Question 1

Solve.
-$5 m ^ { 2 } + 12 m + 5 = 0$

Accepted Answer

A)  $\frac { - 6 \pm \sqrt { 11 } } { 5 }$ 
B)  $\frac { - 12 \pm \sqrt { 11 } } { 5 }$ 
C)  $\frac { - 6 \pm \sqrt { 11 } } { 10 }$ 
D)  $\frac { - 6 \pm \sqrt { 61 } } { 5 }$ 
A)  $\frac { - 6 \pm \sqrt { 11 } } { 5 }$ 
B)  $\frac { - 12 \pm \sqrt { 11 } } { 5 }$ 
C)  $\frac { - 6 \pm \sqrt { 11 } } { 10 }$ 
D)  $\frac { - 6 \pm \sqrt { 61 } } { 5 }$ A

Question 2

Solve.
-The area of a square is 81 square centimeters. If the same amount is added to one dimension and removed from the other, the resulting rectangle has an area 9 square centimeters less than the area of the square. How much is
Added and subtracted?

Accepted Answer

A) 9 cm 
B) 4 cm 
C) 12 cm 
D) 3 cm 
A) 9 cm 
B) 4 cm 
C) 12 cm 
D) 3 cm D

Question 3

Solve. Give exact solutions.
-$$( x + 16 ) ^ { 2 } - 3 = 0$$

Accepted Answer

A)  $- 4 \pm \sqrt { 3 }$ 
B)  $16 \pm \sqrt { 3 }$ 
C)  $- 13,19$ 
D)  $- 16 \pm \sqrt { 3 }$ 
A)  $- 4 \pm \sqrt { 3 }$ 
B)  $16 \pm \sqrt { 3 }$ 
C)  $- 13,19$ 
D)  $- 16 \pm \sqrt { 3 }$ D

Question 4

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers.
-$$S = \frac { 1 } { 2 } g t ^ { 2 } \text { for } t$$

Accepted Answer

A)  $t = \sqrt { \frac { g } { 2 S } }$ 
B)  $t = 2 \sqrt { g s }$ 
C)  $t = 2 g S$ 
D)  $t = \sqrt { \frac { 2 S } { g } }$ 
A)  $t = \sqrt { \frac { g } { 2 S } }$ 
B)  $t = 2 \sqrt { g s }$ 
C)  $t = 2 g S$ 
D)  $t = \sqrt { \frac { 2 S } { g } }$

Question 5

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers.
-$v ^ { 2 } = 2 a s$ for $v$

Accepted Answer

A)  $v = \frac { 2 a } { s }$ 
B)  $v = 2 a \sqrt { s }$ 
C)  $v = \sqrt { \frac { 2 a } { s } }$ 
D)  $v = \sqrt { 2 a s }$ 
A)  $v = \frac { 2 a } { s }$ 
B)  $v = 2 a \sqrt { s }$ 
C)  $v = \sqrt { \frac { 2 a } { s } }$ 
D)  $v = \sqrt { 2 a s }$

Question 6

Solve. Round results to the nearest thousandth.
-$$x ^ { 2 } - 10 x - 36 = 0$$

Accepted Answer

A)  $23.276 , - 13.276$ 
B)  $12.810 , - 2.810$ 
C)  $13.276 , - 23.276$ 
D)  $2.810 , - 12.810$ 
A)  $23.276 , - 13.276$ 
B)  $12.810 , - 2.810$ 
C)  $13.276 , - 23.276$ 
D)  $2.810 , - 12.810$

Question 7

Solve. Give exact solutions.
-$$( x - 3 ) ^ { 2 } = 4$$

Accepted Answer

A)  7 
B)  $1 , - 5$ 
C)  5,1 
D)  $2 , - 2$ 
A)  7 
B)  $1 , - 5$ 
C)  5,1 
D)  $2 , - 2$

Question 8

Solve the equation by completing the square.
-$$z ^ { 2 } + 10 z + 12 = 0$$

Accepted Answer

A)  $5 \pm 2 \sqrt { 3 }$ 
B)  $5 + \sqrt { 13 }$ 
C)  $- 5 \pm \sqrt { 13 }$ 
D)  $- 10 + 2 \sqrt { 3 }$ 
A)  $5 \pm 2 \sqrt { 3 }$ 
B)  $5 + \sqrt { 13 }$ 
C)  $- 5 \pm \sqrt { 13 }$ 
D)  $- 10 + 2 \sqrt { 3 }$

Question 9

Solve. Give exact solutions.
-$$x ^ { 2 } + 3 = 172$$

Accepted Answer

A)  $\pm 12$ 
B)  86 
C)  $\pm 13$ 
D)  13 
A)  $\pm 12$ 
B)  86 
C)  $\pm 13$ 
D)  13

Question 10

Solve.
-A picture 13 inches by 23 inches is to be mounted on a piece of matboard so that there is an even amount of mat all around the picture. How wide will the border be if the area of the border is 252 square inches?

