Accepted Answer

A)  $\left( - \infty , - \frac { 13 } { 2 } \right)$ 
B)  $\left[ - \frac { 13 } { 2 } , \frac { 13 } { 2 } \right]$ 
C)  $\left( - \infty , \frac { 13 } { 2 } \right]$ 
D)  $\left( - \frac { 13 } { 2 } , \frac { 13 } { 2 } \right)$ 
E)  No solution 
A)  $\left( - \infty , - \frac { 13 } { 2 } \right)$ 
B)  $\left[ - \frac { 13 } { 2 } , \frac { 13 } { 2 } \right]$ 
C)  $\left( - \infty , \frac { 13 } { 2 } \right]$ 
D)  $\left( - \frac { 13 } { 2 } , \frac { 13 } { 2 } \right)$ 
E)  No solution

Question 8

Solve the inequality. $- 2 < | x | < 9$

Accepted Answer

A)  $( - 9 , - 2 ) \cup ( 2,9 )$ 
B)  $( - 9,9 )$ 
C)  $( - 2,9 )$ 
D)  $( - \infty , - 2 ) \cup ( 9 , \infty )$ 
E)  $( 0,9 )$ 
A)  $( - 9 , - 2 ) \cup ( 2,9 )$ 
B)  $( - 9,9 )$ 
C)  $( - 2,9 )$ 
D)  $( - \infty , - 2 ) \cup ( 9 , \infty )$ 
E)  $( 0,9 )$

Question 9

Simplify the expression. $\frac { 3 a ^ { 2 } + 20 a + 25 } { a ^ { 4 } - 625 } \div \frac { 9 a ^ { 2 } + 30 a + 25 } { a ^ { 2 } - 5 a }$

Accepted Answer

A)  $\frac { a } { \left( a ^ { 2 } - 25 \right) ( 3 a - 5 ) }$ 
B)  $\frac { a } { \left( a ^ { 2 } + 25 \right) ( 3 a - 5 ) }$ 
C)  $\frac { 1 } { \left( a ^ { 2 } - 25 \right) ( 3 a + 5 ) }$ 
D)  $\frac { a } { \left( a ^ { 2 } + 25 \right) ( 3 a + 5 ) }$ 
E)  $\frac { a } { \left( a ^ { 2 } - 25 \right) ( 9 a + 5 ) }$ 
A)  $\frac { a } { \left( a ^ { 2 } - 25 \right) ( 3 a - 5 ) }$ 
B)  $\frac { a } { \left( a ^ { 2 } + 25 \right) ( 3 a - 5 ) }$ 
C)  $\frac { 1 } { \left( a ^ { 2 } - 25 \right) ( 3 a + 5 ) }$ 
D)  $\frac { a } { \left( a ^ { 2 } + 25 \right) ( 3 a + 5 ) }$ 
E)  $\frac { a } { \left( a ^ { 2 } - 25 \right) ( 9 a + 5 ) }$

Question 10

Simplify the expression. $\left( \frac { - 243 x ^ { 5 } } { y ^ { - 10 } } \right) ^ { \frac { 2 } { 5 } }$

Accepted Answer

A)  $- 3 x ^ { 2 } y ^ { 4 }$ 
B)  $- 9 x ^ { 2 } y ^ { 4 }$ 
C)  $9 x ^ { 2 } y ^ { 4 }$ 
D)  $3 x ^ { 2 } y ^ { 4 }$ 
E)  $- 9 x ^ { 4 } y ^ { 2 }$ 
A)  $- 3 x ^ { 2 } y ^ { 4 }$ 
B)  $- 9 x ^ { 2 } y ^ { 4 }$ 
C)  $9 x ^ { 2 } y ^ { 4 }$ 
D)  $3 x ^ { 2 } y ^ { 4 }$ 
E)  $- 9 x ^ { 4 } y ^ { 2 }$

Question 11

A large grain silo is to be constructed in the shape of a circular cylinder with a hemisphere attached to the top (see the figure). The diameter of the silo is to be 36 feet, but the height is yet to be determined. Find the height h of the silo that will result in a capacity of 15,876 π ft  3 .

