Free Printable Algebra 2 Final Exam

1.

Multiply:
$(4–3i)(-7–2i)$

a)

$-23+13i$

b)

$-23-29i$

c)

$-34-29i$

d)

$-34+13i$

2.

What is the complex conjugate of $4-3i$ ?

a)

$\frac{1}{4-3i}$

b)

$\frac{1}{4+3i}$

c)

$-4+3i$

d)

$4+3i$

3.

Simplify. $u^{-\frac{5}{4}}\cdot\left(u^{\frac{3}{2}}\right)^{\frac{3}{2}}$

a)

$u^{\frac{1}{4}}$

b)

$u$

c)

$u^{\frac{7}{4}}$

d)

$u^3$

4.

Simplify the expression:
$3^{\frac{1}{3}}\cdot9^{\frac{1}{3}}$

a)

3

b)

9

c)

1/3

d)

27

5.

Simplify:
$32^{\frac{3}{5}}$

a)

2

b)

8

c)

16

d)

32

6.

Factor
$2x^2-13x-70$

a)

$(2x-7)(x+10)$

b)

$(7x+5)(x+2)$

c)

$(2x+7)(x-10)$

d)

$2(x+7)(x+10)$

7.

Factor:
$x^2+16$

a)

$\left(x+4\right)\left(x+4\right)$

b)

$(x-4i)(x+4i)$

c)

$(x-8)(x+8)$

d)

$(x-4)(x+4)$

8.

Solve By Completing the Square:

$p^2-10p-52=0$

a)

$5\pm\sqrt{77}$

b)

$-5\pm\sqrt{77}$

c)

$5\pm77$

d)

$5+i\sqrt{77}$

9.

Solve:
$x^2+12x-5=0$

a)

$6\pm\sqrt{41}$

b)

$-6\pm2\sqrt{41}$

c)

$-6\pm\sqrt{41}$

d)

$-6\pm\sqrt{164}$

10.

Solve:
$(2x+1)^{\frac{1}{3}}+3=6$

a)

1

b)

13

c)

4

d)

16

11.

Solve:
$\sqrt{5-x}=x+1$

a)

No solution

b)

2

c)

1

d)

$-4$

12.

Solve:
$\sqrt{10-13x}=x-4$

a)

$x=2,3$

b)

$x=-2,-3$

c)

$x=-1,-6$

d)

No solution

13.

Find the domain and range:
$y=-\sqrt{x-1}+4$

a)

Domain: $\left(-\infty,\ \infty\right)$ Range: $\left(-∞,4\right]$

b)

Domain: $[1,∞)$ Range: $(-∞,4]$

c)

Domain: $[-1.∞)$ Range: $[4,∞)$

d)

Domain: $[4,∞)$ Range: $[-1,∞)$

14.

Given $f(x)=x^2+1$
and
$g(x)=2x-5$ ,
Find $f(x)-g(x)$ .

a)

$x^2-2x+6$

b)

$-x^2+2x+4$

c)

$-x^2-2x-6$

d)

$x^2-2x-4$

15.

Given $p(x)=3x+4$ and
$q(x)=2x^2$ ,
Find $q(p(-2))$ .

a)

8

b)

$-8$

c)

28

d)

22

16.

Given $f(x)=2x$ and $g(x)=x^2+3$
find $f(g(x))$ .

a)

$x^2+2x+3$

b)

$4x^2+3$

c)

$2x^2+3$

d)

$2x^2+6$

17.

Find the inverse of $y=\left(x-4\right)^2+3$ .

a)

$y=\sqrt{x-3}+4$

b)

$y=\sqrt{x+3}-4$

c)

$y=\sqrt{x-3+4}$

d)

$y=\sqrt{3x+1}$

18.

Classify by degree and number of terms: $-5n^4+10n-7$

a)

cubic trinomial

b)

quadratic trinomial

c)

quartic trinomial

d)

quintic trinomial

19.

