MATH 95 EXAM 1



MATH 95 EXAM 1

FALL 2008

[pic]

▪ You have 1 hour and 50 minutes to complete the exam

▪ Please show all work for credit. Partial credit will be given for clear, organized progress toward a solution

▪ You may use your calculator and a 3x5 notecard

▪ You may not use your textbook, neighbor or cell phone.

[pic]

1. Fill in the blanks

a. To square a number, you multiply it by itself

b. Two lines are parallel if they have the same slope

c. The slope of a horizontal line is 0

d. The slope of a vertical line is undefined

e. The slope of the line [pic] is 1

f. The slope of the line [pic] is -1

g. The expression [pic]corresponds to what point on the graph of f? (3,8)

h. If a system is inconsistent and independent, it has no solution(s)

i. If a system is consistent and independent, it has one solution(s)

j. A function is a relation for which every input corresponds to one output(s)

For the following four problems, please give your final answer in slope intercept form.

2. Find the equation of the line which has slope -2 and passes through the point [pic]

y = -2x + 1

3. Find the equation of the line which passes through the points [pic] and [pic]

[pic]

4. Find the equation of the line which passes through the point [pic] and is parallel to the line [pic]

y = -3x +3

5. Find the equation of the line which passes through the point [pic] and is perpendicular to the line [pic]

[pic]

6. Solve the following system by graphing: [pic] Solution: (6, 3)

7. Solve the following system algebraically: [pic] Solution: [pic]

8. Solve the following system algebraically: [pic] Infinite # of solutions

9. Judy had two mochas. One was 20% coffee and the other was 60% coffee. How many ounces of each must she mix to make a 16 oz. mocha that is 49% coffee? (round your answer to two decimal places)

11.6 ounces of 60% coffee and 4.4 ounces of 20% coffee

10. Let [pic]and [pic], evaluate each of the following:

a. [pic]= -13

b. [pic] = 14

c. [pic]= 3t + 5

d. [pic]= 12

e. [pic]

f. [pic]

11. Find the domain of each function. Give your answers in interval notation

a. [pic]

(-∞, ∞)

b. [pic]

(-∞, -1/4) U (-1/4, ∞)

c. [pic]

[4/9, ∞]

12. For each graph, determine if the graph represents a function, and find the domain and range.

a. Domain:(-∞, ∞)

Range: (-∞, 1]

Function? no

[pic]

b. Domain: (-∞, 1] U [3, ∞)

Range: (-∞, ∞)

Function? no

[pic]

c. Domain: [-24, 1]

Range: [-14,14]

Function? no

[pic]

d. Domain: [2, ∞)

Range: [1, ∞)

Function? yes

[pic]

13. For each relation, determine if the relation is a function and find the domain and range

a. {(-2,4), (-1,2), (0,0), (1,-2), (2,-4)}

Domain: {-2, -1, 0, 1, 2}

Range: {4, 2, 0, -2, -4}

Is this relation a function? yes

b. {(2,2), (-1,3), (2,0), (4,4)}

Domain: {2, -1, 4}

Range: {2, 3, 0, 4}

Function? no

c. {(1,6), (-1,3), (0,2), (8,6), (3,0),(-2,0)}

Domain:{1, -1, 0, 8, 3, -2}

Range: {6, 3, 2, 0}

Is this relation a function? yes

d.

A 1 6

B 2 7

C 3 8

D 4 9

E 5 10

Domain: {A, B, C, D, E}

Range: {1, 2, 3, 4, 5}

Is this relation a function? no

MATH 95 EXAM 2

FALL 2008

Name: __________________________ Score: _______/100

[pic]

▪ You have 1 hour and 50 minutes to complete the exam

▪ Please show all work for credit. Partial credit will be given for clear, organized progress toward a solution

▪ You may use your calculator and a 3x5 notecard

▪ You may not use your textbook, neighbor or cell phone.

[pic]

2. Fill in the blank/short answer

a. Rewrite [pic] without fractional exponents: [pic]

b. Rewrite [pic] without negative or fractional exponents: [pic]

c. [pic] if [pic]

d. True or False: [pic] is a solution to [pic]

e. True or False: [pic]is a solution to [pic]

f. The square root of a negative number is a(n) imaginary number

g. The cube root of a negative number is a(n) real number

h. The complex conjugate of [pic] is – 4 + 9i

14. Simplify (Your answers should not contain any negative or fractional exponents)

a. [pic] = [pic]

b. [pic]

c. [pic]

d. [pic]

e. [pic]

f. [pic]

g. [pic]

h. [pic]

i. [pic]

j. [pic]

15. Perform each of the operations and give your answer in standard form of a complex number

a. [pic]

b. [pic]

c. [pic]

d. [pic]

e. [pic]

16. Solve for x

a. [pic]

x = 1, x = 7/2

b. [pic]

x = 9

c. [pic]

x = 4

d. [pic]

x = -12, x = 1

e. [pic]

x = -8

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