Honors Geometry Summer Work
Name: _________________________________
Please complete each of the following questions. You may use a calculator but you should show all steps to problem
solving. You will turn this in to your teacher on the first day of your class.
Please seek tutoring if topics covered in this packet are unfamiliar or you do not remember the concepts. It is
expected that ALL students entering Honors Geometry have had exposure to this material. We will not be covering
this material in our class, but you will be tested on these concepts.
1. Determine which answer choice below is equivalent to the given expression by completing the square.
A.
B.
C.
D.
2. Caesar measured the depth of the stage in the theater at his school. He discovered that his measurement had a margin of
error of 0.5 inch. Which of the following could be the measured depth of the stage?
A. 365.2 inches
B. 365 inches
C. 365.23 inches
D. 365.232 inches
3. Find the value of f(5) for the function
4. Solve for x.
5. Simplify:
A.
B.
C.
D.
-
6. What is the domain of the function graphed?
7. Helen went to the grocery store to buy potatoes. The store charges $1.19 for each pound of potatoes. On the way out of
the store, Helen picked up a gallon of ice cream at a cost of $4.33. If Helen spent $11.47 at the store, how many pounds of
potatoes did she purchase? Assume tax is included in the given price.
8. What type of function is graphed?
A. even function
B. not a function
C. neither even nor odd
D. odd function
9. Find the minimum or maximum of the function f(x) = 3x2 - 7
10. Add the following.
A.
B.
C.
D.
11. Solve the following.
A.
B.
C.
D.
12. Simplify the following expression. (2x + 1)(x - 5)
13. Simplify the following expression.
A.
B.
C.
D.
14. The Tennis Club decided to buy T-shirts for its members. Action Sports Apparel quoted the following prices for the Tshirts.
Number of T-Shirts Total Cost (dollar)
14
170
19
225
24
280
Which equation best describes the relationship between the total cost and the number of T-shirts, t?
A. f(t) = 16t
B. f(t) = 154t
C. f(t) = 16 + 11t
D. f(t) = 11 + 11t
15. Solve for x in the following equation.
16. Mr. Robertson was looking at the test grades of two of his students, shown in the table below.
Test 1 Test 2 Test 3 Test 4
Jimmy
76
84
83
81
Brian 72
76
64
64
Which statement below best describes the students' grades?
A. Jimmy's median test score is greater than Brian's median test score by 13 points.
B. Jimmy's mean test score is less than Brian's mean test score by 12 points.
C. Jimmy's mean test score is greater than Brian's mean test score by 12 points.
D. Jimmy's median test score is less than Brian's median test score by 11 points.
17. Rewrite the following equation as a function of x.
A.
B.
C.
D.
18. What is the domain of the function:
19. Hannah is an architect, and she drew a blueprint of a house she is designing. The table below shows the length of the
walls of the house on the blueprint along with their actual lengths.
8
11
14
17
Blueprint Length (cm) 5
Actual Length (ft)
What scale did Hannah use for her blueprint?
7.5
20. Find the zeros of the function by completing the square.
21. Add the following
22. Which expression is the factored equivalent of x2 - 7x + 12?
A. (x - 3)(x - 4)
B. (x - 1)(x - 3)
C. (x + 4)(x + 3)
D. (x + 3)(x - 4)
12
16.5
21
25.5
23. Determine which answer choice below is equivalent to the expression by completing the square.
A.
B.
C.
D.
24. Autumn had a math homework assignment each day last week. Each assignment had a different number of problems
and took her a different amount of time to complete, as shown by the table below. If Autumn spent the same amount of
time on each problem, how long did it take her to complete one math problem?
Time to
Number of
Complete
Problems
(min)
5
10
10
20
15
30
20
40
25
50
25. Melissa rode her bike for 1.5 hours and traveled 16.4 miles. Nick rode his bike for 2.5 hours and traveled 18.4 miles.
Determine who was riding at a faster speed, and by how many miles per hour (round to the nearest hundredth).
26. Add the following.
27. Factor the following polynomial completely. 0.6x2 - 6.6x + 10.8
28. The functions f(x) and g(x) are defined below. Determine where f(x) = g(x) by graphing.
29. Determine which answer choice below is equivalent to the given expression by completing the square.
A.
B.
C.
D.
30. Multiply the following.
A.
B.
C.
D.
