Math 7A
CHAPTER 1 TEST
FALL 2013
Using a pencil, copy the problem from the test form to the blue book.
Complete ALL work for this test in your blue book; only the work in the blue book will be graded. You may write on this
test form, but nothing written on this test form will be graded
You DO NOT need to copy the directions, pictures, words, word problems, or problems with *.
Show all required work for the problem in a neat and organized way as presented in class and in the book.
Skip a line after completing each problem.
Begin the following problem beneath the completed problem.
(There should only be one column of problems with work per page)
Once you reach the bottom of the page, continue working on the next page. (You may write on the back)
You may write on the test form, but only the work in the blue book will be graded.
Any extra work should be completed next to the problem in an organized format; not in the margin., not between the lines
of the problem.
Complete, organized, and correct work using the methods taught in class including the correct use of symbols is required
in order to receive full credit. Partial or no credit will be given when work is incomplete. Each problem is worth 5 points,
unless otherwise indicated.
SHOW ALL WORK. DO NOT ROUND ANSWERS UNLESS INSTRUCTED TO DO SO. Express answers in simplest
form.
Solve the equation.
4
x 19
+ =
1)
15 2 10
30
4
x
19
+
=
30
15 2
10
8 + 15x = 57
15x = 49
x=
49
15
49
15
2) (x + 9)(x - 1) = (x + 1) 2
x2 + 8x - 9 = x 2 + 2x + 1
8x - 9 = 2x + 1
6x = 10
x=
10
6
x=
5
3
5
3
3)
3
2
4
+
=
x + 5 2x + 1 x - 2
x + 5 2x + 1 x - 2
3
2
4
+
=
x + 5 2x + 1 x - 2
x + 5 2x + 1
x-2
3 2x + 1 x - 2 + 2 x + 5 x - 2 = 4 x + 5 2x + 1
3 2x 2 - 3x - 2 + 2 x 2 + 3x - 10 = 4 2x 2 + 11x + 5
6x 2 - 9x - 6 + 2x 2 + 6x - 20 = 8x 2 + 44x + 20
8x 2 - 3x - 26 = 8x 2 + 44x + 20
- 3x - 26 = 44x + 20
- 46 = 47x
-
46
=x
47
-
46
47
Find the real solutions of the equation by factoring.
OR
4) x3 + 9x 2 - x - 9 = 0
x3 + 9x 2 - x - 9 = 0
x2 x + 9 - x + 9 = 0
x2 x + 9 - x + 9 = 0
x + 9 x2 - 1 = 0
x + 9 x2 - 1 = 0
x+9=0
x2 - 1 = 0
x+ 9 x- 1 x+1 =0
x=- 9
x2 = 1
x+9=0
x+1=0
x-1=0
x=±1
x=- 9
x=- 1
x=1
- 9, ± 1
- 9, ± 1
Solve the equation by completing the square. Find all real or imaginary solutions.
5) 5x 2 - 2x - 4 = 0
5x 2 - 2x = 4
x2 -
2
4
x=
5
5
x2 -
2
1 4
1
x+
= +
5
25 5 25
x-
1 2 21
=
5
25
x-
1
=±
5
x=
1
±
5
x=
1 ±
1 ±
5
21
5
21
5
5
21
21
Solve the equation. Find all real or imaginary solutions.
6) 4x 2 + 1 = 3x
4x 2 - 3x + 1 = 0
x=
x=
x=
- -3 ±
3±
3±
- 3 2- 4 4 1
24
9 - 16
8
8
-7
x=
3±i
8
7
x=
3
7
±
i
8
8
3
7
±
i
8
8
Solve the equation.
7) 3 - 2|x 2 - 4x - 4| = - 13
- 2|x2 - 4x - 4| = - 16
|x 2 - 4x - 4| = 8
x2 - 4x - 4 = 8
x2 - 4x - 4 = - 8
x2 - 4x - 12 = 0
x2 - 4x + 4 = 0
x-6 x+2 =0
x-22 =0
x-6=0
x+2=0
x-2=0
x=6
x=- 2
x=2
6, ± 2
Write the expression in the standard form a + bi.
9 + 5i
8)
7 - 8i
9 + 5i 7 + 8i
·
7 - 8i 7 + 8i
63 + 72i + 35i + 40i 2
49 + 64
63 + 107i - 40
113
23 + 107i
113
23
107
+
i
113 113
9)
10
8
6
i +i +i +1
-1+1+ -1 +1
0
Find the real solutions of the equation.
10) x 2 - 3x + 81 - 6 = x
x 2 - 3x + 81 = x + 6
x2 - 3x + 81 = x 2 + 12x + 36
- 3x + 81 = 12x + 36
45 = 15x
3=x
3
11)
x - 36 +
x=2
x - 36 = 2 -
x
x - 36 = 4 - 4 x + x
4 x = 40
x = 10
x = 100
12)
x + 10 -
x-2=2
x + 10 = 2 +
x-2
x + 10 = 4 + 4 x - 2 + x - 2
10 = 2 + 4 x - 2
8= 4 x- 2
2=
x-2
4=x- 2
6=x
6
13)
1
(x - 2) 2
(x - 2) 2
-
2
=3
x-2
1
(x - 2) 2
-
2
= 3(x - 2) 2
x-2
1 - 2(x - 2) = 3(x - 2)2
5 - 2x = 3 x 2 - 4x + 4
5 - 2x = 3x2 - 12x + 12
0 = 3x2 - 10x + 7
0 = 3x - 7 x - 1
3x - 7= 0
x - 1= 0
3x = 7
x=1
x=
7
3
7
,1
3
Solve the inequality. Express your answer using interval notation and graph the solution.
14) |7x - 8| - 1 > -5
|7x - 8| > - 4
- ,
15) 6 +
3 9x + 18
5
2
3 9x + 18
5
2
9
3
9x + 18
2
3
9x + 18
2
5
5
3
-5
9x + 18
2
5
- 10
9x + 18
10
- 28
9x
-
-
28
9
x
-8
-
8
9
28
8
,9
9
16) 5 - 7x > 12
5 - 7x > 12
5 - 7x < - 12
- 7x > 7
- 7x < - 17
x<- 1
- ,- 1 U
x>
17
,
7
17
7