Name: ________________________ Class: ___________________ Date: __________
ID: A
Algebra 1 SEM 1 Final REVIEW Determine the independent and dependent quantities in each scenario.
2. Gavin works for a skydiving company. Customers pay $200 per jump to skydive in tandem skydives with Gavin.
1. Selena is driving to visit her grandmother who lives 325 miles away from Selena’s home. She travels an average of 60 miles per hour. Choose the graph that best models each scenario. 3. Kylie is filling her backyard pool to get ready for the summer. She is using a garden hose to fill the pool at a rate of 14 gallons per minute. Graph A
Graph B
Graph C
4. Jasmine is saving for college. She has invested $500 in a mutual fund that is expected to earn an average of 7% annually. Graph A
Graph B
Graph C
6
Name: ________________________
ID: A
5. Each day Maria starts her walk to school at 7:45 AM. At 7:50 AM she stops at her friend Jenna’s house. Jenna is usually late and Maria must wait at least 5 minutes for her to get ready. At 7:55 AM Maria and Jenna leave Jenna’s house and arrive at school at 8:10 AM. Graph A
Graph B
Graph C
Label the axes of the graph that models each scenario with the independent and dependent quantities. 6. Madison enjoys bicycling for exercise. Each Saturday she bikes a course she has mapped out around her town. She averages a speed of 12 miles per hour on her journey.
2
Name: ________________________
ID: A
Match each definition to its corresponding term. a. b. c. d. e. f. g.
discrete graph continuous graph relation function domain range Vertical Line Test
7. A graph with no breaks in it 8. The mapping between a set of inputs and a set of outputs 9. The set of all input values of a relation 10. The set of all output values of a relation 11. A graph of isolated points
12. A visual method used to determine whether a relation represented as a graph is a function 13. A relation between a given set of elements for which each input value there exists exactly one output value
Each pair of graphs has been grouped together. Provide a rationale to explain why these graphs may have been grouped together. 14. Graph A
Graph B
Graph A
Graph B
15.
3
Name: ________________________
ID: A
16. Graph A
Graph B
Determine if each graph represents a function by using the Vertical Line Test.
18.
17.
Choose the graph that represents each function. Use your graphing calculator. 19. f(x)
2 x2 3
Graph A
Graph B
Graph C
4
Name: ________________________
ID: A
20. f(x) x 2 4 Graph A
Graph B
Graph C
Graph B
Graph C
Graph B
Graph C
21. f(x) 2 x 5 Graph A
22. f(x) x 6 Graph A
Determine whether each graph represents a linear function, a quadratic function, an exponential function, a linear absolute value function, a linear piecewise function, or a constant function.
24.
23. 25.
5
Name: ________________________
ID: A
Create an equation and sketch a graph for a function with each set of given characteristics. Use values that are any real numbers between 10 and 10.
27. Create an equation and sketch a graph that: • is linear, • is discrete, and • is decreasing across the entire domain.
26. Create an equation and sketch a graph that: • is a smooth curve, • is continuous, • has a minimum, and • is quadratic.
Problem Set Identify the independent and dependent quantities in each problem situation. Then write a function to represent the problem situation. 28. Sophia is walking to the mall at a rate of 3 miles per hour. 29. Shanise plays on the varsity soccer team. She averages 4 goals per game. Use each scenario to complete the table of values and calculate the unit rate of change. 30. Miguel is riding his bike to lacrosse practice at a rate of 7 miles per hour. Independent Quantity
Dependent Quantity
Quantity Units Expression 0 0.5 1 1.5 2
6
Name: ________________________
ID: A
31. Terell plays on the varsity basketball team. He averages 12 points per game. Independent Quantity
Dependent Quantity
Quantity Units Expression 1 3 5 7 9 Use the graph to determine the input value for each given output value. The function D(t) 40t represents the total distance traveled in miles as a function of time in hours.
Identify the input value, the output value, and the rate of change for each function. 32. Cisco mows lawns in his neighborhood to earn money. He earns $16 for each lawn. The function A(m) 16m represents the total amount of money earned as a function of the number of lawns mowed. Solve each function for the given input value. The function A(t) 7t represents the total amount of money in dollars Carmen earns babysitting as a function of time in hours. 33. A(3) __________ 34. A(4.5) __________
35. D(t) 120 36. D(t) 320 37. D(t) 240 38. D(t) 160
7
Name: ________________________
ID: A
What Goes Up Must Come Down Analyzing Linear Functions Problem Set Complete the table to represent each problem situation. 39. A hot air balloon cruising at 1000 feet begins to ascend. It ascends at a rate of 200 feet per minute. Independent Quantity
Dependent Quantity
Quantity Units 0 2 4 2200 2600 Expression Identify the input value, the output value, the y-intercept, and the rate of change for each function.
