Math 1014, Spring 2002

# Practice Exam 1

Disclaimer: This is a practice exam only and contains many more questions than the actual exam. The actual final will be close to this exam, but may contain questions that are different from the questions in this practice test. The final exam takes place as scheduled on Wed, Feb. 20.

1.     State, in your own words, the definition of the following terms:

a)     slope of a line through two points (x, y) and (x, y)

b)     function

c)     range and domain

d)     linear function

e)     monomial

f)      polynomial

2.     Find the slope and y-intercept of the following lines, if possible, and graph them in the coordinate system provided:

a)

b)     -5y – 2x = 7

c)     y + 5 = 7

d)     3 = x - 1

3.     Find the linear equation describing the following lines

a)     line with slope 4 containing (-2, -4)

b)     line through (3, -1) and (4, -2)

c)     line containing (-3, 2) and parallel to the line 2x – 5y = 8

d)     line containing (-3, 2) and perpendicular to the line 2x – 5y = 8

e)     line through (1, 2) and perpendicular to the line through (-2, -2) and (3, 1)

f)      line through (-2, -2) and (3, -2)

g)     line through (-2, -2) and (-2, 3)

4.     For the following problems, evaluate the given function at the indicated position.

a)      - find f(0), f(3), f(-1), and f(a + h)

b)      - find g(0), g(-1), g(2a), and  (simplify all answers)

5.     Which of the following graphs represent a functions, which ones not? For each graph representing a function, determine the range and domain of that function.

6.     Solve the following systems of linear equations.

a)

b)

c)

d)

e)

f)

7.     Solve the following inequalities and draw the solution set on a number line.

a)

b)

c)

d)

e)     3x – 2 < 7 or x – 2 > 4

f)      | 4x – 1 | < 4.5

g)     | -5t - 3 | > 10

h)     | 2.1x – 7.9 | < -2

8.     Find the domains of the following functions:

a)

b)

c)

9.     Perform the following operations

a)      (simplify if possible)

b)      (simplify if possible)

c)      (simplify if possible)

d)      (simplify if possible)

e)     Factor the expression:

f)      Factor the expression:

g)     Factor the expression:

10.  If a given function f has a graph as indicated, please graph the modified function

a)     f(x) – 2

b)     f(x + 1)

c)     f(x – 2) + 1

d)     -f(x)

e)     f(-x)

11.  Solve the following story problems. Make sure to provide your answer as a complete sentence.

a)     The perimeter of a rectangle is 96. The length of the rectangle is 6 less than twice the width. Find the dimensions of the rectangle.

b)     500 tickets were sold for a fundraising dinner. The receipts totaled \$3312.50. Adult tickets were \$7.50 each and children's tickets were \$4.00. How many tickets of each type were sold?

c)     Yolanda wants 14 L of fruit punch that is 10% juice. At the store she finds punch that is 15% juice and punch that is 8% juice. How much of each should she purchase?

d)     A freight train leaves Chicago at midnight traveling south at a speed of 44mph. One hour later, a passenger train, going 55 mph, travels south from Chicago on a parallel track. How many hours will the passenger train travel before it overtakes the freight train?