Accepted Answer

A)  $h = 55$ feet 
B)  $h = 60$ feet 
C)  $h = 110$ feet 
D)  $h = 43$ feet 
E)  $h = 57$ feet 
A)  $h = 55$ feet 
B)  $h = 60$ feet 
C)  $h = 110$ feet 
D)  $h = 43$ feet 
E)  $h = 57$ feet

Question 12

Solve the inequality. $( x + 2 ) ( x - 4 ) ( 11 - x ) \leq 0$

Accepted Answer

A)  $( - \infty , 4 ] \cup [ 2 , \infty )$ 
B)  $( - 2,4 ) \cup ( 11 , \infty )$ 
C)  $[ - 2,4 ] \cup [ 11 , \infty )$ 
D)  $( - \infty , - 2 ] \cup [ 4,11 ]$ 
E)  $( - \infty , 4 ) \cup ( 2 , \infty )$ 
A)  $( - \infty , 4 ] \cup [ 2 , \infty )$ 
B)  $( - 2,4 ) \cup ( 11 , \infty )$ 
C)  $[ - 2,4 ] \cup [ 11 , \infty )$ 
D)  $( - \infty , - 2 ] \cup [ 4,11 ]$ 
E)  $( - \infty , 4 ) \cup ( 2 , \infty )$

Question 13

Express the inequality $- 1 \geq x > - 8$ as an interval.

Accepted Answer

A)  $[ - 1 , - 8 )$ 
B)  $[ - 8 , - 1 )$ 
C)  $[ - 8 , - 1 ]$ 
D)  $( - 8 , - 1 ]$ 
E)  $( - 8 , - 1 )$ 
A)  $[ - 1 , - 8 )$ 
B)  $[ - 8 , - 1 )$ 
C)  $[ - 8 , - 1 ]$ 
D)  $( - 8 , - 1 ]$ 
E)  $( - 8 , - 1 )$

Question 14

Find the solutions of the equation. $x ^ { 3 } - 343 = 0$

Accepted Answer

A)  $7$ 
B)  $7 , \pm 7 i$ 
C)  $7 , - \frac { 7 } { 2 } \pm \frac { 7 } { 2 } \sqrt { 3 } i$ 
D)  $7 , \frac { 7 } { 2 } \pm \frac { 7 } { 2 } \sqrt { 3 } i$ 
E)  $7 , - 7 \pm 7 \sqrt { 3 } i$ 
A)  $7$ 
B)  $7 , \pm 7 i$ 
C)  $7 , - \frac { 7 } { 2 } \pm \frac { 7 } { 2 } \sqrt { 3 } i$ 
D)  $7 , \frac { 7 } { 2 } \pm \frac { 7 } { 2 } \sqrt { 3 } i$ 
E)  $7 , - 7 \pm 7 \sqrt { 3 } i$

Question 15

Rewrite the expression using a radical. $8 - y ^ { \frac { 1 } { 8 } }$

Accepted Answer

A)  $8 - \sqrt { y }$ 
B)  $\sqrt { 8 - y }$ 
C)  $\sqrt [ 8 ] { 8 - y }$ 
D)  $\sqrt [ 8 ] { y } - \sqrt [ 8 ] { y }$ 
E)  $8 - \sqrt [ 8 ] { y }$ 
A)  $8 - \sqrt { y }$ 
B)  $\sqrt { 8 - y }$ 
C)  $\sqrt [ 8 ] { 8 - y }$ 
D)  $\sqrt [ 8 ] { y } - \sqrt [ 8 ] { y }$ 
E)  $8 - \sqrt [ 8 ] { y }$