Sketch the line for the dependent value to estimate each intersection point. 41. f(x) 40x 1200 when f(x) 720
40. A helicopter flying at 3505 feet begins its descent. It descends at a rate of 470 feet per minute. The function f(t) 470t 3505 represents the height of the helicopter as it descends.
8
Name: ________________________
ID: A
42. f(x) 6x 15 when f(x) 75
Substitute and solve for x to determine the exact value of each intersection point. 43. f(x) 40x 1200 when f(x) 720 44. f(x) 4x 7 when f(x) 8
Elena works at the ticket booth of a local playhouse. On the opening night of the play, tickets are $10 each. The playhouse has already sold $500 worth of tickets during a presale. The function f(x) 10x 500 represents the total sales as a function of tickets sold on opening night.
Use the graph of the function to answer each question. Graph each solution on the number line. 45. How many tickets must Elena sell in order to make at least $1000?
46. How many tickets must Elena sell in order to make less than $800?
9
Name: ________________________
ID: A
47. How many tickets must Elena sell in order to make at least $1200?
48. How many tickets must Elena sell in order to make exactly $1400?
49. How many tickets must Elena sell in order to make less than $600?
50. How many tickets must Elena sell in order to make exactly $900?
Write a compound inequality for each situation.
Problem Set Write each compound inequality in compact form.
53. People with a driver’s license are at least 16 years old and no older than 85 years old.
51. All numbers less than or equal to 22 and greater than 4
54. Kyle’s car gets more than 31 miles per gallon on the highway or 26 miles or less per gallon in the city.
52. All numbers less than 55 and greater than 45
Represent the solution to each part of the compound inequality on the number line. Then write the final solution that is represented by each graph. 55. x 2 and x 7 56. x 10 or x 6 57. x 5 or x 3
Solve each compound inequality. Then graph and describe the solution. 58. 3 x 7 17 59. 4 2x 2 12
10
Name: ________________________
ID: A
60. x 5 14 or 3x 9
Solve each linear absolute value equation.
Define variables and write an equation to represent each situation.
61. x 9 2
66. A florist sells carnations for $10.99 a dozen and lilies for $12.99 a dozen. During a weekend sale, the florist’s goal is to earn $650. Write an equation that represents the total amount the florist would like to earn selling carnations and lilies during the weekend sale.
62. x 12 5 Solve each linear absolute value equation. 63. x 3 7 40 64. 2 x 6 48
The basketball booster club runs the concession stand during a weekend tournament. They sell hamburgers for $2.50 each and hot dogs for $1.50 each. They hope to earn $900 during the tournament. The equation 2.50b 1.50h 900 represents the total amount the booster club hopes to earn. Use this equation to determine each unknown value.
Graph the function that represents each problem situation. Draw an oval on the graph to represent the answer. 65. A jewelry company is making 16-inch bead necklaces. The specifications allow for a difference of 0.5 inch. The function f(x) x 16 represents the difference between the necklaces manufactured and the specifications. Graph the function. What necklace lengths meet the specifications?
67. If the booster club sells 315 hamburgers during the tournament, how many hot dogs must they sell to reach their goal? 68. If the booster club sells 420 hot dogs during the tournament, how many hamburgers must they sell to reach their goal? 69. If the booster club sells 0 hot dogs during the tournament, how many hamburgers must they sell to reach their goal? 70. If the booster club sells 0 hamburgers during the tournament, how many hot dogs must they sell to reach their goal? Determine the x-intercept and the y-intercept of each equation. 71. 20x 8y 240 72. 15x 3y 270 73. y 8x 168
11
Name: ________________________
ID: A
Determine the x-intercept and y-intercept. Then graph each equation.
Solve each equation for the variable indicated. 81. The formula for the area of a triangle is A
74. 5x 6y 90
1 bh . 2
Solve the equation for h. 82. The formula for the area of a circle is A r 2 . Solve the equation for r. 83. The formula for the volume of a cylinder is V r 2 h . Solve the equation for h. Problem Set Write a system of linear equations to represent each problem situation. Define each variable. Then, graph the system of equations and estimate the break-even point. Explain what the break-even point represents with respect to the given problem situation.
75. 12x 9y 36
84. Eric sells model cars from a booth at a local flea market. He purchases each model car from a distributor for $12, and the flea market charges him a booth fee of $50. Eric sells each model car for $20.
