Free Printable FnT Final Exam Review

1.

Solve. Select BOTH solutions.
$\left|-4+x\right|=10$

a)

$6$

b)

$14$

c)

$\frac{5}{2}$

d)

$-6$

2.

Solve. Select BOTH solutions.
$\frac{\left|-1+x\right|}{5}=1$

a)

$-4$

b)

$7$

c)

$-5$

d)

$6$

3.

Solve. Select BOTH solutions.
$4\left|10x\right|-3=117$

a)

$\frac{57}{20}$

b)

$12$

c)

$3$

d)

$-3$

4.

What is the correct first step?

a)

divide both sides by 10

b)

multiply both sides by 10

c)

make it two inequalities with an "or"

d)

make it two inequalities with and "and" or a between statement

5.

| x + 3 | ≤ 2

a)

No Solution

b)

x ≤ -1

c)

-5 ≤ x and x ≤ -1

d)

1 ≤ x and x ≤ 5

6.

a)

no solution

b)

x > 2 or x < -22

c)

-22 < x < 2

d)

all real numbers

7.

Solve for n.

a)

n ≥ 10 and n ≤ -6

b)

n > 10 and n < -6

c)

n ≥ 10 or n ≤ -6

d)

n > 10 or n < -6

8.

Convert x²-9x+20 to factored form and solve.

a)

(x-4)(x-5); x=-4, -5

b)

(x+4)(x+5); x=-5, -4

c)

(x-4)(x-5); x=4, 5

d)

Not factorable

9.

Solve
(4a + 3)(4a - 3) = 0

a)

a = ^-3/₄, ³/₄

b)

a = ^-4/₃, ⁴/₃

c)

a = ^-9/₁₆, ⁹/₁₆

d)

a = ^-16/₉, ¹⁶/₉

10.

Identify the a, b and c values for this equation:
3x² - 8x + 15 = 0

a)

a=3, b=8, c=0

b)

a=3, b=-8, c=15

c)

a=3, b=8, c=15

11.

Convert x²-9x+20 to factored form and solve.

a)

(x-10)(x+2); x=-2, 10

b)

(x+4)(x+5); x=-5, -4

c)

(x-4)(x-5); x=4, 5

d)

Not factorable

12.

Which is the correct quadratic formula?

a)

b)

c)

d)

13.

Identify a, b and c for the given equation: $2x^{2\ }-5x+3=0$

a)

a: 2, b: 5, c: 3

b)

a: -2, b: 5, c: -3

c)

a: 2, b: -5, c: -3

d)

a: 2, b: -5, c: 3

14.

Solve using the quadratic formula & simplify completely.

$2x^{2\ }-4x+7=0$

a)

$\frac{2\pm2i\sqrt{10}}{2}$

b)

$\frac{2\pm i\sqrt{10}}{2}$

c)

$\frac{4\pm\sqrt{40}}{4}$

d)

$\frac{2\pm2i\sqrt{40}}{4}$

15.

The discriminant is

a)

ax² + bx + c

b)

b - 4ac

c)

b² - 4ac

d)

b² + 4ac

16.

Which graph has a discriminant = 0?

a)

None of them

b)

Red

c)

Blue

d)

Green

17.

If the discriminant is negative, then the quadratic has:

a)

1 Real Solution

b)

2 Real Solutions

c)

Half a Solution

d)

2 Complex (imaginary) Solutions

18.

Determine the value of the discriminant and describe the number and type roots for the following:

x² + 7x + 13

a)

101, 2 real roots

b)

3, 2 real roots

c)

-101, 2 imaginary roots

d)

-3, 2 imaginary roots

19.

Use the discriminant to determine the number of solutions: $-9x^2-7x+2$

a)

no real solutions (imaginary)

b)

1 real solution

c)

2 real solutions

d)

more than 2 solutions

20.

What is the correct solution to x² - 12x + 4 = 20?

a)

x = 12.48, -0.48

b)

x = 48

c)

x = 27, -15

d)

x = 12.48

21.

