Review for Exam #2
Math 10 Fall 2012
For attendance, turn in solutions to any two of the problems marked with a F.
Chapter 3, Sections 3,4,5
1. Write the equation for the line that passes through the following pair of points in both point-slope
form and slope-intercept form. If the line is vertical or horizontal, write the appropriate equation for
the line:
(a) (6, 4) and (4, −2)
(b) (−1, 3) and (2, 4)
(c) (3, −4) and (3, 5)
(d) (8, −7) and (9, 10)
(e) (−1, 6) and (5, 6)
2. In slope-intercept form, write an equation for the line that is parallel to the line 2x + y = 8 and has a
y-intercept of -4.
3. In point-slope form, write an equation for the line that passes through the point (-4,2) and is perpendicular to the line y = 31 x + 7.F
4. In slope-intercept form, write an equation for the line that has x-intercept of -2 and y-intercept of 6.
1
5. Draw the graphs of the lines whose equations are 3x − 2y = 12 and y = − 23 x + 5.
Chapter 4, Sections 2,3
1. Solve the following systems of linear equations, using either the substitution method or the addition
method.
(a) 2x + 3y = 11
x − 4y = 0
(c) 4x + 3y = 0
2x − y = 0
(b) 2x + 4y = 5
(d) 2x − 7y = 17
3x + 6y = 6
4x − 5y = 25
2
(e) 4x = 36 + 8y
3x − 6y = 27
(f) 6x = 5(x + y + 3) − x
3(x − y) + 4y = 5(y + 1)
2. Each Halloween, Iowa State University’s chapter of The League of Extraordinary Algebraists puts
together a Haunted Hayride for ISU students and the public. The tickets for the hayride cost $1 for
ISU students and $5 for non-students. On Halloween night, the attendance was 1281 people and The
League collected $3425. How many ISU students went on the hayride?F
Chapter 7, Sections 3,4,5,6
1. Perform the following operation(s), and simplify the result.
30b − 20
4 − 2b
22b + 15
+
−
12b2 + 52b − 9 12b2 + 52b − 9 12b2 + 52b − 9
2x + 3
x−2
x
x−4
(b) 2
+
(d) 2
−
2
x − x − 30 30 + x − x
x − 10x + 25 2x − 10
8
2
x+8
x+2 x−2
(c)
−
(e) 2
−
+
x+6 x−6
x −9 x+3 x−3
(a)
3
2. Simplify each complex rational expression:
1 1
−
9 y
(a)
9−y
9
7
x
(b)
4
x−6+
x
12
y
(c)
16
1− 2
y
x+9−
3+
3. Solve the following rational equations:
(a)
10
5y
=3−
y+2
y+2
(b)
x2 + 4x − 2
4
=1+
x2 − 2x − 8
x−4
1
25
4
−
=
y−2 2−y
y+6
1 1
1
(d) + = (solve for q and simplify)
p q
f
(c)
C
describes the selling price, S, of a product in terms of its cost to the retailer,
1−r
C, and its markup, r, usually expressed as a percent (1=100%). A small television cost a retailer $140
and was sold for $200. Find the markup, and express the answer as a percent.F
4. The formula S =
4
Chapter 8, Sections 1,2,3,4
1. Determine whether the following relations are functions:
(a) {(5, 6), (5, 7), (6, 6), (6, 7)}
(b) {(−7, −7), (−5, −5), (−3, −3), (0, 0)}
(c) {(4, 1), (5, 1), (6, 1)}
2. Let f (x) =
3x − 1
. Find the following function values:
x−5
(a) f (0)
(c) f (−3)
(e) f (3x)
(b) f (3)
(d) f (10)
(f) f (a + h)
(g) What is the domain of f ?
3. Draw the graph of a function f whose domain is {x|x ≥ 1} and whose range is [−2, 2], such that
f (x) < 0 for all values x that lie in the interval (3, 5).F
4. Let f (x) = x2 − 3x and g(x) = x + 9. Find the following function values:
(a) (f + g)(1)
(b) (f − g)(−2)
(c) (f g)(4)
5
(d) ( fg )(−5)
5. Let f (x) = 7x + 1 and g(x) = 2x2 − 9. Find (f ◦ g)(x), (g ◦ f )(x), and f −1 (x).
Chapter 9, Section 3
Find the solution sets for the following equations and inequalities:
1. 3|y + 5| = 12
3. |3x − 2| + 4 = 4
5. |3x + 5| < 17
7. |x + 4| ≥ −12
2. |3y − 2| + 8 = 1
4. |4x − 9| = |2x + 1|F
6. |x − 2| > 5
8. 3|2x − 1| + 2 ≤ 8
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