precalculus midterm practice test (2008...

PRECALCULUS MIDTERM PRACTICE TEST (2008-2009) Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the distance d( , ) between the points and . 1) = ( 7, -3); = ( 3, -1) 1) _______

A) 12 B) 12 C) 2 D) 6

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

2) Find the length of each side of the triangle determined by the three points , , and

. State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both.

= (-5, -4), = (-3, 4), = (0, -1)

2) _____________

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

Find the midpoint of the line segment joining the points and . 3) = ( 0.9, 0.6); = ( 2.5, 1.9) 3) _______

A) ( 1.25, 1.7) B) ( 0.8, 0.65) C) ( 1.7, 1.25) D) ( 0.65, 0.8)

Solve the problem. 4) If ( 9, -1) is the endpoint of a line segment, and ( 14, -4) is its midpoint, find the other

endpoint. 4) _______

A) ( -1, 5) B) ( 3, 9) C) ( 19, 2) D) ( 19, -7)

List the intercepts for the graph of the equation. 5) + y - 81 = 0 5) _______

A) (0, -9), (81, 0), (0, 9) B) ( 9, 0), (0, 81), (0, -81) C) (-9, 0), (0, 81), ( 9, 0) D) (-9, 0), (0, -81), ( 9, 0)

Solve the equation algebraically. Verify the solution using a graphing utility.

6) 15( 2x - 6) = 5x - 9 6) _______ A)

{ }

B)

{- }

C)

{ }

D)

{ }

7) 7x + 1 - 7(x + 1) = -2x + 3 7) _______ A)

{ }

B) { -2} C)

{ }

D)

{ - }

8) 5 = -3x + 2 8) _______

A)

{ , 1}

B)

{- , - 1}

C)

{ , - 1}

D)

{- , 1}

9) = 6 9) _______

A) { 37} B) { 49} C) { 36} D) { 35}

Find an equation for the line with the given properties. Express the answer using the slope-intercept form of the equation of a line.

10) horizontal; containing the point ( 2.5, -7.7) 10) ______

A) y = 2.5 B) y = 5.2 C) y = 0 D) y = -7.7

Find the equation of the line in slope-intercept form. 11)

11) ______

A) y = - 5x + 17 B) y = - 5x - 23 C) y = - 5x - 19 D)

y = - x -

Find the slope and y-intercept of the line. 12) 3x + 11y = 33 12) ______

A)

slope = - ; y-intercept = 3

B)

slope = ; y-intercept = -3 C)

slope = - ; y-intercept = 33

D)

slope = ; y-intercept = 3

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the intercepts of the graph of the equation, then graph the equation.

13) 4x + 3y = 15

13) _____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find an equation for the line with the given properties. Express the answer using the slope-intercept form of the equation of a line.

14) Perpendicular to the line ; containing the point ( 2, 2) 14) ______ A) y = - 7x - 16 B) y = 7x - 16 C) y = - 7x + 16 D)

y = - x -

15) Parallel to the line y = -7; containing the point ( 9, 8) 15) ______ A) y = 9 B) y = -7 C) y = 8 D) y = -8

Find an equation for the line with the given properties. Express the answer using the general form of the equation of a line.

16)

Slope = ; containing the point ( 0, 4)

16) ______

A) -3x + 7y = -28

B) -3x + 7y = 28 C) 7x - 3y = -28 D) -3x - 7y = 28

Determine whether the relation represents a function. If it is a function, state the domain and range.

17) {( -1, 8), ( 2, 4), ( 4, -5), ( 8, -2)} 17) ______ A) function

domain: { -1, 2, 4, 8} range: { 8, 4, -5, -2}

B) function domain: { 8, 4, -5, -2} range: { -1, 2, 4, 8}

C) not a function

Find the value for the function.

18) Find f(2x) when f(x) = . 18) ______

A) B) C) D) 2

Find the domain of the function. 19)

19) ______

A) {x|x > 4} B) all real numbers C) {x|x ≠ 4} D) {x|x ≥ 4}

For the given functions f and g, find the requested function and state its domain.

20) f(x) = 9x + 8; g(x) = 2x + 6 Find f ∙ g.

20) ______

A) (f ∙ g)(x) = 18x2 + 22x + 48; {x|x ≠ 48} B) (f ∙ g)(x) = 18x2 + 48; {x|x ≠ 48} C) (f ∙ g)(x) = 18x2 + 70x + 48; all real numbers D) (f ∙ g)(x) = 11x2 + 70x + 14; all real numbers

21) f(x) = ; g(x) = 5x - 4

Find .

21) ______

A)

( )(x) = ; {x|x ≠ 0}

B)

( )(x) = ; {x|x ≠ } C)

( )(x) = ; {x|x ≥ 0}

D)

( )(x) = ; {x|x ≥ 0, x ≠ }

The graph of a function is given. Decide whether it is even, odd, or neither. 22)

22) ______

A) even B) odd C) neither

23)

23) ______


Determine algebraically whether the function is even, odd, or neither. 24) f(x) = 24) ______


25) f(x) = 3 - 25) ______


Solve the problem. 26) The cost C, in dollars, to produce graphing calculators is given by the function C(x) = 53x +

2500, where x is the number of calculators produced. How many calculators can be produced if the cost is limited to $ 129,700?

26) ______

A) 2494 calculators

B) 2400 calculators

C) 2200 calculators

D) 2680 calculators

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.

27) f(x) =

27) _____________

28) f(x) = + 1

28) _____________

29) f(x) = |x + 3| + 4

29) _____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Match the graph to one of the listed functions without using a graphing utility.

