Question 1

Find the reciprocal of 7.

Accepted Answer

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

Question 2

Evaluate the expression $- 6 ^ { 2 }$ .

Accepted Answer

A) -64 
B) 64 
C) -12 
D) 36 
E) -36 
A) -64 
B) 64 
C) -12 
D) 36 
E) -36

Question 3

Find the distance between -4 and 0 on the real number line.

Accepted Answer

A) 1 
B)  2 
C)  -4 
D)  4 
E) 0 
A) 1 
B)  2 
C)  -4 
D)  4 
E) 0

Question 4

Find the product 1(2) .

Accepted Answer

A) 2 
B) 1 
C) -1 
D) -2 
E) 3 
A) 2 
B) 1 
C) -1 
D) -2 
E) 3

Question 5

Determine which of the numbers in the set below are rational. $\left\{ - 11,33 , \frac { 1 } { 11 } , 5.5 , - 4.25 \right\}$

Accepted Answer

A)  $\left\{ \frac { 1 } { 11 } \right\}$ 
B)  $\{ 5.5 , - 4.25 \}$ 
C)  $\{ - 11,33 \}$ 
D)  $\left\{ - 11,33 , \frac { 1 } { 11 } , 5.5 , - 4.25 \right\}$ 
E) none are rational 
A)  $\left\{ \frac { 1 } { 11 } \right\}$ 
B)  $\{ 5.5 , - 4.25 \}$ 
C)  $\{ - 11,33 \}$ 
D)  $\left\{ - 11,33 , \frac { 1 } { 11 } , 5.5 , - 4.25 \right\}$ 
E) none are rational

Question 6

Find the opposite of the real number $ \frac{5}{9} $ .

Accepted Answer

A)  $ \frac{9}{5} $ 
B)  -$ \frac{9}{5} $ 
C)  $ \frac{5}{9} $ 
D)  -$ \frac{5}{9} $ 
E)  -4 
A)  $ \frac{9}{5} $ 
B)  -$ \frac{9}{5} $ 
C)  $ \frac{5}{9} $ 
D)  -$ \frac{5}{9} $ 
E)  -4

Question 7

Evaluate the algebraic expression $x - 3 ( x - y )$ when x=9 and y=-6 .

Accepted Answer

A)  -24 
B)  -36 
C)  20 
D)  37 
E)  -56 
A)  -24 
B)  -36 
C)  20 
D)  37 
E)  -56

Question 8

Translate the phrase into an algebraic expression. The ratio of $120$ and a number x

Accepted Answer

A)  $120 - x$ 
B)  $\frac { 120 } { x }$ 
C)  $120 x$ 
D)  $\frac { 1 } { 120 x }$ 
E)  $\frac { x } { 120 }$ 
A)  $120 - x$ 
B)  $\frac { 120 } { x }$ 
C)  $120 x$ 
D)  $\frac { 1 } { 120 x }$ 
E)  $\frac { x } { 120 }$

Question 9

Add the fractions $\frac { 2 } { 12 } + \frac { 9 } { 12 }$ and write the result in simplest form.

Accepted Answer

A)  $\frac { 1 } { 8 }$ 
B)  $\frac { 11 } { 24 }$ 
C)  $\frac { 3 } { 4 }$ 
D)  $\frac { 11 } { 12 }$ 
E)  $\frac { 3 } { 2 }$ 
A)  $\frac { 1 } { 8 }$ 
B)  $\frac { 11 } { 24 }$ 
C)  $\frac { 3 } { 4 }$ 
D)  $\frac { 11 } { 12 }$ 
E)  $\frac { 3 } { 2 }$

Question 10

Write an algebraic expression that represents the sum of three consecutive integers, the first of which is n .

Accepted Answer

A)  $3 n + 4$ 
B)  $3 n + 5$ 
C)  $6 n$ 
D)  $n + 3$ 
E)  $3 n + 3$ 
A)  $3 n + 4$ 
B)  $3 n + 5$ 
C)  $6 n$ 
D)  $n + 3$ 
E)  $3 n + 3$

Question 11

Evaluate the expression $25 - 5 + 14$ .

Accepted Answer

A) 16 
B) -6 
C) 6 
D) 44 
E) 34 
A) 16 
B) -6 
C) 6 
D) 44 
E) 34

Question 12

Write $4 \left( \frac { 4 } { 12 } \right)$ as repeated addition.

