2ND G

RADING P

ERIOD

DISTR

ICT

ASSESSMENT

QUESTIONS

F AL L

20

12

RATIONALS

If and x 2, x -2, then what must x equal? 

F.

G.

H. 1

J. 2

If    is true, then

n = ? 

A.

B. 5

C.

D.

GRAPHS/SYSTEMS

The figure below shows the graph of a function in the xy-plane.  Which of the following could be the type of function?

A. Absolute Value

B. Quadratic

C. Linear

D. Ellipse

In which direction does the graph  shift as p increases? 

A. Right

B. Left

C. Up

D. Down 

Which of the following sentences is true about the graphs of and ? 

A. Their vertices are maximums.

B. The graphs have the same shape with different vertices.

C. The graphs have different shapes with the same vertices.

D. One graph has a vertex that is a maximum, while the other graph has a vertex that is a minimum.

Find the minimum of C = 2x + 3y for the constraints:                                                          

A. (1, 0))

B. (0, 2)

C. (6, 0)

D. (8, 2)

Solve the following system of equations: 

 

F. (-3, 0)

G. (0, -1)

H. (-3, 0) and (0, -1)

J. No Solution

The figure below shows the graph of a function in the xy-plane.  Which of the following could be the type of function?

A. Absolute Value

B. Quadratic

C. Linear

D. Ellipse

5. In which direction does the graph  shift as z decreases? 

A. Right

B. Left

C. Up

D. Down

Solve the following system of equations:  

F. (0, 0)

G. (2,2) and (2, -2)

H. (0, 0) and (4, 0)

J. No Solution

Find the minimum of P = 4x + 6y for the constraints:                                                                                                                                                                             

A. (0, 4)

B. (4, 0)

C. (3, 1)

D. (0, 1)

It costs Bryson $ 7 per day to drive his truck to work and $3 per day to drive his motorcycle to work.  He drives to work at least 20 days each month.  He must drive the truck at least 8 days, but no more than 12 days, per month.  He can drive the motorcycle no more than 14 days per month.   Given these constraints, what is the minimum gas bill that Bryson can have per month? 

F. $84

G. $92

H. $98

J. $108

A statistician solved the following system of quadratic equations:  She found two ordered pair solutions to the system of equations.  The x-coordinate of the first ordered pair was -3.  What was the x-coordinate of the other ordered pair? 

A. - 9

B. -1

C.

D. 3

FUNCTIONS

Given  , find  . 

A.

B.

C.

D.   does not exist

Given that    and   . What is the value of ? 

F.

G.

H.

J. 2

Given:                        

Are   and  inverse functions?  Justify your answer. 

F. Yes, because

G. Yes, because

H. No, because  .

J. No, because .

Given ,

find . 

A.

B.

C.

D.  does not exist.

Given   and

what is ?

F.

G.

H.

J.

x

26. For the 2 functions, f(x) and g(x), tables of values are shown below.  What is the value of g( f(3) )?  

F. -5

G. -3

H. -1

J. 7

Given , find . 

A.

B.

C.

D.   does not exist.

7. Given:               Are   and  inverse functions?  Justify your answer. 

A. Yes, because

B. Yes, because .

C. No, because

D. No, because

For the 2 functions, f(x) and g(x), tables of values are shown below.  What is the value of g( f(1) )? 

A. -5

B. -3

C. -1

D. 7

8. To convert a temperature in degrees Celsius to degrees Fahrenheit, the formula is  , where C is the degrees in Celsius.  What temperature, to the nearest degree Celsius, equals a temperature of 59 degrees Fahrenheit? 

F.

G. 15

H. 112.5

J. 138

Given   and  . 

What is ? 

A.

B.

C.

D.

13.

A.

B.

C.

D.

Let f(x) be the equation of the line-of-best-fit used to approximate the data given in the chart.  What is the approximate value of f(6)?  

A. 8.5

B. 9.0

C. 10.5

D. 11

  

1. If      and   , then g( h(2) ) = ? 

A.10

B.17

C.23

D.350

CONICS

What is the equation of the circle with center (3, -6) that contains the point (-2, 0)? 

A.

B.

C.

D.

Given the ellipse described by the equation , what is the length of the minor axis? 

A. 1

B. 2

C. 4

D. 16

35. Which of the following equations describes the conic section below?

A.

B.

C.

D.

What is the equation of the circle with center (-2, 4) that contains the point (5, 2)? 