Convert each equation from standard form to slope-intercept form. 76. 4x 6y 48 77. 3x 5y 25 Convert each equation from slope-intercept form to standard form. 78. y 5x 8 79. y
2 x6 3
80. y 5x 13
12
Name: ________________________
ID: A Problem Set
85. Ramona sets up a lemonade stand in front of her house. Each cup of lemonade costs Ramona $0.30 to make, and she spends $6 on the advertising signs she puts up around her neighborhood. She sells each cup of lemonade for $1.50.
Write a system of equations to represent each problem situation. Solve the system of equations using the linear combinations method. 89. The high school marching band is selling fruit baskets as a fundraiser. They sell a large basket containing 10 apples and 15 oranges for $20. They sell a small basket containing 5 apples and 6 oranges for $8.50. How much is the marching band charging for each apple and each orange? 90. Asna works on a shipping dock at a tire manufacturing plant. She loads a pallet with 4 Mudslinger tires and 6 Roadripper tires. The tires on the pallet weigh 212 pounds. She loads a second pallet with 7 Mudslinger tires and 2 Roadripper tires. The tires on the second pallet weigh 184 pounds. How much does each Mudslinger tire and each Roadripper tire weigh? Solve each system of equations using the linear combinations method.
Solve each system of equations by substitution. Determine whether the system is consistent or inconsistent.
ÏÔ Ô 3x 5y 8 91. ÔÌÔ ÔÔÓ 2x 5y 22
ÔÏÔ y 2x 3 86. ÔÔÌ ÔÔÓ x 4 ÏÔ Ô 2x y 9 87. ÔÌÔ ÔÔÓ y 5x 2
ÔÏÔ 2x 4y 4 92. ÔÔÌ ÔÔÓ 3x 10y 14
ÏÔ ÔÔ 1 3 ÔÔ x y 7 2 2 88. ÔÌÔ ÔÔ 1 ÔÔ y 2x 10 ÔÓ 3
13
Name: ________________________
ID: A Graph each linear inequality.
Which Is the Best Method? Using Graphing, Substitution, and Linear Combinations
96. y 10 x
Problem Set Write a system of equations to represent each problem situation. Solve the system of equations using any method and answer any associated questions. 93. Stella is trying to choose between two rental car companies. Speedy Trip Rental Cars charges a base fee of $24 plus an additional fee of $0.05 per mile. Wheels Deals Rental Cars charges a base fee of $30 plus an additional fee of $0.03 per mile. Determine the amount of miles driven for which both rental car companies charge the same amount. Explain which company Stella should use based on the number of miles she expects to drive.
Graph each inequality and determine if the ordered pair is a solution for the problem situation.
Problem Set
97. Noah plays football. His team’s goal is to score at least 15 points per game. A touchdown is worth 6 points and a field goal is worth 3 points. Noah’s league does not allow teams to try for the extra point after a touchdown. The inequality 6x 3y 15 represents the possible ways Noah’s team could score points to reach their goal. Is the ordered pair (6,1) a solution for the problem situation?
Write a linear inequality in two variables to represent each problem situation. 94. Tanya is baking zucchini muffins and pumpkin muffins for a school event. She needs at least 500 muffins for the event. 95. Hiro needs to buy new pens and pencils for school. Pencils cost $1 each and pens cost $2.50 each. He has $10 to spend.
14
Name: ________________________
ID: A Graph each system of linear inequalities and identify two solutions.
98. Lea has $5 to buy notebooks and pens. Notebooks cost $1.25 each and pens cost $0.75 each. The inequality 1.25x 0.75y 5 represents the possible ways Lea could spend her $5. Is the ordered pair (5, 2) a solution for the problem situation?
ÏÔ Ô y 3x 5 103. ÔÌÔ ÔÔÓ y x 3
ÏÔ Ô y 2x 3 104. ÔÌÔ ÔÔÓ y 2x 5
Problem Set Write a system of linear inequalities that represents each problem situation. Remember to define your variables. 99. The maximum capacity for an average passenger elevator is 15 people and 3000 pounds. It is estimated that adults weigh approximately 200 pounds and children under 16 weigh approximately 100 pounds. 100. Pablo’s pickup truck can carry a maximum of 1000 pounds. He is loading his truck with 20-pound bags of cement and 80-pound bags of cement. He hopes to load at least 10 bags of cement into his truck.
ÔÏÔ ÔÔ y 1 x 4 3 105. ÔÌÔ ÔÔ ÔÔ y 2x 5 Ó
Determine whether each given point is a solution to the system of linear inequalities.
ÏÔ Ô 2x y 4 101. ÔÌÔ ÔÔÓ x y 7 Ponits: (2,10) ÔÏÔ x 5y 1 102. ÔÌÔ ÔÔÓ 2y 3x 2 Point: (0,1)
15
