1
MATH 082 FINAL - PRACTICE TEST #4
Revised 12/03/07
DO NOT WRITE ON THIS PAPER. RETURN IT TO THE OFFICE WHEN YOU ARE READY TO
TAKE THE OFFICIAL TEST.
Give all answers in simplest form.
-5
2
1. Perform the indicated operation and simplify: 8 + 3
2. Simplify: 3(x + 2) – 8 – 5(x – 1)
3. Simplify. Write all answers without negative or zero exponents.
-10x5y5
2x3y6
4. Solve for x: 3(7x + 2) = 5(4x + 1) + 17
11
1
8
19
5. Solve for x: 3 x – 6 = 3 x – 6
6. Solve the inequality 5x > 3x + 8
7. Solve for S if D = ST. Given D = 42 and T = 6
8. In the equation, A = KW – 1, solve for W.
9. Graph the line x – 3y = 8
5
10. Graph the line y = -8 x – 2
11. Find the slope of the line passing through the points (6, -2) and (-7, -5)
12. Calculate the slope of the following graph.
10
8
6
4
2
-10 -8 -6 -4 -2
2
4
6
8 10
-2
-4
-6
-8
-10
13. Write the equation of the line that passes through the points (1, -4) and (-2 , 11).
2
Math 082 Final - Practice Test #4 cont
In problems 14 & 15, solve the system of equations.
14. 2x – y = 1
-2x + 3y = 5
15. y = 3x + 8
3x – 2y = -10
16. Simplify. Write all answers without negative or zero exponents. (3x-5y2)(-4x3y5)
17. Simplify. Write all answers without negative or zero exponents (x-5)2
18. Simplify the following radical:
24
19. Write the following in Scientific Notation: 421
20. Multiply and simplify (x – 2)(3x + 7)
21. Multiply and simplify (x + 5)(x2 – 7x + 4)
22. Factor completely: 2x3 + x2 – 3x
23. Factor completely: 6x2 – 19x + 10
24. Factor completely: 4x2 – 36
25. Solve by factoring: x2 – 18x = 0
26. Solve by factoring: x2 + 15 = 8x
27. Use the Pythagorean Theorem to find the missing side of the right triangle. Round your answer to
two decimal places if necessary.
12
4
28. The tennis team bought 25 dinners for the Athletic Banquet. A steak dinner costs $15 and a
shrimp dinner costs $22. If the total cost was $459, how many of each kind was ordered? Set
up a system of equations that models the situation and solve the system to find how many of
each dinner were ordered.
3
Math 082 Final - Practice Test #4 cont.
PRACTICE TEST SOLUTIONS
-5
2
-15
16
1
1. 8 + 3 = 24 + 24 = 24
2. 3(x + 2) – 8 – 5(x – 1)
3x + 6 – 8 – 5x + 5
3x – 5x + 6 – 8 + 5
-2x + 3
Distribute the 3 and -5
Combine like terms
-5
-10x5y5 -10x5y5 -5x5-3y5-6 -5x2y-1 -5x2
3.
=
=
= 1 = y
1
2x3y6
2x3y6
1
4. 3(7x + 2) = 5(4x + 1) + 17
21x + 6 = 20x + 5 + 17
21x + 6 = 20x + 22
-6
-6
Subtract 6 from both sides
21x
= 20x + 16
-20x
= -20x
Subtract 20x from both sides
x = 16
5.
11x 1
8x
19
3 – 6 = 3 – 6
Find the common denominator. Then multiply the common denominator by each term of the equation.
11
1
6· 3x – 6·6
8
19
= 6 · 3x – 6 · 6
22x – 1 = 16x – 19
Add 1 to both sides
22x
Subtract 16x from both sides
= 16x -18
6x = -18
Divide by 6 on both sides
x = -3
6.
5x
5x – 3x
2x
x
> 3x + 8
>8
> 8
>4
Subtract 3x from both sides
Divide by 2 on both sides
7. D = ST, D = 42, T = 6
42  S (6)
Substitute given values
42 = 6S
Divide by 6 on both sides
7=S
4
Math 082 Final - Practice Test #4 cont
A = KW – 1
+1
+1
A + 1 = KW
A+1
KW
K = K
A+1
W =
K
8.
Add one to both sides
Divide both sides by K
9. Graph x – 3y = 8
Take arbitrary values of x and get the
corresponding values of y.
x
-1
2
5
-1–3y = 8
- 3y = 9
y = -3
2-3y=8
- 3y = 6
y=-2
5 – 3y = 8
-3y = 3
y = -1
10
8
6
y
-3
4
2
-2
-10 -8 -6 -4 -2
2
4
-2
-1
-4
-6
-8
-10
10.
