ACP ALGEBRA II MIDTERM REVIEW PACKET 2015- ... ACP ALGEBRA II MIDTERM REVIEW PACKET 2015-16 Name _____

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  • ACP ALGEBRA II MIDTERM REVIEW PACKET 2015-16

    Name _____________________________ Per__ Date______

    This review packet includes new problems and a list of problems from the textbook. The answers to the problems from

    the textbook can be found in the back of the textbook and a detailed solution on www.hotmath.com.

    Section 1-4 Solving Absolute Value Equations

    Vocabulary: Absolute value, empty set, equation, solution, variable

    p.30-31 #5-13odd,17-43odd,47,49,53

    1. Solve each equation. Remember to check your solutions!

    a. 7 4 1p    b. 4 1 5 37w w  

    Section 2-1 Relations and Functions

    Vocabulary: Dependent and independent variable, domain/range, relation/function, function notation, vertical line test

    p.60-61 #3-31odd,35,36,37,47-53odd

    2. Find the value of each of the following for the functions:   4 8f x x   and   26 25g x x x  .

    a.  9f  b. (3 )g a c. 𝑔(𝑥 + 1)

    3. Determine whether each relation is a function. Also, identify the domain and range.

    a.         2,1 , 2,1 , 3,4 , 8,0 b. 6 7y x 

    c. d.

    Section 2-6 Special Functions (graphing absolute value functions and piecewise functions)

    x y

    -5 6

    4 7

    -3 8

    0.5 9

    4 5

    http://www.hotmath.com/

  • Vocabulary: Absolute value function, constant function, identity function, parent graph, piecewise function

    p.93-94 #8-11all,15,16,19,20,32-41all,44

    4. Graph each function. Identify the x-intercepts, y-intercepts, vertex, domain, and range

    a. ( ) 3 9g x x  b. ( ) 2 1 6g x x   

    5. Graph each function. Identify the domain and range. Be sure to use proper notation.

    a.

      4 , 0

    5 , 0

    x x f x

    x x

       

       b.

     

    , 0 3

    2 6 , 0 2

    1 , 2

    x x

    g x x x

    x

     

            

  • 6. Write the definition (the equations) of the function shown in the graph below. Identify the range of the graph also.

    Section 5-1 Monomials

    Vocabulary: Coefficient, constant, degree, monomial, power, scientific notation, simplify, standard notation,

    p.226-7 #3-41odd,45-57odd

    7. Simplify the expression. Assume that no variable equals zero. Remember: leave no negative exponents.

    a.    

    2 3 4 23 2x y x y

    b.

    2 18 10

    9 20

    32

    16

    x y

    x y

         

    Section 5-2 Polynomials

    Vocabulary: Binomial, FOIL method, like terms, polynomial, terms, trinomial

    p.231-2 #5-33odd,37-51odd,57

    8. Find  5p for the polynomial:   5 4 25 5 10 6 1p x x x x x    

    9. Simplify.

    a.    4 3 4 23 4 9 6 5 1x x x x     b.    2 2 213 6 12 9 4x xy y x xy   

    c.  3 2 2 2 33 2 9 3a ab a b a b  d.   4 8x x 

    e.   2 5 3 7x x  f.   4 5 4 5x x 

    g.   2

    5 6x  h.   24 3 2x x x  

  • Section 5-3 Dividing Polynomials

    Vocabulary: Long division, synthetic division

    p.236-7 #3,5,7,11-43odd,49

    10. Simplify.

    a.

    3 218 30

    3

    a a

    a

     b.    6 2 3 2 324 40 4mn m n m n 

    11. Simplify by synthetic or long division.

    a.    3 23 7 4 3 3w w w w     b. 4 36 15 28 6

    2

    y y y

    y

      

    Section 5-4 Factoring Polynomials

    Vocabulary: Difference of cubes, difference of squares, greatest common factor, grouping, perfect square trinomial, sum

    of cubes

    p.242-3 #5-37odd,47,49

    12. Factor completely.

    a. 27 5 18x x  b.

    220 12 11x x 

    c. 38 125x  d.

