Question 1

Solve the equation by completing the square.
-$$x ^ { 2 } + 8 x = 7$$

Accepted Answer

A)  $\{ - 4 \pm \sqrt { 23 } \}$ 
B)  $\{ - 1 \pm \sqrt { 23 } \}$ 
C)  $\{ - 4 \pm 1 \sqrt { 23 } \}$ 
D)  $\{ 4 + \sqrt { 23 } \}$ 
A)  $\{ - 4 \pm \sqrt { 23 } \}$ 
B)  $\{ - 1 \pm \sqrt { 23 } \}$ 
C)  $\{ - 4 \pm 1 \sqrt { 23 } \}$ 
D)  $\{ 4 + \sqrt { 23 } \}$

Question 2

Solve the problem.
-A square plywood platform has a perimeter which is 9 times the length of a side, decreased by 30. Find the length of a side.

Accepted Answer

A)  6 
B)  11 
C)  1 
D)  5 
A)  6 
B)  11 
C)  1 
D)  5

Question 3

Solve the equation for the indicated variable. Assume no denominator is 0.
-$A = 3 \pi a ^ { 2 }$, for $a$

Accepted Answer

A)  $a = \frac { \pm \sqrt { A \pi } } { 3 }$ 
B)  $a = \frac { \pm \sqrt { 3 \pi A } } { 3 \pi }$ 
C)  $a = \sqrt { 3 \pi A }$ 
D)  $\mathrm { a } = \frac { \pm \mathrm { A } \sqrt { 3 \pi } } { 3 \pi }$ 
A)  $a = \frac { \pm \sqrt { A \pi } } { 3 }$ 
B)  $a = \frac { \pm \sqrt { 3 \pi A } } { 3 \pi }$ 
C)  $a = \sqrt { 3 \pi A }$ 
D)  $\mathrm { a } = \frac { \pm \mathrm { A } \sqrt { 3 \pi } } { 3 \pi }$

Question 4

Solve the problem.
-The height of a box is 7 inches. The length is three inches more than the width. Find the width if the volume is 280.

Accepted Answer

A)  40 in. 
B)  5 in. 
C)  8 in. 
D)  7 in. 
A)  40 in. 
B)  5 in. 
C)  8 in. 
D)  7 in.

Question 5

Decide what values of the variable cannot possibly be solutions for the equation.
-$$x ^ { 2 / 3 } = 4 x ^ { 1 / 3 }$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ 0,4 \}$ 
C)  $\{ 0 , - 64 \}$ 
D)  $\{ 0,64 \}$ 
A)  $\varnothing$ 
B)  $\{ 0,4 \}$ 
C)  $\{ 0 , - 64 \}$ 
D)  $\{ 0,64 \}$

Question 6

Solve the formula for the indicated variable.
-$P = s _ { 1 } + s _ { 2 } + s _ { 3 }$, for $s _ { 2 }$

Accepted Answer

A)  $s _ { 2 } = P - s _ { 1 } - s _ { 3 }$ 
B)  $s _ { 2 } = s _ { 1 } + P - s _ { 3 }$ 
C)  $s _ { 2 } = P + s _ { 1 } + s _ { 3 }$ 
D)  $s _ { 2 } = s _ { 1 } + s _ { 3 } - P$ 
A)  $s _ { 2 } = P - s _ { 1 } - s _ { 3 }$ 
B)  $s _ { 2 } = s _ { 1 } + P - s _ { 3 }$ 
C)  $s _ { 2 } = P + s _ { 1 } + s _ { 3 }$ 
D)  $s _ { 2 } = s _ { 1 } + s _ { 3 } - P$

Question 7

Multiply or divide, as indicated. Simplify the answer.
-$$\frac { \sqrt { - 7 } } { \sqrt { 63 } }$$

Accepted Answer

A)  $\frac { 1 } { 3 } \mathrm { i }$ 
B)  $- \frac { 1 } { 3 }$ 
C)  $\frac { 1 } { 3 }$ 
D)  $- \frac { 1 } { 3 } \mathrm { i }$ 
A)  $\frac { 1 } { 3 } \mathrm { i }$ 
B)  $- \frac { 1 } { 3 }$ 
C)  $\frac { 1 } { 3 }$ 
D)  $- \frac { 1 } { 3 } \mathrm { i }$

