Download Name Math 1302 College Algebra Exam I March 6, 2003 1

________________________
Name
Math 1302
College Algebra
Exam I
March 6, 2003
1. Complete each of the following blanks.
a) The set of _________________ is made up entirely of the set of whole numbers and their opposites.
b) Every ___________________ number can be written as a fraction and there is no other real number that can be
written as a fraction except for these numbers.
c) Real numbers are made of numbers that must be members of one of two sets, the
set of
___________________________
or the set of _____________________
2. Complete the following by using the
a) commutative law of addition:
3 + x = ______________
b ) the distributive law: ( - 3 ) ( x + b ) = ____________________
3. Give me an example of the associative law of multiplication. ________________
4. Simplify to a single number in simplest form.
a) -42 = _______
b) 02 = __________
e) -4- 2 = _________
e)
c) - 16 ½ = _________
- 2 0 = ________
d) ( 4/ 9 ) – 3/2 = _______
f) (-8 )-2/3 = _______
5. Evaluate if x = -1 and y = - 2, z = - 3, and r = 0
a) xy = _______
b) ( y r )z = __________
6. Find each of the following absolute values. Do not combine any of the numbers. Write without
absolute values and without parenthesis or grouping symbols of any kind.
__
a) | 4 - 7 | = ___________
b) | 8 - \/ 50 | = _____________
c)
- | 4 | - | - 2 | = _____________
d) | 7 - 2 | = ___________
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7. True or False.
_____________ a. Every integer can be written as a fraction.
_____________ b. all rational numbers are either positive or negative
_____________c. 1 is the smallest positive whole number
_____________d. ( x + 2y )2 = x2 + 4y2
_____________ f. two is the smallest prime number
8. Perform the given operations and simplify.
a) 4 – 3 [ 2 – ( 4 – 5 ) ] = __________________
b) 4 – 22  3 + 8  2 = _________
9. Use the rules of exponents to simplify
a) ( 3x2 )3 = ________________
c) ( - 2x - 2 )2  ( 4x3 )2 = ________
f)
h) (
4x2y4
----------- = ___________
8xy7
- 6 x - 2y - 3
-----------2x 2y – 4
)2
b) ( 4x2 ) ( - 2x4 y ) = _____________
d) ( 4x-2)-1/2 = ____________
e) ( 2/3)-2 = _________
-4x -1y -3
g) -------------------- = ______________
2x - 3y2
=____________________
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10. Use the rules of radicals and fractional exponents to simplify.
_______
3 _____
a) \/ 16x4y2 = ______________
b) \/ 8x6 = ________________
___
c) 4 - 2 \/ 9
= _____________
d)
( 16x24y8 )1/4 = _____________
11. Perform the given operation -- Do not factor.
a) ( 3x2 - 4x + 6 ) - 2(x2 - 2x + 3) =_________________________
b) 3x2y ( x + 2y ) = _______________________
c)
2x + 3 ( x + 2 ) = _____________
12. Factor each of the following polynomials - All of these should factor. Factor completely !
a) 4x2 + 4x - 15 = __________________
c) 5x4 - 20x2y2 = __________________________
b) 3( x – 2y ) + 5( x – 2y ) = ____________________
d) x4 - 16y4 = ___________________________
e) x4 - 8x = _________________________________
13. Find the GCF of the following
a) GCF( 80, 120 ) = _____________
b) GCF( 12x2y4, 16xy5 ) = ___________
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14. Find the LCM of
b) LCM ( 12xy2, 8x3y4 ) = _______
a) LCM (24, 30 ) = ________________
15. Find the degree of each of the following polynomials.
a) 4  _____________
b) 82x3y5  _____________
c) 1 + 5x8 - 2x4y5  _______________
16. Simplify.
a) ( 9 ) – 3/2 = ___________
c)
- 8- 2/3 = _____________
18. A polynomial that has three factors but only one term is called a ________________________
A monomial will always have only one ____________
19. Reduce each of the following algebraic fractions to lowest terms.
a)
x3 - y3
----------------- = _____________
x2 - y2
3 - xy
b) ---------------- = _______________
xy - 3
20. Simplify by performing the given operation and reducing to lowest terms.
3- x
x -1
a) --------- ---------- = ______________
x- 2
x -2
4
x2 - 4x
3x2 + 3x
b) ------------  ------------------ = ________________
x2 - 16
x2 + 5x + 4
c)
x2 - 4x - 12
x2 - 4
-------------------  ------------------- = ____________________
x2 - 12x + 36
x2 - 5x - 6
21. More radicals
a) \/ 64x6y4
b)
\/ 4x6y4 = ____________
c) \/ 24 = ____________
d) \/ 8 + 2 \/18 = __________
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c) --------- =
\/ 9x
22. A dress sells for $60 and there is an 8 % sales tax. How much change will you
get back if you paid with three twenties and a ten dollar bill ?
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23. Simplify by using the rules of exponents. No radicals in your final solution. No
negative exponents in your final solution.
b) x1/4  x1/2 = _______________
a) x1/2 x1/4 = ____________
c) ( -2x1/3y-1/2 )
-6
= ____________
24. Find the solution of each of the following equations. Complex solutions are acceptable – make sure
not to use the phrase “ no real solution”
a)
2 – x ( x – 2 ) = ( 3 – x )(3 + x ) 
b) 3/x = 3
-
1/x
 x = ___________
c) 4 / ( 1 – x ) = 2 / x
d) x/2 + x/3 = 1
x = ___________
 x = _________________
==> x = __________
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25. Write in standard form of a quadratic equation.
4 - x2 = - 2x
find a = _______
b= _______
c = ___________
25. Find the solution of each of the following equations.
a) x2 = 4x ,
x = ___________
b) 9 - 16x2 = 0 , x = ______________
c) 2x ( x + 4 ) = 0 , x = _________________
d) x2 – x – 6 = 0 , x = _________________
26. Simplify by performing the given operation and reducing to simplest form.
a) 4 – x
------ +
2–x
2
--------- = ____________
x–2
x2 - x
3x2 – 9x
b) -----------  --------------- = _____________
x2 + 2x - 3
x2 - 9
c) 1
+
1
---------- = __________________
1 - 1/x
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