When solving a quadratic equation, when do you use the plus or minus (±) symbol?

a)

After taking the square root of both sides

b)

After adding the square to both sides

c)

After taking half of b

d)

After setting the equation equal to zero

22.

When solving the equation x² - 12x + 4 = 20

by completing the square , what values would go in the two blanks?

(________)² = ______

a)

x - 12; 52

b)

x - 6; 16

c)

x - 6; 52

d)

x - 6; 56

23.

What number goes in the blank to complete the square for this trinomial?

x² – 8x + ___

a)

-4

b)

-16

c)

4

d)

16

24.

Use the graph of y=-x²+6x-5 to solve the equation -x²+6x-5=0

a)

{-1,5}

b)

{3,4}

c)

{1,5}

d)

{2,4}

25.

a)

A

b)

B

c)

C

d)

D

26.

Simplify √-48

a)

4i

b)

-4√3

c)

4i√3

d)

12i

27.

Find the value of c to make it a perfect square trinomial.

x²+5x+c

a)

10

b)

25

c)

25/2

d)

25/4

28.

Solve for $x:$ $\sqrt[]{x}=4$

a)

$2$

b)

$-16$

c)

$16$

d)

$-2$

29.

Solve for $x:$ $\sqrt[]{\frac{x}{5}}=5$

a)

$5$

b)

$25$

c)

$\frac{1}{125}$

d)

$125$

30.

Solve for $x:$ $\sqrt[]{x-4}=3$

a)

7

b)

$13$

c)

$-5$

d)

$-5$

31.

Solve for $x:$ $\sqrt[]{x-3}-14=-2$

a)

$147$

b)

$144$

c)

$102$

d)

$No\ solution$

32.

Solve for $x:$ $-8+\sqrt[]{5x-5}=-3$

a)

$-6$

b)

$8$

c)

$6$

d)

$No\ solution$

33.

Solve for $x:$ $-4\sqrt[]{9x}=-24$

a)

$4$

b)

$-4$

c)

$\frac{1}{9}$

d)

$No\ solution$

34.

Solve for $x:$ $-6\sqrt[]{x+4}=-12$

a)

$-2$

b)

$2$

c)

$0$

d)

$No\ solution$

35.

Solve for $x:$ $\sqrt[]{3x+12}=\sqrt[]{x+8}$

a)

$-2$

b)

$2$

c)

$-1$

d)

$No\ solution$

36.

Solve for $x:$ $\sqrt[]{6-x}=x$

a)

$2,\ -3$

b)

$2,\ 3$

c)

$2$

d)

$3$

37.

What would be the first step in solving the equation $\sqrt{4x}=8$

a)

square both sides of the equation

b)

take the square root of both sides

c)

divide both sides by 4

d)

multiply both sides by 8

38.

What would be the first step in solving the equation $\sqrt{y}+6\ =\ 12$

a)

subtract the six from both sides

b)

add the six to both sides

c)

take the square root of both sides

d)

square both sides

39.

Solve the equation $\sqrt{5p+1}=\sqrt{2p+7}$

a)

p = 2

b)

p = 4

c)

p = 1

d)

p = - 2

40.

x^3/2=27

a)

9

b)

-9,9

c)

3

d)

-3,3

41.

x⁴=256

a)

-2,2

b)

3

c)

-4,4

d)

16

42.

64x^3/4-125=0

a)

64/25

b)

625/256

c)

5/2

d)

25/16

43.

Solve the Rational Exponent Equation:

a)

A

b)

B

c)

C

d)

D

44.

Solve for m.

a)

A

b)

B

c)

C

d)

D

45.

Solve for k.

a)

A

b)

B

c)

C

d)

D

46.

What is the first step in the following equation? 27x^2/3 = 81

a)

divide by 27 on both sides

b)

minus 27 on both sides

c)

raise both sides to the power of 3/2

d)

raise both sides to the power of 2/3

47.

What is the first step in the following equation? x^3/4 = 8

a)

multiply both sides by 4/3

b)

raise both sides to the power of 3/4

c)

raise both sides to the power of 4/3

d)

multiply both sides by 3/4

48.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

49.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

50.

log₅25 = ?

a)

2

b)

5

c)

125

51.

