Question 1

Solve the equation.
-$$\frac { x } { x - 4 } - 4 = \frac { 4 } { x - 4 }$$

Accepted Answer

A)  $\{ 4 , - 4 \}$ 
B)  $\{ 4 \}$ 
C)  no solution 
D)  $\{ - 4 \}$ 
A)  $\{ 4 , - 4 \}$ 
B)  $\{ 4 \}$ 
C)  no solution 
D)  $\{ - 4 \}$ C

Question 2

Decide what number must be added to the binomial to make a perfect square trinomial.
-$$x ^ { 2 } + 14 x$$

Accepted Answer

A) 7 
B) 25 
C) 49 
D) 98 
A) 7 
B) 25 
C) 49 
D) 98 C

Question 3

Solve the problem.
-The square of the difference between a number and 9 is 9. Find the number(s).

Accepted Answer

A) 6, 12 
B) 78, 84 
C) 12 
D) 90 
A) 6, 12 
B) 78, 84 
C) 12 
D) 90 A

Question 4

Decide what number must be added to the binomial to make a perfect square trinomial.
-$$x ^ { 2 } - 18 x$$

Accepted Answer

A) 162 
B) 41 
C) -9 
D) 81 
A) 162 
B) 41 
C) -9 
D) 81

Question 5

Write the expression in the standard form a + bi.
-$\frac { 2 } { 2 - 6 i }$

Accepted Answer

A)  $- \frac { 1 } { 8 } + \frac { 3 } { 8 } \mathrm { i }$ 
B)  $- \frac { 1 } { 8 } - \frac { 3 } { 8 } \mathrm { i }$ 
C)  $\frac { 1 } { 10 } + \frac { 3 } { 10 } \mathrm { i }$ 
D)  $\frac { 1 } { 10 } - \frac { 3 } { 10 } \mathrm { i }$ 
A)  $- \frac { 1 } { 8 } + \frac { 3 } { 8 } \mathrm { i }$ 
B)  $- \frac { 1 } { 8 } - \frac { 3 } { 8 } \mathrm { i }$ 
C)  $\frac { 1 } { 10 } + \frac { 3 } { 10 } \mathrm { i }$ 
D)  $\frac { 1 } { 10 } - \frac { 3 } { 10 } \mathrm { i }$

Question 6

Solve the equation by completing the square.
-$$x ^ { 2 } + 10 x + 14 = 0$$

Accepted Answer

A)  $\{ - 10 + \sqrt { 14 } \}$ 
B)  $\{ 5 + \sqrt { 11 } \}$ 
C)  $\{ 5 - \sqrt { 14 } , 5 + \sqrt { 14 } \}$ 
D)  $\{ - 5 - \sqrt { 11 } , - 5 + \sqrt { 11 } \}$ 
A)  $\{ - 10 + \sqrt { 14 } \}$ 
B)  $\{ 5 + \sqrt { 11 } \}$ 
C)  $\{ 5 - \sqrt { 14 } , 5 + \sqrt { 14 } \}$ 
D)  $\{ - 5 - \sqrt { 11 } , - 5 + \sqrt { 11 } \}$

Question 7

Perform the desired operation. Write the answer in the form a + bi.
-$- 3 i ( - 4 + 9 i )$

Accepted Answer

A)  $27 + 12 \mathrm { i }$ 
B)  $12 i - 27 i ^ { 2 }$ 
C)  $- 27 + 12 \mathrm { i }$ 
D)  $12 i + 27 i ^ { 2 }$ 
A)  $27 + 12 \mathrm { i }$ 
B)  $12 i - 27 i ^ { 2 }$ 
C)  $- 27 + 12 \mathrm { i }$ 
D)  $12 i + 27 i ^ { 2 }$

Question 8

Solve the problem.
-As part of a physics experiment, Ming drops a baseball from the top of a 330-foot building. To the nearest tenth of a second, for how many seconds will the baseball fall? (Hint: Use the formula h $$= 16 t ^ { 2 }$$ , which gives the distance h, in feet, that a free-falling object travels in t seconds.)

