Elementary Math (5003) - Algebraic Thinking

On June 1, a tomato plant is 3 cm tall and a kale plant is 5 cm tall. If the tomato plant grows 1.5 cm each day and the kale grows 0.5 cm each day, which of the following is the difference in height of the plants on August 1? (59 cm) (62 cm) (63 cm) (58 cm)

59 cm

Mrs. Fields' science class takes care of a plant at school. The class is responsible for watering the plant and measuring its growth. The students' measurements are charted in the table. Number of Months (m) 1 2 3 4 Height of the Plant (h) in inches 8 13 18 23 Which of the following equations relates the height of the plant, h, and the number of months, m, assuming a constant rate of growth? (3m + 5 = h) (8m - 5 = h) (5m + 3 = h) (4m = h)

5m + 3 = h

Which of the following correctly simplifies the left side of the equation below? 3x - 4 + 6x + 5 - 4x - 2 = 16 ((3x - 4) + (6x + 5) - (4x + 2) = 16) (14x - 10 = 16) (13x - 11 = 16) (5x - 1 = 16)

5x - 1 = 16

Simplify the expression: 3x + 2(3x - 2) + 5 - 2(2x + 1) (5x + 4) (8x + 6) (13x + 11) (5x-1)

5x-1

The 4th term in a sequence of numbers is 162. If each term in the sequence is three times the previous term, what is the value of the initial term in the sequence? (18) (2) (27) (6)

6

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? (5 shirts and 4 pants) (6 shirts and 3 pants) (3 shirts and 6 pants) (4 shirts and 5 pants)

6 shirts and 3 pants

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 expression the number of cookies she had left over? (6 • 12 - (2 • 28 - 2 • 6)) (6 • 12 - 2 • 28 + 2 • 6) (6 • 12 - (2 • 28 + 2 • 6)) (6 • 12 - 2 • 28 - 6)

6 • 12 - (2 • 28 + 2 • 6)

What is the value of the expression below when x = 6? 7x + 3x (45) (10) (25) (60)

60

Which of the following is equivalent to 8(8 + y + y) - 16y for all values of y? (48y) (48) (64) (64 - 8y)

64

The number of mice in a field doubles approximately every 20 days. If there are d mice in the field on day 1, how many mice are there likely to be on day 120? (12 d) (64d) (32d) (2 d⁶)

64d

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 $d per candy bar, which expression could be used to represent how many candy bars Billy sold? (650 + 3d) (650 X d) (650/d) (650 - d)

650/d

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? (x - 6) (x + 6) (x/6) (6x)

6x

Which of the following options shows a logical and correct first step to solving the algebraic equation given? 3(2x + 1) - 5(x + 4) = 11 (-2(3x + 5) = 11) (6x + 3 - 5x + 20 = 11) (6x + 3 - 5x - 20 = 11) (6x + 1 - 5x + 4 = 11)

6x + 3 - 5x - 20 = 11

In January, Jim enrolled in a new gym membership this year which required a $50 membership fee and a $70 monthly fee. In April, Jim wrote an equation in the form y = mx + b to find the total amount he has spent on his gym membership so far that year. What is the meaning of the $70 monthly fee in his equation? (70 is the y-intercept of the line) (70 is the x-intercept of the line) (70 is the slope of the line) (70 is the total amount he has spent this year)

70 is the slope of the line

Larry started the following number pattern: 900, 888, 876, 864, ... Which number could not be a part of Larry's pattern? (756) (736) (816) (624)

736

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? (60 × 50 ÷ 750) (750 ÷ 60) (3.45 X 750 ÷ 5) (750 ÷ 50)

750 ÷ 50

A teacher presents a right triangle to her class. She declares that the hypotenuse can be written as either 4x + 30 or as 6x + 14. Given this relationship, what is the value of x? (12) (6) (10) (8)

8

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?) (A dog named Daisy had a litter of 8 puppies, then a litter of 5 puppies. 3 of the puppies were adopted and taken to their new homes. How many puppies stayed with Daisy?) (Molly's mom made 8 hot dogs for the BBQ. 5 were eaten by her cousins and 3 by Molly and her two brothers. How many hot dogs are left?) (n children were sitting at a table. 5 got up and left and 3 more sat down. How many children are now at the table?)

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?

