Algebra 2
Cumulative QUIZ review
2015-16
Name _________________________
Block _________________________
2015 - 2016 Algebra 2 Mid-Year Quiz Review Packet
Due:
1/15/16 (A Day Classes)
1/14/16 (B Day Classes)
The mid-year review quiz will be on all units we have studies this year. The BEST way to study for the
quiz will be to complete this packet, review old tests and quizzes, and look over you notes.
The review packet will be graded on:
 Completion (10 points) – On January 15th and 14th this packet will be collected in class for a
completion grade. Completion means every problem has been attempted to the best of your ability
and work has been shown. Late packets will be assessed a penalty.
 Accuracy (10 points) -- On January 22th and 21st, we will have a 10 point quiz on problems from
this packet. I will randomly select 5 problems to grade on accuracy. You will be able to use your
packet on this quiz.
Completion
10
GOOD LUCK!!!
The cumulative quiz will cover all material in Units 2 - 4 and regression that we have covered in class
prior to the end of first semester.
Be sure to study your old tests and quizzes from all units.
Name _________________________________
Cumulative Review
Date _________________________
Circle your final solutions!!
UNIT 2: Investigating Functions
1. Use your calculator to graph y = 𝒙𝟑 + 𝟔𝒙𝟐 + 𝟗𝒙
Relative minimum/maximum? ____________________________
Absolute minimum/maximum?____________________________
Zeros? ___________________
Y-intercept? _________________
2. Sketch the inverse of the function shown below, using three points from the graph.
3.
Use the graph to the right to answer the following:
What is the Domain?
Interval Notation: __________________
Inequality Notation: _________________
What is the Range?
Interval Notation: __________________
Inequality Notation: _________________
What are the zeros? ______________________________________________
Is the INVERSE a function? ___________ Explain _______________________________________
Identify:
Relative Minimums ___________________ Relative Maximums __________________
Absolute Minimums __________________Absolute Maximums ___________________
4. Use the graph to the right to answer the following:
Number of turning points: ___________________________________
Identify the Relative Minimums or Maximums _______________________________
Identify the Absolute Minimums or Maximums _______________________________
Increasing Interval (s) _______________________________
Decreasing Interval (s) ______________________________
End Behavior:
As 𝑥 → −∞, 𝑓(𝑥) → ________________
As 𝑥 → +∞, 𝑓(𝑥) → ________________
5. Use the graph to the right to answer the following:
What is the Domain?
Interval Notation: __________________
Inequality Notation: _________________
What is the Range?
Interval Notation: __________________
Inequality Notation: _________________
What is the type of discontinuity shown? ___________________________
UNIT 3: Absolute Value Functions
1.
Fill in the table based on each given absolute value equation. For vertex, domain, and range WRITE in your answer.
For direction and dilation clearly CIRCLE your answer.
Function
Vertex
a.
y  x 2 3
b.
y  2 x  4
c.
y   x  3 1
d.
y  x 5
e.
y   x 6
Direction
Dilation
Up
Dilation
Standard
Down
Up
Down
Up
1
4
Down
Up
Down
Up
Down
Domain
Range
Dilation
Standard
Dilation
Standard
Dilation
Standard
Dilation
Standard
2. Graph y  x  2  5 using at least five distinct points. Then complete the information on
the right based on the graph. (Be sure you can do this without a calculator!)
Domain:
Range:
 y

Vertex:

Y-intercept:


    

x





Zeros:
Increasing:

Decreasing:

End Behavior:


As x    then f (x)  _____
As x    then f (x)  _____
Solve the following equations for the indicated variable.
3. |q + 3| = 1
5.
|2x + 12| = 4x
4.
25+ 2x- 7 = 15
6. |x - 5| = -8
Solve and graph the following inequalities.
7. 5 < 2x + 3 < 11
9.
2
x5  5
3
8.
2 x  4  12
3 x  5  7  11
10.
UNIT 4: Quadratics – GRAPHING PART 1
Function
Form
Direction
Dilation
y = ½ (x + 1)2 - 2
Standard
Vertex
Intercept
Up
Down
Dilation
f(x) = x2 - 6x + 5
Standard
Vertex
Intercept
Up
Down
Dilation
y = (x – 4) (x + 6)
Standard
Vertex
Intercept
Up
Down
Dilation
Standard
Vertex
Intercept
Up
Down
Dilation
y = - 2x2 - 8x + 5
Vertex
Domain
Range
Shrink
Shrink
Shrink
Shrink
1. Complete the table.
2. Graph each quadratic function. (Be sure you can do this without a calculator!)
 y






1
2
 x  2  5
2
 y


    
y
y   x  4 x  2
Y = x2 – 2x - 8








x

 y
    









x






    





x





3. Graph the following using your calculator and fill in all blanks. Round values to 2 decimal places.
f ( x) 
1 2
x  x  3.
2
Vertex: ______
x - Intercepts: ____________
 y

Axis of Symmetry: ________

Y-intercept: ______________

Domain: _____________________

    





x
Range: _______________________

Increasing: ____________________

Decreasing: ___________________

End Behavior:
As x    , f ( x)  _____
As x    , f ( x)  _____


Maximum Value of function: _____
Minimum Value of function: _____
UNIT 4: Quadratics – REAL & COMPLEX NUMBERS PART 2
Exponent Rules
1. 5a(6a )
3 2
24 x y
2 6
4. 3x y
4
5
2.
5.
1
3
x x
3
3
3
5
4 x y 5xy

2 xy
2y
2
3.
4x3y-5z
6.
 16 3 
 4x y 




4
Simplifying Square Roots
Simplify using the product rule. Assume all variables are positive.
7.
8. √24𝑎2 𝑏 7 𝑐 6
108
9. √−144
11.
13.
48
3
10.
1
2
12.
8
10
14.
16 2
64

1
2
75
Operations with Square Roots
15.
3 2 + 4 18
18. 7 6  2
16.
3 2  4 18
17.
19. 2 12  18
20.
2 50  32
2
3 7
Complex Numbers: Simplify the following.
21. (3 + 2i) (4 – 3i)
23.
2
3i
22. (3 + 4i) – (5 – 8i)
24.
3  2i
5i
+ 3 2
UNIT 4: Quadratics – Solving quadratics PART 3
Solve using the square root method:
1. (2x - 3)2 = 121
2.
5 (x – 2)2 – 6 = 24
3. (x – 3)2 = - 144
4. -3 (x + 1)2 = 81
Solve using factoring (zero product property):
5.
7.
4x2 + 24x = 0
6.
x2 – 16 = 0
x2 - x – 12 = 0
8.
4x2 - 7x – 2 = 0
Solve using the quadratic formula:
9.
x2 + 2x + 7 = 0
10. x2 – 5x = 4
Solve by completing the square:
11.
x2 – 6x – 7 = 0
12. x2 + 4x + 8 = 0
Solve using any method:
13.
x2 – x = 6
14.
x2 + 8x – 13 = 0
15. If x2 – 10x + c is a perfect square trinomial, what is the value of c? Then, write the trinomial in
factored form, i.e, as a square binomial.
16. How many real and imaginary solutions does the equation 5x2 – 3x + 7 = 0 have? Explain by
finding the discriminant.
17. Find the solution set for the following
system of equations using graphing.
y

y=½x–3
y = x2 + 4x – 14


    


y = x2 + 1
y = - x2 + 9




x




 y

    








Solutions: ______________________
x



Solutions: ______________________


