Patterns and Algebra

An electronics store is offering a 20% discount on a pair of noise-cancelling headphones that normally cost $169.79. What is the price of the headphones, before tax, after the discount is applied?

$135.83

The Booster Club at Martin MS is selling spirit buttons for homecoming. The buttons cost $0.75 to make and will be sold for $2 each. How many buttons, b, must be sold to make a profit of $500?

$500 = $2b - $0.75b

A sweater is on sale for $43.75. It is 30% off the original price. What is the original price?

$62.50

Which of the following are equivalent to dividing 144 by 9? Select all answers that apply.

(121 ÷ 11) + (55 ÷ 11) (16 ÷ 4)^2 (24 ÷ 12)(64 ÷ 8)

Evaluate the expression: 5(4 - 1)^2 - (4 + 3)^2

-4

Simplify the expression: 30 - 2 × 50 + 70

0

Simplify the expression: 82 - 100 ÷ 4 + 6× 12

129

In Anytown ISD, 13 out of every 20 students ride the bus. Which ratio compares the number or students who ride the bus to those who do not?

13:7

What is the next number in the sequence? 5, 10, 20, 40, 80...

160

At Memorial High School, 60 of the 240 freshmen students are on an athletic team sponsored by the school. If the ratio is the same for the sophomore class, how many of the 220 sophomores are NOT athletes?

165

Simplify: 200 - 3(6 - 2)³ + 10

18

If the 5th term in a geometric sequence is 162, and the common ratio is 3, what is the first term in the sequence?

2

A pancake recipe requires 1 tablespoon of baking powder per 2 cups of flour. If 2 cups of flour make 4 pancakes, how many tablespoons of baking powder are needed to make 12 pancakes?

3

How many terms are in the expression 3x² + 6x +3?

3

Simplify: 15 - 3(8 - 6)²

3

The state sales tax is 7.5%. Which number could also represent 7.5%?

3/40

Simplify the expression: 3(10)2

300

Jenny is baking cookies. Each dozen cookies requires 2 cups of flour and 0.75 lbs of butter. How many cookies can she make with 6 cups of flour and 3 lbs of butter?

36

Susan is planning for volunteer day at the high school. Every person that signs up gets a free lunch for volunteering. This year, lunch includes 3 slices of pizza and a soda. If x = number of volunteers and one pizza has 8 slices, which equation can help her to determine the correct number of pizzas (n) to order?

3x/8 = n

Simplify the expression: 4(10)3

4000

A sixth-grade class is asked to estimate the answer to the following question: 75.8 + 326.79 + 488.92 ÷ 11 = _____. Which of the following would be the best answer?

450

The sequence has the 4th and 5th terms of 33 and -51 respectively. Each term is found by adding the previous 2 terms and multiplying by -3. What is the value of a2? a2, a3, 33, -51...

5

Which equation below models xª•xᵇ = xª⁺ᵇ?

5³ • 5⁴ = 5⁷

A gas pump can pump a quarter gallon of gas every five seconds. If a person is filling up an empty gas tank that can hold 18 gallons of gas, how long will it take the gas pump to fill the empty gas tank?

6 minutes

There was a big sale and Branden bought 9 items of clothing. Shirts were selling for $15 each and pants were $20. If he bought at least one of each item and spent $150, how many of each did he purchase?

6 shirts and 3 pants

A school fundraiser is selling candy bars to raise money for a new gymnasium. If Billy sells a total of $650 worth of candy bars for $x per candy bar, which expression could be used to represent how many candy bars Billy sold?

650 / x

A runner is running a 10k race. The runner completes 30% of the race in 20 minutes. If the runner continues at the same pace, what will her final time be?

67 minutes

Anthony sold x boxes of popcorn for $6.00 per box for his Cub Scout troop. Which expression will help him determine the amount of money he earned for his troop?

