Unit 1 Tests
Chapter One
Chapter 1 Equations and Inequalities
Word Problems
COFFEE SHOP COSTS
You decide to join a coffee club that charges a $30 membership fee. Each cup of coffee costs $4.15. What is the total cost to join and buy 15 cups of coffee? TEKS 2A.2.A
A $90.25
B $82.50
C $92.25
D $67.50
AMUSEMENT PARK TICKETS
You plan a trip to an amusement park with $60 to spend. Admission to the park is $25, and each ride costs $5. How many rides can you enjoy after paying for admission? TEKS 2A.2.A
F 5
G 7
H 8
J 11
BASKETBALL STATS
In basketball, a player’s efficiency rating is calculated by taking the total points scored and subtracting missed shots and turnovers. Which list shows the players in order from lowest to highest efficiency rating? TEKS a.1
Player Efficiency Rating
Kobe Bryant 27
Michael Jordan 29
LeBron James 32
Shaquille O’Neal 24
Larry Bird 26
A Bryant, O’Neal, Bird, Jordan, James
B O’Neal, Bird, Bryant, Jordan, James
C Bird, O’Neal, Bryant, Jordan, James
D Bird, Bryant, O’Neal, Jordan, James
BOOK SALES
A local bookstore sold fiction and non-fiction books with a total revenue of $48,000 in one month. The price of fiction books is $12 each and non-fiction books are $20 each. If the total number of books sold was 3,600, how many non-fiction books were sold? TEKS 2A.2.A
F 900
G 1000
H 500
J 600
GROCERY SHOPPING BUDGET
You are shopping for groceries with a budget of $50 for fruits and vegetables. Apples cost $2 per pound and bananas cost $1.00 per pound. If you want to buy equal amounts of apples and bananas, how many pounds can you buy in total without going over your budget? TEKS 2A.2.A
A 16 pounds
B 20 pounds
C 28 pounds
D 30 pounds
SUMMER CAMP JOBS
You have two summer camp jobs: one as a lifeguard earning 15 per hour and another as a camp counselor earning 10 per hour. If you earn a total of $480 after working for 40 hours that week, which equation represents the hours worked as a lifeguard? TEKS a.5
F 480 = 15x + 10x
G 480 = 15x + 10(40 – x)
H 480 = 15(40 – x) + 10x
J 480 = 15(x + 40) + 10x
FOSSIL LENGTHS
The therizinosaur could grow up to approximately 10 meters long. Using the conversion factor that 1 meter is about 3.28 feet, convert this length to feet and round your answer to the nearest foot. TEKS a.1
ROAD TRIP DISTANCE
You are driving from New York City to Boston, which is about 215 miles apart. If you maintain an average speed of 55 miles per hour, how long will your trip take? Round your answer to the nearest tenth of an hour. TEKS 2A.2.A
GYM MEMBERSHIP COSTS
You decide to join a gym that charges a 40 membership fee. Each workout class costs 6. How much will it cost to join and attend 10 workout classes? TEKS 2A.2.A
A 100
B 80
C 60
D 90
ZOOM ZOO TICKETS
You are planning a visit to the Zoom Zoo with a budget of 50. Admission to the zoo is 20, and each animal encounter costs $7. How many animal encounters can you enjoy after paying for admission? TEKS 2A.2.A
F 4
G 3
H 2
J 5
FOOTBALL STATS
In football, a player’s quarterback rating is determined by various performance metrics. Which list shows the players in order from lowest to highest quarterback rating? TEKS a.1
Player Quarterback Rating
Tom Brady 95
Aaron Rodgers 104
Peyton Manning 98
Russell Wilson 92
Drew Brees 102
A Wilson, Brady, Manning, Brees, Rodgers
B Wilson, Brady, Manning, Rodgers, Brees
C Wilson, Manning, Brady, Brees, Rodgers
D Wilson, Brady, Manning, Brees, Rodgers
CANDY SALES
A local candy shop sold chocolates and gummies with total revenue of $36,000 last month. Chocolates are priced at $15 each and gummies at $5 each. If the total number of candies sold was 3,000, how many gummies were sold? TEKS 2A.2.A
F 900
G 1,200
H 2,100
J 1,500
SHOPPING SPREE BUDGET
You have a budget of $75 for shopping for clothes. T-shirts cost 10 each and jeans cost $25 each. If you want to buy equal amounts of T-shirts and jeans, how many items can you buy in total? TEKS 2A.2.A
A 5 items
B 4 items
C 6 items
D 3 items
PART-TIME JOBS
You have two part-time jobs: one as a cashier earning 12 per hour and another as a delivery driver earning 15 per hour. If you earn a total of $540 after working for 45 hours that week, which equation represents the hours worked as a cashier? TEKS a.5
F 540 = 12x + 15x
G 540 = 12x + 15(45 – x)
H 540 = 12(45 – x) + 15x
J 540 = 12(x + 45) + 15x
REPTILE LENGTHS
The komodo dragon can grow up to about 3 meters long. Using the conversion factor that 1 meter is about 3.28 feet, convert this length to feet and round your answer to the nearest foot. TEKS a.1
TRAVEL TIME ESTIMATION
You are driving from Los Angeles to San Francisco, which is about 380 miles apart. If you maintain an average speed of 65 miles per hour, how long will your trip take? Round your answer to the nearest ten of an hour.