Question 8

Solve the equation using the quadratic formula.
-$( 2 x - 1 ) ( x + 1 ) = 6$

Accepted Answer

A)  $\left\{ \frac { - 1 \pm \sqrt { 57 } } { 4 } \right\}$ 
B)  $\left\{ \frac { 1 \pm \sqrt { 57 } } { 2 } \right\}$ 
C)  $\left\{ \frac { - 1 \pm \sqrt { 17 } } { 2 } \right\}$ 
D)  $\left\{ \frac { 1 \pm \sqrt { 57 } } { 4 } \right\}$ 
A)  $\left\{ \frac { - 1 \pm \sqrt { 57 } } { 4 } \right\}$ 
B)  $\left\{ \frac { 1 \pm \sqrt { 57 } } { 2 } \right\}$ 
C)  $\left\{ \frac { - 1 \pm \sqrt { 17 } } { 2 } \right\}$ 
D)  $\left\{ \frac { 1 \pm \sqrt { 57 } } { 4 } \right\}$

Question 9

Solve the equation for the indicated variable. Assume no denominator is 0.
-$\mathrm { Ve } = \frac { 1 } { 2 } \mathrm { mv } ^ { 2 }$, for $\mathrm { v }$

Accepted Answer

A)  $v = \frac { \pm \sqrt { 2 m V e } } { m }$ 
B)  $v = \pm 2 \frac { \sqrt { \mathrm { Ve } } } { \mathrm { m } }$ 
C)  $v = \pm \sqrt { \frac { V e } { 2 m } }$ 
D)  $v = \pm \sqrt { 2 V e }$ 
A)  $v = \frac { \pm \sqrt { 2 m V e } } { m }$ 
B)  $v = \pm 2 \frac { \sqrt { \mathrm { Ve } } } { \mathrm { m } }$ 
C)  $v = \pm \sqrt { \frac { V e } { 2 m } }$ 
D)  $v = \pm \sqrt { 2 V e }$

Question 10

Solve the problem.
-An airplane leaves Los Angeles for Denver at a speed of 420 mph. Thirty minutes later, a plane going from Denver to Los Angeles leaves Denver, which is 850 miles from Los Angeles, at a speed
Of 520 mph. When they meet, how far are they from Denver?

Accepted Answer

A)  61 mi 
B)  354 mi 
C)  123 mi 
D)  307 mi 
A)  61 mi 
B)  354 mi 
C)  123 mi 
D)  307 mi

Question 11

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$24 x + 15 = 3 ( 3 x - 35 )$$

Accepted Answer

A)  Identity; {all real numbers} 
B)  Conditional; $\{ - 8 \}$ 
C)  Contradiction; $\varnothing$ 
D)  Conditional; $\{ 6 \}$ 
A)  Identity; {all real numbers} 
B)  Conditional; $\{ - 8 \}$ 
C)  Contradiction; $\varnothing$ 
D)  Conditional; $\{ 6 \}$

Question 12

Solve the problem.
-The height of a box is 10 inches. Its length is 4 inches more than its width. Find the length if the volume is 320.

Accepted Answer

A)  10 in. 
B)  4 in. 
C)  32 in. 
D)  8 in. 
A)  10 in. 
B)  4 in. 
C)  32 in. 
D)  8 in.

Question 13

Multiply or divide, as indicated. Simplify the answer.
-$$\frac { \sqrt { - 150 } } { \sqrt { - 6 } }$$

Accepted Answer

A)  5 
B)  $- 5 \mathrm { i }$ 
C)  $- 5$ 
D)  $5 i$ 
A)  5 
B)  $- 5 \mathrm { i }$ 
C)  $- 5$ 
D)  $5 i$

Question 14

Find the quotient. Write the answer in standard form.
-$$\frac { 8 + 5 i } { 6 - 9 i }$$