Accepted Answer

A) 20.6 sec 
B) 82.5 sec 
C) 1.1 sec 
D) 4.5 sec 
A) 20.6 sec 
B) 82.5 sec 
C) 1.1 sec 
D) 4.5 sec

Question 9

Find the real solutions, if any, of the equation. Use the quadratic formula.
-$$x ^ { 2 } - 4 x - 7 = 0$$

Accepted Answer

A)  $\{ 4 + \sqrt { 11 } , 4 - \sqrt { 11 } \}$ 
B)  $\{ 2 + \sqrt { 11 } , 2 - \sqrt { 11 } \}$ 
C)  $\{ - 2 + \sqrt { 11 } , - 2 - \sqrt { 11 } \}$ 
D)  $\{ 2 + \sqrt { 7 } , 2 - \sqrt { 7 } \}$ 
A)  $\{ 4 + \sqrt { 11 } , 4 - \sqrt { 11 } \}$ 
B)  $\{ 2 + \sqrt { 11 } , 2 - \sqrt { 11 } \}$ 
C)  $\{ - 2 + \sqrt { 11 } , - 2 - \sqrt { 11 } \}$ 
D)  $\{ 2 + \sqrt { 7 } , 2 - \sqrt { 7 } \}$

Question 10

Determine whether the equation is linear or nonlinear.
-$$26 x - \frac { 1 } { 15 } = 19$$

Accepted Answer

A) linear 
B) nonlinear 
A) linear 
B) nonlinear

Question 11

Solve the inequality. Express your answer using interval notation.
-$| 7 k - 7 | - 2 < 6$

Accepted Answer

A)  $\left( - \infty , - \frac { 1 } { 7 } \right)$ 
B)  $\left( - \frac { 1 } { 7 } , \frac { 15 } { 7 } \right)$ 
C)  $\left( - \infty , \frac { 15 } { 7 } \right)$ 
D)  $\left( - \infty , - \frac { 1 } { 7 } \right) \cup \left( \frac { 15 } { 7 } , \infty \right)$ 
A)  $\left( - \infty , - \frac { 1 } { 7 } \right)$ 
B)  $\left( - \frac { 1 } { 7 } , \frac { 15 } { 7 } \right)$ 
C)  $\left( - \infty , \frac { 15 } { 7 } \right)$ 
D)  $\left( - \infty , - \frac { 1 } { 7 } \right) \cup \left( \frac { 15 } { 7 } , \infty \right)$

Question 12

Solve the rational inequality. Express the solution in interval notation.
-$$\frac { ( x - 2 ) ^ { 2 } } { x ^ { 2 } - 25 } > 0$$

Accepted Answer

A)  $( - 5,2 ) \cup ( 2,5 )$ 
B)  $( - \infty , - 5 ) \cup ( 2,5 )$ 
C)  $( - 5,2 ) \cup ( 5 , \infty )$ 
D)  $( - \infty , - 5 ) \cup ( 5 , \infty )$ 
A)  $( - 5,2 ) \cup ( 2,5 )$ 
B)  $( - \infty , - 5 ) \cup ( 2,5 )$ 
C)  $( - 5,2 ) \cup ( 5 , \infty )$ 
D)  $( - \infty , - 5 ) \cup ( 5 , \infty )$

Question 13

Determine whether the equation is linear or nonlinear.
-$$\frac { x - 4 } { 7 x + 4 } = 10$$

Accepted Answer

A) linear 
B) nonlinear 
A) linear 
B) nonlinear

Question 14

Solve the polynomial inequality. Express the solution in interval notation.
-$x ^ { 3 } - 2 x ^ { 2 } - 35 x > 0$

Accepted Answer

A)  $( - 5 , \infty )$ 
B)  $( - 5,0 ) \cup ( 7 , \infty )$ 
C)  $( - \infty , - 5 ) \cup ( 0,7 )$ 
D)  $( - 7,0 ) \cup ( 5 , \infty )$ 
A)  $( - 5 , \infty )$ 
B)  $( - 5,0 ) \cup ( 7 , \infty )$ 
C)  $( - \infty , - 5 ) \cup ( 0,7 )$ 
D)  $( - 7,0 ) \cup ( 5 , \infty )$

Question 15

Find the real solutions, if any, of the equation. Use the quadratic formula.
-$$4 x ^ { 2 } - x + 7 = 0$$