Answers
COFFEE SHOP COSTS
Answer: C $92.25
AMUSEMENT PARK TICKETS
Answer: G 7 (After paying for admission, you have 35 left for rides, allowing you to enjoy 7 rides: 35 ÷ $5 = 7 rides)
BASKETBALL STATS
Answer: B O’Neal, Bird, Bryant, Jordan, James (Order from lowest to highest efficiency rating: Shaquille O’Neal 24, Larry Bird 26, Kobe Bryant 27, Michael Jordan 29, LeBron James 32)
BOOK SALES
Answer: J 600 (Let x be the number of non-fiction books. You can set up the equations based on revenue and total books sold: 12(3600 – x) + 20x = 48,000)
GROCERY SHOPPING BUDGET
Answer: C 28 (Total cost equation: 2x + 1.50x = $50; solving gives 3.5x = $50; x = 14.28 pounds of each type; 14.28 x 2 = $28.57 and is over the budget. 14 pounds of banana is 14 x 1.5 = $21 and apples 14 x 2 = $28; totaling 28 pounds for $21 + $28 = $49 and under budget.)
SUMMER CAMP JOBS
Answer: G 480 = 15x + 10(40 – x) (This equation represents the hours worked as a lifeguard in relation to total hours)
FOSSIL LENGTHS
Answer: 33 feet (10 meters × 3.28 feet/meter = 32.8 feet, rounded to the nearest foot is 33 feet)
ROAD TRIP DISTANCE
Answer: Approximately 3.9 hours (215 miles ÷ 55 mph = approximately 3.909 hours, rounded to the nearest tenth is about 3.9 hours)
GYM MEMBERSHIP COSTS
Answer: A 100 (Calculation: 6 × 10 + 40 = 100)
ZOOM ZOO TICKETS
Answer: F 4
(After paying for admission, you have 30 left, which allows for 3 animal encounters: 30 ÷ $7 ≈ 4.29, rounded down to 4)
FOOTBALL STATS
Answer: A Wilson, Brady, Manning, Brees, Rodgers
(Order from lowest to highest quarterback rating: Russell Wilson 92, Tom Brady 95, Peyton Manning 98, Drew Brees 102, Aaron Rodgers 104)
CANDY SALES
Answer: A 900
(Set up equations based on revenue: Let x be the number of gummies. Then (15(3000 – x) + 5x = 36,000). Solving gives x = 900.)
SHOPPING SPREE BUDGET
Answer: B 4 items
(Total cost equation: 10x + 25x = $75. Solving gives x = 2 for T-shirts and jeans each, totaling 4 items.)
PART-TIME JOBS
Answer: G 540 = 12x + 15(45 – x)
(This equation represents the hours worked as a cashier in relation to total hours.)
REPTILE LENGTHS
Answer: 10 feet
(3 meters × 3.28 feet/meter = 9.84 feet, rounded to the nearest foot is 10 feet)
TRAVEL TIME ESTIMATION
Answer: Approximately 5.8 hours
(380 miles ÷ 65 mph = approximately 5.846 hours, rounded to the nearest tenth is about 5.8 hours)
Chapter 2 Linear Equations and Functions
Mixed Review
In Exercises 1 and 2, determine if the given relations are functions. Provide an explanation.
- (1, 25), (0, 4), (2, 3), (21, 2), (2, 7), (1, 2)
- (23, 4), (2, 5), (1, 0), (0, 4), (22, 23), (3, 6)
- Evaluate ( f(x) = 3x2 – 2x + 11 ) when ( x = 26 ).
For the points provided, calculate the slope of the line passing through them and indicate whether the line rises, falls, is horizontal, or is vertical.
- (3, 22), (5, 4)
- (6, 27), (13, 27)
- (22, 1), (1, 24)
- (24, 9), (24, 8)
Graph the following equations:
- ( x = 4 )
- ( y = 3/2x + 3 )
- ( x + 2y = 6 )
- ( 3y = 2x – 12 )
Write the equation of the line that goes through the specified point and meets the given condition.
- Point: (9, -21); Condition: parallel to ( y = -1/3x – 8 )
- Point: (10, 2); Condition: perpendicular to ( y = -5x + 7 )
Given that ( x ) and ( y ) vary directly, write an equation that relates ( x ) to ( y ). Then find ( x ) when ( y = 6 ).
