Question 1

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

Accepted Answer

A)  $S = \frac { - b + b ^ { 2 } - 4 a c } { 2 a }$ 
B)  $S = \frac { - b + b ^ { 2 } + 4 a c } { 2 a }$ 
C)  $S = \frac { - b + \sqrt { b ^ { 2 } + 4 a c } } { 2 a }$ 
D)  $S = \frac { - b + \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$ 
A)  $S = \frac { - b + b ^ { 2 } - 4 a c } { 2 a }$ 
B)  $S = \frac { - b + b ^ { 2 } + 4 a c } { 2 a }$ 
C)  $S = \frac { - b + \sqrt { b ^ { 2 } + 4 a c } } { 2 a }$ 
D)  $S = \frac { - b + \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$

Question 2

Solve by completing the square.
-$$x ^ { 2 } + 4 x = 3$$

Accepted Answer

A)  $- 2 \pm 2 \sqrt { 7 }$ 
B)  $- 1 \pm \sqrt { 7 }$ 
C)  $- 2 \pm \sqrt { 7 }$ 
D)  $2 + \sqrt { 7 }$ 
A)  $- 2 \pm 2 \sqrt { 7 }$ 
B)  $- 1 \pm \sqrt { 7 }$ 
C)  $- 2 \pm \sqrt { 7 }$ 
D)  $2 + \sqrt { 7 }$

Question 3

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

Question 4

Solve the problem. Give the answer to the nearest tenth.
-The hang-time function $\mathrm { V } ( \mathrm { T } ) = 48 \mathrm {~T} ^ { 2 }$, relates vertical leap to hang time. A player has a vertical leap of 39 in. What is his hang time?

Accepted Answer

A)  $0.8 \mathrm { sec }$ 
B)  $43.3 \mathrm { sec }$ 
C)  $1.1 \mathrm { sec }$ 
D)  $0.9 \mathrm { sec }$ 
A)  $0.8 \mathrm { sec }$ 
B)  $43.3 \mathrm { sec }$ 
C)  $1.1 \mathrm { sec }$ 
D)  $0.9 \mathrm { sec }$

Question 5

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers.
-$q = \frac { p } { \sqrt { p ^ { 2 } + 1 } }$, for $p$

Accepted Answer

A)  $p = \frac { q } { q ^ { 2 } + 1 }$ 
B)  $p = \frac { q } { 1 - q ^ { 2 } }$ 
C)  $p = \frac { q } { \sqrt { q ^ { 2 } - 1 } }$ 
D)  $p = \frac { q } { \sqrt { 1 - q ^ { 2 } } }$ 
A)  $p = \frac { q } { q ^ { 2 } + 1 }$ 
B)  $p = \frac { q } { 1 - q ^ { 2 } }$ 
C)  $p = \frac { q } { \sqrt { q ^ { 2 } - 1 } }$ 
D)  $p = \frac { q } { \sqrt { 1 - q ^ { 2 } } }$

Question 6

Solve the equation by completing the square.
-$$7 x ^ { 2 } + 2 x - 5 = 0$$

Accepted Answer

A)  $\frac { 7 } { 5 } , 1$ 
B)  $\frac { 7 } { 5 } , - 1$ 
C)  $\frac { 7 } { 5 } , 0$ 
D)  $\frac { 5 } { 7 } , - 1$ 
A)  $\frac { 7 } { 5 } , 1$ 
B)  $\frac { 7 } { 5 } , - 1$ 
C)  $\frac { 7 } { 5 } , 0$ 
D)  $\frac { 5 } { 7 } , - 1$

Question 7

Solve.
-A square has an area of 49 square inches. If the same amount is added to the length and removed from the width, the resulting rectangle has an area of 45 square inches. Find the dimensions of the rectangle.

Accepted Answer

A) 3 in. by 4 in. 
B) 4 in. by 9 in. 
C) 5 in. by 10 in. 
D) 5 in. by 9 in. 
A) 3 in. by 4 in. 
B) 4 in. by 9 in. 
C) 5 in. by 10 in. 
D) 5 in. by 9 in.