6X

Jim enrolled in a new gym membership this year which required a $50 membership fee and a $70 monthly fee. Jim wrote an equation in the form y=mx+b to find the total amount he has spent on his gym membership this year. What is the meaning of the $70 monthly fee in his equation?

70 is the slope of the line

John's car can drive 50 miles per gallon of gas, he wants to take a trip that is 750 miles. Gas currently costs $3.45 per gallon. He drives an average of 60 miles per hour during the trip. Which of the following expressions can solve for how many gallons of gas must he purchase for the trip?

750 ÷ 50

Which of the following word problems is a valid question to prompt writing the equation: 8 - 5 + 3 = n?

8 birds were sitting on a fence. 5 birds flew away and 3 more birds landed on the fence. How many birds are on the fence now?

Jemma likes to earn spending money through babysitting her neighbor's child and helping with extra chores at home. The expression 8b + 6c represents the total amount of money (in dollars) that Jemma can earn, where b is the number of hours of babysitting she completes and c is the number of chores she finishes. Which term represents the total amount of money that she earns from babysitting?

8b

A painter charges $10 fixed initial charge plus $20 per hour of painting. If the total bill comes to $190, how many hours did he paint for?

9

The function f(x) = 26.00 + 13.75x describes the rental fee for an air compressor, where f(x) is the total cost and x is the number of rental hours. The equation models which of the following situations?

A fixed rental charge of $26.00 plus an additional charge of $13.75 per hour.

What is the 10th term of the geometric sequence 50, 40, 32, 25.6, 20.48,...?

A(10) ≈ 6.71

What is the 8th term of the geometric sequence -3, 6, -12, 24, -48,...?

A(8) = 384

Mrs. Dobbs is teaching students to skip-count by 2, 5 and 10 in her second-grade class. Earlier in the year, she evaluated her students learning style and assigns them one task based on this evaluation. Visual learners have been given a number line and they are to draw the hops across the top. Auditory learners have been given a list of the even number to 20, numbers divisible by 5 to 50 and numbers ending in 0 up to 100. They are told to say them over and over aloud to memorize the skips. Kinesthetic learners have been given a large number line on the floor. They are jumping to the next number as they skip-count. What can Mrs. Dobbs do to improve her teaching?

Allow all students to participate in all three activities by rotating through them.

Maria baked 6 dozen cookies for her classmates. There are 28 students in her class, each child received 2 cookies and Maria gave 6 cookies each to her teacher and her principal. Which equation could be used to find C, the number of cookies she had left over?

C = 6 • 12 - (2 • 28 + 2 • 6)

Which of these statements correctly describes the coefficients and degrees of the polynomial shown? 5x^7 + 5x^5 - 3x - 2

Coefficients: 5, -3, -2 Degrees: 7, 5, 1, 0

A restaurant charges $7.00 for a bowl of noodles and $1.25 for each topping selected. Let D represent the total cost of a meal and let T represent the number of toppings selected. Which of the following is an equation for the total cost of a meal in dollars, D?

D=7.00+1.25T

Mr. Sudu is a waiter. His total weekly earnings consist of a wage of $6 per hour plus approximately 15% in tips on his total sales for the week. One week Mr. Sudu worked 25 hours and had total sales of z dollars. Which of the following represents his total weekly earning in dollars, E, for that week?

E=0.15z+150

Peter babysits in the evenings for neighborhood children. He charges a flat rate of $12 per evening plus $7 for each hour he sits. If E represents his total earnings for an evening of babysitting and t is the number of hours that Peter babysits that evening, which of the following equations represent the relationship between the amount of time he babysits and his total earnings?

E=7t + 12

Which of the following comparisons between equations and inequalities is NOT true?

Equations are solved using inverse operations while inequalities cannot be solved with inverse operations.

A teacher prompted her class to write an expression that matches the phrase "3 less than 2x." One student wrote the expression 3-2x on his paper. What suggestion should the teacher give the student to help him realize his mistake?

Identify key phrases and write the math symbols above the words.

