A formula sheet is attached at the beginning of the packet. Problems
109, 129-130, 138-139, and 142 are extra credit and the formulas
needed to solve these problems are included.
Algebra 1 – Final Review Packet
What You Must Memorize For Final
1) Quadratic Formula:
x=
–b ±
b2 – 4ac
2a
2) Standard Form: ax2 + bx + c = 0
3) Perfect Squares from 0 to 169: √0 , √1 , √4 , √16 … ,
4) Discriminant:
b2 - 4ac
5) Complete the Square: x2
5x + ___
5
2
25
2
4
6) Direct Variation: y=kx
7) Inverse Variation:
8) Vertex:
9) Pythagorean Theorem: a2 + b2 = c2
10) X and Y Intercepts: To find y-intercept, set x’s equal to zero. To
find, x-intercepts, set y equal to zero and solve for x.
2
Algebra 1 – Final Review Packet
*** show your work wherever applicable for full credit ***
Chapter 5
Match each of the following polynomials with its special term name.
1.
4x2 + 27x – 8
_____
a)
trinomial
2.
5x3y10
_____
b)
binomial
3.
3x + 5x3
_____
c)
monomial
Add or subtract the following polynomials.
4.
(8t2 – 10t + 2) + (8t + 13)
_________________________
5.
(x2 + 5x – 1) – (7x2 + 2)
_________________________
6.
(x4 + 7x3 + 7) – (2x4 – 4x3 + 1)
_________________________
7.
(3n3 + n2 – n – 4) + (5n3 – 4n2 + 11)
_________________________
Write in decimal form (standard notation).
8.
8 × 104
10.
9 × 10-3
11.
7.24 × 10-6
Write in scientific notation.
12.
400,000
14.
0.00056
13.
15.
0.0000814
9.
9.82 × 105
5412
3
Algebra 1 – Final Review Packet
Simplify the following. Leave all answers with positive exponents.
22.
(2w2x4)3
16.
x2 • x7
17.
(a4)12
18.
(3b)3
23.
28x 2
y −9
24.
x14
x6
25.
⎛x⎞
⎜⎜ ⎟⎟
⎝y⎠
8
19.
9770
20.
1
5−3
26.
7d4 d6
•
df 5 f 5
21.
–6x8y–8
27.
3t4 v3
21t2 v6
Multiply or Divide. Express your answers in scientific notation.
28.
(2.3 × 102)(4.5 × 10–7)
4.8 × 102
29.
1.2 × 105
4
Algebra 1 – Final Review Packet
Multiply.
30.
3x(4x – 9)
_________________________
31.
4x2(x + 6)
_________________________
32.
2x2(15x3 – 10)
_________________________
Multiply the following. Use your choice of methods, but show your work!!
33.
(x + 9)(x – 6)
(x – 6)(x – 8)
36.
34.
(x + 3)(4x + 5)
37.
(7x + 3)(7x – 2)
35.
(3x – 1)(8x + 1)
38.
(3x3 – 2x2 + 6)(x + 5)
5
Algebra 1 – Final Review Packet
Chapter 6
Factor out the largest possible monomial.
39.
5x2 – 15
40.
8a + 10b – 16
41.
3c4 – 6c2 – 15c
Factor completely (remember – they are not always “ready” to go…).
42.
x2 + 9x + 14
43.
y2 – 15y + 54
44.
t2 + 8t + 15
45.
m2 + 23m – 24
46.
x2 – x – 12
Factor the following differences of squares completely.
48.
x2 – 121
49.
100a2 – 144
6
47.
x2 + xy – 42y2
50.
5m2 – 20
Algebra 1 – Final Review Packet
Factor the following perfect square trinomials completely.
51.
x2 + 18x + 81
52.
25m2 + 30m + 9
53.
4y3 – 16y2 + 16y
Factor completely (remember – they are not always “ready” to go…).
54.
3y2 – 20y + 12
55.
2x2 – 13x – 45
56.
18n3 + 33n2 – 6n
Solve for the given variable.
57.
(a – 5)(a + 2) = 0
58.
x(x – 3) = 0
7
59.
y2 + 23y – 24 = 0
Algebra 1 – Final Review Packet
Chapter 10
Multiply or Divide.