Write in exponential form.
log₂(¹/₈) = -3

a)

2^-3 = ¹/₈

b)

2^1/8= -3

c)

-3² = ¹/₈

d)

-3^1/8 = 2

52.

Condense: log₂6+log₂3=

a)

log₂18

b)

log₂2 = 1

c)

log₂3

d)

log₂9

53.

Write as a single log: log 12 + 2 log x

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x²)

54.

Write in logarithmic form.
2^-4 = ¹/₁₆

a)

log₂(¹/₁₆) = -4

b)

log_-4(¹/₁₆) = 2

c)

log_-4 2 = ¹/₁₆

d)

log₂(-4) = ¹/₁₆

55.

Write log_b(x/y) as two logs

a)

log_bx-log_by

b)

log_bx+log_by

c)

log_bx*log_by

d)

log_bx/log_by

56.

Write log_b(xy) as two logs

a)

log_bx+log_by

b)

log_bx-log_by

c)

log_bx*log_by

d)

log_bx/log_by

57.

Rewrite log_b(xⁿ)

a)

nlog_bx

b)

(log_bx)ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

58.

a)

6log₈(xyz)

b)

log₈(x) - log₈(y) - 6log₈(z)

c)

log₈(x) + log₈(y) - log₈(z)

d)

log₈(x) + log₈(y) + 6log₈(z)

59.

Condense

a)

A

b)

B

c)

C

d)

D

60.

Factor:
25x²- 100y²

a)

(5x - 10y) (5x + 10y)

b)

( 5x - 10y)²

c)

Prime

d)

( 5x - 50y) (5x + 50y)

61.

Factor:
x²+ 81

a)

Prime (not factorable)

b)

( x - 9 ) ( x + 9 )

c)

( x + 9 ) ( x + 9 )

d)

( x - 9 ) ( x - 9 )

62.

$16x^2-81$ Factor:

a)

$\left(4x-9\right)\left(4x-9\right)$

b)

$\left(2x-9\right)\left(2x+9\right)$

c)

$\left(4x\ +\ 9\right)\left(4x+9\right)$

d)

$\left(4x+9\right)\left(4x-9\right)$

63.

$64x^2+112x+49$ Factor:

a)

$\left(8x-7\right)\left(8x+7\right)$

b)

$\left(8x-7\right)^2$

c)

$\left(16x+7\right)^2$

d)

$\left(8x+7\right)^2$

64.

$a^2-10a+25$ Factor:

a)

$\left(a-5\right)\left(a+5\right)$

b)

$\left(a+5\right)^2$

c)

$\left(a-5\right)^2$

d)

$\left(a-10\right)^2$

65.

What is ALWAYS the first step when factoring?

a)

Look for the GCF

b)

Write a, b, and c

c)

Difference of squares

d)

Group

66.

Factor x³+125

a)

(x+5)(x²-25)

b)

(x-5)(x²+25)

c)

(x+5)(x²-5x+25)

d)

(x-5)(x²+5x+25)

67.

Factor 8z³+125

a)

(2z+5)(4z²-25)

b)

(2z+5)(4z²+10z+25)

c)

(2z+5)(4z²-10z+25)

d)

4z+5)(2z²-5z+25)

68.

Factor 8x³+27y³

a)

(2x+3y)(4x²-9y²)

b)

(2x+3y)(4x²-36xy+81y²)

c)

(2x+3y)(4x²-6xy+9y²)

d)

(2x-3y)(4x²+6xy+9y²)

69.

Factor by grouping:

4p^3+8p^2+3p+6

a)

$\left(2p^2+3\right)\left(p+2\right)$

b)

$\left(2p^2+6\right)\left(p+4\right)$

c)

$\left(4p^2+3\right)\left(p+2\right)$

d)

$\left(4p^2+8p\right)\left(3p+6\right)$

70.

Factor the Polynomial

63x³+ 54x² - 105x - 90

a)

3(3x² - 5) (7x + 6)

b)

3(3x² + 5) (7x - 6)

c)

5(3x² - 5) (7x + 6)

d)

5(3x² + 5) (7x - 6)

71.