    225 20 4p p 

    e. 22 18 40x x  f.

    249 81n

    g. 4 16c 

  • Section 5-5 Roots of Real Numbers

    Vocabulary: cube root, nth root, principal root, square root

    p.248 #5-55odd

    13. Simplify.

    a. 8144x b.

    6 6 42729m n

    c. 9 123 27x y

    d. 196

    e.

    8625

    49

    x

    f.  

    2 8x 

    Section 5-6 Radical Expressions

    Vocabulary: Conjugates, like radical expressions, rationalizing the denominator

    p.254-5 #5-45odd,49

    14. Simplify

    a. 23 12288x y b. 200 300

    c. 9 143 128x y

    d.

    20

    10

    64

    11

    y

    y

    e.

    2

    3

    25

    5

    x

    x f.  

    2

    8 7

    g. 5 5 2 80 3 45  h. 20 125 169 45  

    i.  3 3 32 4 12

    j.   2 3 4 5 

  • k.

    7

    3 l.

    2 5

    6

    m.

    2 7

    3 7

    Section 5-7 Rational Exponents

    Vocabulary: Rational exponents

    p.261 #5-15odd,21-47odd

    15. Write

    2

    310 in radical form.

    16. Write each expression using rational exponents.

    a. 647d b.

    3 5 23a b

    17. Evaluate each expression.

    a.

    2

    327 b.

    2 3

    3 28 4

    18. Simplify each expression.

    a.

    4 6

    5 5x x b.

    3 2 4 3y

         

    c.

    3

    4

    1

    6

    y

    y d.

    21

    32

    1

    6

    a a

    a

  • Section 5-9 Complex Numbers

    Vocabulary: Complex conjugates, complex number, imaginary unit, pure imaginary numbers

    p.273-274 #5-41odd,49-61odd

    19. Simplify

    a.    11 3 15i i   b.     11 12 21 8i i  

    c.   4 4 3 3i i    d.     2 7 8i i 

    e. 2 5

    3

    i

    i

      f.

    3

    6 7i

    g. 6 3

    8 11

    i

    i

     h.

    27i

    i. 49  j. 200 300  

    20. Solve 22 18 0x  

    21. Find the values of m and n that makes the equation true:8 15 2 3i m ni  

    Section 6-1 Graphing Quadratic Functions

    Vocabulary: Axis of symmetry, constant term, linear term, maximum value, minimum value, parabola, quadratic

    function, quadratic term, vertex

    p.290-292 #2,3-47odd,51

    22. State whether the graph of the quadratic function opens up or down. Then, state whether the function has a

    maximum or minimum value. Find the minimum or maximum value.

    a.   27 14 11f x x x    b.   23 2 10f x x x   

  • 23. SOLVE A souvenir shop sells about 200 coffee mugs each month for $6 each. The shop owner estimates that for

    each $0.50 increase in the price, he will sell about 10 fewer coffee mugs per month.

    a. Write the function,  I x , where x is the number of increases or decreases.

    b. How much should the owner charge for each mug in order to maximize the monthly income from their

    sales?

    c. What is the maximum monthly income the owner can expect to make from these items?

    24. Complete the following pieces for each function.

    a. Find the y-intercept, the equation of the axis of symmetry, and the vertex.

    b. Use this information to graph the function.

    i.   2 3 4f x x x  

    ii.   2 4 1f x x x   

  • Section 6-2 Solving Quadratic Equations by Graphing

    Vocabulary: Quadratic equation, roots, solutions, x-intercepts, zeros

    p.297-299 #5-43odd,49

    25. Use the formula   2 016h t t v t   , where  h t is the height of an object in feet, 0v is the object’s initial

    velocity in feet per second, and t is the time in seconds.

    ARCHERY An arrow is shot upward with a velocity of 64 feet per second. Ignoring the height of the archer,

    how long after the arrow is released does it hit the ground?

    26. Use the related graph of each equation to determine its solution(s). If exact roots cannot be found, state the

    consecutive integers between which the roots are located.

    a.   22 2 4f x x x   b.   2 3 5f x x x   

    Section 6-3 Solving Quadratic Equations by Fact