Question 1

How many prime numbers are there between -6 and 14 on the number line?

Accepted Answer

A)  19 
B)  13 
C)  0 
D)  14 
E)  6
F) 5 
A)  19 
B)  13 
C)  0 
D)  14 
E)  6
F) 5

Question 2

Perform the operations and simplify. $$\frac { 5 a } { 3 } \cdot \frac { 2 } { 7 b }$$
Assume that no denominators are 0 .

Accepted Answer

A)  $\frac { 3 a } { b 7 }$ 
B)  $\frac { 5 } { 2 }$ 
C)  $\frac { 2 } { 5 }$ 
D)  $\frac { 10 a } { 21 b }$ 
A)  $\frac { 3 a } { b 7 }$ 
B)  $\frac { 5 } { 2 }$ 
C)  $\frac { 2 } { 5 }$ 
D)  $\frac { 10 a } { 21 b }$

Question 3

Simplify the expression. $\frac { x ^ { 4 } x ^ { 2 } } { x ^ { 3 } x }$ Write the answer without using negative exponents.Assume that the variable is restricted to those numbers for which the expression is defined.

Accepted Answer

A)  $x ^ { 4 }$ 
B)  $x ^ { 3 }$ 
C)  $\quad x ^ { 2 }$ 
D)  $x ^ { 10 }$ 
A)  $x ^ { 4 }$ 
B)  $x ^ { 3 }$ 
C)  $\quad x ^ { 2 }$ 
D)  $x ^ { 10 }$

Question 4

Factor the expression completely. $6 x ^ { 2 } + 3 x ^ { 3 }$

Accepted Answer

A)  $\quad 3 x ^ { 2 } ( 3 + x )$ 
B)  $\quad 3 x ^ { 2 } ( 2 + x )$ 
C)  $\quad 3 x ^ { 2 } \left( 2 + x ^ { 2 } \right)$ 
D)  $\quad 3 x ^ { 2 } ( 2 - x )$ 
A)  $\quad 3 x ^ { 2 } ( 3 + x )$ 
B)  $\quad 3 x ^ { 2 } ( 2 + x )$ 
C)  $\quad 3 x ^ { 2 } \left( 2 + x ^ { 2 } \right)$ 
D)  $\quad 3 x ^ { 2 } ( 2 - x )$

Question 5

Simplify the expression. $$\left( x ^ { 6 } \right) ^ { 4 } \left( x ^ { 2 } \right) ^ { 2 }$$

Accepted Answer

A)  $x ^ { - 8 }$ 
B)  $x ^ { 6 }$ 
C)  $x ^ { 14 }$ 
D)  $x ^ { 28 }$ 
A)  $x ^ { - 8 }$ 
B)  $x ^ { 6 }$ 
C)  $x ^ { 14 }$ 
D)  $x ^ { 28 }$

Question 6

Simplify the expression. $\frac { a ^ { 2 / 5 } a ^ { 2 / 5 } } { a ^ { 1 / 5 } }$ Write all answers without using negative exponents.Assume that all variables represent positive numbers.

Accepted Answer

A)  $\quad a ^ { 3 / 5 }$ 
B)  $\quad a ^ { 4 / 5 }$ 
C)  $\quad a ^ { 5 / 5 }$ 
D)  $\quad a ^ { 3 / 10 }$ 
E)  $\quad a ^ { 3 / 8 }$ 
A)  $\quad a ^ { 3 / 5 }$ 
B)  $\quad a ^ { 4 / 5 }$ 
C)  $\quad a ^ { 5 / 5 }$ 
D)  $\quad a ^ { 3 / 10 }$ 
E)  $\quad a ^ { 3 / 8 }$

Question 7

Perform the operations and simplify. $$\frac { 1 } { x - 6 } + \frac { 3 } { x + 6 } - \frac { 3 x - 6 } { x ^ { 2 } - 36 }$$
Assume that no denominators are 0 .