Accepted Answer

A)  $\left\{ \frac { - 1 - \sqrt { 113 } } { 8 } , \frac { 1 + \sqrt { 113 } } { 8 } \right\}$ 
B)  $\left\{ \frac { - 1 + \sqrt { 113 } } { 8 } , \frac { 1 + \sqrt { 113 } } { 8 } \right\}$ 
C)  no real solution 
D)  $\left\{ \frac { - 1 - \sqrt { 113 } } { 8 } , \frac { - 1 + \sqrt { 113 } } { 8 } \right\}$ 
A)  $\left\{ \frac { - 1 - \sqrt { 113 } } { 8 } , \frac { 1 + \sqrt { 113 } } { 8 } \right\}$ 
B)  $\left\{ \frac { - 1 + \sqrt { 113 } } { 8 } , \frac { 1 + \sqrt { 113 } } { 8 } \right\}$ 
C)  no real solution 
D)  $\left\{ \frac { - 1 - \sqrt { 113 } } { 8 } , \frac { - 1 + \sqrt { 113 } } { 8 } \right\}$

Question 16

Find the product of the given complex number and its conjugate. Write the answer in the form a + bi.
-$$\frac { \sqrt { 2 } } { 3 } + \frac { 2 } { 3 } \mathrm { i }$$

Accepted Answer

A)  $\frac { 2 } { 9 } + \frac { 4 } { 9 } \mathrm { i }$ 
B)  $\frac { 4 } { 3 }$ 
C)  $\frac { 2 } { 9 } - \frac { 4 } { 9 } \mathrm { i }$ 
D)  $\frac { 2 } { 3 }$ 
A)  $\frac { 2 } { 9 } + \frac { 4 } { 9 } \mathrm { i }$ 
B)  $\frac { 4 } { 3 }$ 
C)  $\frac { 2 } { 9 } - \frac { 4 } { 9 } \mathrm { i }$ 
D)  $\frac { 2 } { 3 }$

Question 17

Solve the equation.
-$$| 3 - 6 x | = 9$$

Accepted Answer

A)  $\{ - 5,1 \}$ 
B)  $\{ - 1,2 \}$ 
C)  $\{ - 1,5 \}$ 
D)  $\{ - 2,1 \}$ 
A)  $\{ - 5,1 \}$ 
B)  $\{ - 1,2 \}$ 
C)  $\{ - 1,5 \}$ 
D)  $\{ - 2,1 \}$

Question 18

Decide what number must be added to the binomial to make a perfect square trinomial.
-$$( 2 x + 5 ) ^ { 2 } = 49$$

Accepted Answer

A)  $\{ - 6,1 \}$ 
B)  $\{ - 27,27 \}$ 
C)  $\{ 1,6 \}$ 
D)  $\{ 0,1 \}$ 
A)  $\{ - 6,1 \}$ 
B)  $\{ - 27,27 \}$ 
C)  $\{ 1,6 \}$ 
D)  $\{ 0,1 \}$

Question 19

Solve the linear inequality. Express the solution in set-builder notation.
-$$- 4 ( 2 x + 12 ) < - 12 x - 36$$

Accepted Answer

A)  $\{ x \mid x > - 12 \}$ 
B)  $\{ x \mid x  3 \}$ 
A)  $\{ x \mid x > - 12 \}$ 
B)  $\{ x \mid x  3 \}$

Question 20

Solve the equation.
-$$\frac { - 3 x + 5 } { 2 } + 1 = - \frac { 6 x } { 7 }$$

Accepted Answer

A)  $\left\{ \frac { 7 } { 3 } \right\}$ 
B)  $\left\{ \frac { 49 } { 33 } \right\}$ 
C)  $\left\{ \frac { 49 } { 9 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 3 } \right\}$ 
A)  $\left\{ \frac { 7 } { 3 } \right\}$ 
B)  $\left\{ \frac { 49 } { 33 } \right\}$ 
C)  $\left\{ \frac { 49 } { 9 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 3 } \right\}$

Solve the equation. - $\frac { x } { x - 4 } - 4 = \frac { 4 } { x - 4 }$

Decide what number must be added to the binomial to make a perfect square trinomial. - $x ^ { 2 } + 14 x$

Solve the problem. -The square of the difference between a number and 9 is 9. Find the number(s).

