Algebra 1 Spring Final Study Guide

Algebra 1 Spring Final Study Guide
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. A community is building a square park with sides
that measure 120 meters. To separate the picnic
area from the play area, the park is split by a
diagonal line from opposite corners. Determine the
approximate length of the diagonal line that splits
the square. If necessary, round your answer to the
nearest meter. (Hint: Pythagoras could solve this.)
4.Solve the equation
. Check your answer.
a. z = 26
b. z = 676
c. z = 6
d. z =
5. Solve the equation. Check your answer.
120 m
Picnic area
Play area
120 m
a. 28,800 meters
b. 170 meters
c. 240 meters
d. 120 meters
2. Find the perimeter of a triangle whose side lengths
are 7 cm, cm, and cm. Give the answer
as a radical expression in simplest form.
a. ( ) cm
b. ( ) cm
c. ( ) cm
d. cm
3. Simplify the quotient
a.
b.
c.
d.
a. –2
b. 6
c. 4
d. 5
6. Find the excluded values of the rational expression
.
a. The excluded values are –4 and –1.
b. The excluded values are 3 and –5.
c. The excluded values are –5 and 4.
d. The excluded values are 4 and 1.
7. Simplify the rational expression .
a.
b.
c.
d.
8. Multiply. Simplify your answer.
a.
b.
c.
d.
.

9. Subtract and simplify. Find the excluded values.
a.
b.
c.
d.
;
; and
; , and
; and
10. Ting can mow a lawn in 4 hours. Her boss, Renald,
can mow the same lawn in 3 hours. How long will
it take them to mow the lawn if they work together
a. hours
b. hours
c. 1 hour
d. hours
11. A chemist has 600 milliliters of a solution that is
half acid. She needs a solution that is 70% acid.
How many milliliters of acid she should add
a. 300 mL
b. 400 mL
c. 500 mL
d. 600 mL
12. A bullet train travels 30 miles per hour faster than a
passenger train, and it takes the bullet train 3 hours
less time to travel 400 miles. How long does it
takes the passenger train to make the trip.
a. 4 hours
b. 6 hours
c. 8 hours
d. 10 hours
13. Solve .
a. a = –29
b. a = 29
c. a = 15
d. a = –15
14. Solve .
a.
b.
c.
d.
15. Solve . Check your answer.
a. x = 6
b. x = 8
c. x = 5
d. x = 7
16. Solve .
a.
b.
c.
d.
17. Solve .
a. = 4
b. = –11
c. = –1
d. = 5
18. Solve the proportion .
a. x = 36
b. x = 26
c. x = 0.03
d. x = 25
19.Solve the inequality
a. p ≤ –8
–10
–8
b. p ≥ –8
–10
c. p ≤ 8
–10
d. p ≥ 8
–10
–8
–8
–8
–6
–6
–6
–6
–4
–4
–4
–4
–2
–2
–2
–2
≥ 4 and graph the solutions.
0 2 4 6 8 10
0 2 4 6 8 10
0 2 4 6 8 10
0 2 4 6 8 10
20. Mrs. Williams is deciding between two field trips
for her class. The Science Center charges $135 plus
$3 per student. The Dino Discovery Museum
simply charges $6 per student. For how many
students will the Science Center charge less than
the Dino Discovery Museum
a. 132 or more students
b. 132 or fewer students
c. More than 45 students
d. Fewer than 45 students

21. Solve and graph the solutions of the compound
inequality .
a. AND
b. AND
c. AND
d. AND
22. Solve the inequality.
0 1 2 3 4 5
0 1 2 3 4 5
0 1 2 3 4 5
0 1 2 3 4 5
a. The solution set is .
b. The solution set is .
c. The solution set is OR .
d. The solution set is all real numbers.
23. Give the domain and range of the relation.
6
4
2
y
2 4 6 x
a. D: 0 ≤ x ≤ 7; R: 1 ≤ y ≤ 7
b. D: 1 ≤ x ≤ 6; R: 1 ≤ y ≤ 7
c. D: 2 ≤ x ≤ 6; R: 4 ≤ y ≤ 7
d. D: 1 ≤ x ≤ 7; R: 1 ≤ y ≤ 6
24. For , find when x = –1.
a. –2
b. 6
c. –4
d. 2
25. Find the x- and y-intercepts of .
a. x-intercept: −11, y-intercept: 4
b. x-intercept: −11, y-intercept: 3
c. x-intercept: –8, y-intercept: 3
d. x-intercept: –8, y-intercept: 4
26.Find the slope of the line that contains and
.
− 11
a.
3
c. − 3 Hint:
11
∆y
− 3
b.
5
d. − 5 y =
3
∆x
d. x = 2y + 3 2
27. Tell whether the slope of the line is positive,
negative, zero, or undefined.
y
5
4
3
2
1
–5 –4 –3 –2 –1
–1
1 2 3 4 5 x
–2
–3
–4
–5
a. negative c. undefined
b. positive d. zero
28. Tell whether the relation is a direct variation.
Explain.
x –10 –9 1
y 20 18 –2
a. This is a direct variation, because it can be
written as , where k = .
b. This is not a direct variation, because it cannot
be written in the form .
c. This is a direct variation, because it can be
written as , where .
d. This is a direct variation, because it can be
written as , where k = –2.
29. Write the equation that describes the line with slope
= 2 and y-intercept = 3 in slope-intercept form.
2
a. 2x + y = 3 2
b. y = 3 x + 2 2
c. y = 2x + 3 2

