Question 1

Divide.
-$$\frac { 4 y ^ { 4 } + 10 y ^ { 3 } + 5 y - 1 } { 2 y ^ { 2 } + 1 }$$

Accepted Answer

A)  $2 y ^ { 2 } - 5 y + 1$ 
B)  $2 y ^ { 2 } - 1$ 
C)  $2 y ^ { 2 } + 5 y$ 
D)  $2 y ^ { 2 } + 5 y - 1$ 
A)  $2 y ^ { 2 } - 5 y + 1$ 
B)  $2 y ^ { 2 } - 1$ 
C)  $2 y ^ { 2 } + 5 y$ 
D)  $2 y ^ { 2 } + 5 y - 1$

Question 2

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { 98 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } }$

Accepted Answer

A)  $7 \mathrm { k } ^ { 3 } q ^ { 4 } \sqrt { 2 }$ 
B)  $7 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } \sqrt { 2 \mathrm { k } }$ 
C)  $7 q ^ { 4 } \sqrt { 2 k ^ { 7 } }$ 
D)  $7 \mathrm { k } ^ { 3 } \mathrm { q } ^ { 4 } \sqrt { 2 \mathrm { k } }$ 
A)  $7 \mathrm { k } ^ { 3 } q ^ { 4 } \sqrt { 2 }$ 
B)  $7 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } \sqrt { 2 \mathrm { k } }$ 
C)  $7 q ^ { 4 } \sqrt { 2 k ^ { 7 } }$ 
D)  $7 \mathrm { k } ^ { 3 } \mathrm { q } ^ { 4 } \sqrt { 2 \mathrm { k } }$

Question 3

Simplify the expression.
-$$\sqrt { ( 3 y - 2 ) ^ { 2 } }$$

Accepted Answer

A)  $3 y - 2$ 
B)  $- 3 y + 2$ 
C)  $| 3 y - 2 |$ 
D)  $3 | y | - 2$ 
A)  $3 y - 2$ 
B)  $- 3 y + 2$ 
C)  $| 3 y - 2 |$ 
D)  $3 | y | - 2$

Question 4

Use the distributive property to rewrite a sum as a product or the product as a sum.
--4(b + a)

Accepted Answer

A)  -4b + a 
B) -4b - 4a 
C)  -4b + 4a 
D)  -4ba 
A)  -4b + a 
B) -4b - 4a 
C)  -4b + 4a 
D)  -4ba

Question 5

Find the distance between two points given their coordinates.
-Find the distance between points $\mathrm { R }$ and $\mathrm { S }$ on a number line, with coordinates $- 6$ and 11 , respectively.

Accepted Answer

A)  $d ( R , S ) = - 5$ 
B)  $d ( R , S ) = - 17$ 
C)  $d ( R , S ) = 17$ 
D)  $d ( R , S ) = 5$ 
A)  $d ( R , S ) = - 5$ 
B)  $d ( R , S ) = - 17$ 
C)  $d ( R , S ) = 17$ 
D)  $d ( R , S ) = 5$

Question 6

Factor the trinomial, if possible.
-$$7 x ^ { 2 } - 9 x y - 10 y ^ { 2 }$$

Accepted Answer

A)  prime 
B)  $y ( 7 x + 5 ) ( x - 2 )$ 
C)  $( 7 x + 2 y ) ( x - 5 y )$ 
D)  $( 7 x + 5 y ) ( x - 2 y )$ 
A)  prime 
B)  $y ( 7 x + 5 ) ( x - 2 )$ 
C)  $( 7 x + 2 y ) ( x - 5 y )$ 
D)  $( 7 x + 5 y ) ( x - 2 y )$

Question 7

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 4 ] { 81 a ^ { 4 } }$$

Accepted Answer

A)  $3 \sqrt { a }$ 
B)  $3 a$ 
C)  $3 a ^ { 2 }$ 
D)  $81 a$ 
A)  $3 \sqrt { a }$ 
B)  $3 a$ 
C)  $3 a ^ { 2 }$ 
D)  $81 a$

