STUDY GUIDE FOR EXAM ONE. The exam will cover Sections 2.1, 2.2, 2.3, 2.5, and 3.2. NO CALCULATORS! Not
multiple-choice. Bring pencils/pens and paper.
Solve the inequality. State the solution set in interval
notation.
8x - 5 53
< 1)
8
6
2) 13y + 6 ≤ 12y + 16
3) -4 < 4y ≤ 12
4) a + 4 < -8
5) -3z - 2 > -4z + 3
6) 4 < 1 - 4x ≤ 12
Solve the percent problem.
7) Midtown Antiques collects 2% sales tax on all
sales. If total sales including tax are $1790.78,
find the portion that is the tax. Round your
answer to the nearest cent.
8) If Gloria received a 8 percent raise and is now
making $24,840 a year, what was her salary
before the raise?
9) After spending $3850 for tables and $4050 for
chairs, a convention center manager finds that
45% of his original budget remains. Find the
amount that remains. Round your answer to
the nearest dollar, if necessary.
Solve the equation.
10) 3m + 7 + 5(2m - 3) = 3(m + 3)
Solve the mixture problem.
16) It is necessary to have a 40% antifreeze
solution in the radiator of a certain car. The
radiator now has 40 liters of 20% solution.
How many liters of this should be drained and
replaced with 100% antifreeze to get the
desired strength?
17) How many liters of a 30% alcohol solution
must be mixed with 60 liters of a 50% solution
to get a 40% solution?
18) A merchant has coffee worth $4 a pound that
she wishes to mix with 90 pounds of coffee
worth $8 a pound to get a mixture worth $7 a
pound. How many pounds of the $4 coffee
should be used?
Solve the equation for y.
19) 4x + 5y = 6
Solve the investment problem.
20) Roberto invested some money at 6%, and then
invested $5000 more than twice this amount at
11%. His total annual income from the two
investments was $4190. How much was
invested at 11%?
21) Mardi received an inheritance of $70,000. She
invested part at 10% and deposited the
remainder in tax-free bonds at 8%. Her total
annual income from the investments was
$6200. Find the amount invested at 10%.
Solve the equation for y.
22) -5x + 7y = 3
11) -0.08y + 0.13(9000 - y) = 0.29y
7x
3x + 8 7
+ = - 12)
5
4
5
13) 23t - 16 = 15t - 10
14) 14x - 7 = 11
15) 5(x + 5) = (5x + 25)
Solve the problem.
23) Find the length of a rectangular lot with a
perimeter of 124 m if the length is 8 m more
than the width.
24) A printer priced at $581 is sold for $411. What
was the percent of price reduction? Round to
the nearest tenth of a percent, if necessary.
25) Jay drove 355 km at an average rate of 71
km/hr. How long did the trip take?
26) In a recent school board election, the two
candidates for president received 2398 votes.
The loser received 1406 fewer votes than the
winner. How many votes did the winner
receive?
Decide whether the equation is conditional, an identity,
or a contradiction. Give the solution set.
27) 20k + 3 = 5(4k - 1)
35)
y
10
5
-10
-5
5
10
-5
28) 5(2f - 31) = 10f - 155
-10
29) 16m + 6 = 2(5m + 21)
Find the slope of the line through the given pair of points,
if possible. Based on the slope, indicate whether the line
through the points rises from left to right, falls from left
to right, is horizontal, or is vertical.
30) (-9, -8) and (4, 9)
Graph the line described.
36) Through (0, 4); m = 1
4
y
10
31) (-8, -5) and (6, -7)
5
32) (-5, 8) and (-3, 8)
-10
-5
33) (6, -9) and (6, 9)
-5
Find the slope of the line.
34)
-10
5
10
x
5
10
x
y
10
37) Through (0, 3); m = - 5
y
10
5
-10
10
x
-10
-5
-5
-10
-10
x
Answer Key
Testname: ONEST
1) -∞, 179
32
36)
y
10
2)
3)
4)
5)
(-∞, 10]
(-1, 3]
(-∞, -12)
(5, ∞)
3
11
6) - , - 4
4
7) $35.11
8) $23,000
9) $6464
17
10)
10
11) {2340}
60
12) - 47
13)
3
4
14)
9
7
15) {All real numbers}
16) 10 liters
17) 60 liters
18) 30 lb
6 - 4x
19) y = 5
20) $31,000
21) $30,000
3 + 5x
22) y = 7
23) 35 m
24) 29.3%
25) 5 hr
26) 1902 votes
27) Contradiction; ∅
28) Identity; {all real numbers}
29) Conditional; {6}
17
; rises
30)
13
1
31) - ; falls
7
32) 0; horizontal
33) Undefined; vertical
34) 0
35) -1
5
-10
-5
5
10
x
5
10
x
-5
-10
37)
y
10
5
-10
-5
-5
-10