Download MATH 0305

MATH 0305
REVIEW FOR TEST #1 (1.5 – 1.7, 2.1 – 2.6)
1. Consider the following list:  48, 25,  7.24, 0,
5
1
,  , 4, 21, 69,  , 9.01, 1, 64
7
8
a) List all rational numbers _________________________________________
b) List all natural numbers _________________________________________
c) List all whole numbers __________________________________________
d) List all irrational numbers ________________________________________
e) List all integers _________________________________________________
2. List all the factors of 42.
3. Find the prime factorization of each number.
a) 98
b) 375
c) 234
4. Perform the indicated operations.
a)
13 4


18 27
b)
d)
5 4
 
12 9
e) 
g) –14 – (– 99 ) =
i) 
k)
9
1


10 16
2  6
   
9  21 
11 44


132 36
c) 4 
5
0 
9
f) 
3

8
2 1


3 12
h) –3.8 + 5.1 + (–12) + (– 4.3) +10 =
j) 3(- 7) (- 4) 5=
b)  3 
5. Evaluate. a)  5 2 
6. Simplify.
a)
c)  2  
4
72
27
b)
82
210
5
c)
17
85
7. Use the order of operations to simplify.
9 16 4
3 2
 

 
81 27 9
4 3
a) 
b)
6  3 4  5  26   4 


2
c)  1  3 4  3  6 
36  7   4  3  11  20 
3
d)
3  43

8. Translate to an algebraic expression.
a) One fourth of the difference of two numbers increased by five ____________________
b) Five less that the product of a number and two ________________________________
c) The ratio of a number cubed to negative nine __________________________________
d) The sum of a number and three, all raised to the fifth power ______________________
9. Evaluate.
a) 14 xy  7 x  15 y , for x  68 and y  32
b)
3x  7 y
, for x  17 and y  5
5
c)  4 x  y 2 , for x  3 and y  2
10. Multiply. a) – 7( 13x – 4)
b) 0.3 x( 7.4 m + 5.3)
11. Combine like terms.
a) 8 x 3  4 x  6 x 2  10 x 3  1.4 x  2.8 x 2
b) 5 x 
4 2
3
2
y  5  x  y2  9
5
4
7
12. Mary has the following test scores: 86, 95, 78, 82, and 84. Find the average of her test
scores.
13. Hardwood floors are to be installed in a bedroom that measures 14 feet by 15 feet. If the
contractor charges $34.50 per square foot to install the floors, what will be the cost of this
improvement?
14. A kitchen floor that is 15 feet by 16.5 feet is to be re-covered with granite tiles. There is a
fixed island in the center of the floor. The dimensions of the island are 2 feet by 3.5 feet. If the
contractor charges $28.80 per square foot to install the new floor, what will be the installation
cost?
15. A family began a trip of 516 miles at 8am. They arrived at their final destination at 5:30pm.
If they took two 15-minute breaks and took one hour for lunch, what was their average driving
rate?
16. Solve: 4y – 4 + y + 24 = 6y + 20 – 4y
17. Clear fractions or decimals, solve, and check.
5
1
1 3
a) x  x  2 x   x
4
4
2 4
b)
1
2 4 3
2
x 
 x
3
5 15 5
3
c) 1.7t  8  1.62t  0.4t  0.32  8
d) 19  2 x  3  2x  3  x
e)
13
1

 x  2  
64
5

f) 0.7 (3x + 6) = 1.1 – (x + 2)
g) 5  2 x  3  2 5  4 x  2
18. Find each solution set. Then classify each equation as a conditional equation, an
identity, or a contradiction.
a) x + 8 = 3 + x + 7
b) 3t + 5 + t = 5 + 4t
c) 1 + 9x = 3(4x + 1) – 2
n
,
15
where n is the total number of credits for which students have enrolled in a given semester.
Determine the number of full-time-equivalent students on a campus in which students
registered for a total of 21,345.
19. At many colleges, the number of “full-time-equivalent” students f is given by f 
20. Solve each formula for the indicated letter.
a) F = bt – 2, for b
b) A 
1
bh , for b
2
c) Q 
pq
, for p
2
d) A  mt  bt , for t
21. Five times the sum of 3 and some number is 70. What is the number?
22. The circumference of Earth along the equator is approximately 40,053.84 kilometers. What
is the equatorial radius?
23. The formula C  0.3m  25 , describes the total cost of using a digital phone over 100
minutes, where m represents the number of minutes beyond 100 minutes. Pam’s bill shows
that she used the phone for 187 minutes. What is the total cost of her use of the phone?
24. Translate each sentence to an equation and then solve.
a) Negative three times the difference of a number and two is twelve.
b) Two-fifths of a number is equal two less than one-half the number.
c) The difference of a number and 12 is subtracted from the difference of twice the number and
eight so that the result is eleven.
d) The product of negative four and the difference of two and a number is six less than the
product of two and the difference of four and three times the number.
25. Solve an inequality, graph the solution set, and write the answer in both set-builder
and interval notation.
a) 0.96 y  0.79  0.21y  0.46
b) 1.7t  8 1.62t  0.4t  0.32  6
c) 3 r  6  2  4 r  2  21
d)
3
1 2 1
 3x    
4
2 3 3
2. Translate to an inequality and solve.
Three increased by twice a number is less than three times the difference of a number and five.