Summer 2009
Math 260
Test 1
Name: _____________________
Show all necessary work neatly, clearly, and logically. Any understatement and/or incorrect statement will be penalized.
Answer-by-guessing (i.e., without proper work) will receive at most 1 point. Total points: 115 Good Luck 
Solve: 5 x 2  x  2  x 2  6 x  3
1.
(8)
2.
(8)Solve: 6
3.
(8)Solve:
x  2
2
3
 7 x  2 
1
3
2x  5  x  2  5 .
5
5
2
x 1


1
2x  x  3 2x  3 x  1
4.
(8)Solve:
5.
(10)Simplify
the expressions:
 12  74
x y
a. 
5
 y 4






6.
(8)Two
2
4
b.
2 x( x  6) 4  x 2 (4)( x  6) 3
x  68
planes leave Los Angeles at the same time. One heads south to San Diego, while the other heads
north to San Francisco. The San Diego plane flies 50 mph slower than the San Francisco plane. In ½
hours, the planes are 275 mi apart. What are their speeds?
7.
(16) Find
a. (3)
the domain of the following functions:
x3 1
f ( x)  2
 1
x 4 x
b. (7) f ( x) 
c. (3) f ( x) 
6 x
x3
x2  4
d. (3) f ( x) 
8.
x2
(8) Factor the following completely:
3
1
1
a. x 2  3x 2  10 x 2
b. 5( x 2  4) 4 (2 x)( x  2) 4  ( x 2  4) 5 (4)( x  2) 3
2 x
3 x
 x  2, x  0

9. (10)Let f ( x)   2, 0  x  1
 3  x, 1  x

a.
(2)Find
1
f   and f(10)
2
b.
(6)Graph
the function f.
c.
(2)What’s
the range of f?
10. (8)The resistance of a wire varies directly as its length and inversely as the square of its diameter. A wire
50 meter and 0.01 meter in diameter has resistance of 25 ohms. Find the resistance of a wire made of the
same material that is 20 meters long and has diameter of 0.02 meters.
11. (15)Given two points A(-3, 1) and B(-5, -7).
a. (6)Find the equation of the line passes through these two points. Write the equation in standard form.
b.
(3)Find
the distance between the two points.
c.
(3)Find
the midpoint of the segment AB.
d.
(3)If
segment AB is the diameter of a circle. Find the equation of the circle. (Use results from part b
and part c)
12. (8)Let f ( x)   x 2  3
a. (2)Find f (2)
b.
(6)
Find
f ( a  h)  f ( a )
.
h
Simplify as much as possible.