Factor the Polynomial

12x³+ 2x² - 30x - 5

a)

(2x² - 5) (6x + 1)

b)

(2x² + 5) (6x - 1)

c)

(6x² - 5) (2x + 1)

d)

(6x² + 5) (2x - 1)

72.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

73.

What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x³- 5x²+ 2x - 10

a)

0

b)

2x-10

c)

-2x-10

d)

2x+10

74.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x-12

b)

2x⁴-x³-25x²-12x+0

75.

What is the remainder of (3x³ -5x² -4x +1) ÷ (x + 3)?

a)

-25

b)

25

c)

113

d)

-113

76.

Factor $49r^2-36$

a)

(7r + 6)(7r - 6)

b)

(7r + 6)(7r + 6)

c)

(7r - 6)(7r - 6)

d)

$\left(7r-6\right)^2$

77.

Factor completely (hint: look for the GCF first)

$3x^2-48x+192$

a)

3(x - 8)(x -8)

b)

3(x + 8)(x - 8)

c)

(3x + 8)(x - 8)

d)

(3x - 8)(x + 8)

78.

30x³+15x²-18x-9

a)

(5x²-3)(6x+1)

b)

(5x²-3)(6x+3)

c)

3(5x²+3)(2x-1)

d)

3(5x²-3)(2x+1)

79.

(2x³ - 5x² + 3x + 7) ÷ (x - 2)

a)

2x³ - x² + x + 9

b)

2x² - x + 1

c)

2x² - x + 1 + 9/x-2

d)

2x² - 9x - 15 - 23/x-2

80.

Solve for x:
4x + 1 = 7x - 5

a)

-1

b)

2

c)

6/11

d)

8

81.

Solve for x:
6(2x + 1) = 18

a)

3

b)

17/12

c)

1

d)

2

82.

Solve for x:
2(3x + 4) + 2 = 4 + 3x

a)

2

b)

-2/3

c)

10

d)

-2

83.

Solve for x

a)

x = 1/10

b)

x = 10

c)

x = 4

d)

x = 5

84.

Solve:

a)

-9

b)

-28

c)

9

d)

4

85.

Solve:

a)

3

b)

4

c)

-7

d)

15

86.

Solve using substitution.

a)

(1,3)

b)

(3,-1)

c)

(7,3)

87.

Solve using the most efficient method.

a)

(4/3, 4)

b)

(4, 12)

c)

(14, 17)

88.

Write an inequality for Graph 3.

a)

x ≤ -2 AND x > 5

b)

x ≤ -2 OR x > 5

c)

x ≥ -2 OR x < 5

d)

-2 ≤ x < 5

89.

x + 8 < 3 or - 8x < -40

a)

x > -5 or x < 5

b)

x < -5 and x > 5

c)

x < -5 or x > 5

d)

x > -5 and x < 5

90.

a)

A

b)

B

c)

C

d)

D

91.

−6 < 2t − 5 < 3

a)

−0.5 < t < 4

b)

0.5 < t < −1

c)

−11/2 < t < 2

d)

11/2 < t < −2

92.

When solving inequalities you must _________________ the inequality when ____________________ by a negative.

a)

flip; dividing

b)

ignore; multiplying and dividing

c)

flip; multiplying

d)

flip; multiplying and dividing

93.

Which graph represents a system of equations with no solution?

a)

b)

c)

d)

None of the above

94.

Solve $9a+4=40$

a)

$a=4$

b)

$a=\frac{44}{9}$

c)

$a=27$

d)

$a=35$

95.

Find the trig value rounded to the nearest ten-thousandth.
Tan(42°)

a)

.9004

b)

.8123

c)

88.6361

d)

42

96.

Which Trig function do you use?

a)

Sine

b)

Cosine

c)

Tangent

97.

Find the ratio for sinA. (Reduce the fraction)

a)

36/27

b)

4/5

c)

36/45

d)

3/5

98.

What is the correct ratio?

a)

sin 40 = w/28

b)

cos 40 = w/28

c)

tan 40 = w/28

d)

sin 40 = 28/w

99.

