Question 1

Solve.
-Bill can row 3 mph in still water. It takes him 3 hours 36 minutes to go 3 miles upstream and return. Find the speed of the current.

Accepted Answer

A) 3 mph 
B) 2 mph 
C) 2.5 mph 
D) 1.5 mph

Question 2

Solve.
-$$6 n ^ { 2 } = - 12 n - 1$$

Accepted Answer

A)  $\frac { - 6 \pm \sqrt { 42 } } { 6 }$ 
B)  $\frac { - 6 \pm \sqrt { 30 } } { 12 }$ 
C)  $\frac { - 12 \pm \sqrt { 30 } } { 6 }$ 
D)  $\frac { - 6 \pm \sqrt { 30 } } { 6 }$

Question 3

Solve. Give exact solutions.
-$$4 x ^ { 2 } = 52$$

Accepted Answer

A)  $\pm 13$ 
B)  14 
C)  26 
D)  $\pm \sqrt { 13 }$

Question 4

Solve. Give exact solutions.
-$$x ^ { 2 } - 14 x + 49 = 9$$

Accepted Answer

A)  $3 , - 3$ 
B)  16 
C)  $4 , - 10$ 
D)  10,4

Question 5

Solve by completing the square.
-$$y ^ { 2 } + 8 y - 5 = 0$$

Accepted Answer

A)  $4 + \sqrt { 21 }$ 
B)  $- 1 \pm \sqrt { 21 }$ 
C)  $- 4 \pm \sqrt { 21 }$ 
D)  $- 4 \pm 2 \sqrt { 21 }$

Question 6

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

Accepted Answer

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

Question 7

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers.
-$x = \sqrt { r ^ { 2 } - y ^ { 2 } }$ for $r$

Accepted Answer

A)  $r = \sqrt { x ^ { 2 } - y ^ { 2 } }$ 
B)  $r = \sqrt { x + y }$ 
C)  $r = x + y$ 
D)  $r = \sqrt { x ^ { 2 } + y ^ { 2 } }$

Question 8

Solve the equation by completing the square.
-$$\mathrm { p } ^ { 2 } + 3 \mathrm { p } - 9 = 0$$

Accepted Answer

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

Question 9

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers.
-$c ^ { 2 } + d ^ { 2 } + f ^ { 2 } = g ^ { 2 }$, for $c$

Accepted Answer

A)  $c = g ^ { 2 } - d ^ { 2 } - f ^ { 2 }$ 
B)  $c = - g + d + f$ 
C)  $c = g - d - f$ 
D)  $c = \sqrt { g ^ { 2 } - d ^ { 2 } - f ^ { 2 } }$

Question 10

Solve. Give exact solutions.
-$( p - 2 ) ^ { 2 } = 17$

Accepted Answer

A)  $\sqrt { 17 } - 2 , - \sqrt { 17 } - 2$ 
B)  $\sqrt { 17 } + 2$ 
C)  $\sqrt { 17 } + 2 , - \sqrt { 17 } + 2$ 
D)  $\sqrt { 17 } - \sqrt { - 2 }$

Question 11

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers.
-$\mathrm { H } = \frac { \mathrm { F } } { \sqrt { \mathrm { F } ^ { 2 } + \mathrm { G } ^ { 2 } } }$, for $\mathrm { F }$

Accepted Answer

A)  $F = H \sqrt { F ^ { 2 } + G ^ { 2 } }$ 
B)  $\mathrm { F } = \frac { \mathrm { GH } } { 1 - \mathrm { H } }$ 
C)  $\mathrm { F } = \frac { \mathrm { GH } } { \sqrt { 1 - \mathrm { H } ^ { 2 } } }$ 
D)  $F = \frac { \sqrt { \mathrm { G } ^ { 2 } + \mathrm { H } ^ { 2 } } } { \mathrm { G } }$

Question 12

Solve.
-$$\frac { 1 } { x } + \frac { 6 } { x ^ { 2 } } = - 1$$

Accepted Answer

A)  $\frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 }$ 
B)  $- \frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 } \mathrm { i }$ 
C)  $- \frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 }$ 
D)  $\frac { 1 } { 2 } \pm \frac { \sqrt { 23 } } { 2 } \mathrm { i }$

Question 13

Solve. Give exact solutions.
-$$x ^ { 2 } + 5 = 230$$

Accepted Answer

A)  15 
B)  $\pm 15$ 
C)  $\pm 14$ 
D)  115

Question 14

Solve. Round results to the nearest thousandth.
-$$9 x ^ { 2 } = 2 + 17 x$$

Accepted Answer

A)  $2.000 , - 0.111$ 
B)  $1.763,0.126$ 
C)  $- 0.126 , - 1.763$ 
D)  $0.111 , - 2.000$

Question 15

Solve.
-$$\frac { 4 } { x } + \frac { 4 } { x + 6 } = 1$$

Accepted Answer

A)  6 
B)  4 
C)  $- 4,6$ 
D)  $4 , - 6$

Question 16

Solve.
-A picture 9 inches by 18 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 124 square inches?

Accepted Answer

A) 4.5 in 
B) 4 in 
C) 3 in 
D) 2 in

Question 17

Solve by completing the square.
-$$y ^ { 2 } + 5 y - 5 = 0$$

Accepted Answer

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

Question 18

Solve.
-A lot is in the shape of a right triangle. The shorter leg measures 120 m. The hypotenuse is 40 m longer than the length of the longer leg. How long is the longer leg?