Accepted Answer

A)  $\frac { 1 } { x - 6 }$ 
B)  $\frac { 1 } { x + 36 }$ 
C)  $\frac { 1 } { x + 6 }$ 
D)  $\frac { 6 } { x + 6 }$ 
A)  $\frac { 1 } { x - 6 }$ 
B)  $\frac { 1 } { x + 36 }$ 
C)  $\frac { 1 } { x + 6 }$ 
D)  $\frac { 6 } { x + 6 }$

Question 8

Factor the expression completely. $30 x ^ { 2 } - 13 x y = 56 y ^ { 2 }$

Accepted Answer

A)  $\quad ( 5 x - 8 y ) ( 6 x + 7 y )$ 
B)  $\quad ( 5 x + 8 y ) ( 6 x - 7 y )$ 
C)  $\quad ( 7 x - 8 y ) ( 6 x + 5 y )$ 
D)  $\quad ( 5 x - 8 y ) ( 7 x + 6 y )$ 
A)  $\quad ( 5 x - 8 y ) ( 6 x + 7 y )$ 
B)  $\quad ( 5 x + 8 y ) ( 6 x - 7 y )$ 
C)  $\quad ( 7 x - 8 y ) ( 6 x + 5 y )$ 
D)  $\quad ( 5 x - 8 y ) ( 7 x + 6 y )$

Question 9

Factor the expression completely. $$z ^ { 2 } + 6 z + 9 - 36 y ^ { 2 }$$

Accepted Answer

A)  $\quad ( z + 6 + 3 y ) ( z + 6 - 3 y )$ 
B)  $\quad ( z - 3 + 6 y ) ( z + 3 + 6 y )$ 
C)  $\quad ( z + 3 + 6 y ) ( z + 3 - 6 y )$ 
D)  $\quad ( z - 3 + 6 y ) ( z - 3 - 6 y )$ 
A)  $\quad ( z + 6 + 3 y ) ( z + 6 - 3 y )$ 
B)  $\quad ( z - 3 + 6 y ) ( z + 3 + 6 y )$ 
C)  $\quad ( z + 3 + 6 y ) ( z + 3 - 6 y )$ 
D)  $\quad ( z - 3 + 6 y ) ( z - 3 - 6 y )$

Question 10

Perform the division and write the answer without using negative exponents. $$\frac { 160 x ^ { 5 } y ^ { 7 } - 96 x ^ { 2 } y ^ { 5 } + 32 x y } { 4 x ^ { 5 } y ^ { 4 } }$$

Accepted Answer

A)  $24 y ^ { 3 } - \frac { 40 y } { x ^ { 3 } } + \frac { 32 } { x ^ { 4 } y ^ { 3 } }$ 
B)  $\quad 40 y ^ { 3 } - \frac { 40 y } { x ^ { 4 } } + \frac { 32 } { x ^ { 4 } y ^ { 3 } }$ 
C)  $\quad 24 y ^ { 3 } - \frac { 24 y } { x ^ { 3 } } + \frac { 32 } { x ^ { 4 } y ^ { 9 } }$ 
D)  $\quad 40 y ^ { 3 } - \frac { 24 y } { x ^ { 3 } } + \frac { 8 } { x ^ { 4 } y ^ { 3 } }$ 
A)  $24 y ^ { 3 } - \frac { 40 y } { x ^ { 3 } } + \frac { 32 } { x ^ { 4 } y ^ { 3 } }$ 
B)  $\quad 40 y ^ { 3 } - \frac { 40 y } { x ^ { 4 } } + \frac { 32 } { x ^ { 4 } y ^ { 3 } }$ 
C)  $\quad 24 y ^ { 3 } - \frac { 24 y } { x ^ { 3 } } + \frac { 32 } { x ^ { 4 } y ^ { 9 } }$ 
D)  $\quad 40 y ^ { 3 } - \frac { 24 y } { x ^ { 3 } } + \frac { 8 } { x ^ { 4 } y ^ { 3 } }$

Question 11

Simplify the expression. $$\left( \frac { a ^ { - 2 } } { b ^ { - 4 } } \right) ^ { - 5 }$$
Write the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined.

