Deck 8: An Introduction to Algebra

Question 1

Use a property of equality to solve the equation. Then check the result. = __________

Answer 1

-5

Question 2

Use a property of equality to solve the equation. Then check the result. __________

Answer 2

71

Question 3

In the expression , what is the base?

Answer 3

9

Question 4

In the expression $3 x ^ { 2 } - 2 x - 4$ , what is the constant?

A) $4$
B) $3$
C) $- 4$
D) $- 2$

Question 5

Use a property of equality to solve the equation. Then check the result. __________

Question 6

Use the division or the multiplication property of equality to solve $2 a = 24$ . What is the result?

A) 11
B) 12
C) 48
D) 49
E) 47

Question 7

Use the division or the multiplication property of equality to solve . What is the result? __________

Question 8

Use the division or the multiplication property of equality to solve . What is the result? __________

Question 9

What is the numerical coefficient of the term ?

Question 10

In the expression , what is the exponent?

Question 11

Use a property of equality to solve the equation. Then check the result. __________

Question 12

Use the division or the multiplication property of equality to solve . What is the result? __________

Question 13

Write the addition property of zero using the variable m .

A) $m + 0 = m$
B) $m + 0 = 0$
C) $m \cdot 0 = 0$
D) Non of these

Question 14

In the expression , what is the base and the exponent?

Question 15

Tell whether the given number is a solution of the equation. $5 k + 7 = 7 k - 1$ ; $k = 5$

A) unqualified solution
B) removed solution
C) solution
D) not a solution
E) none of these

Question 16

What is the variable part of the term $- 6 b x$  ?...

A) $b$
B) $- 6$
C) $b x$
D) $- 6 b x$
E) $X$

Question 17

Which of the following formulas illustrates the associative property of multiplication?

A) $( a \cdot b ) \cdot c = a \cdot ( b \cdot c )$
B) $a ( b + c ) = a b + b c$
C) $a + b = b + a$
D) None of these

Question 18

Tell whether the given number is a solution of the equation. $\frac { y } { 5 } = 7$ ; $y = 41$

A) restricted solution
B) not a solution
C) solution
D) conflicting solution
E) none of these

Question 19

Use a property of equality to solve the equation. Then check the result. __________

Question 20

Write the commutative property of multiplication using the variables a and b .

A) $a + b = b + a$
B) $( a + b ) + c = a + ( b + c )$
C) $( a b ) c = a ( b c )$
D) $a b = b a$

Question 21

Use the distributive property to write the expression $x ( x + 8 )$ without parentheses. Simplify the result, if possible.

A) $x ^ { 2 } + 8 x$
B) $x + 8 x$
C) $x + x + 8 x$
D) $2 x + 8$
E) $x ^ { 2 } + 8 x ^ { 2 } + 8 x$

Question 22

Evaluate the following expression for the given value of the variable. $\frac { z - 10 } { 10 - z }$  for $z = 8$

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

Question 23

Simplify and complete the expression.
5( y - 7) + 8 y = 5 y +      - 35 =      - 35

Question 24

Determine the correct statement.

A) $a \cdot ( b + c ) = a \cdot b + c$
B) $a \cdot ( b + c ) = a \cdot b + a \cdot c$
C) $a \cdot ( b + c ) = a \cdot b + a$
D) $a \cdot ( b + c ) = a \cdot b + c \cdot b$
E) $a \cdot ( b + c ) = a \cdot b + \frac { 1 } { b }$

Question 25

Simplify the expression.  $\left( 3 s ^ { 3 } \right) ^ { 3 }$

A) $27 s ^ { 6 }$
B) $27 s ^ { 9 }$
C) $3 s ^ { 9 }$
D) $27 s ^ { 3 }$
E) $3 s ^ { 3 }$

Question 26

Use the distributive property to write the expression $8 x ( d - x )$  without parentheses. Simplify the result, if possible.