Question 16

Solve the inequality. $\frac { 1 } { x - 3 } \geq \frac { 5 } { x + 6 }$

Accepted Answer

A)  $( - \infty , - 6 ) \cup ( 3 , \infty ]$ 
B)  $( - 6,3 )$ 
C)  $( - 6,3 ) \cup \left[ \frac { 21 } { 4 } , \infty \right)$ 
D)  $( - \infty , - 6 ) \cup \left( 3 , \frac { 21 } { 4 } \right]$ 
E)  $( - \infty , - 6 ) \cup ( - 6,3 ) \cup \left[ \frac { 21 } { 4 } , \infty \right)$ 
A)  $( - \infty , - 6 ) \cup ( 3 , \infty ]$ 
B)  $( - 6,3 )$ 
C)  $( - 6,3 ) \cup \left[ \frac { 21 } { 4 } , \infty \right)$ 
D)  $( - \infty , - 6 ) \cup \left( 3 , \frac { 21 } { 4 } \right]$ 
E)  $( - \infty , - 6 ) \cup ( - 6,3 ) \cup \left[ \frac { 21 } { 4 } , \infty \right)$

Question 17

Archeologists can determine the height of a human without having a complete skeleton. If an archeologist finds only a humerus, then the height of the individual can be determined by using a simple linear relationship. (The humerus is the bone between the shoulder and the elbow.) For a female, if x is the length of the humerus (in centimeters), then her height h (in centimeters) can be determined using the formula $h = 65 + 3.14 x$ .
For a male, $h = 73.6 + 3.0 x$ should be used.
A female skeleton having a 31-centimeter humerus is found. Find the woman's height at death.

Accepted Answer

A)  $h = 157.04$ centimeters 
B)  $h = 162.34$ centimeters 
C)  $h = 107.6$ centimeters 
D)  $h = 166.6$ centimeters 
E)  $h = 99.14$ centimeters 
A)  $h = 157.04$ centimeters 
B)  $h = 162.34$ centimeters 
C)  $h = 107.6$ centimeters 
D)  $h = 166.6$ centimeters 
E)  $h = 99.14$ centimeters

Question 18

O'Carroll's formula is used to handicap weight lifters. If a lifter, who weighs $b$ kilograms, lifts $w$ kilograms of weight, then the handicapped weight W is given by: $W = \frac { w } { \sqrt [ 3 ] { b - 35 } }$ Suppose two lifters weighing 73 kilograms and 89 kilograms lift weights of 273 kilograms and 210 kilograms, respectively. Use O'Carroll's formula to determine the superior weight lifter.

Accepted Answer

A)  the 73-kg lifter 
B)  the 89-kg lifter 
A)  the 73-kg lifter 
B)  the 89-kg lifter

Question 19

Solve the equation. $5 x - 16 = 3 ( x - 2 )$

Accepted Answer

A)  $x = 7$ 
B)  $x = - 2$ 
C)  $x = 5$ 
D)  $x = 11$ 
E)  $x = - 11$ 
A)  $x = 7$ 
B)  $x = - 2$ 
C)  $x = 5$ 
D)  $x = 11$ 
E)  $x = - 11$

Question 20

Find the solutions of the equation. $x ^ { 3 } + 3 x ^ { 2 } + 5 x = 0$

Accepted Answer

A)  $0$ 
B)  $0 , - \frac { 3 } { 2 } \pm \frac { 1 } { 2 } \sqrt { 11 } i$ 
C)  $0 , - \frac { 3 } { 2 } \pm \frac { 1 } { 2 } \sqrt { 11 }$ 
D)  $0 , \frac { 3 } { 2 } \pm \frac { 1 } { 2 } \sqrt { 11 t }$ 
E)  no solutions 
A)  $0$ 
B)  $0 , - \frac { 3 } { 2 } \pm \frac { 1 } { 2 } \sqrt { 11 } i$ 
C)  $0 , - \frac { 3 } { 2 } \pm \frac { 1 } { 2 } \sqrt { 11 }$ 
D)  $0 , \frac { 3 } { 2 } \pm \frac { 1 } { 2 } \sqrt { 11 t }$ 
E)  no solutions

Solve the inequality. $\frac { x - 2 } { x ^ { 2 } - 5 x - 14 } \geq 0$

The braking distance d (in feet) of a certain car traveling v mi/hr is given by the equation $d = v + \left( v ^ { 2 } / 40 \right)$ Determine the velocities that result in braking distances of less than 30 feet.