Question 8

Write the expression in lowest terms.
-$$\frac { 3 y ^ { 2 } + 7 y + 2 } { 3 y ^ { 2 } + 11 y + 10 }$$

Accepted Answer

A)  $\frac { y - 1 } { y - 5 }$ 
B)  $\frac { y + 2 } { y + 6 }$ 
C)  $\frac { 3 y + 2 } { 3 y - 2 }$ 
D)  $\frac { 3 y + 1 } { 3 y + 5 }$ 
A)  $\frac { y - 1 } { y - 5 }$ 
B)  $\frac { y + 2 } { y + 6 }$ 
C)  $\frac { 3 y + 2 } { 3 y - 2 }$ 
D)  $\frac { 3 y + 1 } { 3 y + 5 }$

Question 9

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$( 3 x ) ^ { - 2 }$

Accepted Answer

A)  $- \frac { 1 } { 6 x }$ 
B)  $- 9 x ^ { 2 }$ 
C)  $\frac { 1 } { 9 x ^ { 2 } }$ 
D)  $- 6 \mathrm { x }$ 
A)  $- \frac { 1 } { 6 x }$ 
B)  $- 9 x ^ { 2 }$ 
C)  $\frac { 1 } { 9 x ^ { 2 } }$ 
D)  $- 6 \mathrm { x }$

Question 10

Factor the trinomial, if possible.
-$- 24 x ^ { 2 } - 20 x + 24$

Accepted Answer

A)  $( - 3 x + 2 ) ( 8 x + 12 )$ 
B)  $4 ( 3 x + 2 ) ( - 2 x + 3 )$ 
C)  $( - 12 x + 8 ) ( 2 x + 3 )$ 
D)  $- 4 ( 3 x - 2 ) ( 2 x + 3 )$ 
A)  $( - 3 x + 2 ) ( 8 x + 12 )$ 
B)  $4 ( 3 x + 2 ) ( - 2 x + 3 )$ 
C)  $( - 12 x + 8 ) ( 2 x + 3 )$ 
D)  $- 4 ( 3 x - 2 ) ( 2 x + 3 )$

Question 11

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 4 ] { \frac { 7 } { 5 } }$

Accepted Answer

A)  $\frac { \sqrt [ 4 ] { 175 } } { 5 }$ 
B)  $\frac { \sqrt [ 4 ] { 875 } } { 5 }$ 
C)  $\frac { \sqrt [ 4 ] { 125 } } { 5 }$ 
D)  $5 \sqrt [ 4 ] { 875 }$ 
A)  $\frac { \sqrt [ 4 ] { 175 } } { 5 }$ 
B)  $\frac { \sqrt [ 4 ] { 875 } } { 5 }$ 
C)  $\frac { \sqrt [ 4 ] { 125 } } { 5 }$ 
D)  $5 \sqrt [ 4 ] { 875 }$

Question 12

Solve the problem.
-The formula $T = 0.07 D ^ { 1.5 }$ can be used to approximate the duration of a storm, where is the time in hours and $\mathrm { D }$ is the diameter of the storm in miles. A storm that is $17.7$ miles in diameter is heading toward a city. How long can the residents of the city expect the storm to last? Round you answer to the nearest hundredth of an hour.

Accepted Answer

A)  $4.64 \mathrm { hr }$ 
B)  $5.21 \mathrm { hr }$ 
C)  $6.44 \mathrm { hr }$ 
D)  $6.74 \mathrm { hr }$ 
A)  $4.64 \mathrm { hr }$ 
B)  $5.21 \mathrm { hr }$ 
C)  $6.44 \mathrm { hr }$ 
D)  $6.74 \mathrm { hr }$

Question 13

List all the elements of set B that belong to the indicated set.
-$$B = \left\{ 2 , \sqrt { 5 } , - 20,0 , \frac { 0 } { 4 } , \sqrt { 16 } \right\}$$
Whole numbers

Accepted Answer

A)  $2 , - 20,0 , \sqrt { 16 }$ 
B)  2,0 
C)  $2 , - 20,0$ 
D)  $2,0 , \frac { 0 } { 4 } , \sqrt { 16 }$ 
A)  $2 , - 20,0 , \sqrt { 16 }$ 
B)  2,0 
C)  $2 , - 20,0$ 
D)  $2,0 , \frac { 0 } { 4 } , \sqrt { 16 }$