2
3
60.
•
3
16
62.
5x
x
•
15
2
Add or Subtract.
3
7
64.
+
4
4
66.
61.
3
7
÷
4
8
63.
5x
x
÷
15
2
65.
(5x – 7) – (8x – 12)
67.
Simplify Completely.
12x4y6
68.
8x7y2
69.
8
1
5
–
7
3
(4x + 3)
(12x + 4)
–
5
5
3x + 9
3x
Algebra 1 – Final Review Packet
70.
3a + 9b
12a2
72.
14a2 − 14b2
21a − 21b
Multiply.
5
4x
74.
•
2x
17
76.
4x
4x + 4
•
2x + 2
8x
9
71.
6y2 + 3y
3y2 + 6y
73.
b2 − 10b + 21
b2 − 11b + 28
75.
2x2 5
•
2x
x
77.
m2 − 4
4m2
•
5m
m+2
Algebra 1 – Final Review Packet
Divide.
2x
12x
78.
÷
7
21
80.
7
26
÷
x+4
x+4
Add or Subtract.
4x 6x
82.
+
7
7
84.
2w2 + w
9
– 3
w
w3
79.
10x3
2x3y
÷
6x2
5x
81.
4x − 6
6x − 9
÷
25
5
83.
5x + 3 3x + 7
+
x+3
x+3
85.
(4x + 2) (7x − 6)
−
(3x + 1) (3x + 1)
10
Algebra 1 – Final Review Packet
3x2 + 2x − 5
2x2 − x + 6
86.
+
5x + 1
5x + 1
87.
1
5
–
3x
x
88.
5m
3
−
m−1
m(m − 1)
89.
2u
v
− 2 2
uv3
u v
90.
3a
−1
+
a+2
a
91.
1
x+4
− 2
x−4
x − x – 12
93.
15
7
−
b −9
2b − 6
92.
3
3
+ 2
x–2
x + 4x – 12
11
2
Algebra 1 – Final Review Packet
Chapter 11
94.
Estimate which two integers each square root is between:
a)
95.
96.
73 is between ____ and ____
13 is between ____ and ____
Simplify (show work):
a)
180
b)
252
c)
x2y3
d)
196b5
b)
700
7
Simplify to find (show work):
81 •
a)
c)
3
25
7 +8
7
d)
5
3
e)
97.
b)
5
24 − 4
5 (5 +
f)
6
5
)
Find the missing side length for each triangle (show your steps):
a)
b)
13
u
2
12
v
5
12
Algebra 1 – Final Review Packet
98.
99.
Solve (show work):
4x + 7 = 15
a)
b)
x + 5 + 8 = 19
To hang a math poster in his office, Mr. Zito leaned a 10 foot ladder against the wall, placing
the bottom of the ladder on the floor 3 feet away from the wall. How high up on the wall was
the ladder? (Show work. A labeled picture is also required)
Chapter 13
100.
Write the quadratic formula.
Solve the following using the QUADRATIC FORMULA. Complete all blanks.
101.
3x2 + 4 = 8x
_____________________ (standard form)
a = _____
b = _____
substitution
c = _____
solution(s) for x:
13
Algebra 1 – Final Review Packet
102.
6x + 5 = -2x2
_____________________ (standard form)
a = _____
b = _____
substitution
c = _____
solution(s) for x:
103.
Write the formula for the discriminant
For questions 5 – 7, the blanks provided are for the following information:
a)
b)
c)
104.
105.
106.
Substitute values for a, b, & c into the discriminant formula.
Find the discriminant.
Tell how many solutions the quadratic has.
3x2 + 4 = 3x
4x + 2 = 3x2
x2 = 8x – 16
a)
d = __________________ (substitution)
b)
d = __________________ (simplified)
c)
_____________________ (# of solutions)
a)
d = __________________ (substitution)
b)
d = __________________ (simplified)
c)
_____________________ (# of solutions)
a)
d = __________________ (substitution)
b)
d = __________________ (simplified)
c)
_____________________ (# of solutions)
14
Algebra 1 – Final Review Packet
107.
