Deck 6: Algebraic Thinking

Question 1

Add the first 4 Fibonacci numbers. Add the first 5 Fibonacci numbers. Based on those values predict the sum of the first 9 Fibonacci numbers. ​

A) 81
B) 176
C) 89
D) 162
E) 88

Answer 1

88

Question 2

Find a pattern in the following set of equations and predict the next equation. ​ 1 + 2 = 3 4 + 5 + 6 = 7 + 8 9 + 10 + 11 + 12 = 13 + 14 + 15 ​

A) 15 + 16 + 18 + 19 = 21 + 22 + 23
B) 17 + 18 + 19 + 20 = 21 + 22 + 23 + 24
C) 16 + 17 + 18 + 19 + 20 = 21 + 22 + 23 + 24
D) 17 + 18 + 19 + 20 + 21 = 22 + 23 + 24 + 25
E) 16 + 17 + 18 + 19 = 21 + 22 + 23

Answer 2

16 + 17 + 18 + 19 + 20 = 21 + 22 + 23 + 24

Question 3

​Using the table, find a formula for y in terms of n . ​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Answer 3

​

Question 4

What is the next term in the sequence? ​ 1, 4, 7, 10, 13, ... ​

A) 17
B) 26
C) 15
D) 16
E) 19

Question 5

Look at the growing pattern below. How many squares will it take to make the 15 th figure in this pattern? ​ ​

A) 45
B) 226
C) 210
D) 15
E) 230

Question 6

What is the next term in the sequence? ​ 2, 6 , 18 , 54 , 162 , ... ​

A) 972
B) 1,458
C) 512
D) 324
E) 486

Question 7

​The cost of a cab ride is $ 3.20 plus $ 0.32 per each eighth of a mile traveled during the cab ride. Translate the rule that calculates the cost of a cab ride C in terms of the number of miles traveled during the cab ride x into an equation. ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 8

Find a pattern for the following set of equations and predict the next equation. ​ 5 ² + 6 ² + 30 ² = 31 ² 6 ² + 7 ² + 42 ² = 43 ² 7 ² + 8 ² + 56 ² = 57 ²

A) 8 ² + 9 ² + 56 ² = 57 ²
B) 8 ² + 9 ² + 72 ² = 73 ²
C) 8 ² + 9 ² + 80 ² = 81 ²
D) 8 ² + 9 ² + 10 ² = 11 ²
E) 8 ² + 9 ² + 64 ² = 65 ²

Question 9

Find a pattern from the first 3 equations of the following sequence of equations and predict the 11th equation. ​ 1³ + 2³ = 3² 1³ + 2³ + 3² = 6² 1³ + 2³ + 3³ + 4³ = 10 ²

A) 1 ³ + 2 ³ + 3 ³ + 4 ³ +...+ 12 ³ = 78 ²
B) 1 ³ + 2 ³ + 3 ³ + 4 ³ +...+ 12 ³ = 91 ²
C) 1 ³ + 2 ³ + 3 ³ + 4 ³ +...+ 11 ³ = 66 ²
D) 1 ³ + 2 ³ + 3 ³ + 4 ³ +...+ 11 ³ = 22 ²
E) 1 ³ + 2 ³ + 3 ³ + 4 ³ +...+ 12 ³ = 66 ²

Question 10

​A tree grows 3.0 feet during the first year of its life and grows one half foot per year each year after the first year. Translate the rule that calculates the height of the tree H in terms the age of the tree x in years into an equation. ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 11

Find a pattern from the first 2 equations of the following sequence of equations and find the missing part of the last equation. ​ 2(4+5+...+15) = 15(16) - 3(4) 2(5+6+...+20) = 20(216) - 4(5) ..... 2( 7 + 8 +...+ 30 ) = ???? ​ ​

A) 30 ( 31 ) - 7 ( 8 )
B) 24 ( 25 ) - 7 ( 8 )
C) 18 ( 19 ) - 7 ( 8 )
D) 24 ( 25 ) - 6 ( 7 )
E) 30 ( 31 ) - 6 ( 7 )

Question 12

What if we made a pattern by joining pentagons? If the length of each side of the pentagon is 1 unit, then what would be the perimeter of 10 pentagons joined together? ​ ​

A) 32
B) 20
C) 28
D) 50
E) 30

Question 13

Assume there is a functional relationship between the frequency of cricket chirps and the temperature. To find the temperature, the rule is to count the number of chirps in one minute, divide by 4 , and add 40 . Translate the rule into an equation. Let x be the number of cricket chirps in one minute and let y be the temperature. ​