Question 14

Find the product.
-$$4 x ^ { 3 } ( - 11 x + 2 )$$

Accepted Answer

A)  $- 36 x ^ { 4 }$ 
B)  $44 x ^ { 4 } - 8 x ^ { 3 }$ 
C)  $- 44 x ^ { 3 } + 8$ 
D)  $- 44 x ^ { 4 } + 8 x ^ { 3 }$ 
A)  $- 36 x ^ { 4 }$ 
B)  $44 x ^ { 4 } - 8 x ^ { 3 }$ 
C)  $- 44 x ^ { 3 } + 8$ 
D)  $- 44 x ^ { 4 } + 8 x ^ { 3 }$

Question 15

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 4 ] { ( - 4 ) ^ { 4 } }$

Accepted Answer

A)  16 
B)  not a real number 
C)  4 
D)  $- 4$ 
A)  16 
B)  not a real number 
C)  4 
D)  $- 4$

Question 16

Evaluate the expression.
-$| 10 |$

Accepted Answer

A)  0 
B)  $\pm 10$ 
C)  10 
D)  $- 10$ 
A)  0 
B)  $\pm 10$ 
C)  10 
D)  $- 10$

Question 17

Insert ⊆ or ⊈ in the blank to make the statement true.
-{10, 14} ___ {7, -8, 12, -10, 14, 9}

Accepted Answer

A)   
B)   
A)   
B)

Question 18

Decide whether the expression has been simplified correctly.
-$$\left( \frac { x } { 9 } \right) ^ { 6 } = \frac { x ^ { 6 } } { 9 }$$

Accepted Answer

A)  Not simplified correctly 
B)  Simplified correctly 
A)  Not simplified correctly 
B)  Simplified correctly

Question 19

Solve the problem.
-The algebraic expression $$0.07 \mathrm {~d} ^{3 / 2}$$ describes the duration of a storm, in hours, whose diameter is d miles. Use a calculator to determine the duration of a storm with a diameter of 8 miles. Round to
The nearest hundredth.

Accepted Answer

A)  0.2 hr 
B)  0.42 hr 
C)  22.63 hr 
D)  1.58 hr 
A)  0.2 hr 
B)  0.42 hr 
C)  22.63 hr 
D)  1.58 hr

Question 20

Simplify the expression. Assume all variables represent positive real numbers.
-$$\frac { - 5 } { \sqrt [ 3 ] { 3 } } + \frac { 33 } { \sqrt [ 3 ] { 24 } } - \frac { 1 } { \sqrt [ 3 ] { 81 } }$$

Accepted Answer

A)  $\frac { 67 } { 18 } \sqrt [ 3 ] { 9 }$ 
B)  $\frac { 67 } { 6 } \sqrt [ 3 ] { 3 }$ 
C)  $\frac { 11 } { 2 } \sqrt [ 3 ] { 3 }$ 
D)  $\frac { 35 } { 9 } \sqrt [ 3 ] { 9 }$ 
A)  $\frac { 67 } { 18 } \sqrt [ 3 ] { 9 }$ 
B)  $\frac { 67 } { 6 } \sqrt [ 3 ] { 3 }$ 
C)  $\frac { 11 } { 2 } \sqrt [ 3 ] { 3 }$ 
D)  $\frac { 35 } { 9 } \sqrt [ 3 ] { 9 }$

Divide. - $\frac { 4 y ^ { 4 } + 10 y ^ { 3 } + 5 y - 1 } { 2 y ^ { 2 } + 1 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 98 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } }$

Simplify the expression. - $\sqrt { ( 3 y - 2 ) ^ { 2 } }$

Use the distributive property to rewrite a sum as a product or the product as a sum. --4(b + a)

Find the distance between two points given their coordinates. -Find the distance between points $\mathrm { R }$ and $\mathrm { S }$ on a number line, with coordinates $- 6$ and 11 , respectively.

