Free Printable FInal Exam Review

1.

Factor
m²+ 9m + 14

a)

(m + 7)(m + 2)

b)

(m + 14)(m + 1)

c)

m(m + 23)

d)

m(m + 9) + 14

2.

Solve by factoring: x² + 3x + 2 = 0

a)

x = 2 and x = -1

b)

x = -1 and x = -1

c)

x = -2 and x = -1

d)

x = 2 and x = 1

3.

Solve for n.

$5n^2+35=0$

a)

$\pm5i\ \sqrt[]{35}$

b)

$\pm\ \sqrt[]{-7}$

c)

$\pm i\ \sqrt[]{7}$

d)

$-i\ \sqrt[]{7}$

4.

Solve for x by factoring.
$x^2-4x=0$

a)

{2, 2}

b)

{0, 4}

c)

{-4}

d)

{4}

5.

Solve by factoring: x² - 4x - 12 = 0

a)

x = 1 and x = -12

b)

x = 6 and x = -2

c)

x = 4 and x = -3

d)

x = 6 and x = 2

6.

(x + 6)(x + 3)

a)

x²- 6x - 3

b)

x²+ 9x + 18

c)

x² + 9x - 18

d)

x² - 3x - 18

7.

(x + 5)(x - 8)

a)

x² - 3x + 40

b)

x²- 5x + 8

c)

x² - 3x - 40

d)

x² - 13x - 40

8.

(5 - 2i) + (-13 - 8i)

a)

-8 - 10i

b)

-18i

c)

8 - 10i

d)

-8 - 6i

9.

(5 + 2i)(1 + 3i)

a)

11 + 17i

b)

5 + 6i

c)

-1 + 17i

d)

-1

10.

Simplify:
(10+ 15i) - (48 - 30i)

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

11.

(7 - 6i) + (9 + 11i)

a)

16 + 17i

b)

16 + 5i

c)

2 + 5i

d)

16 - 5i

12.

Multiply:
(6 – 4i)(6 + 4i)

a)

12 - 8i

b)

52i

c)

52

d)

$36-16i^2$

13.

Factor

$x^2-11x+18$

a)

(x + 9)(x - 2)

b)

(x - 9)(x - 2)

c)

(x - 6)(x - 3)

d)

(x - 9)(x - 9)

14.

$\sqrt[]{-16}$

a)

4i

b)

4

c)

$8i\ \sqrt[]{2}$

d)

$4i\ \sqrt[]{4}$

15.

Complete the square and rewrite.

$x^2+12x\ +\ c$

a)

$c=64;\ \left(x+8\right)^2$

b)

$c=36;\left(x-6\right)^2$

c)

$c=36;\left(x+6\right)^2$

d)

$c=16;\left(x+4\right)^2$

16.

Complete the square and rewrite.
x² - 20x + ____

a)

$c\ =\ 100;\ \left(x-10\right)^2$

b)

$c\ =\ 20;\ \left(x-10\right)^2$

c)

$c=100;\ \left(x+10\right)^2$

d)

$c=64;\left(x-8\right)^2$

17.

Complete the Square and rewrite.
x² + 11x + ____

a)

$c=\frac{121}{4};\left(x+\frac{11}{2}\right)^2$

b)

$c=\frac{121}{2};\left(x+\frac{11}{4}\right)^2$

c)

$c=\frac{121}{4};\left(x-\frac{11}{2}\right)^2$

d)

$c=121;\left(x+11\right)^2$

18.

$\sqrt{-80}$

a)

$8i\sqrt{10}$

b)

$80i$

c)

$4i\sqrt{5}$

d)

$\sqrt{80}$

19.

$\sqrt[]{-56}$

a)

2i√14

b)

$8i\ \sqrt[]{7}$

c)

$7i\ \sqrt[]{8}$

d)

i√56

20.

$\sqrt{72}$

a)

$9\sqrt{8}$

b)

$6\sqrt{2}$

c)

$2\sqrt{6}$

d)

$\sqrt{72}$

21.

Simplify:
$\left(3x^4+4x^2\right)\left(x^3-2x^2-1\right)$

a)

$3x^{12}-6x^8-11x^4+4x^6-4x^2$

b)

$3x^{12}-6x^8+4x^6-11x^4-4x^2$

c)

$3x^7+6x^6-4x^5+11x^4+4x^2$

d)

$3x^7-6x^6+4x^5-11x^4-4x^2$

22.

How many real solutions does the function have?

a)

0

b)

1

c)

2

d)

3

23.

How many real solutions?

a)

1

b)

2

c)

4

d)

10

24.

