Practice Test I Math 303
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1PRACTICE TEST I
MATH 303
Winter 2006
On the test, you must show your work to receive credit. You should be sure to
work on the problems from the in-class exercises for January 17. I have not included
problems of this type on the practice test as there were plenty on the in-class paper.
You should also go over all of the problems on the homework assignments and the
solutions carefully.
1. Simplify each expression so that it is a single fraction having a polynomial for
the numerator and for the denominator, and no parentheses.
x
2
+
x 2
3
x 1
(a)
+
(b)
2
x
3x
x+1
x
2
2x+1
2. Solve for x, showing each step in your solution:
3x+2
3
2
5
1
2
5
(a)
=
x
(b)
(4x + 1) = 2x + 1
x +
(c)
=
7
5
3
2
6
x 1
2x+1
3. Let f (x) = x
2(x
1)
2
(1
x) + 2( x
1). Find expressions for f ( x)
and for f (2x), simplifying as much as possible. Evaluate f ( 1) and f (2).
4. On a coordinate plane, draw the line having x-intercept
3 and y -intercept 2.
Find the equation of this line. Find the distance between the x-intercept and the
y -intercept. Find the equation of the line parallel to this one and passing through
the point ( 1, 1). Find the equation of the line perpendicular to this one and
passing through the point ( 1, 1).
5. Let L be the line with equation 2x+3y = 5, and let M be the line perpendicular
to L and passing through the point (-1,2). Write the equation of M in slope-point
form, in slope-intercept form, and in standard form with integer coefficients. Graph
M and L on the same coordinate plane.
6. Let L be the line passing through the points (2, 1) and ( 1, 5). Find the slope
m of L. Write the equation of L in point-slope form, in slope-intercept form, and
in standard form with integer coefficients. What is the y -intercept of L? What is
the x-intercept of L? Graph the line in the coordinate plane.
7.
Last year, three fifths of the Journalism Club were girls, but this year the
number of boys doubled, and six new girls joined. There are now as many boys in
the club as there are girls. How many members did the club have last year? Set
up an equation that models this problem, and then solve it to provide the answer.
8. Randy and Sandy have a total of 20 books between them. Sandy loses 3, but
Randy doubles his collection. They now have 30 books. How many did each person
have initially? Set up an equation that models this problem, and then solve it to
provide the answer.
9. Due to a malfunctioning time machine, Derek ended up face to face with a T
Rex. If the dinosaur runs 60 feet per second and Derek runs 8 feet per second, how
long until the dinosaur catches Derek, if it starts 988 feet behind Derek? Set up an
equation that models this problem, and then solve it to provide the answer.
10.
For each of the following problems, indicate if you are finding the percent,
finding the part, or finding the whole. Then set up the relevant proportion and find
the requested value.
(a) What percent of 45 is 10?
(b) What is 16% of 261?
(c) 71% of what is 87?
1
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