Deck 8: An Introduction to Algebra

Question 1

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

Answer 1

not a solution

Question 2

In the expression , what is the base?

Answer 2

9

Question 3

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

Answer 3

-5

Question 4

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

Question 5

In the expression , what is the exponent?

Question 6

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

A) $b$
B) $- 6$
C) $b x$
D) $- 6 b x$
E) $\chi$

Question 7

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 8

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 9

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 10

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 11

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

Question 12

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 13

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

Question 14

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

Question 15

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

Question 16

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

Question 17

What is the numerical coefficient of the term ?

Question 18

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

Question 19

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

Question 20

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

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

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

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 23

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 24

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 25

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 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

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 28

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 29

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 30

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 31

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 32

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 33

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 34

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

Question 35

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 36

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 37

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 38

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 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

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 41

Identify the terms of the expression.

Question 42

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

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

Question 43

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 44

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 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

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 47

Simplify the following expression by combining like terms.

Question 48

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

Question 49

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 50

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

Question 51

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 52

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

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

Question 53

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 54

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

Question 55

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 56

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 57

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 58

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 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

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