Decide what number must be added to the binomial to make a perfect square trinomial. - $x ^ { 2 } - 18 x$

Write the expression in the standard form a + bi. - $\frac { 2 } { 2 - 6 i }$

Solve the equation by completing the square. - $x ^ { 2 } + 10 x + 14 = 0$

Perform the desired operation. Write the answer in the form a + bi. - $- 3 i ( - 4 + 9 i )$

Find the real solutions, if any, of the equation. Use the quadratic formula. - $x ^ { 2 } - 4 x - 7 = 0$

Determine whether the equation is linear or nonlinear. - $26 x - \frac { 1 } { 15 } = 19$

Solve the inequality. Express your answer using interval notation. - $| 7 k - 7 | - 2 < 6$

Solve the rational inequality. Express the solution in interval notation. - $\frac { ( x - 2 ) ^ { 2 } } { x ^ { 2 } - 25 } > 0$

Determine whether the equation is linear or nonlinear. - $\frac { x - 4 } { 7 x + 4 } = 10$

Solve the polynomial inequality. Express the solution in interval notation. - $x ^ { 3 } - 2 x ^ { 2 } - 35 x > 0$

Find the real solutions, if any, of the equation. Use the quadratic formula. - $4 x ^ { 2 } - x + 7 = 0$

Find the product of the given complex number and its conjugate. Write the answer in the form a + bi. - $\frac { \sqrt { 2 } } { 3 } + \frac { 2 } { 3 } \mathrm { i }$

Solve the equation. - $| 3 - 6 x | = 9$

Decide what number must be added to the binomial to make a perfect square trinomial. - $( 2 x + 5 ) ^ { 2 } = 49$

Solve the linear inequality. Express the solution in set-builder notation. - $- 4 ( 2 x + 12 ) < - 12 x - 36$

Solve the equation. - $\frac { - 3 x + 5 } { 2 } + 1 = - \frac { 6 x } { 7 }$

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Exam 1: Equations, Inequalities, and Applications

Solve the equation. - xx−4−4=4x−4\frac { x } { x - 4 } - 4 = \frac { 4 } { x - 4 }x−4x​−4=x−44​

Decide what number must be added to the binomial to make a perfect square trinomial. - x2+14xx ^ { 2 } + 14 xx2+14x

Solve the problem. -The square of the difference between a number and 9 is 9. Find the number(s).

Decide what number must be added to the binomial to make a perfect square trinomial. - x2−18xx ^ { 2 } - 18 xx2−18x

Write the expression in the standard form a + bi. - 22−6i\frac { 2 } { 2 - 6 i }2−6i2​

Solve the equation by completing the square. - x2+10x+14=0x ^ { 2 } + 10 x + 14 = 0x2+10x+14=0

Perform the desired operation. Write the answer in the form a + bi. - −3i(−4+9i)- 3 i ( - 4 + 9 i )−3i(−4+9i)

Find the real solutions, if any, of the equation. Use the quadratic formula. - x2−4x−7=0x ^ { 2 } - 4 x - 7 = 0x2−4x−7=0

Determine whether the equation is linear or nonlinear. - 26x−115=1926 x - \frac { 1 } { 15 } = 1926x−151​=19

Solve the inequality. Express your answer using interval notation. - ∣7k−7∣−2<6| 7 k - 7 | - 2 < 6∣7k−7∣−2<6

Solve the rational inequality. Express the solution in interval notation. - (x−2)2x2−25>0\frac { ( x - 2 ) ^ { 2 } } { x ^ { 2 } - 25 } > 0x2−25(x−2)2​>0

Determine whether the equation is linear or nonlinear. - x−47x+4=10\frac { x - 4 } { 7 x + 4 } = 107x+4x−4​=10

Solve the polynomial inequality. Express the solution in interval notation. - x3−2x2−35x>0x ^ { 3 } - 2 x ^ { 2 } - 35 x > 0x3−2x2−35x>0

Find the real solutions, if any, of the equation. Use the quadratic formula. - 4x2−x+7=04 x ^ { 2 } - x + 7 = 04x2−x+7=0

Find the product of the given complex number and its conjugate. Write the answer in the form a + bi. - 23+23i\frac { \sqrt { 2 } } { 3 } + \frac { 2 } { 3 } \mathrm { i }32​​+32​i

Solve the equation. - ∣3−6x∣=9| 3 - 6 x | = 9∣3−6x∣=9

Decide what number must be added to the binomial to make a perfect square trinomial. - (2x+5)2=49( 2 x + 5 ) ^ { 2 } = 49(2x+5)2=49

Solve the linear inequality. Express the solution in set-builder notation. - −4(2x+12)<−12x−36- 4 ( 2 x + 12 ) < - 12 x - 36−4(2x+12)<−12x−36

Solve the equation. - −3x+52+1=−6x7\frac { - 3 x + 5 } { 2 } + 1 = - \frac { 6 x } { 7 }2−3x+5​+1=−76x​