Accepted Answer

A) 4 in 
B) 3 in 
C) 5 in 
D) 5.5 in 
A) 4 in 
B) 3 in 
C) 5 in 
D) 5.5 in

Question 11

Solve the equation by completing the square.
-$$a ^ { 2 } - 10 a + 9 = 0$$

Accepted Answer

A)  $- 9 , - 1$ 
B)  8,1 
C)  $\sqrt { 9 } , - \sqrt { 9 }$ 
D)  9,1 
A)  $- 9 , - 1$ 
B)  8,1 
C)  $\sqrt { 9 } , - \sqrt { 9 }$ 
D)  9,1

Question 12

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers.
-$$A = \frac { 1 } { 3 } \pi r ^ { 2 } \text { for } r$$

Accepted Answer

A)  $r = \frac { 3 \pi } { \mathrm { A } }$ 
B)  $r = \sqrt { \frac { \mathrm { A } } { 3 \pi } }$ 
C)  $r = 3 \sqrt { \mathrm { A } \pi }$ 
D)  $r = \sqrt { \frac { 3 \mathrm {~A} } { \pi } }$ 
A)  $r = \frac { 3 \pi } { \mathrm { A } }$ 
B)  $r = \sqrt { \frac { \mathrm { A } } { 3 \pi } }$ 
C)  $r = 3 \sqrt { \mathrm { A } \pi }$ 
D)  $r = \sqrt { \frac { 3 \mathrm {~A} } { \pi } }$

Question 13

Solve the equation by completing the square.
-$$x ^ { 2 } - 14 x + 74 = 0$$

Accepted Answer

A)  $7 \pm 5 \mathrm { i }$ 
B)  $- 7 \pm 5 \mathrm { i }$ 
C)  $14 \pm 10 \mathrm { i }$ 
D)  12,2 
A)  $7 \pm 5 \mathrm { i }$ 
B)  $- 7 \pm 5 \mathrm { i }$ 
C)  $14 \pm 10 \mathrm { i }$ 
D)  12,2

Question 14

Solve.
-A lot is in the shape of a right triangle. The shorter leg measures 180 m. The hypotenuse is 60 m longer than the length of the longer leg. How long is the longer leg?

Accepted Answer

A) 300 m 
B) 240 m 
C) 360 m 
D) 180 m 
A) 300 m 
B) 240 m 
C) 360 m 
D) 180 m

Question 15

Solve.
-A rectangular garden has dimensions of 23 feet by 20 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 294 square feet?

Accepted Answer

A) 5.5 ft 
B) 4 ft 
C) 5 ft 
D) 3 ft 
A) 5.5 ft 
B) 4 ft 
C) 5 ft 
D) 3 ft

Question 16

Find the x-intercepts.
-$$f ( x ) = 2 x ^ { 2 } - 13 x - 45$$

Accepted Answer

A)  $x$-intercepts $( 9,0 )$ and $\left( \frac { 5 } { 2 } , 0 \right)$ 
B)  No x-intercepts 
C)  x-intercepts $( 9,0 )$ and $\left( - \frac { 5 } { 2 } , 0 \right)$ 
D)  $x$-intercepts $( - 5,0 )$ and $\left( \frac { 9 } { 2 } , 0 \right)$ 
A)  $x$-intercepts $( 9,0 )$ and $\left( \frac { 5 } { 2 } , 0 \right)$ 
B)  No x-intercepts 
C)  x-intercepts $( 9,0 )$ and $\left( - \frac { 5 } { 2 } , 0 \right)$ 
D)  $x$-intercepts $( - 5,0 )$ and $\left( \frac { 9 } { 2 } , 0 \right)$

Question 17

Solve. Round results to the nearest thousandth.
-$$5 \mathrm { x } ^ { 2 } = 10 + 14 \mathrm { x }$$

Accepted Answer

A)  $1.600,1.200$ 
B)  $0.590 , - 3.390$ 
C)  $- 1.200 , - 1.600$ 
D)  $3.390 , - 0.590$ 
A)  $1.600,1.200$ 
B)  $0.590 , - 3.390$ 
C)  $- 1.200 , - 1.600$ 
D)  $3.390 , - 0.590$

Question 18

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

Accepted Answer

A)  $- 4 \pm \sqrt { 23 }$ 
B)  $4 + \sqrt { 23 }$ 
C)  $- 4 \pm 2 \sqrt { 23 }$ 
D)  $- 1 \pm \sqrt { 23 }$ 
A)  $- 4 \pm \sqrt { 23 }$ 
B)  $4 + \sqrt { 23 }$ 
C)  $- 4 \pm 2 \sqrt { 23 }$ 
D)  $- 1 \pm \sqrt { 23 }$

Question 19

Solve the problem. Give the answer to the nearest tenth.
-The position of an object moving in a straight line is given by $s = 2 t ^ { 2 } - 3 t$, where s is in meters and $t$ is the time in seconds the object has been in motion. How long (to the nearest tenth) will it take the object to move 9 meters?