Accepted Answer

A)  $\frac { 1 } { 39 } + \frac { 34 } { 39 } \mathrm { i }$ 
B)  $- \frac { 31 } { 15 } + \frac { 34 } { 45 } \mathrm { i }$ 
C)  $- \frac { 1 } { 45 } + \frac { 34 } { 45 } \mathrm { i }$ 
D)  $\frac { 31 } { 13 } + \frac { 14 } { 13 } \mathrm { i }$ 
A)  $\frac { 1 } { 39 } + \frac { 34 } { 39 } \mathrm { i }$ 
B)  $- \frac { 31 } { 15 } + \frac { 34 } { 45 } \mathrm { i }$ 
C)  $- \frac { 1 } { 45 } + \frac { 34 } { 45 } \mathrm { i }$ 
D)  $\frac { 31 } { 13 } + \frac { 14 } { 13 } \mathrm { i }$

Question 15

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 5 } { x - 5 } + \frac { 14 } { x - 8 } = \frac { 16 } { x ^ { 2 } - 13 x + 40 }$$

Accepted Answer

A)  $\varnothing$ 
B)  $\left\{ \frac { 126 } { 19 } \right\}$ 
C)  $\left\{ \frac { 94 } { 19 } \right\}$ 
D)  $\left\{ - \frac { 33 } { 13 } \right\}$ 
A)  $\varnothing$ 
B)  $\left\{ \frac { 126 } { 19 } \right\}$ 
C)  $\left\{ \frac { 94 } { 19 } \right\}$ 
D)  $\left\{ - \frac { 33 } { 13 } \right\}$

Question 16

Use these equations to convert between the two systems. $$C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32$$ Round answer to the nearest tenth of a degree if necessary.
-$$C = 1 ^ { \circ }$$

Accepted Answer

A)  $\mathrm { F } = 59.4 ^ { \circ }$ 
B)  $\mathrm { F } = 18.3 ^ { \circ }$ 
C)  $\mathrm { F } = - 17.2 ^ { \circ }$ 
D)  $\mathrm { F } = 33.8 ^ { \circ }$ 
A)  $\mathrm { F } = 59.4 ^ { \circ }$ 
B)  $\mathrm { F } = 18.3 ^ { \circ }$ 
C)  $\mathrm { F } = - 17.2 ^ { \circ }$ 
D)  $\mathrm { F } = 33.8 ^ { \circ }$

Question 17

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\sqrt [ 3 ] { x + 1 } = 2$$

Accepted Answer

A)  $\{ 8 \}$ 
B)  $\{ 3 \}$ 
C)  $\{ 7 \}$ 
D)  $\{ 1 \}$ 
A)  $\{ 8 \}$ 
B)  $\{ 3 \}$ 
C)  $\{ 7 \}$ 
D)  $\{ 1 \}$

Question 18

Solve the problem.
-A toy company uses the linear model $y = - 5 x + 560$ to predict the decline in sales of a toy after it has been on the market more than one year. If $\mathrm { x }$ is the number of months after the first year and $\mathrm { y }$ is the number of toys sold in hundreds during that month, how many toys will be sold 7 months after the first year?

Accepted Answer

A)  $- 279,300$ toys 
B)  $- 11,060$ toys 
C)  59,500 toys 
D)  52,500 toys 
A)  $- 279,300$ toys 
B)  $- 11,060$ toys 
C)  59,500 toys 
D)  52,500 toys

Question 19

Solve the inequality. Write the solution set in interval notation.
-$$| x - 1 | \leq 0$$

Accepted Answer

A)  $\{ - 1 \}$ 
B)  $\{ 1 \}$ 
C)  $( - \infty , 1 )$ 
D)  $\varnothing$ 
A)  $\{ - 1 \}$ 
B)  $\{ 1 \}$ 
C)  $( - \infty , 1 )$ 
D)  $\varnothing$

Question 20

Solve the problem.
-A rock falls from a tower that is 68.6 m high. As it is falling, its height is given by the formula $h = 68.6 - 4.9 t ^ { 2 }$ with t in seconds. How many seconds will it take for the rock to hit the ground (h =0)?

