Algebra 1 Final Exam - Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. One root of the quadratic equation whose related function is graphed lies between which consecutive
integers?
a. 0 and 1
b. 1 and 2
c. 2 and 3
____
2. Which function is quadratic?
a. y = x(3x + 2)
b. y = x3 + 2x2
d. 0 and -1
c. y = 5x – 2
d. x – 5y = 9
3. Jon walks dogs to earn extra money. He charges $5 per hour to walk your dog. He writes the equation y = 5x
to determine how much money he earns from dog walking. What does the independent variable represent in
this situation?
____
4. Which equation corresponds to the graph shown?
a. y = x2
c. y = –x2 – 1
b. y = x2 – 1
d. y = x2 + 1
For questions 5-7, factor if possible.
5. m2 + 13m + 42
6. 4m2 – 25
7. x2 + 16
8. What is the slope of the line through (2, –8) and (4, 1)?
9. A company manufactured 324,000 computers in 2002. The company’s output grows by 5,000 units per year.
Year
Production (thousands)
2002
324
2003
329
2004
334
Write a linear equation to find the company’s production, P, in year, t.
10. Solve 10n – 7(n + 2) > 5n – 12.
Explain each step in your solution.
11. Hector is training to participate in competitive trampoline. In his best jump, he can reach a
maximum height of about 9 meters and can spend about 2 seconds in the air performing tricks.
Choose the graph that best models this scenario.
Determine whether each graph represents a linear function, a quadratic function, an
exponential function, or a linear absolute value function.
12.
13.
Which of the above graphs has an absolute minimum?
14.
15.
Which of the above graphs is decreasing?
d
16. The perimeter of the triangle is 61 inches. If two
sides of the triangle are equal and the third side is
4 inches more than the equal sides, what is the
length of the third side?
17.
A jacket costs $75.00 retail. A warehouse
outlet discounts the price by 20%. If the sales tax
is 6%, find the final price.
18. Which of the following polynomials shows the terms of x2 + 5x3 – 4 – 2x arranged so that the powers of x are
in descending order?
A. x2 + 5x3 – 4 – 2x
B. -4 – 2x + x2 + 5x3
C. 5x3 + x2 – 2x – 4
D. 5x3 – 4 – 2x + x2
19. The sum of two numbers is 54, and their difference is 26. What are the numbers?
20. The width of a box is 1 inch less than its height. The length of the box is 4 inches more than its height. If the
box has a volume of 12 cubic inches and the base has an area of 6 square inches, what are the dimensions of
the box?
21.Simplify
. Assume the denominator is not equal to
zero.
23.Find the next two numbers of the sequence:
7, 11, 8, 12, 9, 13, 10, … .
25.Solve the inequality:
< –3
22. The measures of two sides of a triangle are
given on the triangle below. If the perimeter of
the triangle is 6x2 + 8y, find the measure of the
third side.
24. Evaluate w2 + n(v2 – t) if w = 3, n = 2, v = -3,
and t = -2
26.
Graph
.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
–4
–6
–8
–10
2
4
6
8
10
x
27. Find the volume of the solid and express it as a monomial. Use the formula V = πr2h.
y2
2y 3
28. Arnie hits a golf ball straight up with a speed of 80 feet per second. The acceleration of the ball due to gravity is 16
feet per second. Choose the function that best represents this situation.
a) f(x) = |16x + 80|
b) f(x) = -16x2 + 80x
c) f(x) = -16x + 80
d) -16x + 80
29. Sean is saving money for a new car. He has $1000 already in his savings account and saves $75 each week.
Complete the chart below.
Independent Quantity
Dependent Quantity
Quantity
Units
Expression
w
0
8
2500
2875
30. The pep club at NPHS has decided to order t-shirts to sell at school basketball games. The company gives them a
price of $5 per shirt and set up fee of $20.
a) Write a function to represent the total cost for the t-shirts ____________________________________________
b) Identify the independent and dependent quantities
Independent __________________________
Dependent ________________________________
c) Identify the rate of change and the y-intercept. Explain their meanings in terms of the problem situation.
Rate of change ____________ means ________________________________________________________
y-intercept _______________ means ________________________________________________________
d) The students currently have $250 to spend on t-shirts. Write an inequality for this situation and solve it to find the
greatest number of t-shirts they can purchase.
31.Use substitution to solve the system:
32.
33. A number is divided by four. The result is added to five.
This result is multiplied by three to give 27. What is the
number?
34. Solve and graph the solution.
2x + 7 < 19
35. Simplify
. Assume the denominator is not equal to
zero.
37. Which line shown in the picture is the graph
of x – 2y = 4?
39. A teacher starts the year with $600 for art supplies. He
plans to spend $40 per week on supplies. Write an equation to
show the amount, d, that the teacher has left after w weeks.
36. Find the discounted price:
radio: $45.00 discount: 30%
38. Laurie and Maya sold, at most, $50 worth of
get-well and friendship cards. The friendship
cards, x, were sold for $2 each and the getwell cards, y, were sold for $1.50 each. Which
point represents a reasonable number of cards
sold?
A. (40, -20)
B. (-20, 40)
C. (10, 20)
D. (20, 10)
40. Find (3y – 1)2.
41. Write an equation and describe the slope for the
line that passes through
and
.
42. Which inequality is graphed below?
43. Solve 3(2n – 6) = –4(n – 3)
44. True or False.
The line of x = 5 is a horizontal line.
45. Solve
46. Brian collects baseball cards. His father gave
him 20 cards to start his collection on his
tenth birthday. Each year Brian adds about 15
cards to his collection. About how many
years will it take to fill his collection binder if
it holds 200 cards?