10
5
y = - 8x – 2
8
6
y = mx + b
4
2
5
Slope, m = - 8
y-intercept, b = -2
-10 -8 -6 -4 -2
2
-2
-4
-6
-8
-10
11. Points (6,-2) and (-7, -5)
(y2 – y1)
-5 – (-2)
-5 + 2
-3
3
Slope, m = (x – x ) = -7 – 6 = -7 – 6 = -13 = 13
2
1
4
6
8 10
6
8 10
5
Math 082 Final - Practice Test #4 cont
12.
10
Pick any two points on the line.
(0,1) and (-3,3)
8
6
(y2 – y1)
3 1
2

Slope, m = (x – x ) =
2
1
30 3
4
2
-10 -8 -6 -4 -2
2
-2
-4
-6
-8
-10
13. First, calculate the slope.
m=
=
=
= -5
Then, use the point (-2 , 11) in y = -5x + b to solve for b.
11 = -5(-2) + b
11 =
10 + b
-10
-10
1 = b
14.
EQUATION: y = -5x + 1
2x – y = 1
-2x + 3y = 5
Add the two equations to eliminate the x term.
2y = 6  y = 3
Then substitute y = 3 in one of the two equations to solve for x.
2x – 3 = 1  2x = 4  x = 2
Answer (2,3)
15.
y = 3x + 8
3x – 2y = -10
We use substitution method to solve the problem
3x – 2(3x + 8) = -10
3x – 6x – 16 = -10
-3x – 16 = -10
+ 16 +16
-3x
= 6
-3
-3
x = -2
Add 16 to both sides
Divide both sides by -3
y = 3(-2) + 8
Substitute into one of the original equations
y = -6 + 8
y = 2 Answer (-2,2)
4
6
8 10
6
Math 082 Final - Practice Test #4 cont
16. (3x-5y2)(-4x3y5)
-12x-2y7
1
x-2 = 2
x
-12y7
= 2
x
17.
18.
19.
20.
(x -5)2 = x
24 =
5  2
Multiply by adding exponents of like bases
1
= x -10 = x10
4. 6 = 2 6
421
Move the decimal two places left to get number in scientific form
4.21 x 102
(x – 2)(3x + 7)
x · 3x + x · 7 – 2 · 3x – 2 · 7
FOIL
3x2 + 7x – 6x – 14
Combine like terms
3x2 + x – 14
21.
(x + 5)(x2 – 7x + 4)
x · x2 + x · 7x + x · 4 + 5 · x2 – 5 · 7x + 5 · 4
x3 – 7x2 + 5x2 + 4x – 35x + 20
x3 – 2x2 – 31x + 20
22. 2x3 + x2 – 3x
x(2x2 + x – 3)
2x2 + x – 3
2x2 + 3x – 2x – 3
x(2x + 3) – 1(2x + 3)
(x – 1)(2x + 3)
Distribute
Combine like terms
GCF: factor out a GCF of x
Factor 2x2 + x – 3 using the AC Method: ac = -6 and b = 1
The complete factored form is x(x – 1)(2x + 3)
23.
6x2 – 19x + 10
6x2 – 15x – 4x + 10
3x(2x – 5) – 2(2x – 5)
(3x – 2)(2x – 5)
Factor using the AC Method: ac=60 and b = -19
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Math 082 Final - Practice Test #4 cont
24.
25.
4x2 – 36
4(x2 – 9)
4(x + 3)(x – 3)
Factor out a GCF of 4
Difference of Squares
x2 – 18x = 0
x(x – 18) = 0
x = 0 ; x – 18 = 0
Factor out a GCF: x
Set each factor equal to zero
Solve each equation
x = 0 and x = 1
26.
x2 + 15
= 8x
-8x
-8x
2
x – 8x + 15 = 0
x2 – 3x – 5x + 15 = 0
Set original equation equal to zero
Subtract 8x from both sides
Factor by the AC method
x(x – 3) – 5(x – 3) = 0
(x – 5)(x – 3) = 0
x – 5 = 0; x – 3 = 0
Set each
factor equal to zero
Solve each equation
x = 5; x = 3
27. Pythagorean Theorem: a2 + b2 = c2
42 + b2 = 122
16 + b2 = 144
-16
-16
Subtract 16 from both sides
2
b = 128
Take the square root of both sides
b 2 = 128
b  11.31
28. Let steak dinner = x
Let shrimp dinner = y
x + y = 25
15x + 22y = 459
-15x – 15y = -375
15x + 22y = 459
7 y = 84
y = 12
multiply by -15 to each term
Solution: 13 steak dinners and 12 shrimp dinners
x + 12 = 25
x = 13
Substitute