Accepted Answer

A)  $16 + 16 + 16 + 16$ 
B)  $\frac { 4 } { 12 } + \frac { 4 } { 12 } + \frac { 4 } { 12 } + \frac { 4 } { 12 } + \frac { 4 } { 12 }$ 
C)  $\frac { 16 } { 12 } + \frac { 16 } { 12 } + \frac { 16 } { 12 } + \frac { 16 } { 12 }$ 
D)  $\frac { 4 } { 12 } + \frac { 4 } { 12 } + 4$ 
E)  $\frac { 4 } { 12 } + \frac { 4 } { 12 } + \frac { 4 } { 12 } + \frac { 4 } { 12 }$ 
A)  $16 + 16 + 16 + 16$ 
B)  $\frac { 4 } { 12 } + \frac { 4 } { 12 } + \frac { 4 } { 12 } + \frac { 4 } { 12 } + \frac { 4 } { 12 }$ 
C)  $\frac { 16 } { 12 } + \frac { 16 } { 12 } + \frac { 16 } { 12 } + \frac { 16 } { 12 }$ 
D)  $\frac { 4 } { 12 } + \frac { 4 } { 12 } + 4$ 
E)  $\frac { 4 } { 12 } + \frac { 4 } { 12 } + \frac { 4 } { 12 } + \frac { 4 } { 12 }$

Question 13

Evaluate the expression $- ( - 3 ) + 6 - 10 + 12$ .

Accepted Answer

A) 25 
B) -31 
C) 7 
D) -13 
E) 11 
A) 25 
B) -31 
C) 7 
D) -13 
E) 11

Question 14

Find the difference $- 7 - ( - 7 )$ .

Accepted Answer

A) -14 
B) -7 
C)  0 
D) 14 
E) 7 
A) -14 
B) -7 
C)  0 
D) 14 
E) 7

Question 15

A rectangle has sides of length $4 w$ and $W$ . Write an algebraic expression that represents the area of the rectangle.

Accepted Answer

A)  $8 w$ 
B)  $8 w ^ { 2 }$ 
C)  $5 w$ 
D)  $4 w ^ { 2 }$ 
E)  $10 w$ 
A)  $8 w$ 
B)  $8 w ^ { 2 }$ 
C)  $5 w$ 
D)  $4 w ^ { 2 }$ 
E)  $10 w$

Question 16

If you save $75 every month, how much money will you have after 7 years?

Accepted Answer

A) $525 
B) $6300 
C) $984 
D) $82 
E) $5,250 
A) $525 
B) $6300 
C) $984 
D) $82 
E) $5,250

Question 17

Find the difference $- 128 - ( - 33 )$ .

Accepted Answer

A) 95 
B) -161 
C) -105 
D) 161 
E) -95 
A) 95 
B) -161 
C) -105 
D) 161 
E) -95

Question 18

Identify the property of real numbers illustrated by the statement $( 5 + 9 ) + 7 = 5 + ( 9 + 7 )$ .

Accepted Answer

A) Commutative Property of Multiplication 
B) Commutative Property of Addition 
C) Distributive Property 
D) Associative Property of Multiplication 
E) Associative Property of Addition 
A) Commutative Property of Multiplication 
B) Commutative Property of Addition 
C) Distributive Property 
D) Associative Property of Multiplication 
E) Associative Property of Addition

Question 19

Simplify $- 4 x ( x - 7 ) + x ^ { 2 }$ by eliminating the parentheses and combining like terms.

Accepted Answer

A)  $5 x ^ { 2 } + 28 x$ 
B)  $- 3 x ^ { 2 } - 7 x$ 
C)  $- 3 x ^ { 2 } + 28 x$ 
D)  $5 x ^ { 2 } - 7 x$ 
E)  $- 3 x ^ { 2 } + 28$ 
A)  $5 x ^ { 2 } + 28 x$ 
B)  $- 3 x ^ { 2 } - 7 x$ 
C)  $- 3 x ^ { 2 } + 28 x$ 
D)  $5 x ^ { 2 } - 7 x$ 
E)  $- 3 x ^ { 2 } + 28$

Question 20

Justify step 3 of the solution. $x + 7 = 6$ Original equation $( x + 7 ) + ( - 7 ) = 6 + ( - 7 )$ Step 1 $x + [ 7 + ( - 7 ) ] = 6 - 7$ Step 2 $x + 0 = - 1$ Step 3 x=-1 Step 4

Accepted Answer

A) Associative Property of Addition 
B) Additive Inverse Property 
C) Addition Property of Equality 
D) Additive Identity Property 
E) Cancellation Property of Multiplication 
A) Associative Property of Addition 
B) Additive Inverse Property 
C) Addition Property of Equality 
D) Additive Identity Property 
E) Cancellation Property of Multiplication

Find the reciprocal of 7.

Evaluate the expression $- 6 ^ { 2 }$ .

Find the distance between -4 and 0 on the real number line.

Find the product 1(2) .

Determine which of the numbers in the set below are rational. $\left\{ - 11,33 , \frac { 1 } { 11 } , 5.5 , - 4.25 \right\}$

Find the opposite of the real number $\frac{5}{9}$ .

Evaluate the algebraic expression $x - 3 ( x - y )$ when x=9 and y=-6 .

Translate the phrase into an algebraic expression. The ratio of $120$ and a number x

Add the fractions $\frac { 2 } { 12 } + \frac { 9 } { 12 }$ and write the result in simplest form.

Write an algebraic expression that represents the sum of three consecutive integers, the first of which is n .

Evaluate the expression $25 - 5 + 14$ .

Write $4 \left( \frac { 4 } { 12 } \right)$ as repeated addition.

