Free Printable College Algebra Final Exam

1.

Which one of the following is true?

a)

The point (1, -4) lies in Quadrant II.

b)

The graph of an equation is the set of all points whose coordinates satisfy the equation.

c)

Every graph has at least one intercept.

d)

The graph of y = x^2 - 4 is a line.

2.

Solve the equation for x: 5 - 3(x - 6) = 2(x - 6)

a)

-7

b)

-1/5

c)

1

d)

7

3.

Solve the equation for x: 3/x - 1/4 = 1/3

a)

4/7

b)

36/7

c)

10

d)

21/2

4.

Solve the equation for x: x/(x-3) = 3/(x-3) + 9

a)

0

b)

3

c)

24/9

d)

∅

5.

Solve the equation for x: 3/(x+2) = (x+1)/(x+2) = (11x-2)/(x+2)

a)

5/9

b)

7/9

c)

1

d)

9/7

6.

You inherit $2500 with the stipulation that for the first year the money must be invested into two stocks paying 10% and 6% annual interest, respectively. How much should be invested at the 10% rate if the total interest earned for the year is to be$ 221.92?

a)

$449.50

b)

$702

c)

$1798

d)

$2219.20

7.

After a 7% increase in salary, Laurie makes $1016.50 per month. How much did she earn per month before the increase?

a)

$871.29

b)

$945.35

c)

$950

d)

$1087.66

8.

Solve the formula for the specified variable: A = P + Prt for P.

a)

P = A - Prt

b)

P = A/(1+rt)

c)

P = A(1+rt)

d)

P = A/2rt

9.

Solve the following equation for x. If there are two solutions, state their sum. If there is one solution, state that answer.: $5x^2 = 4$

a)

0

b)

2/5

c)

4/5

d)

2/√5

10.

Solve the following equation for x. If there are two solutions, state their sum. If there is one solution, state that answer.: $3x^2 - 2(x - 2) = 18 - 3x$

a)

-5/3

b)

-1/3

c)

1/3

d)

0

11.

Solve the following equation for x. If there are two solutions, state their sum. If there is one solution, state that answer.: $(2x + 1)^2 = 10x - 1$

a)

-5

b)

-5/2

c)

3/2

d)

5/2

12.

Solve the following equation for x. If there are two solutions, state their sum. If there is one solution, state that answer.

a)

1

b)

3

c)

5

d)

6

13.

Which one of the following is the sum of the solutions for $(x^2 + 3x)^2 - 8(x^2 + 3x) - 20 = 0$ ?

a)

-6

b)

4

c)

6

d)

8

14.

Solve the following equation for x. If there are two solutions, state their sum. If there is one solution, state that answer.: |2x + 3| = 17

a)

-3

b)

0

c)

3

d)

7

15.

Solve the inequality for x: (1/2)x - 4 < (1/3)x + 5

a)

(-∞, 9)

b)

(-∞, 54)

c)

(-∞, 6)

d)

(-∞, 54/5)

16.

Solve the absolute value inequality for x: |4x + 7| < 5

a)

(-3, -1/2)

b)

(-∞, -1/2)

c)

(-∞, -3)

d)

(-∞, -3) or (-1/2, ∞)

17.

Solve the quadratic inequality for x: $x^2 - 2x - 15 \geq 0$

a)

(-∞, -3) or (5, ∞)

b)

(-3, 5)

c)

(-∞, -3] or [5, ∞)

d)

[-3, 5]

18.

Solve the rational inequality for x: $\frac{x - 5}{x^2 + 2x - 8} \leq 0$

a)

(-∞, -4) or [2, 5)

b)

(-4, 2) or [5, ∞)

c)

(-∞, -4) or (2, 5)

d)

(-∞, -4) or (2, 5]

19.

Find the slope of the line containing the pair of points: (5, 2) and (–3, 7):

a)

–5/2

b)

–8/5

c)

–5/8

d)

9/2

20.

Which one of the following is an equation of a line that passes through the point (2, –3) with a slope of 4?

a)

y = 4x + 11

b)

y = 4x – 5

c)

y = (1/4)x – 3

d)

y = 4x – 11

21.

Find the slope of the line described: A line perpendicular to 3x – 2y – 5 = 0

a)

–3/2

b)

–2/3

c)

2/3

d)

3/2

22.

Find the exact distance between the two ordered pairs (0, 5) and (7, 9).

a)

√65

b)

√33

c)

√7

d)

√5

23.

