Instructor: Virginia Davis Course: 78mbhsdavismath.weebly.com/uploads/5/8/1/6/58167697/... · Instructor: Virginia Davis Course: Foundations for College Math (1) Assignment: Final

5/18/2016 Final Exam Review Ch 7-8-Virginia Davis

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Student: _____________________Date: _____________________

Instructor: Virginia DavisCourse: Foundations for College Math(1)

Assignment: Final Exam Review Ch78

Simplify the expression.

x + 3

x2 − 5x − 24

Select the correct choice below and fill in any answer boxes in your choice.

A. (Simplify your answer.)x + 3

x2 − 5x − 24=

B. The expression cannot be simplified.

Find the product and simplify if possible.

•x

11x − 55x2 − 5x

7

•x

11x − 55x2 − 5x

7=

(Simplify your answer. Use integers or fractions for any numbers in the expression.)

Find the product and simplify if possible.

•x2 − 36

x2 − 3x − 18

x + 3

x

(Simplify your answer.)•x2 − 36

x2 − 3x − 18

x + 3

x=

Find the quotient and simplify the result.

÷3w4

2w615w

4w4

÷3w4

2w615w

4w4=




5.

6.

7.

8.

9.

Find the quotient and simplify the result.

÷5x5

2x425x2

4x3

÷5x5

2x425x2

4x3=


Simplify the complex fraction.

104x58x

104x58x

=

Divide.

7x − 727

÷9x − 918

7x − 727

÷9x − 918

=

(Type an integer or a simplified fraction.)

Multiply.

•x2 + 3x

710

5x + 15

•x2 + 3x

710

5x + 15=


Multiply.

•6x + 5y

x2 + 6xy + 9y2x + 3y

2

(Simplify your answer. Factor completely.)•6x + 5y

x2 + 6xy + 9y2x + 3y

2=



10.

11.

12.

13.

14.

Find the area of the rectangle in terms of x.

feet

feet

The area of the rectangle is feet .2

(Simplify your answer.)

Add. Simplify the result if possible.

+2

5 + yy + 45 + y

(Simplify your answer.)+2

5 + yy + 45 + y

=

Subtract. Simplify the result if possible.

−5x2 + 2xx − 8

31x + 88x − 8

(Simplify your answer.)−5x2 + 2xx − 8

31x + 88x − 8

=

Subtract the rational expressions.

−12x − 6

x2 + 4x − 21

11x − 13

x2 + 4x − 21

(Simplify your answer.)−12x − 6

x2 + 4x − 21

11x − 13

x2 + 4x − 21=

Subtract the rational expressions and simplify if possible.

−− 10x2

x − 416 − 11x2

x − 4

(Simplify your answer.)−− 10x2

x − 416 − 11x2

x − 4=

2x

x2 −25

x+55x



15.

16.

17.

18.

19.

Subtract the rational expressions and simplify if possible.

−7x + 3x − 3

5x + 9x − 3

(Simplify your answer.)−7x + 3x − 3

5x + 9x − 3

=

Perform the indicated operation.

+5

x

7

3x2

(Simplify your answer.)+ =5

x

7

3x2

Perform the indicated operation. Simplify if possible.

−9

x + 8

8x

x2 − 64

(Simplify your answer.)−9

x + 8

8x

x2 − 64=


+ 39

x + 2

(Simplify your answer.)+ 3 =9

x + 2


−4xx − 5

3xx − 3

(Simplify your answer.)−4xx − 5

3xx − 3

=



20.

21.

22.

23.

Find the unknown length y in the following pair of similar triangles.

15

17

23

7.5

8.5

y =

Find the unknown length y in the pair of similar triangles.

ft y = (Simplify your answer. Type an integer, fraction, or a mixed number.)

Given that the following pair of triangles are similar, find the missing length.

(Type an integer or decimal.)x =

Graph the linear equation.

f(x) = − 3x + 5

Use the graphing tool to graph the linear equation.

10 8 6 4 2 2 4 6 8 10

10

8

6

4

2

2

4

6

8

10

x

y

6 ft y

20 ft15 ft

13x

24

36

H

G

I

J

K L



24.

25.

26.

27.

28.

29.

30.

Graph the linear equation.

f(x) = x2

3

Use the graphing tool to graph the equation.

10 8 6 4 2 2 4 6 8 10

10

8

6

4

2

2

4

6

8

10

x

y

Find an equation of the line with the given slope and containing the given point. Write the equation using function

notation.

Slope ; through ( , )5 8 6

The equation of the line is f(x) .=

Find an equation of the line with the given slope and containing the given point. Write the equation using function

notation.

Slope ; through ( , )− 9 4 9

The equation of the line is f(x) . =

Find an equation of the line passing through the given points. Use function notation to write the equation.