$Find\ p\left(-4\right)\ if\ p\left(x\right)=3x^2-4x+7$

a)

39

b)

71

c)

7

d)

57

25.

$Find\ f\left(-2\right)\ for\ f\left(x\right)=2x^4-3x^3+x^2-x+5$

a)

19

b)

15

c)

67

d)

63

26.

$\left(2x^2+3x-14\right)\div\left(x-2\right)$

a)

2x+7

b)

(2x + 7)(x - 2)

c)

x + 2

d)

x - 15

27.

$Find\ p\left(-3\right)\ if\ p\left(x\right)=4-x$

a)

4

b)

1

c)

7

d)

12

28.

$Find\ f\left(3\right)\ for\ f\left(x\right)=x^2-9x+5$

a)

-13

b)

-23

c)

-16

d)

41

29.

$\left(5x^2-10x-20\right)+\left(9x^2-4\right)$

a)

14x² - 10x + 24

b)

14x² - 10x - 16

c)

14x² - 24

d)

14x²-10x - 24

30.

$y^7\cdot y^3\cdot y^2$

a)

y⁴²

b)

y²

c)

3y¹²

d)

y¹²

31.

$\frac{15r^{10}-5r^8+40r^2}{5r^4}$

a)

$\frac{1}{3r^6-r^4+8r^2}$

b)

$3r^6-r^4+\frac{8}{r^2}$

c)

$3r^6-r^4+8r^2$

d)

$3r^{14}-r^{12}+\frac{8}{r^6}$

32.

$\left(3a^0b^2\right)\left(2a^3b^2\right)^2$

a)

$36a^6b^8$

b)

$12ab^6$

c)

$12a^6b^6$

d)

$6b^8$

33.

$3x\left(2x^2-y\right)$

a)

12x - y

b)

6x²- 3y

c)

6x³ - 3xy

d)

5x³ + 3xy

34.

$State\ the\ \deg ree\ of\ 2x^2-5x^3+7x^4-9$

a)

4

b)

7

c)

-9

d)

3

35.

$\frac{3y^2z}{15y^5}$

a)

$\frac{y^3z}{5}$

b)

$\frac{z}{5y^3}$

c)

$5y^3z$

d)

$\frac{y^7z}{5}$

36.

$\left(7x^3-2x^2+3\right)+\left(x^2-x-5\right)$

a)

$7x^3-2x^2-2$

b)

$8x^5-3x^3-2$

c)

$7x^3-x^2-x-2$

d)

$7x^3-2x^2-x-2$

37.

$\frac{4a^4b^2c}{12a^2b^5c^3}$

a)

$\frac{a^2b^3}{8c^2}$

b)

$\frac{a^2b^3}{3c^2}$

c)

$\frac{a^2}{2b^3c^2}$

d)

$\frac{a^2c^2}{3b^3}$

38.

$State\ the\ \deg ree\ of\ x^6-6+4x^8-8x^2$

a)

2

b)

6

c)

-8

d)

8

39.

$\left(x^2+2x-5\right)-\left(3x^2-4x+7\right)$

a)

$2x^2-2x-12$

b)

$-2x^2+6x-12$

c)

$4x^2+6x+2$

d)

$4x^2-2x+2$

40.

$\left(x^2-2x-35\right)\div\left(x+5\right)$

a)

x + 5

b)

$x^3+3x^2-45x-175$

c)

$x^2-x-30$

d)

x - 7

41.

Find Inverse

{(-3, 9), (-2, 4), (0, 0), (1, 1)}

a)

{(4, -3), (9, -2), (0, 1), (0, 1)}

b)

{(0, -3), (1, -2), (0, 9), (4, 1)}

c)

{(-3, 9), (-2, 4), (0, 0), (1, 1)}

d)

{(9, -3), (4, -2), (0, 0), (1, 1)}

42.

Find Inverse.

{(8, -2), (10, 5), (12, 6), (14, 7)}

a)

{(8, -2), (10, 5), (12, 6), (14, 7)}

b)

{(-2, 5), (5, 8), (6, 10), (7, 6)}

c)

{(-2, 8), (5, 10), (6, 12), (7, 14)}

d)

{(5, 8), (-2, 10), (7, 12), (6, 14)}

43.

$\sqrt[4]{81a^{32}b^{20}}$

a)

$20.25a^{32}b^{20}$

b)

$3a^{32}b^{20}$

c)

$3a^8b^5$

d)

$20.25a^8b^5$

44.