Accepted Answer

A)  $\quad \frac { b ^ { 10 } } { a ^ { 20 } }$ 
B)  $\quad \frac { b ^ { 20 } } { a ^ { 10 } }$ 
C)  $\quad \frac { a ^ { 20 } } { b ^ { 10 } }$ 
D)  $\frac { a ^ { 10 } } { b ^ { 20 } }$ 
A)  $\quad \frac { b ^ { 10 } } { a ^ { 20 } }$ 
B)  $\quad \frac { b ^ { 20 } } { a ^ { 10 } }$ 
C)  $\quad \frac { a ^ { 20 } } { b ^ { 10 } }$ 
D)  $\frac { a ^ { 10 } } { b ^ { 20 } }$

Question 12

Write the expression without using absolute value symbols. 
$| x + 9 | - | x - 13 | \quad$ for $\quad x < - 13$
$| x + 9 | - | x - 13 | =$ for $x < - 13$

Accepted Answer

A)  $2 x - 22$ 
B)  22 
C)  4 
D)  $22 - 2 x$ 
E)  -22 
A)  $2 x - 22$ 
B)  22 
C)  4 
D)  $22 - 2 x$ 
E)  -22

Question 13

Simplify the expression.Assume that all variables represent positive numbers, so that no absolute value symbols are needed. $$\sqrt [ 4 ] { 2 x y ^ { 5 } } + y \sqrt [ 4 ] { 512 x y } - \sqrt [ 4 ] { 2 x y ^ { 5 } }$$

Accepted Answer

A)  $\quad 4 y \sqrt { 4 x y }$ 
B)  $\quad 4 y \sqrt { 2 x y }$ 
C)  $\quad 12 y \sqrt { 2 x y }$ 
D)  $\quad 8 y \sqrt { 3 x y }$ 
A)  $\quad 4 y \sqrt { 4 x y }$ 
B)  $\quad 4 y \sqrt { 2 x y }$ 
C)  $\quad 12 y \sqrt { 2 x y }$ 
D)  $\quad 8 y \sqrt { 3 x y }$

Question 14

How many natural numbers are there between -16.5 and 6.5 on the number line?

Accepted Answer

A)  0 
B)  7 
C)  12 
D)  6 
E)  23 
A)  0 
B)  7 
C)  12 
D)  6 
E)  23

Question 15

Simplify the radical expression. $\sqrt [ 4 ] { 49 }$

Accepted Answer

A)  $\sqrt [ 8 ] { 7 }$ 
B)  $\sqrt [ 2 ] { 700 }$ 
C)  $\sqrt [ 2 ] { 49 }$ 
D)  $\sqrt [ 4 ] { 7 }$ 
E)  $\sqrt [ 2 ] { 7 }$ 
A)  $\sqrt [ 8 ] { 7 }$ 
B)  $\sqrt [ 2 ] { 700 }$ 
C)  $\sqrt [ 2 ] { 49 }$ 
D)  $\sqrt [ 4 ] { 7 }$ 
E)  $\sqrt [ 2 ] { 7 }$

Question 16

Write the expression without using absolute value symbols. $| x + 4 | - | x - 14 | \quad$ for $\quad x < - 8$
$| x + 4 | - | x - 14 | =ـــــــــــ$ for $x < - 8$

Accepted Answer

A)  10 
B)  $- 18$ 
C)  $\quad 2 x - 18$ 
D)  $\quad 18 - 2 x$ 
E)  18 
A)  10 
B)  $- 18$ 
C)  $\quad 2 x - 18$ 
D)  $\quad 18 - 2 x$ 
E)  18

Question 17

Perform the operation and simplify. $- 3 a ^ { 2 } ( a + 1 ) + 7 a \left( a ^ { 2 } - 4 \right) - a ^ { 2 } ( a + 9 )$