A) $8 d x - 8 d ^ { 2 }$
B) $d x + d - 8 x ^ { 2 }$
C) $8 x + d - x$
D) $8 d x - 8 x ^ { 2 }$
E) $d x - 8 x ^ { 2 }$

Question 27

Find the product. $\left( 6 t ^ { 4 } x ^ { 4 } \right) \left( 5 t ^ { 2 } x ^ { 2 } \right)$

A) $11 t ^ { 6 } x ^ { 6 }$
B) $30 t ^ { 6 } x ^ { 6 }$
C) $30 t ^ { 8 } x ^ { 8 }$
D) $30 t ^ { 2 } x ^ { 2 }$
E) none of these

Question 28

Select the expression that completes the formula below. $( x y ) ^ { k }$

A) $x ^ { k } y ^ { k }$
B) $x ^ { m + k }$
C) $x ^ { m k }$
D) $\frac { x ^ { k } } { y ^ { k } }$
E) none of these

Question 29

Let $y = 5$ and $z = 1$ . Write the phrase as an algebraic expression, and evaluate it. $y$ minus $Z$

A) $y - z$ ; $5$
B) $y - z$ ; $4$
C) $y + z$ ; $5$
D) $y + z$ ; $4$
E) $y - z$ ; $- 4$

Question 30

Evaluate the expression. $6 \cdot 10 ^ { 3 } + 5 \cdot 10 ^ { 2 } + 4 \cdot 10 ^ { 1 } + 8$

A) 6,648
B) 6,548
C) 6,553
D) 6,537
E) 6,546

Question 31

Find the product. $\left( 7 y ^ { 6 } x ^ { 6 } \right) \left( 2 y ^ { 2 } x ^ { 4 } \right)$

A) $16 y ^ { 9 } x ^ { 11 }$
B) $14 y ^ { 8 } x ^ { 10 }$
C) $14 y ^ { 4 } x ^ { 2 }$
D) $14 y ^ { 12 } x ^ { 24 }$
E) $9 y ^ { 8 } x ^ { 10 }$

Question 32

Simplify the following algebraic expression and express your answer using positive exponents only. $\left( a ^ { - 1 } v ^ { - 2 } \right) ^ { 7 }$

A) $a ^ { 8 } v ^ { 9 }$
B) $\frac { 1 } { a ^ { 8 } v ^ { 9 } }$
C) $\frac { 1 } { a ^ { 6 } v ^ { 5 } }$
D) $a ^ { 7 } v ^ { 14 }$
E) $\frac { 1 } { a ^ { 7 } v ^ { 14 } }$

Question 33

Simplify the expression. $\left( 6 t ^ { 3 } \right) ^ { 2 }$

A) $6 t ^ { 6 }$
B) $6 t ^ { 3 }$
C) $36 t ^ { 7 }$
D) $36 t ^ { 6 }$
E) $36 t ^ { 5 }$

Question 34

What is $t ^ { 3 } \cdot t ^ { 3 }$  rewritten using only one exponent?

A) $t ^ { 0 }$
B) $t ^ { 6 }$
C) $t ^ { 3 }$
D) $t ^ { 9 }$
E) none of these

Question 35

Simplify the product. $- 3 x ^ { 2 } c ^ { 5 } \left( - 2 c ^ { 2 } x ^ { 5 } \right)$

A) $6 x ^ { 7 } c ^ { 7 }$
B) $- 6 x ^ { 5 } c ^ { 7 }$
C) $2 x ^ { 7 } c ^ { 7 }$
D) $3 x ^ { 7 } c ^ { 2 }$
E) none of these

Question 36

Write the following statement as a mathematical expression.
Three is less than twenty-three.

A) $3 \geq 23$
B) $3 = 23$
C) $3 \leq 23$
D) $3 < 23$
E) $3 > 23$

Question 37

Evaluate the following expression for the given value of the variable. $\frac { y - 4 } { 5 }$  for $y = 14$

A) $- 10$
B) $6$
C) $10$
D) $2$
E) $- 2$

Question 38

Let x , y , and z represent three real numbers. Write an algebraic expression to denote the product of z , x , and y .

A) $x y - z$
B) $z - y$
C) $x y z$
D) $z - x y$
E) $x + 2 z$

Question 39

Find the product. $\left( 6 b ^ { 5 } \right) \left( 5 b ^ { 6 } \right)$

A) $30 b ^ { 11 }$
B) $30 b ^ { 30 }$
C) $11 b ^ { 11 }$
D) $11 b ^ { 30 }$
E) none of these

Question 40

What is $2 c ^ { 3 } \left( 4 c ^ { 2 } \right) 5 c ^ { 2 }$  rewritten using only one exponent?