Question 8

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

Question 9

Solve.
-$$7 x ^ { 2 } - 3 x + 1 = 0$$

Accepted Answer

A)  $- \frac { 3 } { 14 } \pm \frac { \sqrt { 19 } } { 14 } \mathrm { i }$ 
B)  $- \frac { 3 } { 14 } \pm \frac { \sqrt { 19 } } { 14 }$ 
C)  $\frac { 3 } { 14 } \pm \frac { \sqrt { 19 } } { 14 }$ 
D)  $\frac { 3 } { 14 } \pm \frac { \sqrt { 19 } } { 14 } \mathrm { i }$ 
A)  $- \frac { 3 } { 14 } \pm \frac { \sqrt { 19 } } { 14 } \mathrm { i }$ 
B)  $- \frac { 3 } { 14 } \pm \frac { \sqrt { 19 } } { 14 }$ 
C)  $\frac { 3 } { 14 } \pm \frac { \sqrt { 19 } } { 14 }$ 
D)  $\frac { 3 } { 14 } \pm \frac { \sqrt { 19 } } { 14 } \mathrm { i }$

Question 10

Solve the equation by completing the square.
-$$4 \mathrm {~d} ^ { 2 } + 16 \mathrm {~d} + 15 = 0$$

Accepted Answer

A)  $- \frac { 5 } { 2 } , - \frac { 3 } { 2 }$ 
B)  $- \frac { 2 } { 5 } , - \frac { 3 } { 2 }$ 
C)  $\frac { 5 } { 2 } , \frac { 3 } { 2 }$ 
D)  $\frac { 2 } { 5 } , \frac { 2 } { 3 }$ 
A)  $- \frac { 5 } { 2 } , - \frac { 3 } { 2 }$ 
B)  $- \frac { 2 } { 5 } , - \frac { 3 } { 2 }$ 
C)  $\frac { 5 } { 2 } , \frac { 3 } { 2 }$ 
D)  $\frac { 2 } { 5 } , \frac { 2 } { 3 }$

Question 11

Find the x-intercepts.
-$f ( x ) = 25 x ^ { 2 } - 10 x + 1$

Accepted Answer

A)  $\left( \frac { 1 } { 5 } , 0 \right)$ and $\left( \frac { 1 } { 5 } , 0 \right)$ 
B)  $\left( - \frac { 1 } { 5 } , 0 \right)$ 
C)  $\left( \frac { 1 } { 5 } , 0 \right)$ 
D)  No x-intercepts 
A)  $\left( \frac { 1 } { 5 } , 0 \right)$ and $\left( \frac { 1 } { 5 } , 0 \right)$ 
B)  $\left( - \frac { 1 } { 5 } , 0 \right)$ 
C)  $\left( \frac { 1 } { 5 } , 0 \right)$ 
D)  No x-intercepts

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

Solve by completing the square. - $x ^ { 2 } + 4 x = 3$

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 problem. Give the answer to the nearest tenth. -The hang-time function $\mathrm { V } ( \mathrm { T } ) = 48 \mathrm {~T} ^ { 2 }$ , relates vertical leap to hang time. A player has a vertical leap of 39 in. What is his hang time?

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers. - $q = \frac { p } { \sqrt { p ^ { 2 } + 1 } }$ , for $p$

Solve the equation by completing the square. - $7 x ^ { 2 } + 2 x - 5 = 0$

Solve. -A square has an area of 49 square inches. If the same amount is added to the length and removed from the width, the resulting rectangle has an area of 45 square inches. Find the dimensions of the rectangle.

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. - $7 x ^ { 2 } - 3 x + 1 = 0$

Solve the equation by completing the square. - $4 \mathrm {~d} ^ { 2 } + 16 \mathrm {~d} + 15 = 0$

Find the x-intercepts. - $f ( x ) = 25 x ^ { 2 } - 10 x + 1$

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

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Exam 11: Quadratic Equations and Functions

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers. - aS2+bS=ca S ^ { 2 } + b S = caS2+bS=c , for SSS

Solve by completing the square. - x2+4x=3x ^ { 2 } + 4 x = 3x2+4x=3

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers. - A=13πr2 for rA = \frac { 1 } { 3 } \pi r ^ { 2 } \text { for } rA=31​πr2 for r

Solve the problem. Give the answer to the nearest tenth. -The hang-time function V(T)=48 T2\mathrm { V } ( \mathrm { T } ) = 48 \mathrm {~T} ^ { 2 }V(T)=48 T2 , relates vertical leap to hang time. A player has a vertical leap of 39 in. What is his hang time?

Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers. - q=pp2+1q = \frac { p } { \sqrt { p ^ { 2 } + 1 } }q=p2+1​p​ , for ppp

Solve the equation by completing the square. - 7x2+2x−5=07 x ^ { 2 } + 2 x - 5 = 07x2+2x−5=0