47. What is the equation of the line through (–2, –3)
with an undefined slope?
48. Solve the equation
by either
factoring or using the Quadratic Formula.
49. Steve solved the problem (4a + 6b)2 and got 16a2 + 36b2 as his answer. Is he correct (yes/no)? If not, rework
the problem to find the correct answer.
50. Simplify: (4x + y)(2x2 – xy + 5y2)
52. Simplify 3m2(2m2 – m)
51. A rectangle has an area of 72 square
centimeters. Find the length and width so that
the rectangle has the greatest perimeter.
Assume that the length and width are both
whole numbers.
53. Which of the following is the solution set of
| 3x + 18 | = 12?
A. x = 2, x = 10
B. x = -2, x = 10
C. x = 2, x = -10
54. Identify the x and y intercepts of
3x – 8y = 48
D. x = -2, x = -10
55. Use the graph to find the domain of the relation.
56. The area of the rectangle is
square
units. Find the width of the rectangle.
4 a 2b
57. Bags of sand cost $3 and bags of mulch cost $7. The equation 3x + 7y = 105 represents the number of bags of
sand x and bags of mulch y that can be bought with $105. If no bags of sand are bought, how many bags of
mulch can be bought with $105?
58. Graph the solution set for y < –3 or y < 1.
60. The cost, C, of joining the sports center gym
includes an initial membership fee of $139 plus a
$29 monthly fee. Write an equation in slopeintercept form to find the total cost for m months.
SS
59. Scott bought a pen and received change of
$4.75 in 25 coins, all dimes and quarters. How
many of each kind did he receive?
61. Solve for y. -2y + 10x = 30
63. A rectangle has a length of 25x3 and a width of
5x2. Find the area in square units.
62. Solve. |5x +2| = 17
64. If x – 5 = 12, what is the value of x – 9?
65. Solve 2 + 7y = 44
Solve 2 + 7y =
66. Is (6,25) a solution to the equation y = 3x + 7? Show work to support your answer.
67. The table shows the value of a vending machine over the first five years of use.
0
1
2
3
4
5
Number of Years
2000 1810 1620 1430 1240 1050
Value (dollars)
Write an equation for the relationship between years of use t and value v(t).
68. Tanya solved the (4u – 5v) – (u + v) and got 3u – 4v as her answer. Is she correct (yes/no)? If not, reword the
problem to find the correct answer.
69. A bookstore makes a profit of $3.00 on each book they sell, and $1.00 on each magazine they sell. A book
sells for $7.00 each and a magazine sells for $5.00 each. Each week the store sells x books and y magazines.
The store sold $164 worth of books and magazines and the store’s profit was $52.00.
Write a system of equations that models the situation and solve the problem to find how many books and
magazines are sold. Write your answer in a complete sentence.
70. Solve for y:
Algebra 1 Final Exam Review Answer Section
MULTIPLE CHOICE
1. A
2. A
3. B
4. B
5. (m + 6)(m + 7)
6. (2m + 5)(2m – 5)
7. prime
8.
9.
10.
10n – 7(n + 2) > 5n – 12
10n – 7n – 14 > 5n – 12
3n – 14 > 5n – 12
3n – 14 – 5n > 5n – 12 – 5n
–2n – 14 > –12
–2n – 14 + 14 > –12 + 14
–2n > 2
< 2 ÷ (–2)
n < –1
The solution set is {n| n < –1}.
11.
12.
13.
14.
15.
16.
$63.60
4
23 inches
17.
No; the slopes are 4 and
18.
19.
20.
C
40, 14
2 in. by 1 in. by 6 in.
.
21.
22.
23.
24.
25.
26.
3x2 – x + 14y
14, 11
31
{m | m > 15}
see graph
27.
28.
perpendicular slope =
29.
30.
31.
32.
33.
34.
24 months
42 ft
x = 4, y = 1
6
16
26/60 = 0.43
35.
36. $31.50
37. line p
38. C
39. −3𝑥 + 4𝑦 = 64
Parallel slope = -2
Original inequality
Distributive Property
Combine like terms.
Subtract 5n from each side.
Simplify.
Add 14 to each side.
Simplify.
Divide each side by –2.
Simplify.
40. 9y2 – 6y + 1
41.
; positive slope =
42. y >
x+1
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
3
11/28 = 0.39
x = -3
about 12 years
x = –2
x = 1, x = -5/2
D
8x3 – 2x2y + 19xy2 + 5y3
72 cm, 1 cm
6m4 – 3m3
D
90 different outfits
{–4, –2, –1, 1, 4}
56.
57.
15
units
58.
59.
60.
10 dimes and 15 quarters
C = 29m + 139
61.
; 102.5
62.
63.
64.
65.
66.
67.
68.
HG, HR, HB, HO, TG, TR, TB, TO
125x5
8
(0, 4); maximum
6
v(t) = 2000 – 190t
a. Students should recognize that the v terms were not subtracted correctly. Since –5v – (+ v) = –5v – v = –6v, the right side of the equation should be
3u – 6v.
b. Students should recognize that the pattern for the Square of a Sum was not used correctly. The middle term 2(3a)(5b) was omitted. Since (3a + 5b)2
= (3a)2 + 2(3a)(5b) + (5b)2, the right side of the equation should be 9a2 + 30ab + 25b2.
69. 7x + 5y = 164
3x + 1y = 52
The graph of this system of equations shows the ordered pair that corresponds to weekly sales of $164 and a weekly profit of $52. In order to have a
profit of $52 from magazine and book sales, the store would have to sell 12 books and 16 magazines.
70.
y
mx  s
r
Division by 0 is undefined, so in the original equation m  0, and in the final equation r  0.