F.

G.

H.

J.

6. The graph of  is a hyperbola.  Which set of equations represents the asymptotes of the hyperbola's graph? 

F.

G.

H.

J.

What is the equation of the circle with center (3, -6) that contains the point (-2, 0)? 

A.

B.

C.

D.

6. The graph of  is a hyperbola.  Which set of equations represents the asymptotes of the hyperbola's graph? 

F.

G.

H.

J.

LOGARITHMS

Solve for x:  

F. 0.9

G. 4

H. 8

J. 32

A certain type of bacteria, given a favorable growth medium, doubles in population every 6.5 hours.  Given that there were approximately 100 bacteria to start with, how many bacteria will there be in a day and a half? 

F. approximately 0.1066

G. approximately 46

H. approximately 3,789

J. approximately 4,648

Radium has quite a long half-life.  The scientist put 1 ounce of radium in the bowl and 100 years later only 0.95817 ounce remained.  Assuming exponential decrease, what is the half-life of radium? 

F. Approximately 0.162 years

G. Approximately 427 years

H. Approximately 693 years

J. Approximately 1,622 years

Which of the following is equivalent to  ?

F.

G.

H.

J.

Which is equal to ? 

F. 1

G. x

H. 3

J.

The number of bacteria present at noon was 400, and 9 hours later the bacteria numbered 800.  Assuming exponential growth, which of the following is closest to the number of bacteria present at noon the next day. 

F.0.077

G.806

H.2,539

J.295,680

What is the real value of x in the equation ? 

A.2

B.3

C.8

D.21

12. The amount of substance initially present was 400 grams, and after 90 hours only 380 grams remained.  Assuming exponential decay, which is closest to the half-life of the substance. 

F. -0.00057 hours

G. 3.95 hours

H. 137 hours

J. 1216 hours

12. The amount of substance initially present was 400 grams, and after 90 hours only 380 grams remained.  Assuming exponential decay, which is closest to the half-life of the substance. 

F. -0.00057 hours

G.3.95 hours

H.137 hours

J.1216 hours

16.

Which of the following is equivalent to  ? 

F.

G.

H.

J.

At the beginning of an experiment there are 8,000 bacteria.  A lethal pathogen is introduced into the colony and after 2 hours only 7,000 bacteria remain.  Assuming exponential decrease, what is the half-life of the bacteria to the nearest hour?

F. 6 hours

G. 9 hours

H. 10 hours

J. 12 hours

Solve for x:  

F. 1

G. 2

H. 3

J. 8

Find the approximate value of:          

 

F. 4.58

G. 5.32

H. 8.13

J. 20.0

Which  is equal to ?

 

F. 1

G. x

H.

J. 5x

21. What is the real value of x in the equation ?

 

A. 2

B. 3

C. 8

D. 21

Solve for x:                   

A. -1

B.0

C.3

D.5

Which of the following is equivalent to ?

F.

G.

H.

J.

ARITHMETIC AND GEOMETRIC SEQUENCES

Find the sixteenth term of an arithmetic sequence whose first term is -8 and whose common difference is 3.

A. -34

B. 37

C. 128

D. 232

Find the sum of the first 4 terms in a geometric series whose first term is 8 and whose common ratio is -4. 

A.

B. -32

C. -408

D. -512

Find the twenty-fourth term of an arithmetic sequence whose first term is -3 and whose common difference is 4. 

F. 86

G. 89

H. 93

J. 96

COMBINATIONS AND PERMUTATIONS

Eight books are on the English II summer reading list.  Each student must choose 5 books from the list to read over the summer.   How many different combinations of 5 books can be chosen?

F. 28

G. 56

H. 224

J. 336

3. How many ways can a committee of 5 teachers be selected from a group of 12 teachers? 

A.60

B.792

C.5040

D.3,991,680

A coach needs to know how many ways can a team of 5 basketball players be selected from a team of 10 players? Which of the following will give this information?

 

A.

B.

C.

D.

There are 12 people in the Accounts Payable Department of Bloomington, Incorporated.  The manager needs to know how many different ways 7 people from the department can be chosen to be trained on the new accounting software program.   Which of the following will give this information?

F.

G.

H.

J.

25. A teacher needs to arrange 5 science fair winners in 5 chairs for a picture.  How many different ways can the students be arranged in the chairs for pictures?

A. 5

B. 15

C. 120

D. 125