Accepted Answer

A)  $3.0 \mathrm { sec }$ 
B)  $13.5 \mathrm { sec }$ 
C)  $10.0 \mathrm { sec }$ 
D)  $2.8 \mathrm { sec }$ 
A)  $3.0 \mathrm { sec }$ 
B)  $13.5 \mathrm { sec }$ 
C)  $10.0 \mathrm { sec }$ 
D)  $2.8 \mathrm { sec }$

Question 20

Solve. Give exact solutions.
-$$( x - 1 ) ^ { 2 } = - 16$$

Accepted Answer

A)  $1 \pm 4 \mathrm { i }$ 
B)  $1 \pm 4$ 
C)  $4 \mathrm { i }$ 
D)  $4 \mathrm { i } + 1$ 
A)  $1 \pm 4 \mathrm { i }$ 
B)  $1 \pm 4$ 
C)  $4 \mathrm { i }$ 
D)  $4 \mathrm { i } + 1$

Solve. - $5 m ^ { 2 } + 12 m + 5 = 0$

Solve. -The area of a square is 81 square centimeters. If the same amount is added to one dimension and removed from the other, the resulting rectangle has an area 9 square centimeters less than the area of the square. How much is Added and subtracted?

Solve. Give exact solutions. - $( x + 16 ) ^ { 2 } - 3 = 0$

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers. - $S = \frac { 1 } { 2 } g t ^ { 2 } \text { for } t$

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers. - $v ^ { 2 } = 2 a s$ for $v$

Solve. Round results to the nearest thousandth. - $x ^ { 2 } - 10 x - 36 = 0$

Solve. Give exact solutions. - $( x - 3 ) ^ { 2 } = 4$

Solve the equation by completing the square. - $z ^ { 2 } + 10 z + 12 = 0$

Solve. Give exact solutions. - $x ^ { 2 } + 3 = 172$

Solve. -A picture 13 inches by 23 inches is to be mounted on a piece of matboard so that there is an even amount of mat all around the picture. How wide will the border be if the area of the border is 252 square inches?

Solve the equation by completing the square. - $a ^ { 2 } - 10 a + 9 = 0$

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers. - $A = \frac { 1 } { 3 } \pi r ^ { 2 } \text { for } r$

Solve the equation by completing the square. - $x ^ { 2 } - 14 x + 74 = 0$

Solve. -A lot is in the shape of a right triangle. The shorter leg measures 180 m. The hypotenuse is 60 m longer than the length of the longer leg. How long is the longer leg?

Solve. -A rectangular garden has dimensions of 23 feet by 20 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 294 square feet?

Find the x-intercepts. - $f ( x ) = 2 x ^ { 2 } - 13 x - 45$

Solve. Round results to the nearest thousandth. - $5 \mathrm { x } ^ { 2 } = 10 + 14 \mathrm { x }$

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

Solve. Give exact solutions. - $( x - 1 ) ^ { 2 } = - 16$

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Rational Expressions and Equations

Graphs, Functions, and Applications

Systems of Equations

More on Inequalities

Radical Expressions, Equations, and Functions

Exponential Functions and Logarithmic Functions

Finding Measures of Central Tendency for Prices and Heights

Filters

Exam 11: Quadratic Equations and Functions

Solve. - 5m2+12m+5=05 m ^ { 2 } + 12 m + 5 = 05m2+12m+5=0

Solve. -The area of a square is 81 square centimeters. If the same amount is added to one dimension and removed from the other, the resulting rectangle has an area 9 square centimeters less than the area of the square. How much is Added and subtracted?

Solve. Give exact solutions. - (x+16)2−3=0( x + 16 ) ^ { 2 } - 3 = 0(x+16)2−3=0

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers. - S=12gt2 for tS = \frac { 1 } { 2 } g t ^ { 2 } \text { for } tS=21​gt2 for t

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers. - v2=2asv ^ { 2 } = 2 a sv2=2as for vvv

Solve. Round results to the nearest thousandth. - x2−10x−36=0x ^ { 2 } - 10 x - 36 = 0x2−10x−36=0

Solve. Give exact solutions. - (x−3)2=4( x - 3 ) ^ { 2 } = 4(x−3)2=4

Solve the equation by completing the square. - z2+10z+12=0z ^ { 2 } + 10 z + 12 = 0z2+10z+12=0

Solve. Give exact solutions. - x2+3=172x ^ { 2 } + 3 = 172x2+3=172