Translate the following verbal expression into a mathematical expression. Let the unknown number be n. The product of 8 and the quantity of a third of an unknown number plus 5. (n/3 + 5(8)) (8 X 1/3n + 5) (8(1/3n + 5)) (3/n(8) + 5)

8(1/3n + 5)

Which of the following are correct solutions to the inequality below? 2x + 5 ≥ 15 Select all answers that apply. (4) (2) (8) (5)

8, 5

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? (6c) (8b) ((8b+6c)/2) (8b + 6c)

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? (10) (9) (5) (11)

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 rental charge of $26.00 per hour plus an additional charge of $13.75 per hour.) (A rental charge of $39.75) (A fixed rental charge of $13.75 plus an additional charge of $26.00 per hour.) (A fixed rental charge of $26.00 plus an additional charge of $13.75 per hour.)

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

What is the 8th term of the geometric sequence -3, 6, -12, 24, -48,...? (A(8) = 384) (A(8) = -384) (A(8) = 279,936) (A(8) = -768)

A(8) = 384

Which of the following sequences of steps will yield the valid solution for x to the equation -8 + 5x = 12? (Combine -8 and 5 to get -3x = 12, then divide by -3 on each side of the equation.) (Add 8 to each side of the equation, then divide by 5 on each side of the equation.) (Subtract 8 from each side of the equation, then divide by 5 on each side.) (Divide by 5 on both sides of the equation, then add 8 to each side.)

Add 8 to each side of the equation, then divide by 5 on each side of the equation.

Dia has 11 apps on her iPad. Sheila has three times as many apps on her iPad. Dia wants to find how many apps they have all together. Which operation should she use last? (addition) (multiplication) (subtraction) (division)

Addition

Klaus is planning his annual garden. He wants to plant 2 carrot plants, 3 pepper plants, and 1 squash plant. If he knows the area that each plant requires to grow and wants to determine the total area his garden will require, which operation will he use last in his calculation? (subtraction) (division) (multiplication) (addition)

Addition

During small group instruction, a kindergarten teacher shows students a necklace with alternating red and blue beads. She asks students to share what they notice about the necklace. In this scenario, the teacher is most likely trying to promote: (recognition of three-dimensional shapes.) (an understanding of patterns.) (rote counting skills.) (observation skills.)

An understanding of patterns.

Jaya and Asha are selling baked goods at the bake sale. Jaya's profit can be found by using the equation P = 2b - 28, where P represents profit and b represents the amount of baked goods Jaya sells. Asha's profit can be found by using the equation P = 2.5b - 39, where P represents profit and b represents the amount of baked goods Asha sells. Which of the following conclusions can be made based on the two equations? (To make the same amount of profit, both girls need to sell 24 baked goods.) (Asha will make a higher profit.) (Asha is selling her baked goods for fifty cents more than Jaya.) (Jaya spent more on ingredients for the bake sale than Asha.)

Asha is selling her baked goods for fifty cents more than Jaya.

Two painting companies charge for work completed with a linear equation, where C is Total Cost and t is time in hours worked. Company A charges C = 150 + 80t while company B charges C = 300 + 40t. For 0 ≤ t ≤ 20, which of the following statements is true? (Company B charges more initially and charges more per hour.) (Company B charges more initially, but charges less per hour.) (Company A charges more initially and charges more per hour.) (Company A charges more initially, but charges less per hour.)

Company B charges more initially, but charges less per hour.

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) ([(0.5)(3) - 20]b) ([(0.5)(3) + 20]b) ([(0.5)(20) -3]b)

[(0.5)(20) -3]b

For the bake sale, students sold c dozen cupcakes. It cost $0.98 to make a batch of 12 cupcakes and they charged $0.50 per cupcake. Which expression, in terms of c, represents the profit, p, made from the cupcake sales? Assume the students sold all cupcakes made. ([(12)(c) - 0.98]/0.5 = p) ([(12)(0.5) - 0.98]/c = p) ([(12)(c) - 0.98]0.5 = p) ([(12)(0.5) - 0.98]c = p)

[(12)(0.5) - 0.98]c = p

The table shows Jenna's scores in her math class. Quiz 1 Quiz 2 Unit Test 1 Quiz 3 Unit Test 2 Midterm 86% 81% 85% 91% 87% 88% The tests count twice as much as the quizzes, and the midterm counts three times as much as the quizzes. To find her average score in the class at midterm, Jenna uses the following expression: (86 + 81 + 85 + 85 + 91 + 87 + 87 + 88 + 88 + 88) X (1/10) Which of the following is another way to find her average score at midterm? ([86 + 81 + 2(85) + 91 + 2(87) + 3(88)] X 10) (10 ÷ (86 + 81 + 85 + 85 + 91 + 87 + 87 + 88 + 88 + 88) (86 + 81 + 85 + 85 + 91 + 87 + 87 + 88 + 88 + 88 ÷ 10) ([86 + 81 + 91 + 2(85 + 87) + 3(88)] ÷ 10)