31. Solve the following equation for x. x2 + 6x = 7
32. What is the factored form of the following expression? 9x2 - 12x + 4
33. What is the domain of the function graphed?
34. The Riddell High Football Booster Club sells bags of popcorn at the home games to raise money for their annual steak
cook-out. For each game they purchase enough supplies to make 450 bags of popcorn. The popcorn costs $18, the bags
cost $7, and the butter for the popcorn costs $8. They sell the bags of popcorn for $2.75 each, regardless of whether or not
the customer has asked for butter. The profit for the popcorn sales is graphed below.
Over which of the following intervals is the Booster club making a profit to go towards the steak cook-out?
A.
B.
C.
D.
35. Find the extreme value of the following quadratic function by completing the square.
36. Simplify: (2x + 7)(7x2 - 8x + 6)
37. What is the factored form of the following expression? x2 - 10x + 25
38. Multiply the following.
39. Solve the following.
40. The functions f(x) and g(x) are defined below. By graphing, determine where f(x) = g(x).
41. Given the following formula, solve for r.
42. Solve for x.
43. Factor the polynomial x2 + 8x + 15
44. Solve for x in the following equation.
45. What is the domain of the function?
46. Find the solution to the system of equations below.
47. Two orders are placed at a T-shirt design store. In the first order, two long-sleeved shirts and four short-sleeved shirts
cost $80. In the second order, five long-sleeved shirts and eight short-sleeved shirts cost $176. Which system of linear
equations below can be used to determine the price of each type of shirt? Let x represent the cost of a long-sleeved shirt,
and let y represent the cost of a short-sleeved shirt.
2x + 4y = 176
A. 5x + 8y = 80
2x + 5y = 80
B. 4x + 8y = 176
2x + 4y = 80
C. 5x + 8y = 176
D.
7x + 12y = 256
48. What type of function is graphed below?
A. odd function
B. even function
C. neither even nor odd
D. not a function
49. Which expression is the factored equivalent of 3x2 + 17x + 10?
A. (x + 2)(3x - 5)
B. (3x + 2)(x + 5)
C. (x + 10)(3x - 2)
D. (3x + 5)(x + 2)
50. Cathie is making a dress with a sash. The sash needs to be 72.2 inches long, but Cathie's measuring tape is only in
centimeters. Which of the following shows the number of centimeters, with the correct number of significant digits, that
Cathie needs to measure in order for the sash to be 72.2 inches long? (1 inch = 2.54 centimeters)
51. At what point does the line given by the following equation cross the x-axis?
52. Simplify the following expression. (2x - 10)2
53. Solve for x.
54. Solve for x in the following equation. x(x - 6) = 72
55. Determine the answer choice below is equivalent to the expression by completing the square.
A.
B.
C.
D.
56. A reptile park technician counted the lizards at the park. The officials at the park expect the number of lizards to
increase every three months. The approximate number of lizards at the park, t years after the count was taken, is shown by
the following expression.
Which statement below best describes the coefficient, 1,300?
A. the rate at which the number of lizards is increasing
B. the increase in the number of lizards at the park in a three-month period
C. the number of times the number of lizards has compounded since it was counted
D. the initial lizard count
57. Determine which answer choice below is equivalent to the given expression by completing the square.
A.
B.
C.
D.
58. At what value of x does the minimum or maximum occur for the function below? f(x) = -5(x - 1)2 - 3
59. Which of the following relations is NOT a function?
A.
B.
C.
D.
(9, 4), (-1, 2), (1, 1), (-8, 2)
(1, 4), (-1, 2), (1, 1), (-8, 2)
(-8, 4), (1, 3), (-1, 1), (9, 2)
(-1, 4), (1, 2), (9, 1), (-8, 5)
60. Complete the square.
61. Find the zeros of the following function.
62. What is the y-intercept of the equation below?
63. Find the value of h(26) for the function below.
64. Which expression is the factored equivalent of x2 + 5x - 24?
65. What type of number will result from the following sum?
A. Cannot be determined
B. Rational number
C. Whole number
D. Irrational number
66. Solve for x.
67. Jim is opening an interest-accruing checking account which compounds interest monthly. The amount in the account,
in dollars, after t years, is shown by the following expression.
Which statement below best describes the base, 1.07?
A. the number of times the account has compounded since it was opened
B. the amount of the yearly earnings
C. the rate at which the account is increasing
D. the amount of the initial deposit
68. The momentum, p, of an object is represented by the formula p = mv, where m is the mass of the object and v is the
velocity of the object. If p has units of kilograms·meters per second and m has units of kilograms, what must be the units
of v?