Express as a sum of terms of the form $a x ^ { \gamma }$ , where r is a rational number. $\frac { \left( x ^ { 2 } + 6 \right) ^ { 2 } } { x ^ { 5 } }$

Express the interval (2, 11) as an inequality in the variable x.

The two given numbers are coordinates of points $A$ and $\mathcal { B }$ , respectively, on a coordinate line. Express the indicated statement as an inequality involving the absolute value symbol. $\chi$ , $- 3 ; d ( A , B )$ is at least $6$

Express as a quotient. $x ^ { - 1 / 5 } - x ^ { 9 / 5 }$

Solve the inequality. $| 2 x + 13 | \leq - 13$

Solve the inequality. $- 2 < | x | < 9$

Simplify the expression. $\frac { 3 a ^ { 2 } + 20 a + 25 } { a ^ { 4 } - 625 } \div \frac { 9 a ^ { 2 } + 30 a + 25 } { a ^ { 2 } - 5 a }$

Simplify the expression. $\left( \frac { - 243 x ^ { 5 } } { y ^ { - 10 } } \right) ^ { \frac { 2 } { 5 } }$

A large grain silo is to be constructed in the shape of a circular cylinder with a hemisphere attached to the top (see the figure). The diameter of the silo is to be 36 feet, but the height is yet to be determined. Find the height h of the silo that will result in a capacity of 15,876 π ft ³.

Solve the inequality. $( x + 2 ) ( x - 4 ) ( 11 - x ) \leq 0$

Express the inequality $- 1 \geq x > - 8$ as an interval.

Find the solutions of the equation. $x ^ { 3 } - 343 = 0$

Rewrite the expression using a radical. $8 - y ^ { \frac { 1 } { 8 } }$

Solve the inequality. $\frac { 1 } { x - 3 } \geq \frac { 5 } { x + 6 }$

Solve the equation. $5 x - 16 = 3 ( x - 2 )$

Find the solutions of the equation. $x ^ { 3 } + 3 x ^ { 2 } + 5 x = 0$

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series, and Probability

Topics From Analytical Geometry

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Exam 1: Topics From Algebra

Solve the inequality. x−2x2−5x−14≥0\frac { x - 2 } { x ^ { 2 } - 5 x - 14 } \geq 0x2−5x−14x−2​≥0

The braking distance d (in feet) of a certain car traveling v mi/hr is given by the equation d=v+(v2/40)d = v + \left( v ^ { 2 } / 40 \right)d=v+(v2/40) Determine the velocities that result in braking distances of less than 30 feet.

Express as a sum of terms of the form axγa x ^ { \gamma }axγ , where r is a rational number. (x2+6)2x5\frac { \left( x ^ { 2 } + 6 \right) ^ { 2 } } { x ^ { 5 } }x5(x2+6)2​

Express the interval (2, 11) as an inequality in the variable x.

The two given numbers are coordinates of points AAA and B\mathcal { B }B , respectively, on a coordinate line. Express the indicated statement as an inequality involving the absolute value symbol. χ\chiχ , −3;d(A,B)- 3 ; d ( A , B )−3;d(A,B) is at least 666

Express as a quotient. x−1/5−x9/5x ^ { - 1 / 5 } - x ^ { 9 / 5 }x−1/5−x9/5

Solve the inequality. ∣2x+13∣≤−13| 2 x + 13 | \leq - 13∣2x+13∣≤−13

Solve the inequality. −2<∣x∣<9- 2 < | x | < 9−2<∣x∣<9

Simplify the expression. 3a2+20a+25a4−625÷9a2+30a+25a2−5a\frac { 3 a ^ { 2 } + 20 a + 25 } { a ^ { 4 } - 625 } \div \frac { 9 a ^ { 2 } + 30 a + 25 } { a ^ { 2 } - 5 a }a4−6253a2+20a+25​÷a2−5a9a2+30a+25​

