Download Algebra I Final Exam Review Packet

Algebra I Final Exam Review Packet.
1. Which graph shows the best trend line for the following data.
a.
c.
Violin Competition
60
54
54
48
48
42
42
36
36
Score
Score
Violin Competition
60
30
30
24
24
18
18
12
12
6
6
2
4
6
8
10
12
14
16
18
20
2
4
Practice (weeks)
b.
d.
54
54
48
48
42
42
36
36
30
24
18
18
12
12
6
6
8
10
12
14
Practice (weeks)
10
12
14
16
18
20
16
18
20
30
24
6
8
Violin Competition
60
Score
Score
Violin Competition
4
6
Practice (weeks)
60
2
16
18
20
2
4
6
8
10
12
14
Practice (weeks)
2. Gloria makes and sells handmade greeting cards. The scatter plot shows the number of cards she made over a
10-hour period. Find the equation of a trend line and use it to predict the number of cards Gloria can make in
12 hours.
50
45
40
35
Cards
____
30
25
20
15
10
5
1
2
3
4
5
6
7
Hours
8
9 10 11
Write an equation for each translation of
.
3. 6 units down
4. 6 units left
Graph each system. Tell whether the system has no solution, one solution, or infinitely many solutions.
5. y = 5x – 4
y = 5x – 5
Solve the system of equations using graphing.
6. y = x + 6
y = –2x – 3
Solve the system of equations using substitution.
7. 3x + 2y = 7
y = –3x + 11
8. The sum of two numbers is 82. Their difference is 24. Write a system of equations that describes this
situation. Solve by elimination to find the two numbers.
9. Sharon has some one-dollar bills and some five-dollar bills. She has 14 bills. The value of the bills is $30.
Solve a system of equations using elimination to find how many of each kind of bill she has.
Solve the system using elimination.
10. 5x + 8y = –29
7x – 2y = –67
11. 2x – 2y = –8
x + 2y = –1
12. An ice skating arena charges an admission fee for each child plus a rental fee for each pair of ice skates. John
paid the admission fees for his six nephews and rented five pairs of ice skates. He was charged $32.00.
Juanita paid the admission fees for her seven grandchildren and rented five pairs of ice skates. She was
charged $35.25. What is the admission fee? What is the rental fee for a pair of skates?
Graph the inequality.
13.
Write the linear inequality shown in the graph.
14.
y
4
2
–4
–2
O
2
4
x
–2
–4
Solve the system of linear inequalities by graphing.
15.
Simplify the expression.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
Write the number in scientific notation.
28. 0.0805
Write the number in standard notation.
29.
Simplify the expression. Write the answer using scientific notation.
30.
31.
32. Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms.
2 – 11x2 – 8x + 6x2
33. Write the polynomial in standard form.
4g – g3 + 3g2 – 2
Find the degree of the monomial.
34. 7m6n5
35.Find the perimeter of the figure.
3x + 2
6x
5x
not to scale
Simplify.
36. (–7x – 5x4 + 5) – (–7x4 – 5 – 9x)
37. 3p4(4p4 + 7p3 + 4p + 1)
38.
39. (2k + 3)(2k2 – 4k – 3)
40. (2x – 6)2
41. (4p – 6)(4p + 6)
Factor the polynomial.
42. 40w11 + 16w6
43. d2 + 10d + 9
44.
45. 16j2 + 24j + 9
46. r2 – 49
47. 6g3 + 8g2 – 15g – 20
Solve the equation using the zero-product property.
48.
49.
50.
Simplify the radical expression.
51.
52.
53.
54.
55. (6 –
11 )(6 +
11 )
56.
57.
58.
Solve the equation. Check your solution.
59.
60.
61.
Find the length of the missing side. If necessary, round to the nearest tenth.
62.
5
c
14
63.
20
10
b
Determine whether the given lengths can be sides of a right triangle.
64. 18 m, 24 m, 30 m
65. In how many ways can 12 basketball players be listed in a program?
66. A yogurt shop offers 6 different flavors of frozen yogurt and 12 different toppings. How many choices are
possible for a single serving of frozen yogurt with one topping?
67. You own 6 hats and are taking 4 on vacation. In how many ways can you choose 4 hats from the 6?
68. 9 students volunteer for a committee. How many different 7-person committees can be chosen?
69. Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function.
70. Graph
. Label the axis of symmetry and vertex.
Solve the equation using square roots.
71. 7
+ 6 = 13
72.
Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
73.
74.
75. Find the area of the shaded region. Show all your work.
Algebra I Final Exam Review Packet
Answer Section
MULTIPLE CHOICE
1. C
SHORT ANSWER
2. Answers may vary. Sample given:
y = 3x; 36 cards
3. y = | x | – 6
4. y = | x + 6 |
5. no solutions
6. (–3, 3)
7. (5, –4)
8. x + y = 82
x – y = 24
53 and 29
9. 4 five-dollar bills, 10 one-dollar bills
10. (–9, 2)
11. (–3, 1)
12. admission fee: $3.25
skate rental fee: $2.50
13.
y
4
2
–4
–2
O
–2
–4
14.
2
4
x
15.
y
4
2
–4
–2
O
2
4
–2
–4
16. 1
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
31.
33.
34.
35.
36.
37.
90,000
6.3  1017
6.25  1018
–5x2 – 8x + 2; quadratic trinomial
–g3 + 3g2 + 4g – 2
11
14x + 2
2x4 + 2x + 10
12p8 + 21p7 + 12p5 + 3p4
x
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
4k3 – 2k2 – 18k – 9
4x2 – 24x + 36
16p2 – 36
8w6(5w5 + 2)
(d + 9)(d + 1)
2(5x – 2)(2x + 3)
(4j + 3)2
(r – 7)(r + 7)
(2g2 – 5)(3g + 4)
x = –1 or x = 1
1
49. n = 0 or n =
10
50.
51.
52.
53.
54.
55. 25
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
144
116
5
14.9
17.3
yes
479,001,600
72
15
36
; vertex:
70.
y
6
4
2
–6
–4
–2
2
4
6
x
–2
–4
–6
Axis of symmetry:
Vertex:
71.
72. no real number solutions
73. 9, 14
74. 1.82, –0.22
ESSAY
75.
[4]
(2x + 2)(3x – 4) – (x – 3)(x – 6)
[3]
[2]
[1]
one minor computational error
error in formula with correct computation
correct answer without work shown
=
=
=
(6x2 –8x + 6x – 8) – (x2 –6x – 3x + 18)
(6x2 – 2x – 8) – (x2 – 9x + 18)
5x2 + 7x – 26