A)
B)
C)
D)
E)

Question 14

Determine the following products: 1 x 1089, 2 x 1089,.3 x 1089. ​ Now predict the product 5 x 1089. ​

A) 9801
B) 5445
C) 6534
D) 7623
E) 4356

Question 15

Find a pattern in the following set of equations and predict the next equation. ​ 1² + 2² + 2² = 3² 2² + 3 ² + 6² = 7² 3² + 4² + 12² = 13² ​

A) 4 ²+ 5²+ 20² = 21²
B) 5 ² + 6 ² + 30 ² = 32 ²
C) 4 ² + 5 ² + 15 ² = 16 ²
D) 5 ² + 7 ² + 72 ² = 73 ²
E) 4 ² + 6 ² + 24 ² = 25 ²

Question 16

Find a pattern in the following set of equations and predict the next equation. ​ 1³+ 2³ = 3² 1³+ 2³+ 3³ = 6² 1³+ 2³+ 3³+ 4³ = 10² ​

A) 1 ² + 2 ² + 3 ² + 4 ² + 5 ² = 15 ³
B) 1 ² + 2 ³ + 3 ² + 4 ³ + 5 ² = 15 ²
C) 1 ³ + 2 ³ + 3 ³ + 4 ³ + 5 ³ = 15 ²
D) 1 ³ + 2 ³ + 3 ³ + 4 ³ = 12 ²
E) 1 ³ + 2 ³ + 3 ³ + 4 ³ + 5 ³ = 15 ³

Question 17

​Which of the following relationships is not a functional relationship? ​

A) ​The amount a babysitter, making $15 per hour, earns is determined by the number of hours she babysits during a particular job.
B) ​The height of a particular individual is determined by her age.
C) ​The age of a particular adult, who has lost weight, is determined by his weight.
D) ​The temperature of chicken baking in a oven at 350°F is determined by the length of time it has been in the oven.
E) ​The distance a runner has run at a constant speed is determined by the amount of time she has been running.

Question 18

​Using the table, find a formula for y in terms of n . ​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 19

​Which of the following relationships is not a functional relationship? ​

A) ​The cost of rst class postage is determined by the weight of the package.
B) ​The amount of a particular drug in the blood stream is determined by the length of time since the drug had been administered.
C) ​The amount of sales tax one pays on a durable good is determined by the cost of the durable good.
D) ​The cost of purchasing a particular pattern of new carpet is determined by the area of carpet that is purchased.
E) ​The number of hours a college student studies per week is determined by the amount of tuition she pays out of pocket.

Question 20

Suppose a family of 2 parents and their 11 children decides that each person will buy a gift for each member of the family for Christmas. How many gifts will be under the Christmas tree? ​

A) 110
B) 132
C) 156
D) 143
E) 22

Question 21

​Jerry scored 39 points in his basketball game today, which is 9 less than three times as many points than he scored in yesterday's game. How many points did he score in yesterday's game?

A) ​ 16 points
B) ​ 10 points
C) ​ 30 points
D) ​ 48 points
E) ​ 39 points

Question 22

What is the next term of the sequence? ​ 9 , 16 , 25 , 36 , 49 , .... ​

A) 85
B) 64
C) 81
D) 67
E) 74

Question 23

​The school auditorium has 470 seats. At least 20 seats will be saved for community members and donors without children in the school play. If each family with children in the play receive five tickets, at most how many families will be able to receive tickets?

A) ​ 94 families
B) ​ 90 families
C) ​ 89 families
D) ​ 98 families
E) ​ 86 families

Question 24

Examine the following phrase made famous by Fred Flintstone: ​
Y a b b a d a b b a d o o ​
If this pattern is repeated over and over, what letter will be in the 66 th position? ​

A) y
B) o
C) d
D) a
E) b

Question 25

​Sarah ate two thirds of the carrot sticks in her lunch yesterday and saved them for today. Her father added 8 more carrot sticks to her lunch for today. Now she has 17 carrot sticks in her lunch today. If x is the number of carrot sticks Sarah originally had in her lunch yesterday, write an equation that can be used to solve for x .

A) ​
B) ​
C) ​
D) ​
E) ​

Question 26

Determine the following products: 67 x 67 and 667 x 667. ​ Now, predict the product of 666667 x 666667. ​

A) 4444444488888889
B) 444444888889
C) 4444488889
D) 44448889
E) 44444448888889

Question 27

What is the next term in the sequence? ​ 10, 1, 9, 2, 8, 3,..... ​

A) 5
B) 7
C) 6
D) 3
E) 4

Question 28

Examine the following phrase made famous by Fred Flintstone: ​
Y a b b a d a b b a d o o ​
If this pattern is repeated over and over, what letter will be in the 221st position? ​

A) y
B) d
C) b
D) a
E) o

Question 29

​Ari has $ 1900 in a savings account at the beginning of the year. He wants to keep at least $ 800 in the account for a safety net. He withdraws $ 100 each week for spending money. How many weeks can he withdraw money?