30. Write the equation that describes the line in slopeintercept
form.
slope = 4, point (3, –2) is on the line
a. y = 4x + 14
b. y = 4x – 14
c. y = 4x + 10
d. y = 4x – 2
31. Write an equation in point-slope form for the line
that has a slope of 6 and contains the point (–8, –7).
a. x – 8 = 6(y – 7)
b. y + 8 = 6(x + 7)
c. y – 7 = 6(x – 8)
d. y + 7 = 6(x + 8)
32. Write an equation in slope-intercept form for the
line parallel to y = 5x – 2 that passes through the
point (8, –2).
a. y = − 1 5 x – 2
b. y = − 1 5 x – 2 5
c. y = 5x + 32
d. y = 5x – 42
33. Tell whether the ordered pair (5, –3) is a solution of
the system .
a. no
b. yes
34. Solve by substitution. Express your
answer as an ordered pair.
a. ( 3, −2)
b. (− 8 3 , –3)
c. (− 4 3 , 1)
d. (−2, 3)
35. Solve by elimination. Express your
answer as an ordered pair.
a. (–2, –3)
b. (–2, 0)
c. (0, –2)
d. (–8, –6)
36. Solve by elimination. Express your
answer as an ordered pair.
a. (3, 4)
b. (4, 3)
c. (3, 2)
d. ( 4 7 , 8 5 )
37. An airplane travels 900 miles from Houston to
Miami in 6 hours against the wind. On its return
trip, with the wind, it takes only 5 hours. Find the
rate of the airplane with no wind. Find the rate of
the wind.
a. The airplane flies at 155 mi/h with no wind.
The rate of the wind is 135 mi/h.
b. The airplane flies at 165 mi/h with no wind.
The rate of the wind is 135 mi/h.
c. The airplane flies at 155 mi/h with no wind.
The rate of the wind is 15 mi/h.
d. The airplane flies at 165 mi/h with no wind.
The rate of the wind is 15 mi/h.
38. The sum of the digits of a two-digit number is 12.
When the digits are reversed, the new number is 18
less than the original number. Find the original
number. Check your answer.
a. The original number is 75.
b. The original number is 84.
c. The original number is 57.
d. The original number is 93.
39. The planet Mars has an average distance from the
sun of about 141,600,000 miles. Write this number
in scientific notation.
a. 14.16 × 10
b. 1.416 × 10 7
c. 1.416 × 10 8
d. 0.1416 × 10
40. Simplify .
a.
b.
c.
d.

41. Simplify .
a.
−
b.
−
c. –
d.
−
42. Simplify .
a.
b.
c.
d.
43. Simplify the expression .
a. 29
b. 9
c. 13
d. 10
44. Multiply.
a.
b.
c.
d.
45. Multiply.
a.
b.
c.
d.
46. Factor by grouping.
a.
b.
c.
d.
47. Factor .
a.
b.
c.
d.
48. Determine whether is a difference of two
squares. If so, factor it. If not, explain why.
a.
b.
c.
d. Not a difference of squares because –49n 4 is
not a perfect square.
49. Factor completely.
a.
b.
c.
d.
50. Solve the quadratic equation by
factoring.
a. –4 and 2
b. 4 and 2
c. –4 and –2
d. 4 and –2
51. Solve 64x 2 – 121 = 0 by using square roots.
a. ± 11
8
b. ± 64
121
c. No solution
d. ± 8 11
52. Solve by completing the square.
a. The solution is –5.
b. There is no solution.
c. The solutions are –1 and 5.
d. The solutions are –1 and –5.
53. Solve by using the Quadratic Formula.
a. x = 9 or x = −1
b. x = 1 or x = −9
c. x = 54 or x = −46
d. x = 18 or x = −2

