Download MAT150T1

MAT 150 Fall 2005
Test #1
Name:_________________________
Directions: Do all of your work on the “work and answer” document provided. DO NOT WRITE ON THIS PAPER. No calculators
are allowed on this test. The number in parentheses , (#), in front of each problem, indicate how many points that problem is worth.
Show work on all problems that are not matching or true/false!!!!!!!!!!
PROBLEM 1: Write roman numerals I – V on your answer document. Next to each roman numeral write a letter A-E to indicate
which “rule of Algebra” is being demonstrated.
( 1) I. 2 x   2 x   0
A. Distributive Property
(1) II. 3  2  x   2  x   3
B. Commutative Property of Addition
(1) III. 3  2  x   3  x  2
(1) IV. 3  2  x   3  2  3  x
C. Associative Property of Addition
D. Additive Inverse Property
(1) V. (3  2)  x  3  2  x 
E. Commutative Property of Multiplication
PROBLEM 2: Simplify COMPLETELY. Be sure to show ALL steps or you will lose points!
(1) I. 4 27  75
9
(2) II.  
4

1
2
(2) III.
3
2 5
PROBLEM 3: Find the simplified expression that represents the shaded area in the diagram below. Write your result as a polynomial
in standard form. (Lines that look perpendicular ARE perpendicular)
(5)
3x
x
x+2
x+3
PROBLEM 4: Factor Completely:
(2) I. 3x 3  12 x
(1) II. 3x 2  10 x  8
(2)
III. 5x 3  10 x 2  3x  6
PROBLEM 5: Write an expression in completely factored form for the area of the shaded portion of the figure below. This figure
consists of a circle inscribed within a square (this means that the circle only touches the square at four places…the midpoint of each
side).
2x
PROBLEM 6: Divide.
x 2  14 x  49 3x  21

x7
x 2  49
(5)
PROBLEM 7: Subtract.
x
3

x

2
x 4
(5)
2
PROBLEM 8: Describe and correct the error.
(2) I. 2 x  2 y  3  2 x  2 y  3
(3) II.
2x 2  4
=
2
2x 2  4
 x2  4
2
PROBLEM 9:
(1) I. Graph the two points 2,1 and 2,2 on the same coordinate system.
(2) II. Find the midpoint of the line segment that joins these two points.
(2) III. Find the length of the line segment that joins these two points.
PROBLEM 10:
Write down the formula for factoring
(1) I. The difference of two squares
(2) II. The difference of two cubes
(2) III. The sum of two cubes
a 2  b2 
a 3  b3 
a 3  b3 