1
MATH 082 FINAL - PRACTICE TEST #3
Revised 06/23/09
Give all answers in simplest form.
1. Simplify 4 (9x – 3) – (7 – 2x) – 2 + x
2. Simplify. Write all answers without negative or zero exponents.
 12 x 4 y 7
21x 5 y 6
3. Solve for x: 7 – 2 (x + 8) + 9x = -3
1
3
1
5
4. Solve for x: 3x + 4 = 6x – 2
5. Solve the inequality and graph the solution 15 – 6x < 9
6. Solve for V if PV = nRT. Given P = 50, n = 5, R = 16, and T = 0.125
7. Graph the line 4x – 2y = 8
8. Graph the line y = 
1
x5
2
9. Find the slope of the line passing through the points (-1,5) and (2,-7)
10. Write the equation of the line that passes through the points (-2, 5) and (3 , -15).
11. Multiply  4 x(3x 2  5 x  2)
12. Simplify:
(6 x  4) 2
13. Multiply:
(2 x  3 y )(3 x  2 y )
In problems 14 & 15, solve the system of equations.
14. 3x + y = 1
-6x -4y = -10
15. 3x + 10y = -7
-5x – 2y = -3
16. Simplify:
(2 x 3 y 5 ) 5
2
Math 082 Final - Practice Test #3 cont.
17.
a)
Write the following in Scientific Notation: 0.00058
b)
Convert 2.673  10 5 to decimal notation.
c)
Multiply. Give your answer in scientific notation form. (3.7  10 5 )  (7.2  10 2 )
18. Factor completely: x 2  36
19. Factor completely: 4a 3b  6a 2 b  10ab
20. Factor completely: x 2  4 x  45
21. Solve by factoring: x 2  x  12  0
22. Translate into an equation using one variable and solve: the difference of five times a
number and three is nine added to the product of two and the number.
23. I bought 4 T-shirts and 4 pairs of sweatpants from Target for a total of $148. My friend
bought 6 T-shirts and 5 pairs of sweatpants from Target for a total of $200. Set up a
system of equations that models the situation and solve the system to find how much each
T-shirt and pair of sweatpants cost.
24. Solve for y :
4 x  6 y  18
25. The slope of a line is 3 and one point on a line is (2, 3). Find the equation of the line
and write the answer in slope-intercept form.
26. Solve by graphing:
1
y  x2
2
1
y x
2
3
Math 082 Final - Practice Test #3 cont.
PRACTICE TEST SOLUTIONS
1. 4 (9x – 3) – (7 – 2x) – 2 + x
36x – 12 – 7 + 2x – 2 + x
39x – 21
2.
Distribute the 4 and -1
Combine like terms
 12 x 4 y 7  4 x 9

21x 5 y 6
7 y 13
3. 7 – 2(x + 8) + 9x = -3
7 – 2x – 16 + 9x = -3
-9 + 7x = -3
7x = 6
6
x=
7
Distribute the -2
Combine like terms
Add 9 to both sides of the equation
Divide both sides of the equation by 7
1
3
1
5
4. 3x + 4 = 6x – 2 ;
Find the common denominator. Then multiply each term of the equation by the common denominator.
1
3
1
5
12 · 3x + 12 · 4 = 12 · 6x – 12 · 2
4x + 9 = 2x – 30
Subtract a 2x from both sides of the equation.
2x + 9 = -30
Subtract a 9 from both sides of the equation.
2x = -39
-39
x=
Divide both sides of the equation by 2.
2
5. 15 – 6x < 9
-6x < -6
x>1
6.
50 . V = 5 . 16 . (0.125)
50V = 10
10
V=
50
V = 0.2
Subtract 15 from both sides
Divide both sides by -6 and flip inequality symbol.
Substitute all given values into the equation.
Multiply 5 . 16 . (0.125)
Divide both side of the equation by 50.
Write the fraction in lowest terms
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Math 082 Final - Practice Test #3 cont.
7. Graph the line 4x – 2y = 8; Find the x- and y- intercepts.
x
0
2
y
-4
0
(2,0)
(0,-4)
To find ordered pairs, choose a value for x or y,
then substitute this value into the equation to solve
for the missing value of the variable.
