Mathematics 6

MTH 125 MIDTERM EXAM WEEK 6

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the inequality. Give the solution set in both interval and graph forms.

1) -10 y + 6 > -11 y - 2

1) _______

A) ( 4, ∞)

B) (-∞, 4)

C) (-∞, -8)

D) ( -8, ∞)

2) < -

2) _______

A)

B)

-

C)

-

D)

Solve the problem.

3) A car rental company has two rental rates. Rate 1 is per day plus per mile. Rate 2 is per day plus

per mile. If you plan to rent for one day, how many miles would you need to drive to pay less by taking Rate 2?

3) _______

A) more than 1800 miles B) more than 1000 miles

C) more than 900 miles D) more than 450 miles

4) Behemoth Back Packs, Inc. finds that the cost to make x back packs is while the revenue produced from

them is (C and R are in dollars). What is the smallest whole number of back packs, x, that must be sold for the

company to show a profit? 4) _______

A) 533,115 B) 36 C) 55 D) 823,905

For the compound inequality, give the solution set in both interval and graph forms.

5) -11 < 4x + 9 and 2x - 5 < -7

5) _______

A) ( -5, -1]

B) [ -5, -1]

C) [ -5, -1)

D) ( -5, -1)

Name the quadrant, if any, in which the point is located.

6) ( -11, -5) 6) _______

A) IV B) None C) III D) II

Complete the table for the equation.

7) y = -9x - 65

7) _______

A) 7; -79; 1 B) 7; -65; 1 C) 7; 0; 1 D) -8; -65; 1

Graph the equation by determining the missing values needed to plot the ordered pairs.

8) x - 2y = -8; (0, ), ( , 0), ( 3, ), ( , 3)

8) _______

A)

B)

C)

D)

Find the x- and y-intercepts. Then graph the equation.

9) -6x - 12y = 24

9) _______

A) ( -2, 0); (0, -4)

B) ( -4, 0); (0, -2)

C) ( 4, 0); (0, -2)

D) ( -2, 0); (0, 4)

Suppose that segment PQ has the given coordinates for one endpoint P and for its midpoint M. Find the coordinates

of the other endpoint Q.

10) P( 4, 8) and M 10) ______

A) Q B) Q C) Q( -3, -3) D) Q

Provide an appropriate response.

11) Determine the quadrants in which the given point (x, y) may lie when xy > 0. 11) ______

A) II or III B) I or II C) II or IV D) I or III

Find the slope of the line.

12)

12) ______

A) -5 B) 5 C) 1 D) -1

Graph the line described.

13) Through (0, 5); m = - 4

13) ______

A)

B)

C)

D)

Solve the problem.

14) A motorcycle daredevil is planning a stunt to perform at a county fair. A ramp must be built to give him a 20% grade,

or slope. If the vertical height at the end of the ramp must be 15 ft to assure that the stunt is a success, what must be the

length of the horizontal run?

14) ______

A) 15 ft B) 2.7 ft C) 270 ft D) 75 ft

Find the slope and the y-intercept of the line.

15) 4x - 5y = 5 15) ______

A) Slope 1; y-intercept (0, 1) B) Slope - ; y-intercept (0, 1)

C) Slope -1; y-intercept (0, -1) D) Slope ; y-intercept (0, -1)

Decide whether the relation is a function.

16)

16) ______

A) Function B) Not a function

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

17) The equation y = x2 is satisfied by the points (2, 4) and (-2, 4). A horizontal line may be drawn between these two

points. Is y = x2 a function? Explain. 17) _____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine whether or not the function is one-to-one.

18) f(x) = 3x2 - 5 18) ______

A) No B) Yes

Find the indicated value.

19) Let f(x) = . ( 8) 19) ______

A) 2 B) C) D) 3

Find the slope of the line.

20)

20) ______

A) 0 B) 2 C) -2 D) Undefined

Solve the problem.

21) A motorcycle daredevil is planning a stunt to perform at a county fair. A ramp must be built to give him a 20% grade,

or slope. If the vertical height at the end of the ramp must be 13 ft to assure that the stunt is a success, what must be the

length of the horizontal run?

21) ______

A) 234 ft B) 65 ft C) 13 ft D) 2.34 ft

Find the slope and the y-intercept of the line.

22) 3x - 4y = 4 22) ______

A) Slope ; y-intercept (0, -1) B) Slope ; y-intercept (0, 1)

C) Slope - ; y-intercept (0, 1) D) Slope - ; y-intercept (0, -1)

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.

23) 8y - 8 = -x

2x - 5y = -5 23) ______

A) {(0, 0)} B) {(0, 1)} C) {(1, 1)} D) {(1, 0)}

24) x + y = 4

x - 2y = 21 24) ______

A) {(6, -8)} B) {(-6, 8)} C) {(6, 8)} D) {(-6, -8)}

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.

25) x - 4y = -4

-4x - 3y = -3 25) ______

A) {(-1, 0)} B) {(1, 0)}

C) {(0, 1)} D) ∅; inconsistent system

26) -7x + 9y = -42

-5x + 2y = -30 26) ______

A) {( 6, 1)} B) {( 6, 0)}

C) {( 5, 1)} D) ∅; inconsistent system

Apply the product rule for exponents, if possible.

27) (-3 y)(-4 ) 27) ______

A) -12 B) 12 C) 12 D) 12

Evaluate the expression.

28) 28) ______

A) 1 B) 0 C) -1 D) -7

29) 29) ______

A) 64 B) 512 C) 24 D) 4096

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all

variables represent nonzero numbers.

30) 30) ______

A) - B) C) D)

31) 31) ______

A) 1 B) - C) D)

Simplify the expression. Write your answer with only positive exponents. Assume that all variables represent nonzero

real numbers.

32) 32) ______

A) B) C) D)

Determine whether or not the function is one-to-one.

33) f(x) = 5x2 + 5 33) ______

A) No B) Yes

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."

34) f(x) = 8 - 4 34) ______

A) Not one-to-one B) (x) =

C) (x) = ± D) (x) =

Find the indicated value.

35) Let f(x) = . ( 243) 35) ______

A) B) 5 C) D) 3

Graph the line described.

36) Through (0, 3); m = -

36) ______

A)

B)

C)

D)