Evaluate the expression $- ( - 3 ) + 6 - 10 + 12$ .

Find the difference $- 7 - ( - 7 )$ .

A rectangle has sides of length $4 w$ and $W$ . Write an algebraic expression that represents the area of the rectangle.

If you save $75 every month, how much money will you have after 7 years?

Find the difference $- 128 - ( - 33 )$ .

Identify the property of real numbers illustrated by the statement $( 5 + 9 ) + 7 = 5 + ( 9 + 7 )$ .

Simplify $- 4 x ( x - 7 ) + x ^ { 2 }$ by eliminating the parentheses and combining like terms.

Justify step 3 of the solution. $x + 7 = 6$ Original equation $( x + 7 ) + ( - 7 ) = 6 + ( - 7 )$ Step 1 $x + [ 7 + ( - 7 ) ] = 6 - 7$ Step 2 $x + 0 = - 1$ Step 3 x=-1 Step 4

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Exam 1: Fundamentals of Algebra

Find the reciprocal of 7.

Evaluate the expression −62- 6 ^ { 2 }−62 .

Find the distance between -4 and 0 on the real number line.

Find the product 1(2) .

Determine which of the numbers in the set below are rational. {−11,33,111,5.5,−4.25}\left\{ - 11,33 , \frac { 1 } { 11 } , 5.5 , - 4.25 \right\}{−11,33,111​,5.5,−4.25}

Find the opposite of the real number 59 \frac{5}{9} 95​ .

Evaluate the algebraic expression x−3(x−y)x - 3 ( x - y )x−3(x−y) when x=9 and y=-6 .

Translate the phrase into an algebraic expression. The ratio of 120120120 and a number x

Add the fractions 212+912\frac { 2 } { 12 } + \frac { 9 } { 12 }122​+129​ and write the result in simplest form.

Write an algebraic expression that represents the sum of three consecutive integers, the first of which is n .

Evaluate the expression 25−5+1425 - 5 + 1425−5+14 .

Write 4(412)4 \left( \frac { 4 } { 12 } \right)4(124​) as repeated addition.

Evaluate the expression −(−3)+6−10+12- ( - 3 ) + 6 - 10 + 12−(−3)+6−10+12 .

Find the difference −7−(−7)- 7 - ( - 7 )−7−(−7) .

A rectangle has sides of length 4w4 w4w and WWW . Write an algebraic expression that represents the area of the rectangle.

If you save $75 every month, how much money will you have after 7 years?

Find the difference −128−(−33)- 128 - ( - 33 )−128−(−33) .

Identify the property of real numbers illustrated by the statement (5+9)+7=5+(9+7)( 5 + 9 ) + 7 = 5 + ( 9 + 7 )(5+9)+7=5+(9+7) .

Simplify −4x(x−7)+x2- 4 x ( x - 7 ) + x ^ { 2 }−4x(x−7)+x2 by eliminating the parentheses and combining like terms.

Justify step 3 of the solution. x+7=6x + 7 = 6x+7=6 Original equation (x+7)+(−7)=6+(−7)( x + 7 ) + ( - 7 ) = 6 + ( - 7 )(x+7)+(−7)=6+(−7) Step 1 x+[7+(−7)]=6−7x + [ 7 + ( - 7 ) ] = 6 - 7x+[7+(−7)]=6−7 Step 2 x+0=−1x + 0 = - 1x+0=−1 Step 3 x=-1 Step 4

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Evaluate the expression $- 6 ^ { 2 }$ .

Determine which of the numbers in the set below are rational. $\left\{ - 11,33 , \frac { 1 } { 11 } , 5.5 , - 4.25 \right\}$

Find the opposite of the real number $\frac{5}{9}$ .

Evaluate the algebraic expression $x - 3 ( x - y )$ when x=9 and y=-6 .

Translate the phrase into an algebraic expression. The ratio of $120$ and a number x

Add the fractions $\frac { 2 } { 12 } + \frac { 9 } { 12 }$ and write the result in simplest form.

Evaluate the expression $25 - 5 + 14$ .

Write $4 \left( \frac { 4 } { 12 } \right)$ as repeated addition.

Evaluate the expression $- ( - 3 ) + 6 - 10 + 12$ .

Find the difference $- 7 - ( - 7 )$ .

A rectangle has sides of length $4 w$ and $W$ . Write an algebraic expression that represents the area of the rectangle.

Find the difference $- 128 - ( - 33 )$ .

Identify the property of real numbers illustrated by the statement $( 5 + 9 ) + 7 = 5 + ( 9 + 7 )$ .

Simplify $- 4 x ( x - 7 ) + x ^ { 2 }$ by eliminating the parentheses and combining like terms.

Justify step 3 of the solution. $x + 7 = 6$ Original equation $( x + 7 ) + ( - 7 ) = 6 + ( - 7 )$ Step 1 $x + [ 7 + ( - 7 ) ] = 6 - 7$ Step 2 $x + 0 = - 1$ Step 3 x=-1 Step 4