Free Printable Math 4 Final Review

1.

-6i+3i

a)

3i

b)

-3i

c)

-2i

d)

-3i²

2.

(5 - 2i) + (-7 + 8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

3.

(10 + 3i) - (2 - 9i)

a)

20 - 27i

b)

12 - 7i

c)

8 + 12i

d)

20 - 27i²

4.

Multiply
3i(-2 + 4i)

a)

-6+12i

b)

-12-6i

c)

-2+7i

d)

12+6i

5.

Simplify: $\left(-4\ -\ 8i\right)^2$

a)

-48 + 64i

b)

81

c)

-55 + 48i

d)

121

6.

$\left(3+2i\right)+\left(4-5i\right)$

(a)

7.

$\left(4-2i\right)-\left(3+6i\right)$

(a)

8.

Find A+B

a)

8 10
8 1

b)

12 25
7 1

c)

10 30
0 1

d)

can't add two together because the rows dont match columns

9.

Subtract

a)

3 -8
0 -1

b)

3 -4
8 -13

c)

-3 8
0 1

d)

3 -8
-8 1

10.

Find B-A

a)

-3 1
7 -1

b)

1 0
1 -4

c)

-4 0
6 -1

d)

not possible because rows do not match columns

11.

What are the dimensions of this matrix?

a)

2 x 3

b)

3 x 2

c)

6 x 1

d)

1 x 6

12.

Find the product of the matrices.

a)

A

b)

B

c)

C

d)

D

13.

Multiply.

a)

A

b)

B

c)

C

d)

D

14.

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

15.

Given u = <3, 7>, find 2u

a)

<21, 2>

b)

<6, 26>

c)

<6, 14>

d)

23

16.

Given u = <3, 7> and v =<-5, 4>, find 2v - 3u

a)

<21, 2>

b)

<-19, -13>

c)

<-15, 3>

d)

23

17.

Find the magnitude of the vector <10, -8>

a)

2

b)

12.81

c)

6

d)

18

18.

Find the magnitude of the vector <2, -3>.

a)

√11

b)

13

c)

√-4

d)

√13

19.

If w = <2, -5> and y = <2, 0>, find 2w + y

a)

<-10, 2>

b)

<4, -5>

c)

<-6, 10>

d)

<6, -10>

20.

If vector a= (4, -5) and vector b= (-7, 4) Find a+b

a)

(3, 9)

b)

(-3, -1)

c)

(11, 1)

d)

(-3, -9)

21.

If vector a= (4, -5) and vector b= (-7, 4) Find a-b

a)

(-11, -9)

b)

(11, 9)

c)

(11, -9)

d)

(-3, -1)

22.

If vector a= (4, -5) and vector b= (-7, 4) Find 2a-3b

a)

(29, -22)

b)

(13, -2)

c)

(1, 7)

d)

(29, -2)

23.

Find the magnitude of the vector <10, -8>

a)

2

b)

12.81

c)

6

d)

18

24.

Find the direction angle for the vector <2, 7>

a)

74.05°

b)

15.95°

c)

195.94°

d)

97.28°

25.

Which parent function matches the graph?

a)

y = |x|

b)

y = ∛(x)

c)

y = x²

d)

y = a⋅b^x

26.

What type of function is shown?

a)

absolute value

b)

quadratic

c)

linear

d)

exponential

27.

What type of function is shown?

a)

linear

b)

quadratic

c)

square root

d)

absolute value

28.

Which parent function matches the graph?

a)

f(x) = x

b)

f(x)= x²

c)

f(x) = |x|

d)

f(x) = ab^x

29.

g(x)=f(x)-4
Describe the transformation to f(x) that results in g(x).

a)

f(x) has been translated down 4.

b)

f(x) has been translated up 4.

30.

g(x)=f(x-3)
Describe the transformation to f(x) that results in g(x).

a)

f(x) has been translated to the right 3.

b)

f(x) has been translated to the left 3.

31.

Match the equation to its description.

a)

Right 2 and up 2

b)

Left 2 and up 2

c)

Right 2 and down 2

d)

Left 2 and down 2

32.

What are the x-intercepts?

a)

0 and 2

b)

-4 and 0

c)

2 and 3

d)

0 and 4

33.

