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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.
3. Solve for x: 7 – 2 (x + 8) + 9x = -3
4. Solve for x: + = –
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 =
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
12. Simplify:
13. Multiply:
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:
Math 082 Final - Practice Test #3 cont.
17. a) Write the following in Scientific Notation: 0.00058
b) Convert to decimal notation.
c) Multiply. Give your answer in scientific notation form.
18. Factor completely:
19. Factor completely:
20. Factor completely:
21. Solve by factoring:
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
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:
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Math 082 Final - Practice Test #3 cont.
PRACTICE TEST SOLUTIONS
1. 4 (9x – 3) – (7 – 2x) – 2 + x
36x – 12 – 7 + 2x – 2 + x Distribute the 4 and -1
39x – 21 Combine like terms
2.
3. 7 – 2(x + 8) + 9x = -3
7 – 2x – 16 + 9x = -3 Distribute the -2
-9 + 7x = -3 Combine like terms
7x = 6 Add 9 to both sides of the equation
x = Divide both sides of the equation by 7
4. + = – ;
Find the common denominator. Then multiply each term of the equation by the common denominator.
12 · + 12 · = 12 · – 12 ·
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
x = Divide both sides of the equation by 2.
5. 15 – 6x < 9
-6x < -6 Subtract 15 from both sides
x > 1 Divide both sides by -6 and flip inequality symbol.
6. 50 . V = 5 . 16 . (0.125) Substitute all given values into the equation.
50V = 10 Multiply 5 . 16 . (0.125)
V = Divide both side of the equation by 50.
V = 0.2 Write the fraction in lowest terms
Math 082 Final - Practice Test #3 cont.
7. Graph the line 4x – 2y = 8; Find the x- and y- intercepts.
x / y0 / -4
2 / 0
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.
8. Graph y =
y-intercept: (0,5)
m =
Graph the line using the Slope and Y-intercept:
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 =
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
Math 082 Final - Practice Test #3 cont.
11.
12.
13.
14. 3x + y = 1 6x + 2y = 2 Multiply by 2 3x + 4 = 1
-6x – 4y = -10 -6x – 4y = -10 Add down 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 3(1) + 10y = -7
-5x – 2y = -3 -25x – 10y = -15 Multiply by 5 and Add down 3 + 10y = -7
-22x = -22 Divide both sides of the equation by -22 10y = -10
x = 1 Substitute x = 1 into the original equation to find y. y = -1 Solution: (1, -1)
16.
17. a) 0.00058 = 5.8 x 10-4
b)
c)
18. Use the difference of two square formula,
19. Greatest Common Factor = 2ab
Factor 2ab from each term
20. Factor using AC Method; a = 1, b = -4, c = -45 -
Math 082 Final - Practice Test #3 cont.
21.
Factor using AC Method
set each factor equal to zero
x = 4 x = -3
22. let x=the number, translate the statement into mathematical equation:
,
23. Let x = the cost of one T-shirt
y = the cost of one pair of sweatpants
4x + 4y = 148 -24x -24y = -888 Multiply by -6 4x + 4(22) = 148
6x + 5y = 200 24x +20y = 800 Multiply by 4, and add the two equations 4x + 88 = 148
-4y = -88 Divide both sides of the equation by -4 4x = 60
y = 22 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.
Subtract 4x from both sides of the equation
divide both sides of the equation by 6
25. ,
, since
Then, use the point (2 , 3) in y = 3x + b to solve for b.
3 = (3)(2) + b,
3 = 6 + b, subtract 6 from both sides of the equation
-3 = b Equation: y = 3x –3
26. Graph the lines of the two equations, then determine the intersection point of two lines.
solution: