Question 1

The three steps shown below were used to find an expression equivalent to $\frac{2}{5}(15x-30y)$ $+ 10x$.
Which expression could be used as Step 1?

Accepted Answer

$6x-12y+10x$

Answer

$15(x-2y)+10x$

Answer

$\frac{2}{5}(25x-30y)$

Answer

$6x-30y+10x$

Question 2

Which expression represents a factorization of $32m+56pm?$

Accepted Answer

$8m(4+7p)$

Answer

$8p(4+7m)$

Answer

$8(4m+7p)$

Answer

$8(4+7)mp$

Question 3

Ben earns $$\$9$$ per hour and $$\$6$$ for each delivery he makes. He wants to earn more than $$\$155$$ in an $8$-hour workday. What is the LEAST number of deliveries he must make to reach his goal?

Accepted Answer

$14$

Answer

$12$

Answer

$11$

Answer

$13$

Question 4

Which expression is equivalent to $8c +6 - 3c -2$?

Accepted Answer

$5c + 4$

Answer

$11c + 4$

Answer

$5c + 8$

Answer

$11c + 8$

Question 5

Salid bought $35\,	ext {feet}$ of window trim at a hardware store. The trim cost $$\$1.75$$ per foot, including sales tax. If Salid paid with a $$\$100.00 $$ bill, how much change should he have received?

Accepted Answer

$$\$38.75$$

Answer

$$\$61.25$$

Answer

$$\$80.00$$

Answer

$$\$20.00$$

Question 6

Ms. Gartland bought $x$ number of shirts for the new members of her chorus. The cost for $x$ number of shirts, including $$\$3.99$$ shipping, was $$\$77.49.$$ Each shirt cost $$\$12.25.$$ There was no sales  tax on this purchase. Which equation could be used to find $x?$

Accepted Answer

$12.25x+3.99=77.49$

Answer

$3.99(x+12.25)=77.49$

Answer

$12.25(x+3.99)=77.49$

Answer

$3.99x+12.25=77.49$

Question 7

The measure of one side of a square is $(s + 3)$ inches long. Which pair of expressions both represent the perimeter of this square?

Accepted Answer

$4(s + 3$)
and
$(s + 3)+(s  +3)+(s + 3)+(s  +3)$

Answer

$2s + 3$
and
$(s + 3)(s  +3)$

Answer

$2(s + 3)$
and
$(s + 3)(s  +3)$

Answer

$4s + 3$
and
$(s + 3)+(s  +3)+(s + 3)+(s  +3)$

Question 8

Winston needs at least $80$ signatures from students in his school before he can run for class president. He has $23$ signatures already. He and two of his friends plan to get the remaining signatures during lunch. If each person gets the same number of signatures, which inequality can Winston use to determine the minimum number of signatures each person should get so he can run for class president?

Accepted Answer

$3x +23 \ge80$

Answer

$3x +80 \ge 23$

Answer

$3x +23 \le80$

Answer

$3x +80 \le23$

Question 9

Which expression makes the equation true for all values of $x$?
$\quad16x-16=4(\,?\,)$

Accepted Answer

$4x - 4$

Answer

$12x - 12$

Answer

$2x - 2$

Answer

$4x - 16$

Question 10

Mr. Santino needs a total of $406$ forks for his restaurant. He currently has $278$ forks.
If each set has $12$ forks, what is the minimum number of sets of forks he should buy?

Accepted Answer

$11$

Answer

$140$

Answer

$12$

Answer

$128$

Question 11

Which expression is equivalent to the expression shown below?
$\quad-\frac{1}{2}[-\frac{3}{2}x+6x+1]-3x$

Accepted Answer

$-5\frac{1}{4}x-\frac{1}{2}$

Answer

$\frac{2}{3}x-\frac{1}{2}$

Answer

$-\frac{3}{4}x+\frac{1}{2}$

Answer

$6\frac{3}{4}x-\frac{1}{2}$

Question 12

Which expression is equivalent to $\frac{7}{2}h-3[5h-\frac{1}{2}]?$

Accepted Answer

$-\frac{23}{2}h+\frac{3}{2}$

Answer

$\frac{37}{2}h+\frac{3}{2}$

Answer

$\frac{37}{2}h-\frac{3}{2}$

Answer

$-\frac{23}{2}h-\frac{3}{2}$

Question 13

The amount of money in a bank account increased by 21.5% over the last year. If the amount of money at the beginning of the year is represented by $n,$ which expression represents the amount of money in the bank account after the increase?

Accepted Answer

$n + 0.215n$

Answer

$21.5n$

Answer

$0.215n$

Answer

$n + 21.5n$

Question 14

A triangle has side lengths of $(5.5x + 6.2y)	ext {centimeters,} (4.3x + 8.3z)	ext {centimeters}, $and$ (1.6z - 5.1y)	ext {centimeters}.$ Which expression represents the perimeter, in centimeters, of the triangle?