Accepted Answer

A)  $\quad 3 a ^ { 2 } + 12 a ^ { 4 } - 28$ 
B)  $\quad 3 a ^ { 3 } - 12 a ^ { 2 } - 28$ 
C)  0 
D)  $\quad 3 a ^ { 3 } - 12 a ^ { 2 } - 28 a$ 
A)  $\quad 3 a ^ { 2 } + 12 a ^ { 4 } - 28$ 
B)  $\quad 3 a ^ { 3 } - 12 a ^ { 2 } - 28$ 
C)  0 
D)  $\quad 3 a ^ { 3 } - 12 a ^ { 2 } - 28 a$

Question 18

How many prime numbers are there between -5 and 20 on the number line?

Accepted Answer

A)  0 
B)  4 
C)  19 
D)  24 
E)  20
F) 8 
A)  0 
B)  4 
C)  19 
D)  24 
E)  20
F) 8

Question 19

Simplify the fraction. $\frac { x y + 6 x + 4 y + 24 } { x ^ { 3 } + 64 }$
Assume that denominator is not 0 .

Accepted Answer

A)  $\frac { y - 6 } { x ^ { 2 } - 4 x - 16 }$ 
B)  $\frac { y + 6 } { x ^ { 2 } - 4 x + 16 }$ 
C)  $\frac { y - 6 } { x ^ { 2 } - 4 x + 16 }$ 
D)  $\frac { y + 4 } { x ^ { 2 } - 4 x + 16 }$ 
A)  $\frac { y - 6 } { x ^ { 2 } - 4 x - 16 }$ 
B)  $\frac { y + 6 } { x ^ { 2 } - 4 x + 16 }$ 
C)  $\frac { y - 6 } { x ^ { 2 } - 4 x + 16 }$ 
D)  $\frac { y + 4 } { x ^ { 2 } - 4 x + 16 }$

Question 20

Perform the division.

Accepted Answer

A)  $\quad 11 x - 13$ 
B)  $11 x - 15$ 
C)  $15 - 11 x$ 
D)  $11 x ^ { 2 } - 13$ 
A)  $\quad 11 x - 13$ 
B)  $11 x - 15$ 
C)  $15 - 11 x$ 
D)  $11 x ^ { 2 } - 13$

How many prime numbers are there between -6 and 14 on the number line?

Perform the operations and simplify. $\frac { 5 a } { 3 } \cdot \frac { 2 } { 7 b }$ Assume that no denominators are 0 .

Simplify the expression. $\frac { x ^ { 4 } x ^ { 2 } } { x ^ { 3 } x }$ Write the answer without using negative exponents.Assume that the variable is restricted to those numbers for which the expression is defined.

Factor the expression completely. $6 x ^ { 2 } + 3 x ^ { 3 }$

Simplify the expression. $\left( x ^ { 6 } \right) ^ { 4 } \left( x ^ { 2 } \right) ^ { 2 }$

Simplify the expression. $\frac { a ^ { 2 / 5 } a ^ { 2 / 5 } } { a ^ { 1 / 5 } }$ Write all answers without using negative exponents.Assume that all variables represent positive numbers.

Perform the operations and simplify. $\frac { 1 } { x - 6 } + \frac { 3 } { x + 6 } - \frac { 3 x - 6 } { x ^ { 2 } - 36 }$ Assume that no denominators are 0 .

Factor the expression completely. $30 x ^ { 2 } - 13 x y = 56 y ^ { 2 }$

Factor the expression completely. $z ^ { 2 } + 6 z + 9 - 36 y ^ { 2 }$

Perform the division and write the answer without using negative exponents. $\frac { 160 x ^ { 5 } y ^ { 7 } - 96 x ^ { 2 } y ^ { 5 } + 32 x y } { 4 x ^ { 5 } y ^ { 4 } }$

Simplify the expression. $\left( \frac { a ^ { - 2 } } { b ^ { - 4 } } \right) ^ { - 5 }$ Write the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined.

