Download Math 120/121

Math 120/121
Review for Exam 1
1) Write the following set in interval notation and graph it on a number line:
 y | 4  y  2
2) Perform the indicated operations:
2 3  (1  2)  2
9(3)  (2)
8  4  32  5  2(1)
3) Perform the indicated operations:
3  23  1
4) Find each square root:
a) 196
b)  225
c)
16
8k  2m2
5) Evaluate
if k  3 , m  3 and r  25
r 2
6) Simplify 3  2k  4  4  3k  5  2  4k
7) Solve for x: 3(2 x  2)  4( x  6)  3 x  8  x
8) Solve for x:
x6 x4 x2


10
15
6
9) Solve for x:
a) 6 x  3(5 x  2)  4(1  x)
b) 3x  (2  x)  4 x  2  8 x  3
c) 4(2 x  6)  5 x  24  7 x
x
5x
x
2 9
d)  7 
3
6
2
10) The 2005 Indianapolis 500 (mile) race was won by Dan Wheldon, who averaged
157.603 miles per hour. What was Wheldon’s time to the nearest thousandth of an
hour?
11) A certificate of deposit pays $2281.25 in simple interest for 1 year on a principal of
$36,500.00. What is the rate of interest?
12) In 2005 there were 37,142 offices, stations and branches of the U.S. Postal Service, of
which 27,385 were actually classified as post offices. What percent, to the nearest
tenth, were classified as post offices?
13) Two cars leave from the same point at the same time, traveling in opposite directions.
One travels 15 mph slower than the other. After 6 hours, they are 630 miles apart.
Find the rate of each car.
14) Tyler invested some money at 3% simple interest and some at 5% simple interest.
The total amount of his investments was $28,000.00 and the interest he earned during
the first year was $1,240.00. How much did he invest at each rate?
15) Solve each inequality. Express your answer in interval notation and graph on a
number line.
a) 4  6( x  3)  2  2( x  6)  3x
4
b)  x  16
7
4
c) 6  x  2  2
3
16) A student must have an average of at least 80 and less than a 90 on the four tests in a
course to get a B. The student had scores of 83, 76 and 79 on the first three tests. What
scores can the student get on the last test in order to earn a B in the class?
17) Solve for k : | 3k  2 | 1  8
18) Find the x and y intercepts, and graph the equation: 3x  2 y  20
19) Find the slope of the line through  6, 4  and  4, 1
20) Determine whether the following pairs of lines are parallel, perpendicular or neither.
5x  y  8
2 y  3 x  12
a)
b)
3y  2x  5
5y  x  3
21) Write the equation of each line in slope intercept form if possible:
a) through  4, 1 ; m  5
b) through  7, 2  parallel to 3 x  5 y  6
c) through  2,3 and  6, 1
d) through  5, 6  ; vertical
e) through  3,14 ; horizontal
f) through
 7, 2 perpendicular to 3x  5 y  6
22) Given f ( x)   x 2  2 x  1
a) find f (2)
b) find f (3)
c) find f (a )
2
x  1 ; What is the domain and range?
3
24) Solve this system of linear equations by graphing.
x y 7
23) Graph the linear function f ( x) 
x y 5
25) Solve each of the following systems by substitution or elimination.
2 x  3 y  24
a)
2
y x
3
b)
3 x  y  8
2x  6 y  3
c)
3x  4 y  8
8 y  7  6x
26) Julia Roberts is one of the biggest box-office stars in Hollywood. As of June 2004,
her two top-grossing domestic films, Ocean’s Eleven and Runaway Bride, earned $335.5
million dollars together. If Runaway Bride grossed $31.3 million less than Ocean’s
Eleven, how much did each film gross?
27) A chemist needs 12 L of a 40% alcohol solution. She must mix a 20% solution and a
50% solution. How many liters of each will be required to obtain what she needs?
28) A local electronics store will sell seven AC adaptors and two rechargeable flashlights
for $86.00, or three AC adaptors and four rechargeable flashlights for $84.00. What is
the price of a single AC adaptor and a single rechargeable flashlight?
Answers
1) (4, 2]
16
2)
7
11
3)
23
4) a) 14 b) -15 c) not a real number
6
5) 
23
6) 10k 10
7) -19
8) all real numbers (infinite solutions)
9) a) -2 b) no solutions c) 0 d) infinite solutions (all real numbers)
10)3.173 hours
11) 6.25%
12) 74%
13) 45 m/hr, 60 m/hr
14) $8,000 at 3% and $20,000 at 5%
15) a) [0, ) b) (, 28) c) [ 3,3]
16) [82,122)
5
17)  or 3
3
20


18)  , 0  ,  0, 10
 3 
1
19)
2
20) a) perpendicular
b) neither
3
11
1
21) a) y  5 x  19
b) y   x 
c) y   x  2
d) x  5
5
5
2
5
41
e) y  14
f) y  x 
3
3
22) a) -1
b) -16
c) a 2  2a  1
23) domain  ,   , range  ,  
24)  6,1
 9 5
b)   ,  c) no solutions
 4 4
26) Ocean’s Eleven $183.4 million, Runaway Bride $152.1 million
27) 4 liters of 20%, 8 liters of 50%
28) AC adaptors $8.00, rechargeable flashlights $15.00
25) a)  6, 4 