A) ​ 27 weeks
B) ​ 8 weeks
C) ​ 19 weeks
D) ​ 11 weeks
E) ​ 20 weeks

Question 30

What is the next term in the sequence? ​ 1, 4, 8, 13, 19, ... ​

A) 24
B) 27
C) 23
D) 26
E) 29

Question 31

In the figure below, the face of each cube is a 1cm by 1 cm square. Determine the surface area of the 19 th figure in the pattern. ​ ​

A) 116 cm²
B) 361 cm²
C) 78 cm²
D) 57 cm²
E) 365 cm²

Question 32

​Jerry scored 28 points in his basketball game today, which is 8 less than three times as many points than he scored in yesterday's game. If x is the number of points he scored in yesterday's game, write an equation that can be used to solve for x .

A) ​
B) ​
C) ​
D) ​
E) ​

Question 33

Jack and Jill decide to start a rumor that there will be no school on the following Monday. If each of them tells 1 person, and each of those people tells exactly 1 other person, and so on, how long will it take until all 1024 students in the school hear the rumor? Assume that everyone who knows the rumor will tell exactly one person every hour. That is, initially Jack and Jill know; after 1 hour, 2 more people know, . . . ​

A) 23 hours
B) 9 hours
C) 10 hours
D) 7 hours
E) 20 hours

Question 34

What is the next term of the sequence? ​ 54, 48, 42, 36, 30, ...... ​

A) 18
B) 24
C) 6
D) 29
E) 22

Question 35

Find four different odd numbers whose sum is 34 . ​

A) 12 + 7 + 13 + 2 = 34
B) 11 + 7 + 13 + 3 = 34
C) 13 + 9 + 13 + 3 = 34
D) 11 + 8 + 12 + 3 = 34
E) 11 + 9 + 13 + 5 = 34

Question 36

​Shoshana has $ 1760 in a savings account at the beginning of the year. She wants to keep at least $ 460 in the account for a safety net. She spent $ 100 on gift for her father on January 1. Additionally, she withdraws $ 60 each week for spending money. How many weeks can she withdraw money?

A) ​ 21 weeks
B) ​ 7 weeks
C) ​ 28 weeks
D) ​ 29 weeks
E) ​ 20 weeks

Question 37

​Sarah ate two thirds of the carrot sticks in her lunch yesterday and saved them for today. Her father added 10 more carrot sticks to her lunch for today. Now she has 21 carrot stick in you lunch today. How many carrot sticks did Sarah originally have in her lunch yesterday?

A) ​ 7 carrots
B) ​ 2 carrots
C) ​ 54 carrots
D) ​ 33 carrots
E) ​ 43 carrots

Question 38

What is the next term of the sequence? ​ 4 , 5 , 8 , 13 , 20 , 29 , 40 ,..... ​

A) 53
B) 59
C) 68
D) 49
E) 55

Question 39

​Solve the following linear equation. ​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 40

​Hester wants to spend no more than $ 48 at the grocery store. She needs to buy a pound of a salmon for $ 12 . A bag of organic apples costs $ 9 . How many bags of organic apples can she buy?

A) ​ 4 bags
B) ​ 10 bags
C) ​ 9 bags
D) ​ 6 bags
E) ​ 5 bags

Question 41

​Solve the following linear equation. ​ ​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 42

​Solve the following linear inequality. ​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 43

Solve the following linear inequality. ​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 44

Find the Celsius temperature when the Fahrenheit temperature is -20 . Use the relationship between Fahrenheit temperature and Celsius temperature, which is given by the formula F = 1.8 C + 32, where F is the Fahrenheit temperature and C is the Celsius temperature. Round your answer to the nearest tenth of a degree. ​

A) -4.0 °C
B) 6.7 °C
C) -24.9 °C
D) -28.9 °C
E) -11.1 °C

Question 45

Find the number of units made during a week when the total cost was $39,000, the cost per unit was $9, and the fixed costs were $3000. Use the formula T = U · N + F , where T is the total cost, U is the cost per unit, N is the number of units made, and F is the fixed cost. ​

A) 39,333 units
B) 27,000 units
C) 12,000 units
D) 4375 units
E) 4000 units

Question 46

​Mark and Anthony run a catering business. Their fee for catering is $ 220 plus $ 20 per person. Their goal is to gross $ 4000 this month. Which of the following strategies would accomplish their goal?