Let's call the graph f(x). Find f(5) = ___

a)

25

b)

30

c)

35

d)

40

34.

Identify the x-intercept intercept of g(x)

a)

(-4, -8)

b)

(4, 0)

c)

(2, -4)

d)

(0, -8)

35.

What is the interval of increase for this function?

a)

(-6, -2)

b)

(negative infinity, infinity)

c)

(-2, -6)

d)

(-1, 3)

36.

List the types of intervals that the graph demonstrates in order.

a)

decreasing, constant, increasing, constant

b)

increasing, decreasing, constant

c)

increasing, constant, increasing, constant

d)

increasing, constant, decreasing, constant

37.

What is g(7) if:

a)

-17

b)

-13

c)

13

d)

17

38.

What is f(-2)?

a)

4

b)

1

c)

1

d)

DNE

39.

What is m(-3) if:

a)

-3

b)

0.5

c)

3

d)

-3.5

40.

Which piecewise function corresponds to this graph? (Take your time)

a)

f(x) = { x if x < 4; -x+1 if x ≥ 4

b)

f(x) = { x if x ≤ 4; -x+1 if x > 4

c)

f(x) = { -x+1 if x < 4; x if x ≥ 4

d)

f(x) = { -x+1 if x ≤ 4; x if x > 4

41.

If f(x) = 5x and g(x) = 2x-1,

what is the composition f(g(x)) ?

a)

10x-1

b)

10x-5

c)

5x²-1

d)

5x²-5

42.

If f(x) = x-1 and g(x) = 2x,

what is and g(f(x)) ?

a)

2x²-1

b)

2x-1

c)

2x-2

d)

x-2

43.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

44.

Find g(- 2).

a)

12

b)

-2

c)

-24

d)

18

45.

Evaluate f(x)=-2x+13 for f(10)

a)

-7

b)

1

c)

-8

d)

7

46.

g(x)=3x+4
h(x)=3x-1
Find (g∘h)(x)

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

47.

f(x) = x² + 3x - 2

g(x) = 2x² +4x + 1

(f + g)(-3) =

a)

-1

b)

-39

c)

5

d)

15

48.

f(x) = x² + 3x - 2

g(x) = 2x² +4x + 1

(g - f)(2) =

a)

25

b)

9

c)

15

d)

-9

49.

Find

f\circ g\left(5\right)

a)

30

b)

242

c)

92

d)

2

50.

Given $f\left(x\right)=5x+7$ and $g\left(x\right)=4x+3$ , find $\left(f\circ g\right)\left(x\right)$ in simplest form.

a)

16x+15

b)

20x+31

c)

25x + 42

d)

20x+22

51.

Given $f\left(x\right)=5x+7$ and $g\left(x\right)=4x+3$ ,

Find $\left(g\circ f\right)\left(x\right)$ in simplest form.

a)

16x+15

b)

20x+31

c)

25x + 42

d)

20x+22

52.

f(n)=n²+4n
g(n)=-n-5
Find f(n)+g(n)

a)

n²+3n-5

b)

-n³+2n-7

c)

n³+3n-3n

d)

n²-3n-5

53.

Given
f(x)=3x²+7x and g(x)=2x²-x-1, find (f+g)(x).

a)

11x² - 1

b)

5x⁴ + 6x² - 1

c)

5x² + 6x - 1

d)

5x² + 8x - 1

54.

f(x) = x²+9
g(x) = x-9
Find f(x)-g(x).

a)

x²+x+9

b)

x²-x+9

c)

x²-x

d)

x²-x+18

55.

$f\left(x\right)\ =\ x^2\ -\ 2\ \ \ \ and\ \ \ \ g\left(x\right)\ =\ 3x\ +\ 5$
Find: $\left(f-g\right)\left(3\right)$

a)

-7

b)

3

c)

11

d)

21

56.

$f\left(x\right)\ =\ x+7\ \ \ \ and\ \ \ \ \ g\left(x\right)\ =\ -2x\ -9$
Find: $\left(g-f\right)\ \left(2\right)$

a)

-2

b)

22

c)

2

d)

-22

57.

a)

9 - √5

b)

√14

c)

16

d)

4

58.