( , ) and ( , )3 2 5 8

f(x) =

Write an equation of the line using function notation.

Horizontal; through (0, − 4)


Find an equation of the line. Write the equation using function notation.

Through ; perpendicular to y x(2, − 5) 5 = − 10


Find an equation of the line. Write the equation using function notation.

Through ; parallel to ( − 2, − 6) 5x + 2y = 7

f(x) =



31.

32.

33.

34.

Use the graph of the function shown to find all positive values of x such that .g(x) = 8

x = (Use a comma to separate answers as needed.)

10 8 6 4 2 2 4 6 8 10

10

8

6

4

2

2

4

6

8

10

x

y

g(x)

The function can be used to predict diamond production. For this function, x is the number of years after 2000, and f(x) is the value (in billions of dollars) of the year's diamond production. Use this function to predict diamond production in

f(x) = 0.42x + 13.4

2010.

The diamond production in is predicted to be $ billion.2010 (Type an integer or a decimal.)

Graph the function.

f(x) =2x, for x < 0

x + 1, for x ≥ 0

Choose the correct graph below.

A.

10 10

10

10

x

y

B.

10 10

10

10

x

y

C.

10 10

10

10

x

y

D.

10 10

10

10

x

y

Sketch the graph of the function.

f(x) = + 1x


A.

10 10

10

10

x

y

B.

10 10

10

10

x

y

C.

10 10

10

10

x

y

D.

10 10

10

10

x

y



35.

36.

37.

Sketch the graph of the function.

y = ( )x − 3 2


A.

16 162

30

x

y

B.

16 16

16

16

x

y

C.

16 16

16

16

x

y

D.

16 162

30

x

y

Find the graph of the function.

g(x) = − + 3x − 1


A.

10 5 5 10

105

510

x

y

B.

10 5 5 10

105

510

x

y

C.

10 5 5 10

105

510

x

y

D.

10 5 5 10

105

510

x

y

Graph the equation.

y = 3


A.

10 10

10

10

x

y

B.

10 10

10

10

x

y

C.

10 10

10

10

x

y

D.

10 10

10

10

x

y



38.

39.

40.

41.

42.

Graph the following equation.

x = 5


A.

10 10

10

10

x

y

B.

10 10

10

10

x

y

C.

10 10

10

10

x

y

D.

10 10

10

10

x

y

Write the domain and range of the function.

h( ) = − |x + 5| + 1x

The domain is . (Type your answer in interval notation.)

The range is . (Type your answer in interval notation.)

Without graphing, find the domain of the function.

f( ) = 3 + 1x x − 16

The domain is . (Type your answer in interval notation.)

If y varies directly as x, find the constant of variation and the direct variation equation for the situation.

y when x= 10 = 4

The constant of variation k is . (Type an integer or a simplified fraction.)

The direct variation equation is y = . (Use integers or fractions for any numbers in the expression.)

If y varies inversely as x, find the constant of variation k and the inverse variation equation for the situation.

y when x= 6 = 5

Find the constant of variation k.

k (Simplify your answer.)=

Write the inverse variation equation.



1.

A. (Simplify your answer.)x + 3

x2 − 5x − 24=

1x − 8

2. x2

77

3. x + 6

x

4. 2w5

5. 2x2

5

6. 4

7. 1427

8. x27

9. 6x + 5y2(x + 3y)

10. 2

5(x − 5)

11. y + 65 + y

12. 5x + 11

13. 1

x − 3

14. x + 4

15. 2



16.

15x + 73x2

17. x − 72

(x + 8)(x − 8)

18. 3x + 15x + 2

19. x2 + 3x

(x − 5)(x − 3)

20. 11.5

21. 4 12

22. 19.5

23.

10 8 6 4 2 2 4 6 8 10

10

8

6

4

2

2

4

6

8

10

x

y



24.

10 8 6 4 2 2 4 6 8 10

10

8

6

4

2

2

4

6

8

10

x

y

25. 5x − 34

26. − 9x + 45

27. 3x − 7

28. − 4

29. − 5x + 5

30. − x − 1152

31. 6

32. 17.6

33. B.

10 10

10

10

x

y



34. C.

10 10

10

10

x

y

35. D. 16 162

30

x

y

36. D.

10 5 5 10

105

510

x

y

37. C.

10 10

10

10

x

y

38. C.

10 10

10

10

x

y

39. ( − , )

( − ,1]

40. [16, )

41. 52

x52



42. 30

y = 30x

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Instructor: Virginia Davis Course: 78mbhsdavismath.weebly.com/uploads/5/8/1/6/58167697/... · Instructor: Virginia Davis Course: Foundations for College Math (1) Assignment: Final