30)

30) ______

A) f(x) = - 4x B) f(x) = - - 4 C) f(x) = - 4 D) f(x) = - - 4x

Find the domain of the rational function. 31)

h(x) =

31) ______

A) {x|x ≠ -3, x ≠ 3} B) all real numbers C) {x|x ≠ 0, x ≠ -9} D) {x|x ≠ -3, x ≠ 3, x ≠ -8}

Use the graph to determine the domain and range of the function.

32)

32) ______

A) domain: {x|x ≠ 5} range: {y|y ≥ 0}

B) domain: {x|x ≥ 0} range: {y|y ≠ 5}

C) domain: {x|x ≠ 5} range: {y|y > 0}

D) domain: {x|x > 0} range: {y|y ≠ 5}

Find the vertical asymptotes of the rational function.

33)

f(x) =

33) ______

A) x = 0, x = 25 B) x = 0, x = -5, x = 5 C) x = 25, x = -11 D) x = -5, x = 5

34)

f(x) =

34) ______

A) x = 1, x = -4 B) x = -1, x = -4 C) x = -1 D) x = -1, x = 4

Give the equation of the horizontal asymptote, if any, of the function. 35)

R(x) =

35) ______

A) y = 0 B) no horizontal asymptotes C) y = -10, y = 5 D) y = -3

Solve the inequality.

36) - 9x ≥ 0 36) ______

A) (-∞, 0] or [ 9, ∞) B) [-9, 0] C) (-∞, -9] or [0, ∞) D) [0, 9]

Use the Factor Theorem to determine whether x - c is a factor of f(x). 37) f(x) = x4 - 45x2 - 196; x - 14 37) ______

A) Yes B) No

List the potential rational zeros of the polynomial function. Do not find the zeros. 38) f(x) = -2 + 3 - 4x + 8 38) ______

A)

± , ± 1, ± 2, ± 4

B)

± , ± 1, ± 2, ± 4, ± 8 C)

± , ± , ± 1, ± 2, ± 4, ± 8

D)

± , ± , ± , ± 1, ± 2, ± 4, ± 8

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. 39) Degree 3; zeros: 1, 4 - i 39) ______

A) -4 + i B) -1 C) 4 + i D) no other zeros

Form a polynomial f(x) with real coefficients having the given degree and zeros. 40) Degree: 3; zeros: -3 and 3 - 2i 40) ______

A) f(x) = x3 - 3x2 + 5x - 52 B) f(x) = x3 - 3x2 - 5x + 39 C) f(x) = x3 - x2 + 11x + 39 D) f(x) = x3 - x2 - 5x + 39

Use the given zero to find the remaining zeros of the function.

41) f(x) = x3 - 3x2 - 5x + 39; zero: -3 41) ______ A) 3 + 2i, 3 - 2i B) 1 + 2 i, 1 - 2 i C) 6 + 4i, 6 - 4i D) 1 + 2i, 1 - 2i

The graph of an exponential function is given. Match the graph to one of the following functions.

42)

42) ______

A) f(x) = B) f(x) = C) f(x) = - D) f(x) = -

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function.

43) f(x) =

43) _____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Approximate the value using a calculator. Express answer rounded to three decimal places.

44) 44) ______ A) 3.262 B) 3.320 C) 3.620 D) 1.641

Solve the system of equations by using substitution.

45)

45) ______

A) x = 0, y = 10 B) x = 10, y = 10 C) x = 10, y = 0 D) x = 0, y = 0

Use the elimination method to solve the system. 46)

46) ______

A) x = 0, y = 0 B) x = 0, y = 1 C) x = 1, y = 1 D) x = 1, y = 0

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Graph the system of inequalities.

47)

47) _____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write a system of linear inequalities that has the given graph.

48)

48) ______

A) x ≤ 4, and y + x ≤ 7 B) y ≥ 0, x ≥ 0, x ≤ 4, and y + x ≥ 7 C) y ≥ 0, x ≥ 0, x ≤ 7, and y + x ≤ 4 D) y ≥ 0, x ≥ 0, x ≤ 4, and y + x ≤ 7

Solve the problem.

49) The liquid portion of a diet is to provide at least 300 calories, 36 units of vitamin A, and 90 units of vitamin C daily. A cup of dietary drink X provides 60 calories, 12 units of vitamin A, and 10 units of vitamin C. A cup of dietary drink Y provides 60 calories, 6 units of vitamin A, and 30 units of vitamin C. Set up a system of linear inequalities that describes the minimum daily requirements for calories and vitamins. Let x = number of cups of dietary drink X, and y = number of cups of dietary drink Y. Write all the constraints as a system of linear inequalities.

49) ______

A)

B)

C)

D)

1) C 2) d( , ) = 2 ; d( , ) = ; d( , ) =

both 3) C 4) D 5) C 6) D 7) A 8) C 9) D

10) D 11) A 12) A 13)

x-intercept: ; y-intercept: 5

14) C 15) C 16) B 17) A 18) B 19) A 20) C 21) D 22) B 23) A 24) C 25) A 26) B 27)

28)

29)

30) B 31) C 32) C 33) A 34) C 35) D 36) A 37) B 38) B 39) C 40) B 41) A 42) D 43)

domain of f: (-∞, ∞); range of f:(0, ∞) horizontal asymptote: y = 0

44) B 45) B 46) B 47)

48) D 49) C

precalculus midterm practice test (2008...

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