Write the expression without using absolute value symbols. $| x + 9 | - | x - 13 | \quad$ for $\quad x < - 13$ $| x + 9 | - | x - 13 | =$ for $x < - 13$

Simplify the expression.Assume that all variables represent positive numbers, so that no absolute value symbols are needed. $\sqrt [ 4 ] { 2 x y ^ { 5 } } + y \sqrt [ 4 ] { 512 x y } - \sqrt [ 4 ] { 2 x y ^ { 5 } }$

How many natural numbers are there between -16.5 and 6.5 on the number line?

Simplify the radical expression. $\sqrt [ 4 ] { 49 }$

Write the expression without using absolute value symbols. $| x + 4 | - | x - 14 | \quad$ for $\quad x < - 8$ $| x + 4 | - | x - 14 | =ـــــــــــ$ for $x < - 8$

Perform the operation and simplify. $- 3 a ^ { 2 } ( a + 1 ) + 7 a \left( a ^ { 2 } - 4 \right) - a ^ { 2 } ( a + 9 )$

How many prime numbers are there between -5 and 20 on the number line?

Simplify the fraction. $\frac { x y + 6 x + 4 y + 24 } { x ^ { 3 } + 64 }$ Assume that denominator is not 0 .

Perform the division.

Equations and Inequalities

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Exam 1: A Review of Basic Algebra

How many prime numbers are there between -6 and 14 on the number line?

Perform the operations and simplify. 5a3⋅27b\frac { 5 a } { 3 } \cdot \frac { 2 } { 7 b }35a​⋅7b2​ Assume that no denominators are 0 .

Simplify the expression. x4x2x3x\frac { x ^ { 4 } x ^ { 2 } } { x ^ { 3 } x }x3xx4x2​ Write the answer without using negative exponents.Assume that the variable is restricted to those numbers for which the expression is defined.

Factor the expression completely. 6x2+3x36 x ^ { 2 } + 3 x ^ { 3 }6x2+3x3

Simplify the expression. (x6)4(x2)2\left( x ^ { 6 } \right) ^ { 4 } \left( x ^ { 2 } \right) ^ { 2 }(x6)4(x2)2

Simplify the expression. a2/5a2/5a1/5\frac { a ^ { 2 / 5 } a ^ { 2 / 5 } } { a ^ { 1 / 5 } }a1/5a2/5a2/5​ Write all answers without using negative exponents.Assume that all variables represent positive numbers.

Perform the operations and simplify. 1x−6+3x+6−3x−6x2−36\frac { 1 } { x - 6 } + \frac { 3 } { x + 6 } - \frac { 3 x - 6 } { x ^ { 2 } - 36 }x−61​+x+63​−x2−363x−6​ Assume that no denominators are 0 .

Factor the expression completely. 30x2−13xy=56y230 x ^ { 2 } - 13 x y = 56 y ^ { 2 }30x2−13xy=56y2

Factor the expression completely. z2+6z+9−36y2z ^ { 2 } + 6 z + 9 - 36 y ^ { 2 }z2+6z+9−36y2

Perform the division and write the answer without using negative exponents. 160x5y7−96x2y5+32xy4x5y4\frac { 160 x ^ { 5 } y ^ { 7 } - 96 x ^ { 2 } y ^ { 5 } + 32 x y } { 4 x ^ { 5 } y ^ { 4 } }4x5y4160x5y7−96x2y5+32xy​

Simplify the expression. (a−2b−4)−5\left( \frac { a ^ { - 2 } } { b ^ { - 4 } } \right) ^ { - 5 }(b−4a−2​)−5 Write the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined.