A) ​3 jobs with 30 people at each banquet and 2 jobs with 20 people at both banquets
B) ​6 jobs with 22 people at each banquet
C) ​2 jobs with 50 people at both banquets and 1 job with at least 68 people
D) ​4 jobs with 30 people at each banquet
E) ​5 jobs with 27 people at each banquet

Question 47

Julio, a sales executive, averages 29 mi/gal on a 749 -mile trip. Find the number of gallons of gasoline used on the trip. Round your answer to the nearest tenth of a gallon. Note: Use the formula D = m · g , where D is the total mileage, m is the average mileage, and g is the total number of gallons used. ​ ​

A) 27.4 gal
B) 26.0 gal
C) 26.4 gal
D) 25.8 gal
E) 28.0 gal

Question 48

The value of an investment in a high-tech company after 1 year was $17,000. The increase in value during the year was $3000. Find the amount of the original investment. Note: Use the formula A = P + I , where A is the value of the investment after 1 year, P is the original investment, and I is the increase in value of the investment. ​

A) $17,800
B) $20,000
C) $14,000
D) $15,000
E) $15,400

Question 49

​Solve the following linear inequality. ​ ​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 50

​Solv e the following linear inequality. ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 51

The original investment in a mutual fund was $ 9,000 . The value of the mutual fund after 1 year was $ 11,670 . Find the increase in value of the investment. Note: Use the formula A = P + I , where A is the value of the investment after 1 year, P is the original investment, and I is the increase in value of the investment. ​

A) $ 2,670
B) $ 2,669
C) $ 20,670
D) $ 2,869
E) $ 2,471

Question 52

Find the time required for a falling object to increase its velocity from 10 ft/s to 474 ft/s. Use the formula V = V ₀ + 32 t , where V is the final velocity of a falling object, V ₀ is the starting velocity of a falling object, and t is the time for the object to fall. ​

A) 32.7 s
B) 2.2 s
C) 15 s
D) 46.5 s
E) 14.5 s

Question 53

​If 3 books cost $ 30 , a book, three pens, and a notebook cost $ 16 , and a book and pen cost $ 11 . Find the cost of a notebook.

A) ​$ 10
B) ​$ 3
C) ​$ 1
D) ​$ 2
E) ​$ 6

Question 54

​Solve the following linear inequality. ​ ​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 55

You estimate that your car can travel 440 miles on 12 gallons of gasoline. Find the miles per gallon. Round your answer to the nearest tenth of a mile per gallon. Note: Use the formula ​D = m · g , where D is the total mileage, m is the average mileage, and g is the total number of gallons used. ​

A) 38.3 mi/gal
B) 34.5 mi/gal
C) 36.7 mi/gal
D) 37.1 mi/gal
E) 35.7 mi/gal

Question 56

​Jerry and Elliot raised money selling popcorn. They raised $ 2100 total. Jerry raised $ 100 more than Elliot. How much did Jerry raise?

A) ​$ 100
B) ​$ 1000
C) ​$ 650
D) ​$ 550
E) ​$ 1100

Question 57

​Solve the following linear inequality. ​ ​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 58

​Solve the following linear inequality. ​ ​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 59

​Solve the following linear inequality. ​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 60

8 adults and 4 children need to cross a river in a small boat that can hold one adult or one or two children. How many one-way trips will it take for all of them to cross the river? ​

A) 37
B) 35
C) 12
D) 32
E) 16

Question 61

A store manager uses a markup rate of 25% on all appliances. Find the cost of a blender that sells for $64.00. Round your answer to the nearest cent. Note: Use the formula S = C + M , where S is the selling price, C is the cost price, and M is the markup. ​

A) $51.20
B) $52.20
C) $49.40
D) $53.00
E) $48.60

Question 62

Jack and Jill run a catering business. Their fee for catering banquets is $ 145 plus $ 6 per person. Their goal is to gross $ 3500 a month. How many 100 person banquets do they need to average in order to make their goal? Round your answer to the nearest whole number. ​

A) 14 banquets
B) 24 banquets
C) 5 banquets
D) 6 banquets
E) 23 banquets

Question 63

​A small tumor in a patient begins to grow a steady rate for two years until the patient was treated. Over the next year, the tumor begins to shrink slowly and then shrinks faster and faster during the fourth year until it is smaller than it was when it began to grow. Sketch a graph that shows the size of the tumor over time.