Find the midpoint of the line segment joining the ordered pairs (–5, –20) and (16, –4).

a)

(11/2, –12)

b)

(5, –12)

c)

(21/2, 8)

d)

(21/2, –8)

24.

The center of the circle with the following equation is: $(x – 4)^2 + (y + 9)^2 = 25$

a)

(–4, 9)

b)

(4, –9)

c)

(–2, 3)

d)

(2, –3)

25.

Which one of the following is the standard form of the equation of the circle whose center is at the point (–5, 1) and whose radius is 4?

a)

$(x – 5)^2 + (y + 1)^2 = 2$

b)

$(x – 5)^2 + (y + 1)^2 = 16$

c)

$(x + 5)^2 + (y – 1)^2 = 2$

d)

$(x + 5)^2 + (y – 1)^2 = 16$

26.

Which one of the following does not define y as a function of x?

a)

$x^2 + y = 16$

b)

y = $(x – 3)^2 – 1$

c)

x + y = 3

d)

$x = y^2$

27.

If g(x) = $–x^2 + 3$ then find g(–4).

a)

19

b)

–13

c)

–5

d)

11

28.

If f(x) = $x^2 + 2x$ , then find f(a + h) – f(a).

a)

$h^2 + 2ah + 2h$

b)

$h^2 + 4a + 2h$

c)

$h^2 + 2ah + 2h$

d)

$h^2 + 2h$

29.

If f(x) = {–x + 1 for x < –1; 2x for x ≥ –1}, then evaluate f(–3).

a)

–8

b)

–6

c)

3

d)

4

30.

State the domain of the following function: y = √3x – 4

a)

(3/4, ∞)

b)

[3/4, ∞)

c)

(4/3, ∞)

d)

[4/3, ∞)

31.

State the domain of the following function in interval notation: f(x) = 5 / (√(x+7))

a)

(-7, ∞ )

b)

[-7, ∞)

c)

(-∞, ∞)

d)

(-∞, -7) ∪ (-7, ∞)

32.

Use the graph below to determine the function’s range. Tick marks along the axes represent one unit each.

a)

(-3,2]

b)

(-3,∞)

c)

(-3,2)

d)

[-2,3]

33.

If f(-x) = -f(x) for every value of x in the domain of the function f, then which one of the following is true about f?

a)

f is called an odd function and its graph is symmetric about the y-axis.

b)

f is called an even function and its graph is symmetric about the y-axis.

c)

f is called an odd function and its graph is symmetric about the origin.

d)

f is called an even function and its graph is symmetric about the origin.

34.

The graph of y = -3√x - 5 can be obtained by doing which of the following transformations of the graph of y = √x?

a)

reflect about the x-axis, stretch by a factor of 3, shift up 5 units.

b)

shift down 5 units, reflect about the y-axis, stretch by a factor of 3.

c)

reflect about the x-axis, stretch by a factor of 3, shift down 5 units.

d)

reflect about the x-axis, shrink by a factor of 3, shift down 5 units.

35.

If f(x) = $x^2 - 9$ and g(x) = $x - 3$ , then (f/g)(5) =

a)

5(x+3)

b)

x+3

c)

1/8

d)

8

36.

If f(x) = 2x - 4 and g(x) = 3x + 1, then (f + g)(x) =

a)

x - 3

b)

$5x^2 - 3x$

c)

-x - 3

d)

5x - 3

37.

If f(x) = $x^2 + 1$ and g(x) = $x - 2$ , then (f ∘ g)(x) =

a)

$x^2 - 4x + 5$

b)

$x^2 - 3$

c)

$x^2 - 1$

d)

$x^2 - 2x + 5$

38.

If f(x) = $-7x + 3$ and g(x) = $x^2 + 4$ , what is (f ∘ g)(2)?

a)

-53

b)

59

c)

125

d)

292

39.

If f(x) = $(3/4)x - 2$ , then f^(-1)(x) =

a)

4/(3x-8)

b)

(4/3)x - 8/3

c)

(4/3)x + 8/3

d)

(-4/3)x + 2

40.

Which one of the following is true about the graph of a one-to-one function of x?

a)

It is symmetric about the y-axis.

b)

It is symmetric about the x-axis.

c)

It will pass through the ordered pair (1, 1).

d)

It will pass the horizontal line test.

41.

Find the coordinates of the vertex of the parabola: $y = 4(x + 3)^2 + 5$

a)

(-3, 5)

b)

(3, 5)

c)

(3, -5)

d)

(-3, -5)

42.