- ( x = 4, y = 28 )
- ( x = -22, y = -21 )
- ( x = 8, y = 18 )
- ( x = 16, y = -26 )
For Exercises 18 and 19: (a) Create a scatter plot for the data, (b) Estimate the best-fitting line, (c) Estimate the value of ( y ) when ( x = 10 ).
- Data:
| x | y |
| 1 | 18 |
| 2 | 40 |
| 3 | 55 |
| 4 | 73 |
| 5 | 91 |
- Data:
| x | y |
| 1 | 97 |
| 2 | 91 |
| 3 | 87 |
| 4 | 81 |
| 5 | 75 |
- Graph the equation ( y = -23|x +1| +3 ). Compare this graph with that of ( y = |x| ).
Graph the following inequalities on a coordinate plane:
- ( y ≥ -2x +4 )
- ( 2x -4y ≤16 )
- ( y < |x -3| +1 )
- ( y > -2|x| -3 )
- Tire Wear: A new set of car tires starts with a tread depth of 8 mm, decreasing by 0.12 mm per 1,000 miles driven. Write an equation representing tread depth as a function of distance driven and predict at what distance the tread depth will reach 2 mm.
- Painting: The amount of paint applied by an electric sprayer varies directly with time; it applies 0.5 gallons in 2.5 minutes. Write an equation that describes the amount of paint as a function of time and determine how much paint is applied if operated for 20 minutes.
- Computer Chips: The table below lists the number of transistors (in millions) and corresponding speed (in gigahertz) for various computer processors. Find an approximation for the best-fitting line for this data.
| Transistors x | Speed y |
|---|---|
| 3.1 | 0.06 |
| 9.5 | 0.45 |
| 28 | 0.50 |
| 37 | 1.50 |
| 42 | 1.50 |
| 55 | 2.00 |
| 106 | 2.40 |
| 125 | 3.60 |
Mixed Review
In Exercises 1 and 2, determine if the given relations are functions. Provide an explanation.
1 (1, 25), (0, 4), (2, 3), (21, 2), (2, 7), (1, 2)
2 (23, 4), (2, 5), (1, 0), (0, 4), (22, 23), (3, 6)
3 Evaluate ( f(x) = 3x2 – 2x + 11 ) when ( x = 26 ).
f(26) = 3(26)2 – 2(26) + 11
For the points provided, calculate the slope of the line passing through them and indicate whether the line rises, falls, is horizontal, or is vertical.
- (3, 22), (5, 4)
- (6, 27), (13, 27)
- (22, 1), (1, 24)
- (24, 9), (24, 8)
Graph the following equations:
- ( x = 4 )
- ( y = 3/2x + 3 )
- ( x + 2y = 6 )
- ( 3y = 2x – 12 )
Write the equation of the line that goes through the specified point and meets the given condition.
- Point: (9, -21); Condition: parallel to ( y = -1/3x – 8 )
- Point: (10, 2); Condition: perpendicular to ( y = -5x + 7 )
Given that ( x ) and ( y ) vary directly, write an equation that relates ( x ) to ( y ). Then find ( x ) when ( y = 6 ).
- ( x = 4, y = 28 )
- ( x = -22, y = -21 )
- ( x = 8, y = 18 )
- ( x = 16, y = -26 )
For Exercises 18 and 19: (a) Create a scatter plot for the data, (b) Estimate the best-fitting line, (c) Estimate the value of ( y ) when ( x = 10 ).
- Data:
- ( x: 1, 2, 3, 4, 5 )
- ( y: 18, 40, 55, 73, 91 )
- Data:
- ( x: 1, 2, 3, 4, 5 )
- ( y: 97, 91, 87, 81, 75 )
- Graph the equation ( y = -23|x +1| +3 ). Compare this graph with that of ( y = |x| ).
Graph the following inequalities on a coordinate plane:
- ( y ≥ -2x +4 )
- ( 2x -4y ≤16 )
- ( y < |x -3| +1 )
- ( y > -2|x| -3 )
- Tire Wear: A new set of car tires starts with a tread depth of 8 mm, decreasing by 0.12 mm per 1,000 miles driven. Write an equation representing tread depth as a function of distance driven and predict at what distance the tread depth will reach 2 mm.
- Painting: The amount of paint applied by an electric sprayer varies directly with time; it applies 0.5 gallons in 2.5 minutes. Write an equation that describes the amount of paint as a function of time and determine how much paint is applied if operated for 20 minutes.
- Computer Chips: The table below lists the number of transistors (in millions) and corresponding speed (in gigahertz) for various computer processors. Find an approximation for the best-fitting line for this data.
https://www.desmos.com/calculator/aw3kbjuvey
| Transistors x | Speed y |
|---|---|
| 3.1 | 0.06 |
| 9.5 | 0.45 |
| 28 | 0.50 |
| 37 | 1.50 |
| 42 | 1.50 |
| 55 | 2.00 |
| 106 | 2.40 |
| 125 | 3.60 |