Study Guide for Bench mark 2

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Benchmark #2 study Guide

1. The diagram shows a block of processed cheddar cheese that has a mass of 227 grams. Find the density of processed cheddar cheese to the nearest hundredth of a gram per cubic centimeter.

2. The diagram shows the dimensions of a cylindrical log from a live oak tree. The wood from a live oak has a density of 0.977 gram per cubic centimeter. Find the mass of the live oak log to the nearest kilogram. Use 3.14 for 

3. Identify and describe the solid produced by rotating the figure around the given axis.

5

10

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340 mi

210 mi

Write a function g whose graph represents the indicated transformation of the graph of f. 5. ; translation 7 units left

6. ; translation 2 units down

7. Two shirt screening companies charge a set up fee and a charge for each shirt made. The table shows the total costs for the company Shirt Express. The total cost y (in dollars) for x shirts made by Shirt Custom is

represented by the equation .

Shirt Express

Number of shirts, x Total cost, y

10 $98

20 $183

30 $268

40 $353

50 $438

Which company initially charges less per shirt? How many shirts must be ordered for the cost to be the same?

8. Use the linear regression feature on a graphing calculator to find the line of best fit for the data in the table. Estimate the height (in centimeters) of a person whose femur is 38 centimeters long.

Femur length (centimeters),

x

Height (centimeters), y

39 171

44 184

31 152

49 196

36 163

40 175

29 142

33 152

46 186

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9. A stadium charges $75 for each seat in section A, $50 for each seat in section B, and $40 for section C. There are three times as many seats in section B as in section A. The revenue from selling all 20,000 seats is

$897,500. Write a system to represent the situation.

Write an equation of the parabola in vertex form.

10.

(8, 7)

(4, –9)

4 8 12 16 –4

–8 –12

–16 x

4 8 12 16

–4

–8

–12

–16 y

Write an equation of the parabola in intercept form.

11.

(–1, –7) (–8, 0) (–2, 0)

4 8 12

–4 –8

–12 x

4 8 12

–4

–8

–12 y

12. x-intercepts of 2 and –8; passes through

13. The table shows the heights h (in feet) of a firework when it explodes for different fuse lengths l (in inches).

Fuse length, l 4 5.5 6 7.5 9

Height, h 440 521 545 571 555

a. Use a graphing calculator to create a scatter plot. Which better represents the data, a line or a parabola? Explain.

b. Use the regression feature of your calculator to find the model that best fits the data.

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Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.

14.

Evaluate the function for the given value of x.

15. ;

Find the sum. 16.

Find the difference. 17.

Find the product. 18.

Use Pascal’s Triangle to expand the binomial. 19.

20. Find the coefficient of in the expansion of .

Divide using polynomial long division. 21.

Divide using synthetic division. 22.

Find all real zeros of the function. 23.

24.

Write a polynomial function f of least degree that has a leading coefficient of 1 and the given zeros. 25.

Describe the transformation of f represented by g. Then graph each function.

26. ,

27. ,

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29.

Match the function below with its correct description, graph, or value.

a. d. polynomial function with a degree of 3

and a leading coefficient of 3 b.

2 4 6

–2 –4 –6 x 4 8 12 –4 –8 –12 y _e.

2 4 6

–2 –4 –6 x 20 40 60 –20 –40 –60 y

c. not a polynomial function f.

____ 30. ____ 31. ____ 32. ____ 33. ____ 34. ____ 35.

36. A box is created from a rectangular piece of cardboard 16 centimeters by 24 centimeters by cutting a square from each corner and folding up the sides, as shown in the diagram. Write an expression for the volume of the box as a polynomial in standard form.

x x x x x x x x cm 24 16cm

37. The table shows the annual profits p (in millions of dollars) of a certain company in the year t, where

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t 1 2 3 4 5 6 7 8 9 10 p 4.3 12.3 21.8 28.5 30.5 28.3 29.0 30.2 33.1 41.7

Find and state the domain. Then evaluate for the given value of x.

38. , ;

Find and state the domain. Then evaluate for the given value of x.

39. , ;

Find and state the domain. Then evaluate for the given value of x.

40. , ;

Find and state the domain. Then evaluate for the given value of x.

41. , ;

Find the inverse of the function. Then graph the function and its inverse. 42.

Determine whether the inverse of f is a function. Then find the inverse. 43.

Evaluate the expression without using a calculator. 44.

45.

Rewrite the equation in logarithmic form. 46.

Evaluate the logarithm. 47.

Condense the logarithmic expression.

48.

49. Determine the type of function represented by the table. Explain your reasoning.

x 2 3 4 5 6

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____ 50. Which statements about the data are true?

x –3 –2 –1 0 1 2 3

f(x) –14 –6 0 4 6 6 4

a. _{A polynomial function that fits the data exactly is} b. _{A polynomial function that fits the data exactly is} c. The third finite differences are constant and equal –28.

d. _{A polynomial function that fits the data exactly is} _. e. The second finite differences are constant and equal –2.

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Benchmark #2 study Guide

Answer Section

1. ANS: 0.95 DIF: Level 2 2. ANS: 13,899

DIF: Level 2 3. ANS:

cylinder with radius 5 DIF: Level 1 4. ANS:

about 10 people per sq mi DIF: Level 1

5. ANS:

Shirt Express charges less per shirt. For the cost to be the same, 74 shirts must be ordered. DIF: Level 2

8. ANS:

; about 167.4 centimeters DIF: Level 1

9. ANS:

a. parabola; not a constant rate of change b.

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polynomial function; ; 2 (quadratic), leading coefficient: –5 DIF: Level 1

15. ANS:

18

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f g

2 4 6

–2 –4

–6 x

2 4 6

–2

–4

–6 y

The graph of g is a horizontal shrink by a factor of and a translation 4 units down of the graph of f.

f

g

2 4 6

–2 –4

–6 x

2 4 6

–2

–4

–6 y

neither

even

DIF: Level 1

30. ANS: F DIF: Level 2

31. ANS: A DIF: Level 2

32. ANS: C DIF: Level 2

33. ANS: D DIF: Level 2

34. ANS: B DIF: Level 2

35. ANS: E DIF: Level 2

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, domain: all real numbers; DIF: Level 1

39. ANS:

, domain: all real numbers; DIF: Level 1

40. ANS:

, domain: ; DIF: Level 1

41. ANS:

, domain: ;

f

g

2 4 6

–2 –4

–6 x

2 4 6

–2

–4

–6 y

yes;

DIF: Level 2 44. ANS: 5

DIF: Level 1 45. ANS: 128

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–3

exponential; The common ratio is 1 2. DIF: Level 1