[86 + 81 + 91 + 2(85 + 87) + 3(88)] ÷ 10

The formula for the perimeter of an isosceles triangle is P = 2a + b. Solve for a. (a = (P - b)/2) (a = 2(P - b)) (a = P/(2 + b)) (a = (b - P)/2)

a = (P - b)/2

The following list shows the first four terms of a sequence: 24, 21, 18, 15, . . . Which of the following formulas represents the arithmetic sequence? (an = 27 + (n - 1)(-3)) (an = 24 ⋅ (-3)^(n-1)) (an = 24 + (n - 1)(3)) (an = 24 + (n - 1)(-3))

an = 24 + (n - 1)(-3)

The following list shows the first three terms of a sequence: 4, 10, 25, . . . Which of the following formulas represents the geometric sequence? (an = 4 + (n - 1)(2.5)) (an = 1.6 ⋅ (2.5)^(n-1)) (an = 4 ⋅ (2/5)^(n-1)) (an = 4 ⋅ (2.5)^(n-1))

an = 4 ⋅ (2.5)^(n-1)

The formula for the area of a triangle is A = 1/2bh. Solve for b. (b = A/(2h)) (b = h/(2A)) (b = 2Ah) (b = (2A)/h)

b = (2A)/h

Which of the following is a solution for b in the inequality: -2b + 4 ≤ 7 - b (b ≤ 3) (b ≤ -3) (b ≥ -3) (b ≥ 3)

b ≥ -3

The number of bacteria in a sample doubles every 45 minutes. If there are b bacteria in a sample at 6 p.m., how many bacteria were there earlier, at noon, that same day? (b/2⁸) (2⁸b) (8²b) (b/8²)

b/2⁸

Austin had d dollars in his bank account. He removed one-fourth of his money from the account. Which expression represents the money remaining in his account after the withdrawal? (3/4) (d - (1/4)d) (d - 1/4) (d - (3/4)d)

d - (1/4)d

The number of tennis shoes, t, in a dorm is 12 more than 5 times the number of dress shoes. Which of the following represents the number of dress shoes in the dorm in terms of t? (d = 5t + 12) (d = (t - 12)/5) (d = (t/5) - 12) (d = 5t - 12)

d = (t - 12)/5

Mrs. Janie asked her class to write their own geometric sequence. As she walked around the room, she noticed Brad had 3, 6, 2, 4, 4/3, 8/3,... written on his paper. When Mrs. Janie asked Brad to explain his sequence, he replied, "My sequence is a geometric sequence because you multiply by 2, then multiply by 1/3, then you multiply by 2 again, then multiply by 1/3 again and so on." What is the best teacher response to Brad's statement?

"Your reasoning has an error. In order for a sequence to be a geometric sequence, you must multiply by the same common ratio each time. You can not use two different ratios."

The table shows the cost of carrots at two different grocery stores in town. Grocery Store #1 Grocery Store #2 Number of Pounds Total Cost Number of Pounds Total Cost 3 $2.64 4 $3.64 5 $4.40 6 $5.46 9 $7.92 8 $7.28 If a recipe requires 7 pounds of carrots, how much money will be saved by shopping at the less expensive store? ($0.88) ($6.37) ($0.21) ($6.16)

$0.21

Ari spent half of the money in his checking account. He then deposited $75.00 and later withdrew $15.00. His new balance is $120.00. How much money did Ari have in his account to begin with? (Note: no other transactions were made and no interest accrued.) ($30.00) ($120.00) ($60.00) ($90.00)

$120.00

John spends his summer working at a retail shop. As a result, he gets a 15 percent employee discount of everything sold in the store. He decides to buy 4 pairs of pants which retail for $30 and 5 shirts which retail for $20. What is the total price he must pay after his employee discount? ($195.50) ($230) ($187) ($220)

$187

Each year as a fundraiser, Angela's scout troop produces and sells tie-dye shirts. Short-sleeved shirts sell for $22 and long-sleeved shirts sell for $30. Last year, Angela's troop sold 35 short-sleeved shirts and 18 long-sleeved shirts. This year they sold 27 short-sleeved shirts and 25 long-sleeved shirts. What is the difference in profit between the two years? ($102) ($34) ($50) ($8)