A) ​
B) ​
C) ​
D) ​
E) ​

Question 64

​Choose the story that best describes the graph.

A) ​A frozen chicken was removed from the freezer and left to thaw until it reached room temperature. The chicken was then left out for another hour before it was placed in the oven to bake for an hour.
B) ​A frozen chicken was removed from the freezer and left to thaw. It was then placed in the oven to bake for an hour.
C) ​A frozen chicken was placed in the oven to bake. It was then removed from the oven and left on the counter for an hour. It was placed back in the oven to cook for another hour.
D) ​A frosen chicken was removed from the freezer and placed ina microwave oven to thaw quickly. The chicken was then left out for another hour before it was placed in the oven to bake for an hour.
E) ​A frozen chicken was placed in the oven to bake. It was then removed from the oven and left on the counter for an hour. It was placed back in a microwave oven to cook for another half hour.

Question 65

​During a two -week period, there were 240,000 births and 120,000 deaths worldwide. What do these numbers tell us about the rate of change in world population during these two weeks?

A) ​The world population increased at a rate of 120,000 individuals per week.
B) ​The world population decreased at a rate of 120,000 individuals per week.
C) ​The world population increased at a rate of 240,000 individuals per week.
D) ​ ​The world population increased at a rate of 60,000 individuals per week.
E) ​ The world population decreased at a rate of 60,000 individuals per week.

Question 66

​A runner begins running at a steady pace on a at path. She speeds up as she starts to run downhill. Once she is at the bottom of the hill, the path is at again, and she resumes a steady pace faster than her previous steady pace. Her run ends with an uphill path, on which she runs slower and slower until she stops at the top of the hill. Sketch a graph of the runner's speed versus time.

A) ​
B) ​
C) ​
D) ​
E) ​

Question 67

Consider the graph below which depicts the depreciation of a copy machine over 5 years. Predict when the value of the copy machine will be $ 200 . Round your answer to two decimal places. ​ ​

A) 12.00 years
B) 6.00 years
C) 5.65 years
D) 4.80 years
E) 6.13 years

Question 68

​A population of bacteria grown in a Petri dish begins to grow slowly but increasingly faster over the fi rst two days. The population then grows faster and faster for three days until the growth begins to slow down for the following two days until the population levels off. Sketch a graph that shows the growth of the bacteria population over time.

A) ​ ​
B) ​
C) ​
D) ​
E) ​

Question 69

​Which of the following is an arithmetic sequence? ​

A) ​ 4 , 8 , 16 , 32 , 64 , ...
B) ​ 5 , 8 , 11 , 16 , 19 , ...
C) ​ 3 , 9 , 27 , 81 , 243 , ...
D) ​ 9 , 15 , 21 , 27 , 33 , ...
E) ​ 2 , 2 , 4 , 6 , 10 , ...

Question 70

​Mario is driving on the highway at a steady rate. He encounters a construction zone and slows down until he is out of the zone and is able to resume his original steady speed. He then slows down as he approaches his exit and comes to a complete stop at the stop sign at the end of the exit ramp. Sketch a graph of Mario's speed versus time.

A) ​
B) ​
C) ​
D) ​
E) ​

Question 71

​Which of the following is a geometric sequence? ​

A) ​ 6 , 14 , 22 , 30 , 38 , ...
B) ​ 2 , 6 , 18 , 54 , 162 , ...
C) ​ 9 , 12 , 17 , 24 , 33 , ...
D) ​ 6 , 12 , 18 , 30 , 36 , ...
E) ​ 9 , 27 , 81 , 729 , 2187 , ...

Question 72

​A road sign says there is an 12 % incline. Choose the correct explain for the meaning of the road sign. ​

A) ​The road makes an angle of 12 degrees with the horisontal direction.
B) ​The road rises 12 feet for every 10 feet in horizontal distance.
C) ​The road rises 12 feet for every 100 feet in horizontal distance.
D) ​The road rises 1 foot for every 12 feet in horizontal distance.
E) ​The road rises 12 feet.

Question 73

Let's say you have a choice between two checking plans. With the first plan, you will be charged $ 3 per month plus 25 ¢ per check. With the second plan, you will be charged $ 4 per month regardless of how many checks you write. If you write only a few checks, the first plan is clearly cheaper. Similarly, if you write many checks a month, the second plan is clearly cheaper. Determine the number x that will enable you to make the following statement: If you write 1 to x checks per month, choose the first plan. If you write more than x checks per month, choose the second plan. ​

A) x = 8
B) x = 10
C) x = 2
D) x = 4
E) x = 16