MAT 1033
REVIEW FOR EXAM #3
This review has been designed to give you more practice before the exam. It is not meant to be
the only thing that you study. Be sure to look at your notes, homework, your book, etc.
Sections 4.1 and 4.3
1. Solve by graphing:
a) x + y = 2
b) 2x + 3y = 6
2
y   x 1
3
x–y=4
y
c) x = 6
y =–2
y
6
y
6
6
x
-6
6
x
-6
-6
2.
Solve by addition:
a)
6x – 6y = -5
10x – 2y = 1
3.
a)
Solve by substitution:
5x + 2y = 15
x=6–y
6
x
-6
6
-6
b)
6x – 4y = 3
3x – 2y = 9
b) 3x + 4y = 14
2x + y = 1
-6
c)
3
5
x + y = 11
4
2
1
3
x - y = -1
16
4
c) –6x + 3y = 3
y = 2x + 1
4.
A science museum charges $10 regular admission and $5 student admission. Last
Saturday, 750 tickets were sold for a total of $5400. How many of each type were sold?
5.
One number is three times a second number, and twice the sum of the numbers is168.
Find the numbers.
6.
A pharmacist needs 500 milliliters of a 20% phenobarbital solution but has only 5% and
25% phenobarbital solutions available. Find how many milliliters of each she should mix
to get the desired solution.
Sections 5.1 – 5.7

 
1. Add: a) 3 x 2  2  x 2  5 x  3

Divide: a)
 

2. Multiply: a) 2a  52
3.

b) 3 x 2  2x  x 2  5 x  3
Subtract:
b) 3x  2 x2  4x  3
32a3b2c  24a2b5  40a 4b3
2 2
8a b

5(x2 + 1) + 3x(x2 + 1)
6.
x2 + xy – 3x – 3y
7.
12a2b – 2ac – 42ab + 7c
8.
x2 + 8x + 12
c) (4mn – 7)(4mn + 7)

b) x3  5x  14  x  3
Factor each of the following:
4.
21a5b4c – 3a7b3c – 6a3b6c3
5.

Check:

9.
x2 – x – 12
Check:
10.
2x2 + 3x – 5
Check:
11.
2x2 – 15x + 18
Check:
12.
2x2 – 7x – 30
Check:
13.
3x2 + 7x + 1
Check:
14.
6x2 + 16xy + 8y2
Check:
15.
25x2 – 10x + 1
Check:
16.
49x2 – 100y2
Check:
17.
27a3 – 125
18.
8x3 + 1
Solve each equation.
19.
x2 – 9 = 0
21.
3x2 – 10x = 8
23.
– 18 = 2x2 – 15x
20.
10x2 + 7x + 1 = 0
22.
4x2 + 12 = – 14x
ANSWER KEY – MAT 1033 Review for Exam #3
Sections 4.1 and 4.3
1.
a) (3, -1)
b) No Solution, lines are parallel
c) (6, -2)
2.
a) (1/3, 7/6) b) No Solution, lines are parallel
c) (8, 2)
3.
a) (1, 5)
4.
$330 regular, $420 students
5.
21 and 63
b) (-2,5)
c) {(x, y) | y= 2x +1}
6. 125 ml of 5%; 375 ml of 25%
Sections 5.1 – 5.7
1.
a) 4 x 2  5 x  5
b) 2 x 2  7 x  3
2.
a) 4a2  20a  25
b) 3x3  14x2  17x  6
3.
a) 4ac  3b3  5a2b
b) x 2  3x  4 
4.
3a3b3c(7a2b – a4 – 2b3c2)
5.
(x2 + 1)(5 + 3x)
6.
(x + y)(x – 3)
7.
(6ab – c)(2a – 7)
8.
(x + 6)(x + 2)
9.
(x – 4)(x + 3)
10.
(2x + 5)(x – 1)
11.
(2x – 3)(x – 6)
12.
(2x + 5)(x – 6)
13.
not factorable
14.
2(3x + 2y)(x + 2y)
15. (5x – 1)2
16.
(7x + 10y)(7x – 10y)
17. (3a – 5)(9a2 + 15a + 25)
18.
(2x + 1)(2x2 – 2x + 1)
19. x = 3, – 3
20.
1 1
x=  ,
5 2
21. x = 
2
,4
3
c) 16m2n2  49
2
x3
22. x = 
3
, –2
2
23. x = 6,
3
2