$34

Every year, Tamera puts 15% of the amount of her income that exceeds $20,000 in a savings account, and the rest of her income goes into her checking account. If she put $37,000 into her checking account last year, what were her total earnings for that year? ($57,000) ($54,000) ($40,000) ($43,530)

$40,000

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 - $0.75b = $2b) ($500 = $2b - $0.75b) ($500 = $2b + $0.75b) ($500 + $2b = $0.75b)

$500 = $2b - $0.75b

Ellie runs a sandwich-only shop out of a food truck that she owns. Each month she sells 6,000 sandwiches for $6 each. She spends $3.50 per sandwich for ingredients and supplies and pays two of her friends $3000 a month to help her run her shop on the weekends. Utilities cost her $550 a month. How much profit does Ellie make per month? ($18,950) ($11,450) ($9,000) ($8,450)

$8,450

If y = 3x - 2 were graphed in the xy plane, which point would fall above the graph? (-1, -6) (-1, -1) (2, 1) (1, -1)

(-1, -1)

The quotient of the sum of four and x, and two, results in the number 3. Which of the following is another way to represent this statement? ((4 + x) - 2 = 3) ((4 + x)/2 X 3) ((4 + x)/2 = 3) ((4 - x) + 2 ÷ 3)

(4 + x)/2 = 3

Mrs. Thompson presents the scenario to her class and asks them to use it to answer the following question: Kirsten wants to rent paddle boats for her group of friends. She will need 4 boats to fit all of her friends and the boat rental company charges $15 per hour for each boat. In addition to the hourly fee, there is a one-time membership fee of $40 to use the facilities, regardless of how many boats are rented. If Kirsten has budgeted $300 for this outing, how many hours will she and her friends enjoy on the lake? If h represents the number of hours, which of the following equations represents the scenario? (15h + 40 = 300) ((4 ⋅ 15h) + 40 = 300) ((4 ⋅ 15h) - 40 = 300) ((4 ⋅ 15h) + 40h = 300)

(4 ⋅ 15h) + 40 = 300

Three of the following expressions, when simplified, equal the same value. Which of the following equations, when simplified, is not equal to the other expressions? (15x + 8y - 3x - 7y) (1/2(20x + 6y) + 8(1/4x) - 2y) (-4y + 3x + x(5 + 4) + 5y) ((4x ⋅ 3x) + y)

(4x ⋅ 3x) + y

Hillary collects stamps and keeps them in tidy envelopes for storing. She has 8 envelopes with s stamps in each one. She decides to divide her collection evenly among herself and 3 of her friends so they can start a collection too. Which expression represents the number of stamps each person receives? ((8s)/3) ((8s)/4) (4/(8s)) ((4s)/8)

(8s)/4

Before purchasing a new car, Branden wants to know his monthly payments, m. He plans to make a down payment, d, and then pay off the rest of the car in 60 months. The total cost of the car plus interest is t. Which equation can Branden use to find his monthly payment? ((d-t)/60 = m) (60/(t-d) = m) ((t-d)/60 = m) (60/(d-t) = m)

(t-d)/60 = m

Which of the following is not an appropriate first step when solving this equation? 6(y - 3) = 2(y - 3) + 8 (3(y - 3) = y - 3 + 4) (-2(y - 3) = 2(y - 3)) (6y - 18 = 2y - 6 + 8) (4(y - 3) = 8)

-2(y - 3) = 2(y - 3)

Solve for x. 10x + 6 = 1/2(4x - 8) (-7/3) (-5/3) (-7/4) (-5/4)

-5/4

If 6(3x+4) = 2(x+2) - 8, what is the value of x? (-7/4) (-5/8) (-5/4) (7/4)

-7/4

Evaluate the expression 4y - 5 when y = -1. (1) (-9) (-2) (20)

-9

Which of the following is equivalent to the expression below? 2x + 4y - 3x + 6 (-x² + 4y + 6) (5x + 4y + 6) (-x + 4y + 6) (9xy)

-x + 4y + 6

Solve for x. (10x + 2)/4 = 5x - 2 (1) (-4/5) (2/5) (-1)

1

A middle school band is selling candy bars and nuts to raise money for a field trip. Each candy bar, b, costs $1.50 and each box of nuts, n, costs $4.00. If they raised $418, what expression shows the portion that came from candy bar sales? (1.5n/418) (1.5b/418) ((4n + 1.5b)/418) ((4n - 1.5b)/418)