54.Find the number of solutions of the equation
by using the discriminant.
a. There is one solution.
b. Cannot determine the number of solutions. The
discriminant can only be used for a quadratic
equation, and
is not a quadratic
equation.
c. There are no real solutions.
d. There are two solutions.
55. Find the domain of the square-root function
a. –8
b. − 9 8
c. −1
d. –8
.
56.Simplify .
a. c.
b. d.
57.Which graph represents a function
a.
y
c.
y
5
5
4
4
3
3
2
2
1
1
–5 –4 –3 –2 –1
–1
1 2 3 4 5 x
–2
–3
–4
–5
–5 –4 –3 –2 –1
–1
1 2 3 4 5 x
–2
–3
–4
–5
b.
y
d.
y
5
5
4
4
3
3
2
2
1
1
–5 –4 –3 –2 –1
–1
1 2 3 4 5 x
–2
–3
–4
–5
–5 –4 –3 –2 –1
–1
1 2 3 4 5 x
–2
–3
–4
–5

58. 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 110 different rug designs.
50000
a. $31,000
b. $0
c. $38,000
d. $35,000
Total Sales ($)
40000
30000
20000
10000
20 40 60 80 100 120 140 160
Number of Designs
Short Answer
59. Solve the inequality and graph the solutions. Then write the solutions as a compound inequality.
60. Write the equation in slope-intercept 63. Graph the system of linear inequalities
form. Then graph the line described by the
equation.
. Give two ordered pairs that are
61. Solve the system by graphing.
62. Graph the solutions of the linear inequality
.
66. Subtract.
solutions and two that are not solutions.
64. Graph . Find the axis of symmetry
and the vertex.
65. Graph the linear equation . Then tell
whether it represents a function.
67. Simplify the expression . All variables represent nonnegative numbers.
68. Solve and graph the compound inequality.
OR
69. Write the inequality shown by the graph.
–7 –6 –5 –4 –3 –2 –1
0 1 2 3 4 5 6 7 m
70. Tell whether the relationship is an inverse variation. Explain.
x y
2 409
3 240
4 194

Algebra 1 Spring Final Study Guide
Answer Section
MULTIPLE CHOICE
1. B
2. B
3. C
4. B
5. D
6. D
7. B
8. A
9. B
10. D
11. B
12. C
13. D
14. C
15. B
16. A
17. C
18. D
19. A
20. C
21. C
22. D
23. B
24. B
25. D
26. D
27. C
28. D
29. C
30. B
31. D
32. D
33. B
34. D
35. C
36. B
37. D
38. A
39. C
40. B
41. A
42. B
43. B
44. C
45. D
46. A
47. D
48. B
49. B
50. A
51. A
52. D
53. A
54. C
55. A
56. A
57. D
58. D
SHORT ANSWER
59.
–27 –24 –21 –18 –15 –12
–9
–6
–3
0 3 6 9 12 15 18 21 24 27 30
68. OR
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1
0 1 2 3 4 5 6 7 8 9 10 s
69. m ≥ –3
70. The product xy is not constant, so the relationship is not an inverse variation.
Note these answers
are out of
order. I was just
trying to conserve
paper ☺.

60.
5
4
y
10
8
6
4
2
y
3
2
1
–5 –4 –3 –2 –1
–1
1 2 3 4 5 x
–2
–3
61.
–8 –6 –4 –2 2 4 6 8 x
–2
–4
–6
–8
–10
y
10
8
6
4
2
–10 –8 –6 –4 –2
–2
2 4 6 8 10 x
–4
–6
–8
–10
62.
y
10
8
6
4
2
–10 –8 –6 –4 –2
–2
–4
2 4 6 8 10 x
64.
–4
–5
y
12
10
8
6
4
2
(1.5, 1.75)
–8 –6 –4 –2 2 4 6 8 10 12 x
–2
–4
The axis of symmetry is . The vertex is .
65.
y
5
4
3
2
1
–5 –4 –3 –2 –1
–1
1 2 3 4 5 x
–2
–3
–4
–5
Yes, represents a function.
–6
–8
–10
63. (0, 0) and ( 4, 5) are solutions.
(2, 2) and (10, 1) are not solutions.
66.
67.