Set up the problem...

a)

sin X = 41/28

b)

tan X = 41/28

c)

cos X = 28/41

d)

sin X = 28/41

100.

A hawk sitting on a tree branch spots a mouse on the ground 15 feet from the base of the tree. The hawk swoops down toward the mouse at an angle of 30 degrees. What is the distance from the tree branch to the mouse?

a)

7.5 ft

b)

15 ft

c)

26 ft

d)

30 ft

101.

Solve for x. Round to the nearest tenth.

a)

25.9

b)

0.6

c)

-0.9

d)

9.9

102.

Find the length of side y.

a)

22.32 cm

b)

36.5 cm

c)

76.34 cm

d)

87.76 cm

103.

Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.

a)

63 ft

b)

65 ft

c)

74 ft

d)

87 ft

104.

What is the ratio for Sine?

a)

Hyp/Opp

b)

Opp/Hyp

c)

Opp/Adj

d)

Adj/Opp

105.

What is the ratio for Cosine?

a)

Opp/Hyp

b)

Opp/Adj

c)

Adj/Opp

d)

Adj/Hyp

106.

What is the ratio for Tangent

a)

Opp/Adj

b)

Adj/Opp

c)

Opp/Hyp

d)

Hyp/Opp

107.

Find the measure of the indicated angle. Round to the nearest tenth.

a)

35.8°

b)

43.8°

c)

46.2°

d)

54.2°

108.

Find the measure of the indicated angle (?) round to the nearest tenth.

a)

9.4

b)

55.2

c)

20.15

d)

19.4

109.

Identify the Law of Sines

a)

Sin²x + Cos²x =1

b)

Sin(A)/a = Sin(B)/b = Sin(C)/c

c)

Sin(A)Sin(B)Sin(C) = 1

d)

Soh-Cah-Toa

110.

Find AB.

a)

A

b)

B

c)

C

d)

D

111.

What is the measure of angle A?

a)

50 degrees

b)

60 degrees

c)

78 degrees

d)

74 degrees

112.

$180\degree\ is\ the\ same\ as$

a)

A. $\frac{1}{2}\pi\ rads$

b)

B. $\pi\ rads$

c)

C. $1.5\pi\ rads$

d)

D. $2\pi\ rads$

113.

$\frac{1}{2}\pi\ rads\ is\$

a)

A. $45\degree$

b)

B. $90\degree$

c)

C. $135\degree$

d)

D. $180\degree$

114.

What is 135° in radians?

a)

3/4

b)

3π/4

c)

3/5

d)

3π/5

115.

What is 11π/12 in degrees?

a)

164

b)

165

c)

162

d)

163

116.

Add

a)

11 8
-4 2

b)

3 2
-6 -6

c)

-3 2
-4 -6

d)

10 8
-6 2

117.

Subtract

a)

3 -8
0 -1

b)

3 -4
8 -13

c)

-3 8
0 1

d)

3 -8
-8 1

118.

Multiply

a)

20 15 -10
30 -5 0

b)

-20 15 -10
30 -5 0

c)

1 8 3
11 4 5

d)

20 -15 10
-30 5 0

119.

Find the product of the two matrices.

a)

1 2
6 -8

b)

-3 -5
-5 -11

c)

-2 8
-6 -12

d)

2 -3
5 -2

120.

Find the product of the matrices.

a)

A

b)

B

c)

C

d)

D

121.

What is the determinant of this matrix?

a)

-2

b)

2

c)

10

d)

24

122.

Find the determinant of the matrix

a)

A

b)

B

c)

C

d)

D

123.

Solve the system for the value of x using a matrix.

5x + 8y = -12

3x + 5y = -7

a)

1

b)

-1

c)

-4

d)

No solution

124.

Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies? Use a matrix

a)

Sugar Cookies $5
Oatmeal Cookies $3

b)

Sugar Cookies $4
Oatmeal Cookies $8

c)

Sugar Cookies $2
Oatmeal Cookies $6

d)

Sugar Cookies $3
Oatmeal Cookies $6

FnT Final Exam Review

Total questions: 124

Worksheet time: 11hrs 36mins

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