Factor the trinomial, if possible. - $7 x ^ { 2 } - 9 x y - 10 y ^ { 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 4 ] { 81 a ^ { 4 } }$

Write the expression in lowest terms. - $\frac { 3 y ^ { 2 } + 7 y + 2 } { 3 y ^ { 2 } + 11 y + 10 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $( 3 x ) ^ { - 2 }$

Factor the trinomial, if possible. - $- 24 x ^ { 2 } - 20 x + 24$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 4 ] { \frac { 7 } { 5 } }$

List all the elements of set B that belong to the indicated set. - $B = \left\{ 2 , \sqrt { 5 } , - 20,0 , \frac { 0 } { 4 } , \sqrt { 16 } \right\}$ Whole numbers

Find the product. - $4 x ^ { 3 } ( - 11 x + 2 )$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 4 ] { ( - 4 ) ^ { 4 } }$

Evaluate the expression. - $| 10 |$

Insert ⊆ or ⊈ in the blank to make the statement true. -{10, 14} ___ {7, -8, 12, -10, 14, 9}

Decide whether the expression has been simplified correctly. - $\left( \frac { x } { 9 } \right) ^ { 6 } = \frac { x ^ { 6 } } { 9 }$

Solve the problem. -The algebraic expression $0.07 \mathrm {~d} ^{3 / 2}$ describes the duration of a storm, in hours, whose diameter is d miles. Use a calculator to determine the duration of a storm with a diameter of 8 miles. Round to The nearest hundredth.

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { - 5 } { \sqrt [ 3 ] { 3 } } + \frac { 33 } { \sqrt [ 3 ] { 24 } } - \frac { 1 } { \sqrt [ 3 ] { 81 } }$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

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Trigonometric Identities and Equations

Applications of Trigonometry

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Analytic Geometry

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Exam 12: Review of Basic Concepts

Divide. - 4y4+10y3+5y−12y2+1\frac { 4 y ^ { 4 } + 10 y ^ { 3 } + 5 y - 1 } { 2 y ^ { 2 } + 1 }2y2+14y4+10y3+5y−1​

Simplify the expression. Assume all variables represent positive real numbers. - 98k7q8\sqrt { 98 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } }98k7q8​

Simplify the expression. - (3y−2)2\sqrt { ( 3 y - 2 ) ^ { 2 } }(3y−2)2​

Use the distributive property to rewrite a sum as a product or the product as a sum. --4(b + a)

Find the distance between two points given their coordinates. -Find the distance between points R\mathrm { R }R and S\mathrm { S }S on a number line, with coordinates −6- 6−6 and 11 , respectively.

Factor the trinomial, if possible. - 7x2−9xy−10y27 x ^ { 2 } - 9 x y - 10 y ^ { 2 }7x2−9xy−10y2

Simplify the expression. Assume all variables represent positive real numbers. - 81a44\sqrt [ 4 ] { 81 a ^ { 4 } }481a4​

Write the expression in lowest terms. - 3y2+7y+23y2+11y+10\frac { 3 y ^ { 2 } + 7 y + 2 } { 3 y ^ { 2 } + 11 y + 10 }3y2+11y+103y2+7y+2​

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - (3x)−2( 3 x ) ^ { - 2 }(3x)−2

Factor the trinomial, if possible. - −24x2−20x+24- 24 x ^ { 2 } - 20 x + 24−24x2−20x+24

Simplify the expression. Assume all variables represent positive real numbers. - 754\sqrt [ 4 ] { \frac { 7 } { 5 } }457​​

List all the elements of set B that belong to the indicated set. - B={2,5,−20,0,04,16}B = \left\{ 2 , \sqrt { 5 } , - 20,0 , \frac { 0 } { 4 } , \sqrt { 16 } \right\}B={2,5​,−20,0,40​,16​} Whole numbers

Find the product. - 4x3(−11x+2)4 x ^ { 3 } ( - 11 x + 2 )4x3(−11x+2)

Simplify the expression. Assume all variables represent positive real numbers. - (−4)44\sqrt [ 4 ] { ( - 4 ) ^ { 4 } }4(−4)4​

Evaluate the expression. - ∣10∣| 10 |∣10∣