Find the coordinates of the vertex of the parabola: $y = 2x^2 + 4x - 3$

a)

(-1, 5)

b)

(-1, -5)

c)

(1, -5)

d)

(1, 5)

43.

Match the correct equation with the parabola. Tick marks along the axes represent one unit each.

a)

$y = 5(x-1)^2 - 2$

b)

$(x-1)^2 + 2$

c)

$y = (x-2)^2 - 1$

d)

$(x+2)^2 - 1$

44.

Find the x and y intercepts for the given quadratic function: y = $x^2 + 3x - 4$

a)

(0, -4), (4, 0), (-1, 0)

b)

(4, 0), (0, 4), (-1, 0)

c)

(0, 4), (-4, 0), (0, 1)

d)

(0, -4), (-4, 0), (1, 0)

45.

Which one of the following equations is a polynomial function of x?

a)

$f(x) = x^{(1/2)} - 2x + 1$

b)

$g(x) = \frac{x^2 + 7}{x^3}$

c)

$h(x) = 7x^2 - 2x + \frac{1}{3}$

d)

$y = x^{-1} + 4$

46.

What information can multiplicity provide about the graph of a polynomial?

a)

Where the graph crosses the x- and y-axis.

b)

Whether the graph will touch and turn at the x-axis or crosses the x-axis at an x-intercept.

c)

The domain of the graph of the polynomial.

d)

The range of the graph of the polynomial.

47.

Which one of the following functions will have a graph whose end behavior indicates that the graph will rise to the left?

a)

$f(x) = -2x^4 + 4x^2 - 6x + 9$

b)

$f(x) = x^5 - 4x^2 - 6x - 9$

c)

$f(x) = -4x^5 - 4x^2 - 6x - 9$

d)

$f(x) = -3x^4 + 4x^2 - 6x + 9$

48.

Find the quotient and remainder for the following: $(5x^4 + 17x^3 + 10x^2 + 13x - 14) ÷ (x + 3)$

a)

$5x^3 + 2x^2 + 9x + 14; -17$

b)

$5x^3 + 2x^2 + 4x + 13$ ; -53

c)

5x^3 + 2x^2 + 4x + 1; -17

d)

5x^3 + 32x^2 + 106x + 331; 979

49.

If the number 3 is a zero of a polynomial function f(x), then which of the following is true?

a)

x - 3 is a factor of f(x)

b)

x + 3 is a factor of f(x)

c)

-3 is a zero of f(x)

d)

f(-3) = 0

50.

Use the rational zero theorem to find all possible rational zeros for the polynomial function. f(x) = $9x^7 + 5x^3 - 7x + 10$

a)

±(1, 3, 9, 1/2, 3/2, 9/2, 1/5, 3/5, 9/5, 1/10, 3/10, 9/10)

b)

±(1, 2, 5, 10)

c)

±(1, 2, 5, 10, 1/3, 2/3, 5/3, 10/3, 1/9, 2/9, 5/9, 10/9)

d)

±(1, 3, 9)

51.

Find the remaining zeros of f(x) = $x^4 + 8x^3 + 2x^2 - 80x - 75 = 0$ , given -5 is a double root. What is the sum of these remaining roots?

a)

2

b)

4

c)

-2

d)

-4

52.

Which one of the following equations have the given roots, 3 and -4?

a)

$x^3 - 3x^2 + 16x - 48$

b)

$x^3 + 3x^2 + 16x + 48$

c)

$x^3 - 3x^2 - 16x + 48$

d)

$x^3 + 3x^2 - 16x - 48$

53.

Write the following as a product of linear factors given that 1 and -3 are zeros: f(x) = $x^4 + 2x^3 + x^2 + 8x - 12$

a)

(x - 1)(x + 3)(x + 2i)(x - 2i)

b)

(x + 1)(x - 3)(x - 2i)(x + 2i)

c)

(x - 1)(x + 3)(x + 2i)(x - 2i)

d)

(x + 2)(x - 2)(x + 3)(x - 1)

54.

State the domain of the following function in interval notation: f(x) = $(x^2 - 4)/(x + 2)$

a)

(-∞, 2) or (2, ∞)

b)

(-∞, -2) or (-2, ∞)

c)

(-∞, ∞)

d)

(-∞, -2) or (-2, 2) or (2, ∞)

55.

Find the horizontal asymptote: f(x) = (4x - 1)/(7x - 9)

a)

y = 9/7

b)

y = 0

c)

x = 1/4

d)

y = 4/7

56.