1
x5
2
y-intercept: (0,5)
1 fall
m = 
2 run
8. Graph y = 
10
8
6
4
2
Graph the line using the Slope and Y-intercept:
-10 -8 -6 -4 -2
2
4
-2
The slope of the line is -½ and the y-intercept is 5.
Plot the y-intercept (0, 5). Then use the slope to find
other points on the line. Starting at (0, 5) fall 1 and run
4 (Move down 1 and right 2). Repeat this (Move down
1 and right 2) to find additional points on the line.
9. m =
-4
-6
-8
-10
y 2  y1  7  5  12


 4
3
x 2  x1 2  (1)
10. First, calculate the slope.
m=
=
=
= -4
Then, use the point (-2 , 5) in y = -4x + b to solve for b.
y = mx + b
5 = -4(-2) + b
5 = 8 + b
-8
-8
-3 = b
Equation: y = -4x – 3
6
8 10
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Math 082 Final - Practice Test #3 cont.
11.
 4 x(3x 2  5 x  2)  12 x 3  20 x 2  8x
12.
(6 x  4) 2  (6 x  4)(6 x  4)  36 x 2  24 x  24 x  16  36 x 2  48x  16
13.
(2 x  3 y)(3x  2 y)  6 x 2  4 xy  9 xy  6 y 2  6 x 2  5xy  6 y 2
14.
3x + y = 1
-6x – 4y = -10
6x + 2y = 2 Multiply by 2
-6x – 4y = -10 Add down
3x + 4 = 1
3x
= -3
-2y = -8 Divide by -2 on both sides of the equation
x = -1
y = 4 Substitute y = 4 into the original equation to find x.
Solution: (-1, 4)
15. 3x + 10y = -7
3x + 10y = -7
-5x – 2y = -3 -25x – 10y = -15 Multiply by 5 and Add down
3(1) + 10y = -7
3 + 10y = -7
-22x = -22 Divide both sides of the equation by -22
x = 1 Substitute x = 1 into the original equation to find y.
10y = -10
y = -1
Solution: (1, -1)
16. (2 x 3 y 5 ) 5  32 x15 y 25
17.
18.
a)
0.00058 = 5.8 x 10-4
b)
2.673  10 5  267300
c)
(3.7  10 5 )  (7.2  10 2 )  26.64  10 7  (2.664  101 )  10 7  2.664  108
Use the difference of two square formula,
x 2  36  ( x  6)( x  6)
19. Greatest Common Factor = 2ab
4a 3 b  6a 2 b  10ab
2ab(2a 2  3a  5)
20.
x 2  4 x  45
 x 2  9 x  5 x  45
 x( x  9)  5( x  9)
 ( x  9)( x  5)
Factor 2ab from each term
Factor x  4 x  45 using AC Method; a = 1, b = -4, c = -45 2
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Math 082 Final - Practice Test #3 cont.
21.
x 2  x  12  0
( x  4)( x  3)  0
x  4  0, x  3  0
x=4
x = -3
Factor using AC Method
set each factor equal to zero
22. let x=the number, translate the statement into mathematical equation:
5x  3  2 x  9 ,
3x  12
x4
23. Let x = the cost of one T-shirt
y = the cost of one pair of sweatpants
4x + 4y = 148
6x + 5y = 200
-24x -24y = -888
24x +20y = 800
-4y = -88
y = 22
Multiply by -6
4x + 4(22) = 148
Multiply by 4, and add the two equations
4x + 88 = 148
Divide both sides of the equation by -4
4x = 60
Substitute y = 22 into the original equation to find x
x =15
The cost of one T-shirt = x = $15
The cost of one pair of sweatpants = y = $22
24.
25.
4 x  6 y  18
6 y  4 x  18
2
y   x3
3
divide both sides of the equation by 6
y  mx  b ,
y  3x  b , since m  3
Then, use the point (2 , 3) in y = 3x + b to solve for b.
3
3
26.
Subtract 4x from both sides of the equation
= (3)(2) + b,
= 6 + b,
subtract 6 from both sides of the equation
-3 = b
Equation: y = 3x –3
Graph the lines of the two equations, then determine the intersection point of two lines.
solution:
x  2, y  1