Simplify the expression. (−243x5y−10)25\left( \frac { - 243 x ^ { 5 } } { y ^ { - 10 } } \right) ^ { \frac { 2 } { 5 } }(y−10−243x5​)52​

A large grain silo is to be constructed in the shape of a circular cylinder with a hemisphere attached to the top (see the figure). The diameter of the silo is to be 36 feet, but the height is yet to be determined. Find the height h of the silo that will result in a capacity of 15,876 π ft 3 .

Solve the inequality. (x+2)(x−4)(11−x)≤0( x + 2 ) ( x - 4 ) ( 11 - x ) \leq 0(x+2)(x−4)(11−x)≤0

Express the inequality −1≥x>−8- 1 \geq x > - 8−1≥x>−8 as an interval.

Find the solutions of the equation. x3−343=0x ^ { 3 } - 343 = 0x3−343=0

Rewrite the expression using a radical. 8−y188 - y ^ { \frac { 1 } { 8 } }8−y81​

Solve the inequality. 1x−3≥5x+6\frac { 1 } { x - 3 } \geq \frac { 5 } { x + 6 }x−31​≥x+65​

Solve the equation. 5x−16=3(x−2)5 x - 16 = 3 ( x - 2 )5x−16=3(x−2)

Find the solutions of the equation. x3+3x2+5x=0x ^ { 3 } + 3 x ^ { 2 } + 5 x = 0x3+3x2+5x=0

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series, and Probability

Topics From Analytical Geometry

Filters

Solve the inequality. $\frac { x - 2 } { x ^ { 2 } - 5 x - 14 } \geq 0$

The braking distance d (in feet) of a certain car traveling v mi/hr is given by the equation $d = v + \left( v ^ { 2 } / 40 \right)$ Determine the velocities that result in braking distances of less than 30 feet.

Express as a sum of terms of the form $a x ^ { \gamma }$ , where r is a rational number. $\frac { \left( x ^ { 2 } + 6 \right) ^ { 2 } } { x ^ { 5 } }$

The two given numbers are coordinates of points $A$ and $\mathcal { B }$ , respectively, on a coordinate line. Express the indicated statement as an inequality involving the absolute value symbol. $\chi$ , $- 3 ; d ( A , B )$ is at least $6$

Express as a quotient. $x ^ { - 1 / 5 } - x ^ { 9 / 5 }$

Solve the inequality. $| 2 x + 13 | \leq - 13$

Solve the inequality. $- 2 < | x | < 9$

Simplify the expression. $\frac { 3 a ^ { 2 } + 20 a + 25 } { a ^ { 4 } - 625 } \div \frac { 9 a ^ { 2 } + 30 a + 25 } { a ^ { 2 } - 5 a }$

Simplify the expression. $\left( \frac { - 243 x ^ { 5 } } { y ^ { - 10 } } \right) ^ { \frac { 2 } { 5 } }$

A large grain silo is to be constructed in the shape of a circular cylinder with a hemisphere attached to the top (see the figure). The diameter of the silo is to be 36 feet, but the height is yet to be determined. Find the height h of the silo that will result in a capacity of 15,876 π ft ³.

Solve the inequality. $( x + 2 ) ( x - 4 ) ( 11 - x ) \leq 0$

Express the inequality $- 1 \geq x > - 8$ as an interval.

Find the solutions of the equation. $x ^ { 3 } - 343 = 0$

Rewrite the expression using a radical. $8 - y ^ { \frac { 1 } { 8 } }$

Solve the inequality. $\frac { 1 } { x - 3 } \geq \frac { 5 } { x + 6 }$

Solve the equation. $5 x - 16 = 3 ( x - 2 )$

Find the solutions of the equation. $x ^ { 3 } + 3 x ^ { 2 } + 5 x = 0$