Download Final Review Problems ~ Math 60

Final Review Problems ~ Math 60
1
2
1. Simplify the following expressions given a  2, b  5, c   , d  .
4
3
a  4c
2
a)
b) 2  a  c   4  b2  d 
b  6d
2. Use set-builder notation (or the roster method depending on appropriateness), interval
notation and a number line to describe the following sets.
a) The set of prime numbers greater than 15 and less than or equal to 83.
b) The set of real numbers greater than or equal to -5.1 and less than 2.3.
3. Write each of the following phrases using symbols.
3
and one third n.
4
b) The product of 5 less than a number and 2 more than the same number.
a) The sum n and 8 divided by the difference of
4. Let A be the set of all positive multiples of 4, B  3, 2,1,5,8,16, 23 and C be the set of all
multiples of 3.
a) Find A  B .
b) Find C  B .
c) Find A  C
5. The product of a number and 2 more than three times the same number is 21. What is the
number?
6. The sum of an even odd and 3 times the next consecutive odd integer is 94 . What are the
two integers?
7. Combine like terms then evaluate.
a) 5a 2  3a  2  6a 2  5, given a  1
1
3
b) 4 x  3 y  2  7 x  6  4 y, given x  , y 
6
2
8. Solve the following. For the inequalities, state your answers using a number line, set-builder
notation, and interval notation.
7
4
 x  18  x  1
3
3
b)
8 x 7 3x 9
 

5 2 5 4
c) 2  3  5x   7 x  6 x  8
d)
3 x 1 11 x
  
2 3 6 4
e) B  P 1  rt  , for t
f)
a)
2D 
C  6s
, for s
n
g)
1
1 5x
5  2x   
3
6 2
h) 4 x  2  3  2 x   6 x  8
i)
x  7  21
j)
3  2 x  7  18
l)
1
5
 3  x  x    2x
3
3
k) 2 3x  4  8
m) The distance between two times a number and 7 is 15.
n) The distance between two thirds a number and -6 is 4.
 15 
9. Which of the ordered pairs  0, 0  , 1,  ,  2, 3 ,  6, 0  are solutions for the equation
 4
3x  4 y  18 .
10. Solve for y where applicable, find at least 3 points that satisfy the equation, graph the
equation, and state the slope and y-intercept of each equation. Label your axis and each line
graphed.
a)
4
5
y   x
3
2
c) 2 x  4 y  11
11.
2
9
b)  x  3 y  
5
2
d)
2
 x  2 y   4  3x  2
3
Find the equation of the line with y-intercept  0, 2  and perpendicular to the line
y  3x  7 .
12.
Find the equation of the line with y-intercept  0, 2  and parallel to the line
2 x  3 y  3x  7 .
13.
Find the equation of the line passing through the points  7,1 and  3, 2 .
14.
1 1
Find the equation of the line passing through the point  ,   and perpendicular to the
2 2
line in 13.
15.
1 1
Find the equation of the line passing through the point  ,   and parallel to the line in
2 2
13.
16.
Shade in the feasible region for the following inequalities.
4
5
a) y   x 
3
2
2
9
b)  x  3 y  
5
2
c) 2 x  4 y  11
d)
2
 x  2 y   4  3x  2
3
For all word problems, clearly define your variable, state the equation, solve, and interpret
your results using complete sentences.
17.
The reception hall where Terri is to be married charges $4000 for the hall and $35 for each
meal. If Terri and her fiancé have $7000 to spend on the reception, what is the maximum
number of people they can invite?
18.
A recreational manufacturer makes two types of tents: a four-person tent that costs $100 to
make and a two-person tent that cost $60 to make. The manufacturer can budget no more
than $9000 to produce the tents. The manufacturer can make no more than 120 tents.
Express the given conditions as linear inequalities and graph the feasible region.
19.
A tool company manufactures two types of electric drills, one which is cordless. The cordtype drill requires 2 labor hours to make, and the cordless drill requires 3 hours. The
company has only 600 labor hours available each day. The packaging department of the
company can package at most 250 drills per day. Express the given conditions as linear
inequalities and graph the feasible region.
20. A plane flying with the wind went 350 mi in 2 hours. The return trip, flying against the
wind, took 2.6 h. Find the rate of the plane in calm air and the rate of the wind.
21.
A clothing manufacturer purchased 60 yd of cotton and 90 yd of wool for a total cost of
$1800. Another purchase, at the same prices include 80 yd of cotton and 20 yd of wool for
a total cost of $1000. Find the cost per yard of the cotton and of the wool.
22.
An average of 70 to 79 in a mathematics class receives a C grade. A student has scores of
56, 91, 83, and 62 on four tests. Find the range of scores on the fifth test that will give the
student a C for the course.
23.
The sum of 5 times a number and twelve added to the product of fifteen and the number is
82. What is the number?
24.
One half the sum of six times a number and twenty two is 50. What is the number?
25.
Eleven more than the square of a number added to the difference between the number and
seventeen.