Accepted Answer

$9.8x + 1.1y + 9.9z$

Answer

$9.8x + 7.8y + 3.5z$

Answer

$11.4xz + 9.4yz$

Answer

$11.7xy + 12.6xz - 3.5yz$

Question 15

Yolanda participated in a walkathon in which each kilometer walked raised $$\$10$$ for charity. Her goal was to raise more than $$\$300$$ on Saturday and Sunday. She raised $$\$50$$ on Saturday. Which graph shows all the distances, in kilometers, that Yolanda could have walked on Saturday to reach her goal?

Accepted Answer

https://uploads.quizalize.com/aff96c32-8f4c-4ae0-a2a1-a9bbeebf8645/question/75f6455c4be289818a86437d3de35553f9ff913c.png

Answer

https://uploads.quizalize.com/aff96c32-8f4c-4ae0-a2a1-a9bbeebf8645/question/80eefc9629fd8af1f90d5a3faef037d33d705e6d.png

Answer

https://uploads.quizalize.com/aff96c32-8f4c-4ae0-a2a1-a9bbeebf8645/question/003b8c4b193f5ac4dd2741688db048055fc3cc4a.png

Answer

https://uploads.quizalize.com/aff96c32-8f4c-4ae0-a2a1-a9bbeebf8645/question/4064ced288ec7cd20e11d4b26a02d7a3c639384d.png

Question 16

An item with an original price of $p$ dollars is on sale at a $25\%$ discount. Which expression is NOT equivalent to the price of the item with the discount?

Accepted Answer

$0.25p$

Answer

$(1.0p - 0.25p)$

Answer

$(1.0 -  0.25)p$

Answer

$0.75p$

Question 17

Bob buys eggs and potatoes at a store.
• He pays a total of $$\$25.92$$.
• He pays $$\$2.57$$ for the eggs.
• He buys 5 bags of potatoes that each cost the same amount.
Which equation can be used to determine the cost, $x$, of each bag of potatoes?

Accepted Answer

$x=(25.92-2.57) \div5$

Answer

$x=25.92 \div 5+2.57$

Answer

$x=25.92\div 5-2.57$

Answer

$x=(25.92+2.57) \div 5$

Question 18

Which expression is equivalent to $(-18)-64n$?

Accepted Answer

$-2(9+32n)$

Answer

$2(9+32n)$

Answer

$2(9-32n)$

Answer

$-2(9-32n)$

Question 19

A farm grew 19.8 tons of wheat in 2013. The farm's wheat output increased by 9.8% from 2013 to 2014 and by 5.1% from 2014 to 2015. Which expression represents a strategy for estimating the total output of wheat, in tons, in 2015?

Accepted Answer

20(1.1) (1.05)

Answer

20 + 1.1 + 1.05

Answer

20(10)(5)

Answer

20 + 10 + 5

Question 20

Which expression is equivalent $n+n -0.18n$?

Accepted Answer

$1.82n$

Answer

$2n-0.82$

Answer

$n-0.18$

Answer

$1.18n$

Question 21

Which expression is equivalent to $-\frac{1}{3}(6x+15)-3$?

Accepted Answer

$-2x-8$

Answer

$-2x+12$

Answer

$-2x+2$

Answer

$-2x-2$

Question 22

Josh has a rewards card for a movie theater.
• He receives 15 points for becoming a rewards card holder.
• He earns 3.5 points for each visit to the movie theater.
• He needs at least 55 points to earn a free movie ticket.
Which inequality can Josh use to determine x, the minimum number of visits he needs to earn his first free movie ticket?

Accepted Answer

$55 \le 3.5x+15$

Answer

$55 \ge 3.5x+15$

Answer

$55 \le 15x+3.5$

Answer

$55 \ge 15x+3.5$

Question 23

At a store, a hat has a regular price of $x$ dollars. During a sale, the price of the hat is discounted by 20%. The expression $0.8x$ describes the discounted price, in dollars, of the hat. Which expression also describes the discounted price, in dollars, of the hat?

Accepted Answer

$x-0.2x$

Answer

$0.2x$

Answer

$x-0.2$

Answer

$x-20$

Question 24

Clara goes miniature golfing. She pays $$\$7.50$$ for an admission ticket and $$\$6.25$$ for each round she golfs. The total amount Clara pays for admission and the number of rounds she golfs is $$\$26.25.$$ Which equation can be used to determine the number of rounds, $x,$ that Clara golfs?

Accepted Answer

$6.25x+7.50=26.25$

Answer

$6.25x-7.50=26.25$

Answer

$7.50x+6.25=26.25$

Answer

$7.50x-6.25=26.25$

Question 25

The regular price of an item at a store is $p$ dollars. The item is on sale for  $20\%$ off the regular price. Some of the expressions shown below represent the sale price, in dollars, of the item.

Which two expressions each represent the sale price of the item?

Accepted Answer

Expression B and Expression D

Answer

Expression C and Expression D

Answer

Expression B and Expression C

Answer

Expression A and Expression E

Question 26

Which expression is equivalent to $7a-8-12a+4$?

Accepted Answer

$-5a-4$

Answer

$31a$

Answer

$-9a$

Answer

$19a+12$

Question 27

Manny goes bowling.
$\quad\bullet\,$ He has  $$\$25.00$$ to spend.
$\quad\bullet\,$  He spends $$\$4.25$$ to rent shoes.
$\quad\bullet\,$  He spends $$\$2.50$$ for each game he bowls.