1.5b/418

Debbie is having a garage sale and prices her shirts, s, at $1.50 each and her pants, p, at $2.00 each. The amount she makes from selling clothes can be expressed as 1.5s + 2p. Which of the following represents the total amount she made from selling shirts? (2p) (1.5s) (2) (1.5)

1.5s

The half-life of a carbon-14 (C-14) is 5730 years. This means that about half of the C-14 in the sample will decay into a new material every 5730 years. If there were x grams of C-14 in a sample 40110 years ago, which of the following is the approximate number of grams that have not yet decayed today? Seven half-lives pass in 40110 years. (1/128x grams) (7/2x grams) (1/2x⁷ grams) (1/7x grams)

1/128x grams

Solve the following equation. Write the solution as a fraction in simplest form. 3(4x - 5) + 8 = 9(2x - 1) (-1/3) (8/3) (3) (1/3)

1/3

Which of the following is equivalent to 1/2(4/3x² - 1/3)? (1/3(2x² - 1/2)) (1/6(x² - 1)) (2/3x² - 2/3) (8/3(x² - 2/3))

1/3(2x² - 1/2)

Marty gets an allowance of $5 each week from his parents. He also can earn extra money by doing additional chores outside of his usual household responsibilities for $1.50 per chore. He has been working on saving his money to buy a new game and thinks he will be close this week. If he would like to get at least $20 from his parents at the end of the week, what is the minimum number of additional chores Marty needs to complete? (10) (17) (14) (13)

10

Solve for a. 2a - 12 + a = 18 (2) (30) (10) (15)

10

A sequence of numbers is generated, and a partial list is shown. What is the value of the 100th term? Term Pattern Value 1 2 2 2⋅3 6 3 12 4 4⋅5 20 5 30 6 42 (10,302) (10,100) (9,900) (201)

10,100

James has $10.95 in nickels, dimes, and pennies. He has an equal number of nickels and dimes. If he has x nickels, which of the following represents the number of pennies he has? (1095 - 15x) ((10.95 - 0.05x)/0.1) ((1095 - 15x)/0.01) (It is not possible to determine because there are 3 types of coins.)

1095 - 15x

Which of the following is equivalent to 5/6(12a³ + 4/15a)? (2a³ + 4/3a) (2a³ + 5/6a) (10a³ + 4/15a) (10a³ + 2/9a)

10a³ + 2/9a

Which of the following is the same as this expression? 1y + 8x - 2 + 2x + 1 - 3y (8xy - 1) (10x + 4y - 3) (7) (10x - 2y - 1)

10x - 2y - 1

Kate and Amelia both get summer jobs. Kate works 3 days a week for 4 hours each and Amelia works 2 days a week for 7 hours each. In addition, Kate makes $100 in tips each week and Amelia makes $75 in tips each week. Kate and Amelia make the same amount of money per week. If k represents the hourly wage Kate earns and a represents the hourly wage Amelia earns, which of the following equations accurately represent this situation? (k(12 + 100) = a(14 + 75)) (100k + 12 = 75a + 14) (12k + 100 = 14a + 75) (14k + 100 = 12a + 75)

12k + 100 = 14a + 75

Given the sequence 16, -20, 25, -125/4, 625/16,... which of the following is closest to the 21st term? (1735) (1388) (-1735) (-1388)

1388

If 1/5x + 3 = 6, what is the value of x? (45) (15) (5) (20)

15

Mr. McDahl has planned a day of independent work for his English students when they next have a substitute teacher. One-third of the students choose to work on an essay. One-half of the remaining students choose to read. The remaining 5 students work on vocabulary. How many students are present in the class on that day? (15) (24) (30) (18)

15

If left unchecked, the number of thistle plants growing in a field doubles every 6 weeks. If T is the number of thistle plants sprouting in early April, which of the following represents that number of thistle plants (T) in the field at the end of September, 24 weeks later? (16 T⁴) (16 T) (6⁴ T) (6⁴ T²)

16 T

Which of the following is equivalent to 4/5 (20m² - 15/2m)? (4m² - 30m) (16m² - 6m) (24/5m² - 19/10m) (16m² - 7.5m)

16m² - 6m

The data table shows the xy-coordinates for a line. x y 0 -5 -10 -15 10 7 4 1 What is the y coordinate for an x coordinate of 15? (-1) (1) (16) (19)

19

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) (2/3) (13,122) (cannot be solved)

2

What is the units digit of 2⁴⁵? (2) (8) (4) (6)