Accepted Answer

A)  8 sec 
B)  3.7 sec 
C)  8.3 sec 
D)  960.4 sec 
A)  8 sec 
B)  3.7 sec 
C)  8.3 sec 
D)  960.4 sec

Solve the equation by completing the square. - $x ^ { 2 } + 8 x = 7$

Solve the problem. -A square plywood platform has a perimeter which is 9 times the length of a side, decreased by 30. Find the length of a side.

Solve the equation for the indicated variable. Assume no denominator is 0. - $A = 3 \pi a ^ { 2 }$ , for $a$

Solve the problem. -The height of a box is 7 inches. The length is three inches more than the width. Find the width if the volume is 280.

Decide what values of the variable cannot possibly be solutions for the equation. - $x ^ { 2 / 3 } = 4 x ^ { 1 / 3 }$

Solve the formula for the indicated variable. - $P = s _ { 1 } + s _ { 2 } + s _ { 3 }$ , for $s _ { 2 }$

Multiply or divide, as indicated. Simplify the answer. - $\frac { \sqrt { - 7 } } { \sqrt { 63 } }$

Solve the equation using the quadratic formula. - $( 2 x - 1 ) ( x + 1 ) = 6$

Solve the equation for the indicated variable. Assume no denominator is 0. - $\mathrm { Ve } = \frac { 1 } { 2 } \mathrm { mv } ^ { 2 }$ , for $\mathrm { v }$

Solve the problem. -An airplane leaves Los Angeles for Denver at a speed of 420 mph. Thirty minutes later, a plane going from Denver to Los Angeles leaves Denver, which is 850 miles from Los Angeles, at a speed Of 520 mph. When they meet, how far are they from Denver?

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $24 x + 15 = 3 ( 3 x - 35 )$

Solve the problem. -The height of a box is 10 inches. Its length is 4 inches more than its width. Find the length if the volume is 320.

Multiply or divide, as indicated. Simplify the answer. - $\frac { \sqrt { - 150 } } { \sqrt { - 6 } }$

Find the quotient. Write the answer in standard form. - $\frac { 8 + 5 i } { 6 - 9 i }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 5 } { x - 5 } + \frac { 14 } { x - 8 } = \frac { 16 } { x ^ { 2 } - 13 x + 40 }$

Use these equations to convert between the two systems. $C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32$ Round answer to the nearest tenth of a degree if necessary. - $C = 1 ^ { \circ }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 3 ] { x + 1 } = 2$

Solve the inequality. Write the solution set in interval notation. - $| x - 1 | \leq 0$

Solve the problem. -A rock falls from a tower that is 68.6 m high. As it is falling, its height is given by the formula $h = 68.6 - 4.9 t ^ { 2 }$ with t in seconds. How many seconds will it take for the rock to hit the ground (h =0)?

Review of Basic Concepts

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 2: Equations and Inequalities

Solve the equation by completing the square. - x2+8x=7x ^ { 2 } + 8 x = 7x2+8x=7

Solve the problem. -A square plywood platform has a perimeter which is 9 times the length of a side, decreased by 30. Find the length of a side.

Solve the equation for the indicated variable. Assume no denominator is 0. - A=3πa2A = 3 \pi a ^ { 2 }A=3πa2 , for aaa

Solve the problem. -The height of a box is 7 inches. The length is three inches more than the width. Find the width if the volume is 280.

Decide what values of the variable cannot possibly be solutions for the equation. - x2/3=4x1/3x ^ { 2 / 3 } = 4 x ^ { 1 / 3 }x2/3=4x1/3

Solve the formula for the indicated variable. - P=s1+s2+s3P = s _ { 1 } + s _ { 2 } + s _ { 3 }P=s1​+s2​+s3​ , for s2s _ { 2 }s2​

Multiply or divide, as indicated. Simplify the answer. - −763\frac { \sqrt { - 7 } } { \sqrt { 63 } }63​−7​​

Solve the equation using the quadratic formula. - (2x−1)(x+1)=6( 2 x - 1 ) ( x + 1 ) = 6(2x−1)(x+1)=6

Solve the equation for the indicated variable. Assume no denominator is 0. - Ve=12mv2\mathrm { Ve } = \frac { 1 } { 2 } \mathrm { mv } ^ { 2 }Ve=21​mv2 , for v\mathrm { v }v