Which inequality can Manny use to determine  $x$, the greatest number of games he can bowl?

Accepted Answer

$4.25+2.5x\le25$

Answer

$2.5+4.25x\ge25$

Answer

$2.5+4.25x\le25$

Answer

$4.25+2.5x\ge25$

Question 28

Which expression is equivalent to $2(x+7)-18x+\frac{4}{5}?$

Accepted Answer

$-16x+\frac{74}{5}$

Answer

$-16x+\frac{139}{5}$

Answer

$20x+\frac{74}{5}$

Answer

$20x+\frac{139}{5}$

Question 29

A coach of a baseball team orders hats for the players on his team. Each hat costs $$\$9.95.$$ The shipping charge for the entire order is $$\$5.00.$$There is no tax on the order. The total cost of the coach's order is less than $$\$125.00.$$ . Which inequality can be used to determine the greatest number of hats, $h,$ the coach orders?

Accepted Answer

$9.95h+5<125$

Answer

$5h+9.95<125$

Answer

$5h+9.95>125$

Answer

$9.95h+5>125$

Question 30

A worker at a snack stand opened a new box of cups. The first day, the worker used $30$ cups from the box. The second day, the worker used $15\%$ of the remaining cups in the box. A total of $90$ cups were used on the second day. What was the original number of cups in the box before any cups were used?

Accepted Answer

$630$

Answer

$570$

Answer

$400$

Answer

$800$

Question 31

Addison wants to ride her bicycle more than $80$ miles this week. She has already ridden her bicycle $18$ miles. Which inequality could be used to determine the mean number of miles, $m,$ she would need to ride her bicycle each day for six more days to achieve her goal?

Accepted Answer

$6m+18>80$

Answer

$6m-18<80$

Answer

$6m+18<80$

Answer

$6m-18>80$

Question 32

The perimeter of a certain pentagon is $10.5$ centimeters. Four sides of this pentagon have the same length, in centimeters, $h,$ and the other side has a length of $1.7$ centimeters, as shown below.

What is the value of $h?$

Accepted Answer

$2.2$

Answer

$3.7$

Answer

$4.8$

Answer

$8.8$

Question 33

A trailer will be used to transport several $40	ext{-kilogram}$ crates to a store. The greatest amount of weight that can be loaded onto the trailer is $1,050\,	ext {kilograms}.$ An $82	ext{-kilogram}$ crate has already been loaded onto the trailer. What is the greatest number of $40	ext{-kilogram}$ crates that can also be loaded onto the trailer?

Accepted Answer

$24$

Answer

$26$

Answer

$27$

Answer

$25$

Question 34

What is the value of the expression below?

$\quad (3\frac{1}{2}-9\frac{3}{4})\div(-2.5)$

Accepted Answer

$2.5$

Answer

$-2.5$

Answer

$2.3$

Answer

$-2.3$

Question 35

Which expression represents the product of $3$ and $(\frac{5}{4}n+1.8)$ ?

Accepted Answer

$3.75n+5.4$

Answer

$5.55n$

Answer

$9.15n$

Answer

$3.75n+1.8$

Question 36

Mike took a taxi from his home to the airport. The taxi driver charged an initial fee of $$\$6$$ plus $$\$3$$ per mile. The total fare was $$\$24,$$ not including the tip. How many miles did Mike travel by taxi on this ride?

Accepted Answer

$6$

Answer

$10$

Answer

$2$

Answer

$8$

Question 37

The original selling price of a share of stock was $d$ dollars. The selling price for a share of the same stock at a later date was represented by the expression $1.15(0.95d).$ Which description could explain what happened to the price of the share of stock?

Accepted Answer

The price decreased by $5\%$ and then increased by $15\%.$

Answer

The price decreased by $5\%$ and then increased by $0.15\%.$

Answer

The price decreased by $95\%$ and then increased by $0.15\%.$

Answer

The price decreased by $95\%$ and then increased by $15\%.$

Question 38

Which expression is equivalent to the expression $-3(4x- 2) - 2x?$

Accepted Answer

$-14x+6$

Answer

$-8x$

Answer

$-14x-2$

Answer

$-16x$

Question 39

Lance bought $n$ notebooks that cost $$\$0.75$$ each and $p$ pens that cost $$\$0.55$$ each. A $6.25\%$ sales tax will be applied to the total cost. Which expression represents the total amount Lance paid, including tax?

Accepted Answer

$(0.75n + 0.55p) + 0.0625(0.75n + 0.55p)$

Answer

$0.75(0.0625n) + 0.55(0.0625n)$

Answer

$0.75(1.0625n) + 0.55(1.0625n)$

Answer

$0.0625(n + p) + 0.0625(0.75n + 0.55p)$

Question 40

When Keisha installed a fence along the $200	ext{-foot}$ perimeter of her rectangular back yard, she left an opening for a gate. In the diagram below, she used $x$ to represent the length, in feet, of the gate.

What is the value of $x?$

Accepted Answer

$10$

Answer

$30$

Answer

$20$

Answer

$25$

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