A) $8 c ^ { 7 }$
B) $40 c$
C) $40 c ^ { 6 }$
D) $40 c ^ { 7 }$
E) $9 c ^ { 7 }$

Question 41

Solve the equation. $5 ( x + 1 ) = 15$

A) $x = 1$
B) $x = 13$
C) $x = 10$
D) $x = 2$
E) $x = 7$

Question 42

The length of a rectangle is 7 times its width. If the perimeter of the rectangle is 112 inches, find its length and width.

A) the length is 980 inches and the width is 49 inches
B) the length is 49 inches and the width is 7 inches
C) the length is 70 inches and the width is 14 inches
D) the length is 343 inches and the width is 49 inches
E) the length is 343 inches and the width is 7 inches

Question 43

Solve the equation. $8.5 = - 10 c + 6$

A) $c = 4.75$
B) $c = - 0.25$
C) $c = - 0.25$ .
D) $c = 0.75$
E) none of these

Question 44

Solve the equation. $3 z + 4 = 13$

A) $z = 11$
B) $z = 3$
C) $z = 1$
D) $z = 5$
E) none of these

Question 45

Solve the equation. $38 = - 4 - 17 b$

A) $b = \frac { 42 } { 17 }$
B) $b = - \frac { 42 } { 17 }$
C) $b = - \frac { 34 } { 17 }$
D) $b = - \frac { 17 } { 42 }$
E) $b = \frac { 34 } { 17 }$

Question 46

Simplify the expression.  $\left( 3 x ^ { 5 } c ^ { 4 } \right) ^ { 3 }$

A) $27 x ^ { 15 } c ^ { 12 }$
B) $3 x ^ { 8 } c ^ { 7 }$
C) $27 x ^ { 5 } c ^ { 4 }$
D) $27 x ^ { 8 } c ^ { 7 }$
E) $3 x ^ { 15 } c ^ { 12 }$

Question 47

Identify the terms of the expression.

Question 48

Use an equation to solve the problem.
One-third of the movie audience left the theater in disgust. If 65 angry patrons walked out, how many were there originally?

A) 195
B) 207
C) 222
D) 230
E) 154

Question 49

Use an algebraic approach to solve the problem. Find three consecutive integers whose sum is 48.

A) -15, -16, -17
B) 15, 14, 13
C) 17, 18, 19
D) 20, 21, 22
E) 15, 16, 17

Question 50

Use an equation to solve the problem.
The average price of homes in one neighborhood decreased 8 % since last year, a drop of $5,800 . What was the average price of a home last year?

A) $69,500
B) $74,500
C) $73,500
D) $72,500
E) $76,500

Question 51

Solve the equation. $3 x - 5 + 6 x - 8 x + 3 = 8$

A) $x = 19$
B) $x = - 10$
C) $x = 6$
D) $x = 10$
E) $x = 14$

Question 52

Simplify the expression.  $\left( y ^ { 5 } y ^ { 5 } \right) ^ { 4 }$

A) $y ^ { 45 }$
B) $y ^ { 29 }$
C) $y ^ { 40 }$
D) $y ^ { 20 }$
E) $y ^ { 14 }$

Question 53

Solve the equation. $5 ( t - 1 ) + 3 ( t - 3 ) = - 2 ( t - 1 ) + 11 ( t + 3 )$

A) $t = - 51$
B) $t = - 53$
C) $t = - 49$
D) $t = - 14$
E) $t = - 48$

Question 54

Simplify the following expression by combining like terms.

Question 55

For a 49-mile trip, Stacy paid the taxi driver $23.00. If $2 was a tip, how much was the fare?
$__________

Question 56

Use an equation to solve the problem.
Sales tax on a $9 compact disc is $0.36. At what rate is sales tax computed?

A) 8%
B) 4%
C) 6%
D) 9%
E) 7%

Question 57

The width of a rectangle is 17 inches less than $\frac { 1 } { 2 }$  of its length. If the perimeter of the rectangle 98 inches, find the area of the rectangle. ( Hint: Find the width and the length first. )

A) $550 \mathrm { in } ^ { 2 }$
B) $5 \mathrm { in } ^ { 2 }$
C) $44 \mathrm { in } ^ { 2 }$
D) $220 \mathrm { in } ^ { 2 }$
E) $110 \mathrm { in } ^ { 2 }$

Question 58

Identify the like terms from the list below and add them.

Question 59

Use an equation to solve the problem.
A sport jacket that sells for $180 has a markup of $90. Find the wholesale price.

A) $70
B) $85
C) $105
D) $90
E) $100

Question 60

Simplify the expression by combining like terms.
12 a + (-12 a )