What type of sequence is the following number sequence? 4, 12, 20, 28, 36, 44...

It is an arithmetic sequence; you add 8 every time to get the next term.

A teacher prompted her students to write an example of an expression on their papers. One student wrote the following on their paper: 2x+3=5 The student raises her hand and wants to know if her answer is correct. Of the following, which is the best teacher response to the student?

It is incorrect; this is an equation because it contains an equal sign. There is an expression on either side of the equal sign, which could be possible correct answers.

Which situation could best be represented by the equation: 12x = 54?

Marty made car payments on her car for 54 months until it was paid off. What is x, the number of years it took Marty to pay off her car?

Miss Wilson's class is learning about unit rates. They are comparing costs from the grocery store to see if the store brand is a better deal than the name brand. Douglas and Kaitlyn are volunteering to answer questions during class, but few others are. What should Miss Wilson do?

Provide wait time before calling on someone to answer

Which of the following activities is the best way for elementary students to learn how to write an equation for a line of best fit on a scatter plot?

Students create a scatter plot of data from a simple experiment where they compare the height to the arm span of various students in class. Students then answer guided questions about the correlation between arm span and height, make predictions, create a line a best fit, and write an equation for the line

A teacher wants to help her students understand the rule of the order of operations. The student simplified the following expression: 3 × (8 - 2) + 6 24 - 2 + 6 22 + 6 28 Which of the following best describes the student's work?

The student multiplied before simplifying the operation within the parentheses.

Students in a math class are working on the following problem: Julio can answer 3 math problems in 10 minutes. He completed his math homework after school, which consisted of 14 questions. Assuming he worked at the same rate the entire time, how long did it take Julio to complete his math homework? One student called the teacher over to see if she set up the problem correctly. The following was on her paper: 3/10=x/14 ​ Which of the following suggestions should the teacher give the student to guide them to realize their mistake?

Write the units of each value in each ratio.

A teacher prompted his class to write their own examples of arithmetic sequences on their papers. As the teacher is circulating, he sees the following written on one Tasha's paper: 2, 3, 5, 8, 12, 17, 23... When asked to explain her work, Tasha explains that the sequence is arithmetic because to get the next number in the sequence, you +1, +2, +3, +4, +5, etc. So you always add one more to get the next number. Which of the following is the best teacher response to Tasha's reasoning?

Your reasoning is incorrect; you must add by the same number every time for the sequence to be arithmetic.

The Parent Teacher Organization at Douglass Elementary baked cookies. The ingredients to make each batch of cookies cost $3. Each batch made 20 cookies. The PTO sold each cookie for $0.50. They produced b batches of cookies, and sold every single one of them. What is a valid expression, in terms of b, for the profit that the PTO made for their cookie sale?

[(0.5)(20) -3]b

If -¼ is the 11th term in a geometric sequence where r = -½, then what is a₁?

a₁ = -256

Sally walks into class and tells her teacher that a local candy store had a "buy one candy bar, get one candy bar free" promotion this weekend. The teacher asks Sally how many candy bars she purchased, but she can only remember how many candy bars she received. The teacher asks the class to create an equation that would help Sally find out how many candy bars a person would receive (r) if for any candy bar they purchased (p), they received one candy bar for free. One student says the equation would be 2p + 1 = r. Which of the following activities would best help Sally recognize the error in her answer?

create a function table

A teacher has her students graph multiple linear equations with the same slope, and then record their observations about the equations and graphs. Which of the following goals is the teacher most likely to achieve?

have students connect the relationship between equations with the same slope and parallel lines

In the formula d = m/V, if density d equals 40 and mass m remains constant, which of the following is equal to volume, V?

m/40

A student-athlete can run 10 yards in 6 seconds. Which equation shows the number of yards that can be run in s seconds?

s/0.6

Which of the following equations is written in slope-intercept form?

y = 3x + 5

Which of the following equations are linear? Select all answers that apply.

y=x−2 y=3 y=−3x−5