Algebra II Honors                                                              

Midyear Exam Review Problem Set

 

From Chapter R:

1.   Factor the following expression fully.  You will need to use multiple methods. 

The following formulas may be needed:  

       Factor  completely. 

 

 

 

 

 

 

 

 

 

 

 

2.      Simplify the mixed quotient below into a single rational expression using only positive exponents.  Be sure to reduce if necessary but you don’t need to put your numerator and denominator into standard form.  In other words, you can leave answer in factored form if you would like. 

 

     

 

 

 

 

 

 

 

 

 

 

 

 

3.      Simplify the radical below.  Assume that all variables are positive.  Give your answer in radical form. 

 

        

 

 

 

 

4.      Use rational exponents to simplify the expression below.                             

Give your answer in either radical form or with a positive rational exponent.

 

        

 

 

 

 

 

 

5.       Subtract the rational expressions below.                                                       

 

           

 

 

 

 

 

 

 

 

6.      Factor the expression below. 

 

           

 

 

 

 

 

 

 

From Chapter 1:

 

1.      Solve the equation below. 

     

             

 

 

 

 

 

 

 

2.      Solve                                                                                

 

 

 

 

 

 

 

3. Solve                                                                                    

 

 

 

 

 

 

4.  Solve                                                                                       

 

 

 

 

 

 

5.      Kevin can overhaul a boat’s diesel inboard engine in 40 hours. His apprentice, Donald, can do the same job in 60 hours.  How long would it take them working together assuming no gain or loss in efficiency?   Show all work!  

 

 

 

 

 

 

6.       Solve the equation below.   (You don’t have to check for extraneous since odd root.  You may leave your answer(s) in un-rationalized radical form. )                                                     

 

          

 

 

 

 

 

 

 

 

 

 

 

From chapter 2:

 

1.      A circle has a center of (2, 4) and the point (−1, 1) lies on the circle.  Write the equation for this circle in standard form. 

 

 

 

 

 

 

 

 

 

2.      Write the equation of the line that has an x-intercept of 4 and is parallel to .  Give answer in standard form. 

 

 

 

 

 

3.      The table below gives the enrollment for the City Year national youth service program from

     1989 to 1998.  Let x be years since 1989 and let y be the number of youth in the program.

 

x

 

0

1

2

3

4

5

6

7

8

9

y

 

57

76

107

234

371

688

678

716

894

918

 

a)     Use your calculator to find the line of best fit.  Round decimals to four places.                   

 

b)     Identify the correlation coefficient. Based on this value, what do you conclude?

 

 

c)      If the pattern continues, how many people will enroll in City Year in the year 2005?  Round up or down since people.  

 

 

 

 

4.      The safety load (S) of a beam varies jointly with the width (W)                  

and the square of the depth (D) and inversely with the length (L) of the

beam.  Suppose k is the constant of proportionality, what is the equation? 

 

            A)               B)             C)                

           

            D)               E)  None of the above choices.

 

 

5.      Identify the center and the radius of the circle given by:                             Center:

 

                                                                                   radius: 

 

 

 

 

 

 

 

 

 

 

6.      Determine the symmetry (x, y, and/or origin) of the equation below.

 

 

 

 

 

 

7.      Write the equation of the line that contains the points (2, 4) and (4, 8) in standard form.

 

 

 

 

 

 

 

From chapter 12:

 

1.  Find x and y such that the two matrices below are equivalent.        1.  x = _________

 

                                                 y = _________

 

 

2.      Multiply the matrices: 

 

 

 

3.      If  and A is a 2x3 matrix, what are the dimensions of matrix B? 

 

 

 

 

 

4.      Mark, Maggie, and Matt all go athletic gear store to stock up on some workout clothes.  Mark buys 3 pairs of socks, 2 t-shirts, and 5 pairs of shorts.  Mark spends $109.50 on his purchase.  Maggie buys 5 pairs of socks, 3 t-shirts, and 3 pairs of shorts.  Maggie spends $93.50 on her purchases.  Matt buys 8 pairs of socks, 2 t-shirts, and 6 pairs of shorts.  Matt spends $138 on his purchases.  Determine the price of each pair of socks, each t-shirt, and each pair of shorts.  Assign variables, write a system, and solve using any method you would like.

 

 

 

 

 

 

 

5.      On graph paper, sketch the system of inequalities below.  Be sure to darkly shade the solution set and be sure it is clear if your lines are solid or dashed. 

 

 

 

6.      Give an example of two equations in standard form that form an inconsistent system. 

 

 

 

7.      Solve the system below.

 

                                                  

 

 

8.      Algebraically, solve the system below.

 

 

 

 

 

 

 

Since Chapter 3 and 4.1 are recent, see your assessments and slide reviews for problems.

Answers to the Midyear Exam Review Problem Set

 

 

Chapter R

 

1)        

2)        

3)        

4)        

5)   

6)  

 

 

Chapter 2

 

1) 

2)  5x + 2y = 20

3)  a)  y = 110.1152 x − 21.6182

b)  r = 0.9739  Positive correlation (m=pos).  Very good fit since so close to1.   One should

trust the model.  The line fits many points.

c)      1740 people

4) B

5)  (0,8) 

6)  Origin

7)  −2x + y =0

 

 

Chapter 1


1) 

2) 

3) x>9 OR x<3

4)  All real numbers

5)  24 hours

6) 

 

 

Chapter 12

 

1)     x = 7, y = ±5

2)    

3)     B is 3x4

4)     Socks $2.50, T is $11, Shorts are $16

5)      

6)     Various answer, two parallel lines

7)     Let x = any real number and then

8)     X = 4; y = −3; z = 1