9-Week Review: Expressions, Radicals, Equations, Inequalities, Functions
1. Joe went to the grocery store with $54 to buy snacks for a party. A six-foot-long submarine sandwich costs $32.95. What is the greatest number of snacks that Joe can buy if each bag costs $2.69?
2. In science class, the lowest point total to earn a B is 412. Jane has a mean score of 82.5 on the first four tests. Her teacher only gives whole number points as test scores. What is the least score she can earn on the fifth test and still get a B in the class?
3. Mr. Lenberg has less than $325 to spend on box lunches for a field trip. The deli charges a fee of $75 to pack the lunches and supply a cooler of lemonade for everyone. Seventy-two students are going on the trip. What is the most that each lunch should cost?
4. Eliseo is fencing in an area where his dogs can play. Eliseo has 60 feet of fencing and he wants one dimension of the area to be twice the length of the other dimension. What are the maximum whole number dimensions that the play area can have?
Name:
5. A year in a dog’s life is not equal to a year in a human’s life. A dog’s age can be estimated using the function d(g) = 21 + 4(g - 2), where “g” is the age in dog years. Ronald’s dog was born 5 years ago. What is the dog’s age in human years?
6. Rafael has a rare baseball card in his collection. It is worth $128, and its value increases by $1.75 every month that the player is in the league. How much will this card be worth in one year if the player is still playing?
7. Solve, then write a number which is and is not a solution of the inequality.
5 – 2x ≥ -7
8. If f(x) = .75x2 + .25x, what is the value of
f(21)?
Record your answer and fill in the bubbles.
9. The side lengths of the figure below are given in centimeters. If the perimeter of this figure is 88 cm, what is the value of x?
10. Write the equation for “six more than the product of 7 and a number is fifty-four?”
11. Alisa buys pizza for $25 and several bottles of water for $1.25 each. Let C represent the total amount of money that Alisa spends and let w represent how many bottles of water she buys. Write the equation which best represents this situation?
12. Which situation is best modeled by
1787 - x?
A My bank account had $1,787 and then I wrote a check to the grocery store for x dollars.
B In 1787 there were x states in the Union.
C The number of states that entered the Union in 1787 was x.
D North Carolina entered the Union x years after Pennsylvania which entered in 1787.
13. The width of a pair of curtain panels is four and a half times the width of the window plus 9 inches. Write a function that models the width of one panel for a window that is x inches wide?
14. The equation C = 35 + 0.12m represents the cost c of renting a car and driving m miles. Write the situation that best describes the cost as a function of the number of mile driven?
15. The volume of this cube can be described by
V = 43.
How would you find the volume of a cube with edges that was g units shorter?
16. Write the functional relationship to model the inequality: Kelsey was offered a new 6% commission on all her sales added to her $350 salary which will earn her at least $650 a week.
17. The volume of four identical cubes is related to the edge length of the cubes. Write a function that represents the combined volume of these cubes?
18. The scatterplot shows the number of free throws that different basketball players attempted and the number that each player made.
Based on the trend in the data, approximately how many free throws would a player be expected to make if he attempted 65 free throws?
19. The scatter plot shows the relationship between the weekly total sales ($) and the number of different rug designs a rug store has. Based on this relationship, predict what the total sales will be when the store has 120 different rug designs.
20. Leonard observes that traffic is getting worse and it’s taking him longer to get to work. He records once a week the following data for several weeks. Graph a scatter plot using the given data. Draw the line of best fit and determine if there is any correlation.
Week / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8Time (min) / 7.2 / 7.8 / 8.2 / 8.5 / 8.9 / 9.5 / 9.4 / 9.9
21. Explain how this scatter plot represents the relationship between the number of students who passed the final exam and the number of students who failed the class.
22. Write a situation that would describe each:
a positive correlation
a negative correlation
no correlation
“+”
“-“
No:
23. The librarian will determine the total number of books to order for the library using the function
L(n) = 2n, where n represents the number of students in the school. What is the dependent quantity in this situation?
24. International travel requires the conversion of American dollars into foreign currency. One dollar can be converted to 6 Croatian Kunas. Jenna is converting ’x’ dollars into ‘y’ Kunas. Which expression is the independent variable in this situation? Which expression is the dependent variable in this situation?
Dependent:
Independent:
25. Which is the dependent variable in the following situation?
“Eliza jogs more often in the summer months than in the winter months.”
