Download Final Exam Review

Final Exam Review
Math 35
From Chapter 2 and 3:
Solve this literal equation for the variable requested.
1.
y = mx + b
(solve for m)
2.
A =
h · (b + c)
(solve for b)
2
3.
Pedro’s company uses an aluminum
alloy to make wheels for cars. He
has 30 pounds of 75% aluminum
alloy and wants to add pure
aluminum to it so that the aluminum
content increases to 80%. What is
the amount of pure aluminum that
must be added?
4.
The three angle measures in a triangle are such that the measure of the largest angle is three times
the measure of the smallest angle; the middle-sized angle is 9° less than the measure of the largest
angle. What are the measures of the three angles?
Solve each of these inequalities. Write the solution in interval notation, and draw its graph on a number
line.
5.
y
y
11
4 – 5 < 3 – 2
10.
1
-1 < 2 q + 3 ≤ 2
8.
|
Solve. Write the solution in a solution set.
7.
|
3x + 15 | = 21
5 – 4p | = 1
Solve. Draw the graph of the solution, and write it in interval notation and set builder notation.
9.
| 6w
+ 15 | ≥ 3
10.
|
7 – 2x | < 1
From the Chapter 4 and 5:
11.
First write the equation 2x + 3y = -3 in slope-intercept form. Then, identify the slope and yrise
intercepts, and use the slope as run to find two other points on the line and draw the graph. Be
sure to label the points on the graph.
12.
Find the equation of the line that passes through (10, 1) and (-15, -9). Write the equation in
slope-intercept form (y = mx + b).
page 1
13.
Find the equation of the line that passes through (8, -5) and is parallel to (has the same slope as) the
line 3x + 4y = -36. Write the equation in standard form (Ax + By = C).
14.
Solve this system by using the
substitution method.
15.
5x – 4y = -12
Solve this system by using the
elimination method.
6x + 5y = 12
3
4x + 3y = 7
y = -4x – 5
From the Chapter 6 and 7:
Multiply and combine like terms. Write each answer in descending order.
16.
(2x – y)(4x2 + 2xy + y2)
17.
Divide using long division.
18.
(x + 3)(x – 3)(x + 5)
Factor this four-term polynomial.
(2x3 – 7x2 + 5) ÷ (2x – 3)
19.
9x3 – 6x2 – 15x + 10
Factor each polynomial completely. If the polynomial is not factorable, write prime.
20.
3x2 + 13x + 12
21.
x2 + 20xy + 36y2
22.
15q6 + 28q3 – 4
23.
5r2 – 20r + 20
24.
81w4 – 16
25.
m3 – 27
26.
4x2 + 25
27.
8p3 + y3
From the Chapter 9:
Simplify. Write all answers with positive exponents only. For this set, assume all variables represent
positive numbers.
26.
121x2
27.
-
180y3
28.
3
-1,000y15
Multiply and simplify. For this set, assume all variables represent positive numbers.
page 2
29.
-
5c ·
15c
Simplify.
31.
-
30.
3
6w4 ·
3
-18w2
Multiply and simplify.
45 +
80
32.
(4
–
10 )(1 + 2 10 )
Graph the function and state its domain and range.
33.
f(x) =
x + 5
Consider that i = -1 . Perform the indicated operation and simplify. Write the answer in the
standard complex number form, a + bi.
34.
- 15 ·
- 20
6 )2
35.
(5 + i
37.
4y2 + 3y = 7y – 1
From the Chapter 10+:
Solve each equation by factoring. (Sec. 7.5)
36.
4x2 + x – 14 = 0
Solve the equation. Be sure to check all answers.
(Sec. 9.6)
38.
39.
5x – 4
+2= x
6 – 2x = x + 9
Solve using the square root property. Write the answers in a solution set.
40.
(2x – 5)2 = 49
41.
(3x + 1)2 = 24
Solve by first completing the square and then applying the square root property.
42.
x2 – 5x + 13 = 0
43.
1
x2 + 2 x = 3
Graph f(x) by first identifying the vertex and the axis of symmetry of the parabola. Then plot two sets of
symmetric pairs. Lastly, state the domain and range.
44.
f(x) = 2(x + 2)2 – 3
45.
f(x) = -(x – 3)2 + 5
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