$8x^3-1$ Factor:

a)

$(2x-1)(4x^2+2x+1)$

b)

$(2x+1)(4x^2-2x+1)$

c)

$(2x-1)(4x^2-2x-1)$

d)

$(2x+1)(4x^2+2x+1)$

20.

Factor completely:
$3x^4-48$

a)

$3(x^2+4)(x^2-4)$

b)

$(x^2+4)(x^2-4)$

c)

$3(x+2)(x-2)\left(x+\sqrt{2}\right)\left(x-\sqrt{2}\right)$

d)

$3(x+2)(x-2)\left(x+2i\right)\left(x-2i\right)$

21.

Factor completely:
$u^4-6u^2+8$

a)

$\left(u-2\right)\left(u+2\right)\left(u-\sqrt{2}\right)\left(u+\sqrt{2}\right)$

b)

$\left(u^2-2\right)\left(u^2-4\right)$

c)

$\left(u^2+4\right)\left(u^2+2\right)$

d)

$\left(u-2\right)\left(u+2\right)\left(u-2i\right)\left(u+2i\right)$

22.

Divide:
$(2x^3+5x^2+9)÷(x+3)$

a)

$2x^2-x+3$

b)

$2x^3-x^2+3x$

c)

$2x^2+11x+33+\frac{108}{x+3}$

d)

$2x^2-5x+12$

23.

If $f(x)=x^3+8x+24$ , find $f(-2)$ using synthetic division.

a)

12

b)

8

c)

0

d)

$-6$

24.

Find all zeros
$P(x)=x^3+6x^2+9x+54$
given that $f\left(-6\right)=0$ .

a)

$6,\ \pm3$

b)

$-6,\ \pm3$

c)

$-6,\ \pm3i$

d)

$6,\ \pm3i$

25.

Find all zeros
$P(x)=x^3-3x^2+12x-10$
given that $\left(x-1\right)$ is a factor.

a)

$1,\ 1\pm3i$

b)

$1,\ -1\pm3i$

c)

$-1,\ -1\pm3i$

d)

$-1,-5,\ 2$

26.

Which equation best describes the graph shown?

a)

$y=x(x-3)(x-2)$

b)

$y=x(x-3)^2(x+2)$

c)

$y=x\left(x+3\right)\left(x-2\right)$

d)

$y=-x(x+3)^2(x-2)$

27.

What is the least degree of the function graphed here?

a)

6

b)

4

c)

3

d)

5

28.

How many REAL zeros does the function have?

a)

None

b)

2

c)

3

d)

4

29.

Simplify:
$\frac{35n-25}{63n-45}\cdot\frac{9n+9}{n^2+7n+6}$

a)

$\frac{20}{n-4}$

b)

$\frac{5}{n+6}$

c)

$5\left(n-9\right)$

d)

$\frac{n+9}{7n}$

30.

Simplify:
$\frac{4}{x+8}+\frac{3}{x-5}$

a)

$\frac{7x+3}{(x-5)(x+8)}$

b)

$\frac{2x+3}{(x-5)(x+8)}$

c)

$\frac{2x+4}{(x-5)(x+8)}$

d)

$\frac{7x+4}{(x-5)(x+8)}$

31.

Simplify: $\frac{\frac{1}{k+2}}{\frac{5}{k^2-4}}$

a)

$\frac{k-2}{5}$

b)

$\frac{k+2}{5}$

c)

$\frac{5}{k-2}$

d)

$k-2$

32.

Solve:
$\frac{5}{x-2}+\frac{x-6}{x^2-2x}=\frac{1}{x}$

a)

5

b)

$\frac{4}{5}$

c)

1

d)

$-4$

33.

Solve:
$\frac{3}{x-5}-\frac{20}{x^2-25}=\frac{2}{x+5}$

a)

$x=-5$

b)

$x=5$

c)

$\frac{5}{\left(x+5\right)\left(x-5\right)}$

d)

No Solution

34.

Solve the rational inequality and state your solution in interval notation.