A. meters per second squared
B. meters per second
C. meters
D. seconds
69. What is the domain of the function?
70. If the graph of f(x) = x is shifted up 7 units, what would be the equation of the new graph?
A. g(x) = x + 7
B. g(x) = x - 7
C. g(x) = 7 - x
D. g(x) = 7x
71. On the last day of the month, Sandra has to pay her daughter's preschool tuition and late pick-up fees. Tutition is
$610.60 per month and each fee for a child who is picked up late is $6.10. If Sandra wrote a check for $647.20, how many
days did she pick up her daughter late from preschool?
72. Dew Water Industries makes honeydew melon flavored water that it sells locally. The company's daily profit is
modeled in the table below where x is the number of cases sold per day.
x
Profit
0
-288
8
0
16
224
24
384
32
480
40
512
48
480
56
384
64
224
Based on the table, over which of the following intervals is the company making a profit?
(8 , 72)
A.
B.
C.
D.
[0 , 8)
[8 , 72]
[72 , 88]
73. Due to winter, the Maxwells want to drain their swimming pool. The function below represents the amount of water in
the pool after t minutes of draining.
What is the domain of V(t)?
A. all real numbers between and including 0 and 3,000
B. all real numbers
C. all positive integers less than or equal to 3,000
D. all real numbers less than 3,000
74. Factor the following polynomial completely. -0.8x2 - 4x + 19.2
77. Simplify the following expression.(8x2 - 9x + 2) - (2x2 - 3x + 6)
78. Subtract the following.
79. Given the following formula, solve for w.
80. Solve for y.
81. A water-storage tank is being emptied for cleaning. The amount of water left in the tank, in liters, is represented by the
function below, where x represents the time elapsed, in minutes.
What is the average rate of change over the interval [2, 4]?
82. Identify the x-intercepts of the function f(x) = x2 + 11x + 24
83. What type of number will result from the following sum?
84. Solve for x in the following equation.
85. In one day, 72 people take group tennis lessons at Cherry Hills Country Club. The club provides 12 lessons each day.
If an average of 84 tennis balls are used in each lesson, determine the average number of tennis balls used per person per
lesson (round to the nearest whole number if necessary).
86. Solve for x.
87. Find the zeros of the following function.
88. If the graph of f(x) = 6x is shifted 7 units to the right, then what would be the equation of the new graph?
A. g(x) = 6x - 7
B. g(x) = 6x + 7
C. g(x) = 6(x - 7)
D. g(x) = 6(x + 7)
89. Which expression is the factored equivalent of 4x2 + 19x + 12?
90. The table below shows the cost of a cell phone plan for different hours. Which equation would be the line of best fit
for this data?
Number of Hours, x
1
2
3
4
5
Cost in Dollars, C $38.80 $47.60 $61.40 $71.20 $81.00
A. C = x2 - 7x + 41.8
B. C = 11.8x + 24
C. C = 13.8x + 22
D. C = 55.6 - 2x2
91. Simplify the following expression. (8p + 4q)(-2p + 11q)
92. Solve for x in the following equation.
93. Jason opened a savings account where the bank pays an annual interest rate of 6%, compounded quarterly. The
function represents the amount of money in his savings account after x years.
A(x) = $2,000(1.015)4x
What does the y-intercept represent?
the amount of money Jason deposits into his savings account quarterly
A.
B.
C.
D.
the initial amount of money Jason deposited into his savings account
the amount of money the bank pays to his savings account quarterly
the time it takes for the initial deposit to increase by 100%
94. Simplify:
95. If the graph of f(x) = 6x is shifted 9 units down, then what would be the equation of the new graph?
A. g(x) = 6(x + 9)
B. g(x) = 6x - 9
C. g(x) = 6x + 9
D. g(x) = 6(x - 9)
96. Myles opened a money market account two years ago with a $3,500 deposit and made no other withdrawals or
deposits. If the account does not meet the minimum account balance of $5,000 each month, a monthly fee is withdrawn
from the account. The equation below shows the balance of the account, where t is equal to the number of months the
account has been open.
M(t) = 3,500 - 50t
Myles creates a graph to show the account balance since the account was opened. Which of the following describes the
end behavior of the graph?
As t approaches positive infinity, M(t) approaches negative infinity.
A.
B.
C.
D.
As t approaches positive infinity, M(t) approaches zero.
As t approaches positive infinity, M(t) approaches positive infinity.
As t approaches positive infinity, M(t) remains constant.