A restaurant sells pizza for the prices in the data table. Calculate the linear regression equation of the data.

a)

y = 1.5x + 12

b)

y = 12x + 1.5

c)

y = 0.67x - 8

d)

y = -8x + 0.67

59.

A person travels by car. They record their miles driven in a data table. Calculate the linear regression equation of this data.

a)

y = 61.93x - 1.79

b)

y = -1.79x + 61.93

c)

y = 0.016x + 0.03

d)

y = 0.03x + 0.016

60.

Find the quadratic regression equation for the relationship of the horizontal distance and the height of the ball in the provided table.

a)

$-18x^2+2.11x+4.21$

b)

$-0.06x^2+1.06x+7.9$

c)

$-6x^2+1.06x+79$

d)

$-0.12x^2+2.11x+4.22$

61.

Find the height of the ball when it traveled a distance of 10 feet.

a)

12.8 ft

b)

13.5 ft

c)

11.1 ft

d)

17 ft

62.

Determine the curve of best fit.

a)

$y=-2.7x+7.4$

b)

$y=0.95x^2-2.08x-0.75$

c)

$y=-.05x-3.26$

d)

$y=0.95x^2+2.08x+0.75$

63.

Find the best fitting Quadratic model for the data

a)

$-0.26x^2-17.3x+222.8$

b)

$-0.26x2^2+22.59x+23.02$

c)

$2.6x^2+22.9x+20.03$

d)

$2.6x^2+2.3x+23.02$

64.

Write the exponential regression equation for the data.

a)

Y=8.16(2.7)^x

b)

Y=81.6(2.7)^x

c)

Y=8.16(.27)^x

d)

Y=8.16(27)^x

65.

A chemist has a 100-gram sample of a radioactive material. He records the amount of radioactive material every week for 6 weeks and obtains the following data: Find the exponential model of the function.

a)

y = 100(8.7)^x

b)

y = 100(1.87)^x

c)

y = 100(.87)^x

d)

y = 100(.13)^x

66.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

67.

log₅25 = ?

a)

2

b)

5

c)

125

d)

10

68.

Rewrite log₂8 = 3 in exponential form.

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

69.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

70.

Solve for x.
3^x = 27

a)

2

b)

4

c)

3

d)

5

71.

Rewrite log_vn = a in exponential form.

a)

v^a = n

b)

n^a = v

c)

vⁿ = a

d)

aⁿ = v

72.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

73.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

74.

a)

A

b)

B

c)

C

d)

D

75.

log (x) + log (x) = log (25)

a)

-5, 5

b)

5

c)

-5

d)

25

76.

Solve: 2^3x = 15

a)

2.3

b)

-2.3

c)

1.3

d)

-1.3

77.

log₂(x + 5) = 3

a)

3

b)

4

c)

5

d)

6

78.

Condense $3\log_{ }x+4\log_{ }y\ +\log_{ }z$

a)

$\log_{ }\ x^3y^4z$

b)

$12\log_{ }\ xyz$

c)

$\log_{ }\ 3x4yz$

d)

logx³y³z³

79.

Condense the Logarithm $5\log_{ }a\ -\ 25\log_{ }b$

a)

$\log\ \left(a^5+b^{25}\right)$

b)

$\log\ \left(a^5-b^{25}\right)$

c)

$\log\ \left(ab\right)^{25}$

d)

$\log_{ }\ \left(\frac{a^5}{b^{25}}\right)$

80.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

81.

log₆(2x + 16) = 3

a)

x = 2

b)

x = 100

c)

x = 116

d)

x = 50

82.

log₈(4x - 4) = 2

a)

18

b)

12

c)

2

d)

5

83.

log₈(4x+4)=2

a)

15

b)

12

c)

10

d)

3

84.

log₈₁x = 3/4

a)

2

b)

3

c)

27

d)

81

85.

Solve for x:
4²^x+ 1 = 17

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

86.

Solve for x:

2^{3x - 1} = 32

a)

0

b)

-1

c)

5/3

d)

2

Math 4 Final Review

Total questions: 86

Worksheet time: 6hrs 58mins

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