108.
Solve each of the following using the zero-product property. SHOW WORK.
a)
(x + 10)(x + 24) = 0
b)
(2x – 6)(5x + 2) = 0
c)
x(x + 158) = 0
d)
5x(4x – 16)(x + 9) = 0
Solve each of the following equations by factoring: SHOW WORK.
a)
109.
b)
x2 + 4x – 21 = 0
b)
u2 – 26u __________
Complete the square for the following:
a)
110.
x2 – 8x + 16 = 0
x2 + 20x __________
Solve using any method you want… show work!!
b)
x2 + 10x = –4
a)
x2 – 49 = 0
15
Algebra 1 – Final Review Packet
Chapter 12
Identify the domain and range for each. Tell if the relation is a function.
111.
h: {(3, 1), (2, 4), (3, 5), (4, 8)}
112.
j: {(2, 7), (3, 6), (4, 5), (5, 4), (6, 3)}
a)
domain: ____________________
a)
domain: ____________________
b)
range:
b)
range:
c)
function / not a function
c)
function / not a function
113.
____________________
k: {(1, 2), (2, 3), (3, 2), (4, 1)}
114.
____________________
m: {(4, 5), (4, 2), (4, 1), (4, 3), (1, 6)}
a)
domain: ____________________
a)
domain: ____________________
b)
range:
b)
range:
c)
function / not a function
c)
function / not a function
____________________
____________________
Find the indicated outputs for the following functions.
115.
f(x) = –4x2 – 2
116.
f(1) =
g(–2) =
f(–3) =
g(–1) =
f(0) =
g(4) =
16
g(x) = –| x – 3 | + 6
Algebra 1 – Final Review Packet
Determine which of the following graphs represent functions.
117.
118.
119.
y
y
x
function / not a function
y
x
function / not a function
function / not a function
State the domain and range for the following graphs.
120.
121.
y
y
x
x
122.
y
x
x
Domain: _________
Domain: _________
Domain: _________
Range: __________
Range: __________
Range: __________
Graph the following functions.
123.
f(x) = | x |
124.
y
g(x) = | x – 3 | – 4
125.
y
h(x) = –
2
x+2
3
y
x
x
17
x
Algebra 1 – Final Review Packet
Graph each of the following quadratic functions, finding all indicated information.
126. f(x) = x2
b
Vertex
–
2a
y-intercept
127.
–
f(x) = x2 – 5
b
2a
Vertex
y-intercept
128.
–
x-intercept(s)
x-intercept(s)
f(x) = x2 – 4x – 12
b
2a
y-intercept
Vertex
x-intercept(s)
18
Algebra 1 – Final Review Packet
129.
Find an equation of variation where y varies directly as x for each pair of values given.
a)
y = 3 when x = 24
b)
y = 50 when x = 25
130.
Find an equation of variation where y varies inversely as x for each pair of values given.
2
a)
y = when x = 27
b)
y = 4 when x = 8
3
19
Algebra 1 – Final Review Packet
132. Write the equation in Standard
Form and then identify a, b, and c.
131. Find the Vertex:
f(x) = 4x2 + 8x + 1
3x2 = -2x + 1
133. Solve using the quadratic formula: 134. Find the x and y intercepts:
3x2 -7x +4 = 0
f(x) = x2 – 3x – 10
135.
136. What is the Domain and the
Range of a relation defined by:
{(5,2), (5,3), (6,2), (3,1)}
y
x
Function? Yes or No
Domain: _________________
Domain: ________________
Range: __________________
Range: _________________
137. Find the indicated outputs for the
function:
f(x) = 3x2 – 1 for f(-2)
138. Find the equation of variation
where y varies directly as x, and y = 14
and x = 2.
20
Algebra 1 – Final Review Packet
140.
139. Find the equation of variation
where y varies inversely with x, and y =
14 and x = 2.
141. ( x + 3) 2 = 16
x −1 = 4
142. What number should be added to
complete the square?
X2 + 6x + __
143.
4
25
144.
25
3
145.
12 − 2 =
146. (2 5 ) 2
147. Find the length of side a.
9
a
3
21