Accepted Answer

A) 160 m 
B) 120 m 
C) 240 m 
D) 200 m

Question 19

Solve. Give exact solutions.
-$$x ^ { 2 } - \frac { 1 } { 2 } x + \frac { 1 } { 16 } = \frac { 7 } { 24 }$$

Accepted Answer

A)  $\frac { 1 } { 2 } + \frac { \sqrt { 42 } } { 6 } , \frac { 1 } { 2 } - \frac { \sqrt { 42 } } { 6 }$ 
B)  $\frac { 1 } { 2 } + \frac { \sqrt { 42 } } { 12 } , \frac { 1 } { 2 } - \frac { \sqrt { 42 } } { 12 }$ 
C)  $\frac { 1 } { 2 } + \frac { \sqrt { 42 } } { 12 } , - \frac { 1 } { 2 } + \frac { \sqrt { 42 } } { 12 }$ 
D)  $\frac { 1 } { 4 } + \frac { \sqrt { 42 } } { 12 } , \frac { 1 } { 4 } - \frac { \sqrt { 42 } } { 12 }$

Question 20

Find the x-intercepts.
-$$4 x ^ { 2 } + 9 = 0$$

Accepted Answer

A)  $x$-intercepts $\left( - \sqrt { \frac { 3 } { 2 } } , 0 \right) , \left( \sqrt { \frac { 3 } { 2 } } , 0 \right)$ 
B)  $x$-intercepts $\left( - i \sqrt { \frac { 3 } { 2 } } , 0 \right) , \left( i \sqrt { \frac { 3 } { 2 } } , 0 \right)$ 
C)  $x$-intercepts $\left( 0 , - i \sqrt { \frac { 3 } { 2 } } \right) , \left( 0 , i \sqrt { \frac { 3 } { 2 } } \right)$ 
D)  No x-intercepts

Exam 11: Quadratic Equations and Functions

Solve. -Bill can row 3 mph in still water. It takes him 3 hours 36 minutes to go 3 miles upstream and return. Find the speed of the current.

Solve. - $6 n ^ { 2 } = - 12 n - 1$

Solve. Give exact solutions. - $4 x ^ { 2 } = 52$

Solve. Give exact solutions. - $x ^ { 2 } - 14 x + 49 = 9$

Solve by completing the square. - $y ^ { 2 } + 8 y - 5 = 0$

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

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers. - $x = \sqrt { r ^ { 2 } - y ^ { 2 } }$ for $r$

Solve the equation by completing the square. - $\mathrm { p } ^ { 2 } + 3 \mathrm { p } - 9 = 0$

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers. - $c ^ { 2 } + d ^ { 2 } + f ^ { 2 } = g ^ { 2 }$ , for $c$

Solve. Give exact solutions. - $( p - 2 ) ^ { 2 } = 17$

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers. - $\mathrm { H } = \frac { \mathrm { F } } { \sqrt { \mathrm { F } ^ { 2 } + \mathrm { G } ^ { 2 } } }$ , for $\mathrm { F }$

Solve. - $\frac { 1 } { x } + \frac { 6 } { x ^ { 2 } } = - 1$

Solve. Give exact solutions. - $x ^ { 2 } + 5 = 230$

Solve. Round results to the nearest thousandth. - $9 x ^ { 2 } = 2 + 17 x$

Solve. - $\frac { 4 } { x } + \frac { 4 } { x + 6 } = 1$

Solve. -A picture 9 inches by 18 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 124 square inches?

Solve by completing the square. - $y ^ { 2 } + 5 y - 5 = 0$

Solve. -A lot is in the shape of a right triangle. The shorter leg measures 120 m. The hypotenuse is 40 m longer than the length of the longer leg. How long is the longer leg?

Solve. Give exact solutions. - $x ^ { 2 } - \frac { 1 } { 2 } x + \frac { 1 } { 16 } = \frac { 7 } { 24 }$

Find the x-intercepts. - $4 x ^ { 2 } + 9 = 0$

Exam 11: Quadratic Equations and Functions

Solve. -Bill can row 3 mph in still water. It takes him 3 hours 36 minutes to go 3 miles upstream and return. Find the speed of the current.

Solve. - 6n2=−12n−16 n ^ { 2 } = - 12 n - 16n2=−12n−1

Solve. Give exact solutions. - 4x2=524 x ^ { 2 } = 524x2=52

Solve. Give exact solutions. - x2−14x+49=9x ^ { 2 } - 14 x + 49 = 9x2−14x+49=9

Solve by completing the square. - y2+8y−5=0y ^ { 2 } + 8 y - 5 = 0y2+8y−5=0

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

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers. - x=r2−y2x = \sqrt { r ^ { 2 } - y ^ { 2 } }x=r2−y2​ for rrr

Solve the equation by completing the square. - p2+3p−9=0\mathrm { p } ^ { 2 } + 3 \mathrm { p } - 9 = 0p2+3p−9=0

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers. - c2+d2+f2=g2c ^ { 2 } + d ^ { 2 } + f ^ { 2 } = g ^ { 2 }c2+d2+f2=g2 , for ccc

Solve. Give exact solutions. - (p−2) 2=17( p - 2 ) ^ { 2 } = 17(p−2) 2=17

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers. - H=FF2+G2\mathrm { H } = \frac { \mathrm { F } } { \sqrt { \mathrm { F } ^ { 2 } + \mathrm { G } ^ { 2 } } }H=F2+G2​F​ , for F\mathrm { F }F

Solve. - 1x+6x2=−1\frac { 1 } { x } + \frac { 6 } { x ^ { 2 } } = - 1x1​+x26​=−1

Solve. Give exact solutions. - x2+5=230x ^ { 2 } + 5 = 230x2+5=230

Solve. Round results to the nearest thousandth. - 9x2=2+17x9 x ^ { 2 } = 2 + 17 x9x2=2+17x

Solve. - 4x+4x+6=1\frac { 4 } { x } + \frac { 4 } { x + 6 } = 1x4​+x+64​=1