$\sqrt[3]{8g^3k^8}$

a)

$2gk^3$

b)

$2gk^2\cdot\sqrt[]{k^2}$

c)

$2gk^2\cdot\sqrt[3]{k^2}$

d)

$2\left|g\right|k^2\cdot\sqrt[3]{k^2}$

45.

Identify the Domain of the graph $y=\sqrt[]{x+3}+9$

a)

$x\le-\frac{1}{3}$

b)

$x\ge3$

c)

$x\ge-3$

d)

$x\ge-\frac{1}{3}$

46.

$\sqrt[3]{125t^6w^2}$

a)

$5t^2\cdot\sqrt[]{w^2}$

b)

$25t^2\cdot\sqrt[3]{w^2}$

c)

$5t^3\cdot\sqrt[3]{w^2}$

d)

$5t^2\cdot\sqrt[3]{w^2}$

47.

$6\sqrt[]{20}+8\sqrt[]{5}-5\sqrt[]{45}$

a)

$9\sqrt[]{-20}$

b)

$5\sqrt[]{-5}$

c)

$5\sqrt[]{5}$

d)

$-5\sqrt[]{5}$

48.

$\left(3\sqrt[]{15}\right)\left(-4\sqrt[]{45}\right)$

a)

$-180\sqrt[]{3}$

b)

$3\sqrt[]{15}-12\sqrt[]{5}$

c)

$-360\sqrt[]{3}$

d)

$-36\sqrt[]{15}$

49.

$\sqrt[]{121}$

a)

Not a Real number

b)

$\sqrt[]{11}$

c)

-11

d)

11

50.

$If\ f\left(x\right)=x+5\ and\ g\left(x\right)=2x,\ find\ \left(f\cdot g\right)\left(x\right).$

a)

$3x^2+10x$

b)

$2x+10$

c)

$2x^2+5$

d)

$2x^2+10x$

51.

$For\ f\left(x\right)=x+5\ and\ g\left(x\right)=2x,\ find\ \left(f+g\right)\left(x\right).$

a)

x + 5

b)

3x + 5

c)

$2x^2+5$

d)

2x + 10

52.

$\left(2+\sqrt[]{5}\right)\left(3-\sqrt[]{5}\right)$

a)

$-1+\sqrt[]{5}$

b)

$1+\sqrt[]{5}$

c)

$1-\sqrt[]{5}$

d)

$-1-\sqrt[]{5}$

53.

$\sqrt[3]{216p^3q^9}$

a)

$6pq^3$

b)

$6\left|pq^3\right|$

c)

$-6pq^3$

d)

$6p^9q^{27}$

54.

$Find\ the\ inverse\ of\ g\left(x\right)=-3x.$

a)

$g^{-1}\left(x\right)=x+1$

b)

$g^{-1}\left(x\right)=-\frac{1}{3}x$

c)

$g^{-1}\left(x\right)=-3x-3$

d)

$g^{-1}\left(x\right)=x-1$

55.

$\sqrt[]{75}+\sqrt[]{12}$

a)

$10\sqrt[]{3}$

b)

$\sqrt[]{87}$

c)

$7\cdot\sqrt[]{3}$

d)

21

56.

$Find\ \left(f+g\right)\left(x\right).$

$f\left(x\right)=4x^2+7x+11$

$g\left(x\right)=9x+7$

a)

$13x^2+14x+11$

b)

$13x^3+14x+11$

c)

$4x^2+16x+18$

d)

$4x^2+16x+11$

57.

$Find\ \left(f-g\right)\left(x\right).$

$f\left(x\right)=x^2+8x$

$g\left(x\right)=3x+5$

a)

$x^2+5x-5$

b)

$x^2+5x+5$

c)

$-x^2-5x+5$

d)

$x^2+11x+5$

58.

Find the inverse.

$f\left(x\right)=2x-7$

a)

$f^{-1}\left(x\right)=x+\frac{7}{2}$

b)

$f^{-1}\left(x\right)=\frac{x+7}{2}$

c)

$f^{-1}\left(x\right)=7x-2$

d)

$f^{-1}\left(x\right)=\frac{1}{2}x+7$

59.

$\sqrt[3]{216x^9}$

a)

$6x^6$

b)

$6x^3$

c)

$36x^3$

d)

$\pm6x^3$

60.

$Find\ \left(f+g\right)\left(x\right).$

$f\left(x\right)=x^2+3x-5$

$g\left(x\right)=2x+1$

a)

$2x^2+4x-5$

b)

$x^2+x-6$

c)

$x^2+5x-4$

d)

$-x^2-5x+4$

FInal Exam Review

Total questions: 60

Worksheet time: 15hrs 0mins

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