Find the vertical asymptote(s): f(x) = $(4x - 9) / (2x^2 + 9x - 5)$

a)

x = -1/2, x = 5

b)

x = 1/2, x = -5

c)

x = 9/4

d)

y = 0

57.

Find the y-intercept: f(x) = $\frac{5x^2 - 4}{x + 3}$

a)

(0, -3)

b)

(0, -4/3)

c)

(-4/3, 0)

d)

(-3, 0)

58.

Find the x-intercept: f(x) = (5 - x) / (x + 5)

a)

(0, 1)

b)

(5, 0)

c)

(1, 0)

d)

(-1, 0)

59.

If P varies inversely as w, and P = 2/3 when w = 1/4, then what is P when w = 1/6?

a)

1

b)

16

c)

4/9

d)

4

60.

Which one of the following is true?

a)

If y varies inversely as x, then for x = 0, we get y = 0.

b)

The area of a rectangle varies directly as its length and inversely as its width.

c)

The number π can be a constant of variation.

d)

If y varies directly as x, then y is not a linear function.

61.

If y varies directly as u and varies inversely as the square of v, and y = 7 when u = 9 and v = 6, then find the constant of variation.

a)

7√6/9

b)

7/4

c)

28/9

d)

28

62.

The number of spiders, S(t), remaining within a 10-foot radius of their birthplace t days after birth is given by the formula: $S(t) = 200(2^{-0.2t})$ . Find the number of spiders present within this radius 10 days after their birth.

a)

0

b)

5

c)

50

d)

800

63.

If $4500 is invested at a rate of 8% compounded quarterly, then how much interest will be earned at the end of 6 years?

a)

$353,235.81

b)

$24,035.31

c)

$7237.97

d)

$2737.97

64.

The growth in the population of a biology experiment fits $A(t) = 445e^{0.13t}$ where t is the number of years since 1987. Estimate the population in the year 2000.

a)

527

b)

451

c)

264

d)

534

65.

What is the range of f(x) = $2^{(x+3)} - 1$ ?

a)

(-∞, ∞)

b)

(-1, ∞)

c)

(-3, ∞)

d)

(3, ∞)

66.

Write the equation in its equivalent logarithmic form: ∛8 = 2

a)

log₂(8) = 3

b)

log₈(2) = 1/3

c)

log₃(2) = 8

d)

log₈(1/3) = 2

67.

Evaluate the expression: log₉(1/729)

a)

-3

b)

3

c)

81

d)

-81

68.

What is the domain for f(x) = log₂(x+1)?

a)

(0, ∞)

b)

[-1, ∞)

c)

(-1, ∞)

d)

(-∞, ∞)

69.

Which one of the following is true?

a)

$e^{ln(x)}$ = x for any real number x.

b)

log₈(8)/log₃(3) = log₈(8) - log₃(3)

c)

log₈(8)/log₈(3) = 8/3

d)

log₂(7) = log(7)/log(2)

70.

Write as a single logarithm whose coefficient is 1: 2 log₈(8) - log₃(3)

a)

log₈(13)

b)

log₈(61)

c)

log₈(64/3)

d)

log₈(10)

71.

Expand the logarithmic expression: ln(3e²)

a)

2 ln(3) + ln(e)

b)

(2 ln 3) + 1

c)

2 + ln(3)

d)

-2 + ln(3)

72.

If 5ˣ = 29, then x equals

a)

ln(29)/ln(5)

b)

ln(5)/ln(29)

c)

ln(29/5)

d)

ln(5/2)

73.

Solve for x: log₇(3x-9) - log₇(2x-6) = 0

a)

3

b)

all real numbers

c)

-3

d)

No solution

74.

Solve for x. If there are two solutions, state their sum. If there is one solution, state that answer. log(x+9) + log(x) = 1

a)

-9

b)

9

c)

-1

d)

1

75.

If $2500 is invested in the account that pays interest compounded continuously at a rate of 4%, how long will it take to double the investment?

a)

2.8 years

b)

13.0 years

c)

14.2 years

d)

17.3 years

76.

The spread of a flu virus through a particular population is modeled by $y = \frac{1000}{1 + 990e^{-0.7t}}$ where y is the total number of people infected after t days. In how many days will 530 people be infected with the virus? (Round your answer to the nearest whole number.)

a)

8 days

b)

9 days

c)

10 days

d)

11 days

77.

When the system of linear equations is solved, what is the x-value of the solution?

a)

-26/17

b)

-34/5

c)

-9/2

d)

-4

College Algebra Final Exam

Total questions: 77

Worksheet time: 39mins

Similar Resources on Wayground