Write the expression without using absolute value symbols. ∣x+9∣−∣x−13∣| x + 9 | - | x - 13 | \quad∣x+9∣−∣x−13∣ for x<−13\quad x < - 13x<−13 ∣x+9∣−∣x−13∣=| x + 9 | - | x - 13 | =∣x+9∣−∣x−13∣= for x<−13x < - 13x<−13

Simplify the expression.Assume that all variables represent positive numbers, so that no absolute value symbols are needed. 2xy54+y512xy4−2xy54\sqrt [ 4 ] { 2 x y ^ { 5 } } + y \sqrt [ 4 ] { 512 x y } - \sqrt [ 4 ] { 2 x y ^ { 5 } }42xy5​+y4512xy​−42xy5​

How many natural numbers are there between -16.5 and 6.5 on the number line?

Simplify the radical expression. 494\sqrt [ 4 ] { 49 }449​

Perform the operation and simplify. −3a2(a+1)+7a(a2−4)−a2(a+9)- 3 a ^ { 2 } ( a + 1 ) + 7 a \left( a ^ { 2 } - 4 \right) - a ^ { 2 } ( a + 9 )−3a2(a+1)+7a(a2−4)−a2(a+9)

How many prime numbers are there between -5 and 20 on the number line?

Simplify the fraction. xy+6x+4y+24x3+64\frac { x y + 6 x + 4 y + 24 } { x ^ { 3 } + 64 }x3+64xy+6x+4y+24​ Assume that denominator is not 0 .

Perform the division.

Equations and Inequalities

The Rectangular Coordinate System and Graphs of Equations

Functions Functions and Function Notation

Exponential and Logarithmic Functions

Solving Polynomial Equations

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Perform the operations and simplify. $\frac { 5 a } { 3 } \cdot \frac { 2 } { 7 b }$ Assume that no denominators are 0 .

Simplify the expression. $\frac { x ^ { 4 } x ^ { 2 } } { x ^ { 3 } x }$ Write the answer without using negative exponents.Assume that the variable is restricted to those numbers for which the expression is defined.

Factor the expression completely. $6 x ^ { 2 } + 3 x ^ { 3 }$

Simplify the expression. $\left( x ^ { 6 } \right) ^ { 4 } \left( x ^ { 2 } \right) ^ { 2 }$

Simplify the expression. $\frac { a ^ { 2 / 5 } a ^ { 2 / 5 } } { a ^ { 1 / 5 } }$ Write all answers without using negative exponents.Assume that all variables represent positive numbers.

Perform the operations and simplify. $\frac { 1 } { x - 6 } + \frac { 3 } { x + 6 } - \frac { 3 x - 6 } { x ^ { 2 } - 36 }$ Assume that no denominators are 0 .

Factor the expression completely. $30 x ^ { 2 } - 13 x y = 56 y ^ { 2 }$

Factor the expression completely. $z ^ { 2 } + 6 z + 9 - 36 y ^ { 2 }$

Perform the division and write the answer without using negative exponents. $\frac { 160 x ^ { 5 } y ^ { 7 } - 96 x ^ { 2 } y ^ { 5 } + 32 x y } { 4 x ^ { 5 } y ^ { 4 } }$

Simplify the expression. $\left( \frac { a ^ { - 2 } } { b ^ { - 4 } } \right) ^ { - 5 }$ Write the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined.

Write the expression without using absolute value symbols. $| x + 9 | - | x - 13 | \quad$ for $\quad x < - 13$ $| x + 9 | - | x - 13 | =$ for $x < - 13$

Simplify the expression.Assume that all variables represent positive numbers, so that no absolute value symbols are needed. $\sqrt [ 4 ] { 2 x y ^ { 5 } } + y \sqrt [ 4 ] { 512 x y } - \sqrt [ 4 ] { 2 x y ^ { 5 } }$

Simplify the radical expression. $\sqrt [ 4 ] { 49 }$

Perform the operation and simplify. $- 3 a ^ { 2 } ( a + 1 ) + 7 a \left( a ^ { 2 } - 4 \right) - a ^ { 2 } ( a + 9 )$

Simplify the fraction. $\frac { x y + 6 x + 4 y + 24 } { x ^ { 3 } + 64 }$ Assume that denominator is not 0 .