$\frac{3x-7}{x+2}>0$

a)

$\left(-2,\ \frac{7}{3}\right)$

b)

$\left(\ \frac{7}{3},\ \infty\right)$

c)

$\left(-\infty,-2\right)\cup\left(\frac{7}{3},\ \infty\right)$

d)

$\left(-\infty,-2\right)\cup\left[\frac{7}{3},\ \infty\right)$

35.

Find the partial fraction decomposition.
$\frac{-5x-41}{x^2+x-12}$

a)

$\frac{3}{x+4}-\frac{8}{x-3}$

b)

$\frac{8}{x+4}-\frac{3}{x-3}$

c)

$\frac{16}{x+4}-\frac{21}{x-3}$

d)

$\frac{-8}{x+4}+\frac{3}{x-3}$

36.

Identify the hole in the graph of $y=\frac{2x^2+6x-8}{x^2-1}$ .

a)

$(-1,\ 3)$

b)

$(1,\ 4)$

c)

$(1,\ 5)$

d)

there is no hole

37.

Which graph has a horizontal asymptote of y = 0?

a)

$y=\frac{2x}{x-5}$

b)

$y=\frac{2x}{x^2-5}$

c)

$y=\frac{2x^2}{x-5}$

d)

$y=\frac{2x}{2x-5}$

38.

Which function is graphed?

a)

$f(x)=-3|x-1|+4$

b)

$f(x)=-|x-1|+4$

c)

$f(x)=-5|x+1|+4$

d)

$f(x)=-3|x-4|+1$

39.

Solve:
$−2|2r+4|=-12$

a)

$1$

b)

$\left\{\pm1\right\}$

c)

$\left\{1,\ -5\right\}$

d)

No Solution

40.

Solve:
$|3n+12|=2n$

a)

No Solution

b)

$-12,-\frac{12}{5}$

c)

$-12$

d)

$-\frac{12}{5}$

41.

Solve:
$|b-8|+10>22$

a)

$-4,\ 20$

b)

$\left(-\infty,\ -4\right)\cup\left(20,\ \infty\right)$

c)

$\left(-4,\ 20\right)$

d)

$\left(-\infty,\ -4\right]\cup\left[20,\ \infty\right)$

42.

What is $f(-2)$ ?

a)

4

b)

1

c)

$-1$

d)

1, 4

43.

Which piecewise function best represents the graph shown?

a)

b)

c)

d)

44.

Write the logarithmic expression as a single logarithm $\log_460-\log_44+\log_4x$

a)

$\log_415$

b)

$\log_415x$

c)

$\log_456x$

d)

$x\log_430$

45.

Expand the logarithmic expression
$\log\frac{5x}{4y}$

a)

$\log5x+\log4y$

b)

$\log5x-4\log y$

c)

$\log5+\log x-\log4-\log y$

d)

$5\log x-4\log y$

46.

Find the inverse of
$f(x)=\log_4(x+4)$

a)

$f^{-1}(x)=4^{(x-4)}$

b)

$f^{-1}(x)=4^x+4$

c)

$f^{-1}(x)=4^x-4$

d)

$f^{-1}(x)=4^x$

47.

Evaluate $\log_520$ to the nearest thousandth.

a)

$0.537$

b)

$2.996$

c)

$1.301$

d)

$1.861$

48.

Solve for x:
$\log_6x+\log_6(x-5)=2$

a)

$\sqrt{7}$

b)

9

c)

4

d)

none of these

49.

Solve for x.
$8+\log_6\left(x-1\right)=6$

a)

$\frac{37}{36}$

b)

$-\frac{1331}{8}$

c)

$-\frac{1}{28}$

d)

11

50.

Solve for x:
$3e^{2x}+1=5$

a)

$x\approx0.131$

b)

$x\approx0.187$

c)

$x\approx0.151$

d)

$x=0.144$

Algebra 2 Final Exam

Total questions: 50

Worksheet time: 4hrs 10mins

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