2

Three of the following equations, when simplified, equal the same value. Which of the following equations, when simplified, is NOT equal to the other equations? (.25 X 100 - 40) (200 X 1/8 - 2(40 - 20)) (2(40 X .2) + 5[.4 X (1/4)]) ([20/(1/5)]-[5/(1/23)])

2(40 X .2) + 5[.4 X (1/4)]

The difference of the number m and four is doubled, resulting in twelve. Which of the following equations is a representation of this statement? (12 = m - (2 X 4)) (2(m - 4) = 12) (4m - 2 = 12) (2 = (4 - m) X 12)

2(m - 4) = 12

A shelter for unhoused people uses the equation t = .45p + 180 to find the total cost, t, of all meals served. If someone donates $1500 for dinner, how many people, p, can be served? (2,933 people) (3,333 people) (3,334 people) (2,934 people)

2,933 people

The 4th term in a sequence of numbers is 181. If each term in the sequence is 3 plus 2 times the previous term, what is the value of the initial term in the sequence? (29) (43) (20) (15)

20

A family took a road trip that required them to drive 560 miles. Mom, Dad, and their oldest son, Alex, took turns driving. Dad drove twice as far as mom and 60 miles more than Alex. How far did Dad drive? (124 miles) (248 miles) (188 miles) (372 miles)

248 miles

The sum of two times a number and 3 less than 4 times the same number is 51. Which of the following expressions matches the verbal description above? (2(3a) - 4a = 51) (2a - (4a - 3) = 51) (2a + 3 - 4a = 51) (2a + (4a - 3) = 51)

2a + (4a - 3) = 51

Which of the following is the equation of the line in the xy-plane that passes through the points (-4,-7) and (-6,-8)? (y - 2x = 4) (2y - x = -10) (2y + x = -18) (y + 2x = 1)

2y - x = -10

Which of the following expressions is equivalent to 19x + 36 for all values of x? (3(7x + 36) - 2x) (3(7x + 12) - 2x) (3(7x + 10) + 6) (3(7x - 2x + 12))

3(7x + 12) - 2x

Consider the algorithm below: Step 1: Select a numerical value for n. Step 2: Subtract 4 from n. Step 3: Square the result Step 4: Multiply the result by 3 Step 5: End Which of the following is an equivalent algebraic expression? ([3(n-4)]²) (3²(n-4)²) (3(n-4)²) (3(n²-16)

3(n-4)²

If 1/6x - 4 = 1, then x = (-18) (5/6) (30) (10)

30

Sarah swam x laps in the pool. Jenny swam 4 more laps than Sarah. Kara swam 2 laps less than Sarah. How many total laps did the three girls swim? (3x+2) (3x-2) (x+2) (3x+6)

3x+2

The Arnolds have x pets. The Riveras have 3 more pets than the Arnolds and 2 less than the Pooles. Which of the following expressions represents the total number of pets the three families own? (3x+8) (3x+5) (3x+1) (3x+3)

3x+8

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 + 1)/8 = n) (3/8x = n) (3x/8 = n) (3/8 X x + 1 = n)

3x/8 = n

What is the first step in solving this equation? 3 (y + 4) - 2(3y - 1) = 10 (3y + 12 + 6y + 2 = 10) (3y + 4 − 6y − 1 = 10) (3y + 4 + 6y + 2 = 10) (3y + 12 − 6y + 2 = 10)

3y + 12 − 6y + 2 = 10

Use the equation below to answer the question that follows. 4x + 8(x-3) = x+20 Which of the following is the correct value of x? (all real numbers) (4) (3) (6)

4

What is the last digit of 4³¹? (6) (1) (4) (31)

4

A teacher writes the problem shown below on the board for a warm-up. 7x + 4 - 3x + 2 = 12 She asks students to combine like terms as the first step in solving the problem. Which equation demonstrates an understanding of the first step? (4x + 6 = 12) (4x - 2 = 12) (x = 2) (10x + 2 = 12)

4x + 6 = 12

Josef, Byron, Carmen, and Andy are training for a marathon. On Saturday, Josef ran x miles, Byron ran 2 less than Josef, Carmen ran 4 more than Josef, and Andy ran 3 more than Josef. Which expression represents the number of miles the four ran on Saturday? (4x-5) (4x+5) (x+5) (3x+2)

4x+5

Which of the following numbers is not a solution to the inequality 8 - y > 2(y - 3)? (2) (3) (4) (5)

5