26. The graph shows the cost of purchasing “x” small flags at a gift shop if the flags are equally priced. Based on this information, determine an ordered pair that would represent an additional point on the graph?
27. A car is traveling at a constant speed. After 3 hours, the car has traveled 195 miles. If the car continues to travel at the same constant speed, how many hours will it take to travel a total of 325 miles? Record your answer and fill in the bubbles.
28. Write a situation that would be represented by a discrete graph? Continuous graph?
29. One type of redwood tree has an average height of 65 feet when it is 20 years old. If the tree is more than 20 years old, the average height, h, can be modeled by the function h = 1.95(a – 20) + 65, where ‘a’ is the age of the tree in years. Which statement about this situation is true?
F Every additional 1.95 ft of length over 20 ft adds 45 years to the age of this type of redwood tree
G For this type of redwood tree, the average height increases by 1.95 ft per year throughout its lifetime
H Each additional year of age over 20 years adds 1.95 ft to the average height of this type of redwood tree
J For this type of redwood tree, the average height increases by 65 ft for every 20 years of growth
30. Which set of ordered pairs represents y as a function of x?
A {(−9,2), (0,6), (0,−2), (−3,6)}
B {(−1,0), (4,3), (−7,−3), (−1,−8)}
C {(3,2), (−4,−2), (3,1), (−4,1)}
D {(5,4), (2,3), (1,1), (-2,4)}
31. Which of the following relations is not a function?
F {(-3, -3), (-3, -2), (-3, -1)}
G {(-4, 2), (-6, 2), (-8, 2)}
H {(5, -1), (-5, -2), (0, -3)}
J {(-3, 1), (0, 0), (3, 1)}
32. Give two ways to write the algebraic expression 8z in words
33. Picture frames are being purchased for favors at the senior prom. To ensure that enough frames are purchased, 1.3 times the number of tickets sold plus a dozen additional frames for the teacher chaperones will be purchased. Which quadrant will the ordered pairs to this function lie in?
34. Express the relation for the math test scoring system {(1, 2), (2, 2), (3, 5), (4, 5), (5, 5)} as a table and as a graph and determine if it is a function.
35. For the function f(x) = 32 x + 1, graph the ordered pairs for the given domain {-6, -4, 0, 4, 6}
36. Use the graph of the function
f(x) = -2x + 1 to find the value of y when x = -1 and 2.
37. The function, f(h) = 60h, describes how far from home Janelle is as she drives from Pittsburg to Daytona Beach. Graph the function and estimate how far from home Janelle is in 9 hours.
38. Which of the following is not a function?
A
B {(-5, 1), (-1, 1), (-1, 2), (-5, 2)}
C
39. The temperature of air in a room that began at 85℉ is decreasing by 3℉ per hour. The function that describes the temperature of the air over time is f(h) = 85 – 3h. Graph the function to show the temperatures for a domain of 0-10 hours.
40. The mapping below represents all of the points on the graph of a function. What is the domain and range of the function ?
41. Function h is graphed below. What is the range and domain of the function?
42. Give the domain and range of the relation.
43. Give the domain and range of the relation. Tell whether the relation is a function and is it a discrete or continuous relation.
x / y0 / –6
1 / –3
0 / 3
1 / 6
44. Glen and Stephanie have 100 flowers for prom decorations. In addition, they are planning to buy some flower arrangements that have 16 flowers each. All of the arrangements cost the same. They are not sure yet about the number of flower arrangements to buy, but they have enough money to buy up to 6 of them. A function rule to describe how many flowers they can buy is f(x) = 16x + 100. Let x represents the number of flower arrangements they can buy. Find a reasonable range for the function.
45. Write an expression is equivalent to:
6c13d-2 – 7(c + 3) + d(c + 5)
46. Solve: 9(x – 23 ) = 1 + x
Record and bubble in your answer.
47. Draw a graph that represents the following situation. A woman poured lemonade from a full pitcher at a constant rate. Then for several seconds, she stopped pouring from the pitcher. Then the woman poured the rest of the lemonade from the pitcher at a slower rate than before.
48. Temperature changes throughout the hours of a day. Early in the morning, temperature increases slowly. At noon, the temperature rises sharply. During the afternoon, the temperature stays the same for several hours. As night falls, the temperature decreases slightly. Draw a graph that best represents this situation.
49. Write the algebraic expression that represents
“k squared less than 14”
50. Write the algebraic expression that represents
“m squared more than 2”
51. Simplify: 64121
52. Simplify: 144400