Download Math 130A

Name _____________________________________________ Math 130A.050 – Exam II – Review – October 13, 2004
1.
2.
Change to
a) an improper fraction: 5 ½ = ___________
b) to a mixed number 25/7 = __________
c) to a decimal: 5/8 = _________________
d) to fraction in simplest form: 0.004 = ___________
Write in words.
201.021 → ______________________________________________________
Write in standard form ( numbers). Five thousand one and 2 ten thousandths. _________________
Round to the nearest ten-thousandth → 30,204.02345 → ____________
3.
Which of the following numbers are real numbers. _________________
-2,
a) 0
2/3,
5
c) 0 and - 2
d) -2, 0, 2/3
0,
b) 0 and 2/3
e) all are
Which of them are not rational ? ____________
Which of them are whole numbers ? ________
4. Match.
___________
a) a + b = b + a
___________
c) (ab) c = a ( bc )
___________
d) a(b + c ) = ab + ac
5.
1) associative law of addition
2) commutative law of addition
3) associative law of multiplication
4) commutative law of multiplication
5)distributive law
6) none of these
We call 1 the multiplicative identity because for any real number x, 1 • x = x • 1 = x
We call ________ the additive identity because for any real number x → x + ___ = ___ + x = x
What is the opposite of - 2/3 ? ______ What is the reciprocal of - 2/3 ? ________
6. Evaluate. Write in simplest form.
a) -ab = ___________
if a = - 2 ¼ and b = 5 ½
b) -2a - b2 = ___________ if
a = 4 1/3 and b = - 2 ½
f) NONE
6c)
ab - b = ____________ if a = 3.12 and b = - 1.2
d) ( a + b ) ÷ b = ______ if a = -1.47 and b = 2.1
7.
Find the solution of each of the following equations.
a) - 2x + 5/2 = - 4/3
x = __________________
b) 2.1 - 2x = 4.9
x = ___________________
c)
x–1
x+2
----------- = -------3
3
d)
x = ________________
0.3x = 62.7 x = _____________
8. Write the correct symbol between the expressions ( < , > , or = )
a)
2/3 __________
c) 1/3 _________
9.
8/13
0.3333
b) 0.21___________ 0.201
d)
2/3 _________ 18 / 27
Find
a) 3/n + 4/n -
c)
8/n = ___________
3/12 ÷ 8/15 ÷ 6/20 = __________
e) 12 - 4 ½ = __________
b) 5 5/12
-
6 ¼
d) 5 • 2 ¼ = _________
f) 8 ÷ 2 2/3
10.
Write as simple fraction.
½ - 1/3
----------------- = ____________
¼
11. Simplify
a) ( 0.1)3 = __________
c)
b)
32.16 ÷ 1.6 = ____________
2.3 - 0.23 = _____________
12. Simplify the following radicals.
___
a) 2 \/ 64 = __________
___
b) 8 - 3 \/ 16
____
c) \/ 9/16 = ________
= __________
_____
d) - \/ 9 + 16 = __________
12.5 More radicals.
a) 2+ 2
9 = ________
13. Plot on a number line.
b)
3  3 = ________
c)
24 = ____
x≤ 3
Write as an inequality
____________
14. Find
a) 4 ( 3x ) = _________
b) ( 2x) ( 3x ) = __________
c) - ( 2 – 3x ) = __________
d) ( -3 ) ( x ) = ___________
15. Word Problems.
a) Your cellular phone company charges $19.99 per month which includes 20 minutes of free air time, and $0.75 for each
additional minute after the first 20. What is your cellular phone service bill for a month in which you had 42 minutes of
calls ?
____________________
15b) The relationship between the velocity of a car and its braking distance is given by the formula v = 20d , where v is
the velocity in miles per hour and d is its braking distance in feet. How fast is a car going when its braking distance is
80 feet ?
_________________
c) A one year subscription to a monthly magazine costs $45. The price of each issue at the newsstand is $4.90. How much
would you save per issue by buying a year’s subscription rather than buying each issue at the newsstand ?
__________
d) Find the length of fencing needed to surround a rectangular dog pen that 20 ½ feet long by 12 ¼ feet wide. ________
e) A bicyclist rode ¾ hours at a rate of 5 ½ mph. How far did he travel ? _____________
f) If a car can go 18 ½ miles per gallon and you traveled ____________ then how many gallons did you use ?
16.
What is the degree of each of the following polynomials
a) 2 + x + x 3 → _________
b) 3 – 2xy + y3 → ____________
c) 4x2 y5
17. Write in scientific notation
23.2 = ____________
18.
0.00345 = ________________
Write in standard form
3.2 x 10-2 = ________________
1.01 x 105 = ____________
19.
Use the rules of exponents to simplify
a) 2x3 • 4x4 = _____________
b) ( -4x5 ) ÷ ( 2x3 y) = _________
c) ( 2x4y2 )3 = _____________
d)
4 xy 3
= ________________
6x 4 y 2
20. More with scientific notation and exponents.
a) ( 2.1 x 102 )
• ( 5.0 x 105 ) = _________________________(in scientific notation )
b) ( 1.2 x 103 ) ÷ ( 6 x 102 ) = __________________________ ( in scientific notation )
21. Perform the given operation and simplify by combining similar terms.
a) 4 + 3a = _________
b) ( 2a + 3 ) ( 2a + 3 ) = _____________
c) ( x +2 )2 = ____________
d) ( 2x2 + 2x + 3 ) - ( x2 – 2x – 3 ) = _____________
e) 2x + x( x – 2 ) = _________
22. Write in simplest form without negative exponents.
a) -40 = _________
b) ( - 2 ) 0 = ________
c) -22 = __________
d) 4-2 = _________
e) - 2-3 = ___________
f) m-2 = _________