MATH 082 FINAL - PRACTICE TEST #1
Revised 06/23/09
Give all answers in simplest form.
1. Simplify. Write all answers without negative or zero exponents.
2. Simplify the expression by combining like terms:
3. Solve for x: 18 – 4(2x – 3) + 5x = 41
2
1
1
4
4. Solve for x: 3 x + 4 = 6 x – 3
5. Solve the inequality and graph the solution: -4x + 3 < 11
6. Solve for A if L = A + (M – 1)D. Given L = 29, M = 6, D = 5.
7. Solve for :
3
8. Graph the line whose slope is 4 and
is
.
9. Find the slope of the line passing through the points (1, -2) and (-3, 10)
10. The slope of a line is 2 and one point on a line is (- 1, 3). Find the equation of the line
and write the answer in slope-intercept form.
11. Write the equation of the line that passes through the points (-3, 11) and (1, 3).
In problems 12 & 13, solve the system of equations.
12. 2x – y = 5
5x + 3y = 18
13. y = 3x + 2
4x – y = 0
14. Simplify (2xy3) 4
251
Math 082 Final - Practice Test #1 cont.
15. a).
Write 350 in Scientific Notation
b).
Convert
to decimal notation.
c).
Multiply. Give your answer in scientific notation form.
16. Multiply:
17. Multiply and simplify: (4x – 3y)(2x + 5y)
18. Simplify: (3x  4) 2
19. Factor completely: 2x3y– 6x2y+ 2xy
20. Factor completely: x2 + 4x – 21
21. Factor completely: x2 – 49
22. Solve for x by factoring: x 2  3 x  28  0
23. Translate into an equation using one variable and solve: the sum of 5 times a number and nine is
three less than the product of two and the number.
24. Solve by graphing:
y  2x  4
3x  2 y  6
25. I bought 3 notebooks and 5 folders for my classes and spent $25. My friend, Alex, bought
8 folders and 5 notebooks and spent $41. Set up a system of equations that models the
situation and solve the system to find the cost of each notebook and folder.
252
PRACTICE TEST SOLUTIONS
1.
2.
=
=
Distribute the -2
combine like terms
3. 18 – 4(2x - 3) + 5x = 41
18 – 8x + 12 + 5x = 41
-3x + 30 = 41
-3x = 11
11
x=3
2
1 1
4
4. 3 x + 4 = 6 x – 3 ;
Distribute the -4
Combine like terms
Subtract 30 from both sides of the equation
Divide both sides of the equation by -3
Find the common denominator. Then multiply the common denominator by each term of the equation.
2
1
12 · 3x + 12 · 4
8x + 3 = 2x – 16
6x + 3 = -16
6x = -19
-19
x=
6
1
-4
= 12 · 6x + 12 · 3
Subtract 2x from both sides of the equation
Subtract 3 from both sides
Divide both sides of the equation by 6
5.
-4x + 3 < 11
-4x < 8
x > -2
6.
L = A + (M – 1)D L = 29, M = 6, D = 5
Subtract a 3 from both sides
Divide both sides by -4 and flip the inequality symbol
29 = A + (6 – 1) . 5 Substitute the given values
29 = A + 25
Subtract (6 – 1), then multiply by 5 (PEMDAS, Use correct order of operations,)
A=4
Subtract 25 from both sides of the equation
7.
Subtract
from both sides
divide both sides by 3
253
Math 082 Final - Practice Test #1 cont.
8.
y
3
x3
4
10
8
Graph the line by Plotting Points:
6
4
x
y
0
-3
4
0
2
3
y  (0)  3  0  3  3
4
-10 -8 -6 -4 -2
2
4
6
8 10
-2
-4
3
y  (4)  3  3  3  0
4
-6
-8
-10
Graph the line using the Slope and Y-intercept:
The slope of the line is ¾ and the y-intercept is –3. Plot the y-intercept (0, -3). Then use the slope to
find other points on the line. Starting at (0, -3) rise 3 and run 4 (Move up 3 and right 4). Repeat this
(Move up 3 and right 4) to find additional points on the line.
9. slope =
10 – (-2)
10 + 2
12
-3 – 1 = -3 – 1 = -4 = -3
10. y  mx  b ,
y  2 x  b , since m  2
Then, use the point (-1 , 3) in y = 2x + b to solve for b.
3 = (2)(-1) + b,
3 = - 2 + b,
Add 2 to both sides of the equation
5 = b
Equation: y = 2x + 5
11. First, calculate the slope.
m=
=
=
= -2
Then, use the point (1 , 3) in y = -2x + b to solve for b.
y = mx + b
12. 2x – y = 5
5x + 3y = 18
Solution: (3,1)
3 = (-2)(1) + b
6x – 3y = 15
5x + 3y = 18
11x
= 33
x =3
3 = -2 + b
+2 +2
5 = b
Equation: y = -2x + 5
Multiply by 3
2(3) – y = 5
Add down
6–y=5
Divide by 11 on both sides
– y = -1
Substitute x = 3 into original equation to find y
y=1
254
Math 082 Final - Practice Test #1 cont.
4x – (3x + 2) = 0 Substitute 3x + 2 for y
4x – 3x – 2 = 0 Distribute the –
x – 2 = 0 Combine like terms
x = 2 Add 2 to both sides
13. y = 3x + 2
4x – y = 0
Solution: (2,8)
Substitute x = 2 into original equation to find x
14. (2xy3) 4 =16x4y12
15.
a) 3 5 0 = 3.5 x 102
b)
c)
16.
17. (4x – 3y)(2x + 5y)= 8x2 + 20xy– 6xy –15y2 = 8x2 +14xy – 15y2
18. (3x  4) 2  (3x  4)(3x  4)  9 x 2  12 x  12 x  16  9 x 2  24 x  16
19. Greatest Common Factor = 2xy
2x3y– 6x2y+ 2xy
=2xy(x2 – 3x + 1)
20.
c = -21
x2 + 4x – 21
= x2 – 3x + 7x – 21
= x(x – 3) + 7(x – 3)
= (x – 3)(x + 7)
21. Factor a Difference of Two Squares:
x2 – 49 = (x)2 – (7)2
= (x + 7)(x – 7)
22. x2 – 3x – 28 = 0
Factor using the AC test (A = 1, B=-3, C=-28)
( x  4)( x  7)  0
Set each factor equal to 0
x – 7 = 0 x + 4 = 0 Solve each equation
x=7
x = -4
23. Let x  the number, translate the statement into a mathematical equation:
5x  9  2 x  3
3x  12
y = 3(2)+2
y = 6+2
y=8
subtract 2x and 9 from both sides
255
Math 082 Final - Practice Test #1 cont.
24. Graph the lines the equations y  2 x  4 and 3x  2 y  6 , then find the intersection point
between two lines.
solution:
25. Let x = the cost of one notebook
y = the cost of one folder
3x + 5y = 25
5x + 8y = 41
15x + 25y = 125 Multiply by 5
-15x – 24y = -123 Multiply by -3
y=2
Substitute into original equation
The cost of one notebook = x = $5 and
The cost of one folder = y = $2
256
3x +5(2) = 25
3x + 10 = 25
3x = 15
x=5