Download Sem 1 Review - A2 - 2016

Name: _____________________________
Date: __________
Hour: _____
ALGEBRA II – 1st Semester Test Review
Objective 9: Review multi-step linear equations.
1.
Solve: 4x + 3(x + 2) – 4 = 6(x – 1) + 3
2.
6(x – 0.8) – 0.2(5x – 4) = 6
Objective 11: Define and distinguish between relations and functions.
3.
Sketch a picture of a graph that is a function. Sketch another that is not a function.
4.
Does the following relation represent a function? Explain why or why not. {(2, -3), (4, 6), (3, -3)}
5.
Mary wants her relation to be a function. Which ordered pair should she delete so that the
relation  4, 2 , 1, 6 ,  0, 0 ,  4,6  is a function?
Objective 12: Use functional notation and specify domain and range.
6.
For f(x) = -6x + 5 and g(x) = 3x – 2, find:
7.
State the domain and range of the function {(2, -3), (4, 6), (3, -3)}.
8.
Find the domain and range and determine whether it is a function.
a) f(x) + g(x)
y
–3
–2
c) f
y
3
2
2
2
1
1
1
–1
–1
1
2
3
x
–3
–2
–1
–1
1
2
3 x
–3
–2
Objective 16: Graph linear equations and write equations of lines.
Graph the equation: 6x – 5y = 30.
–2
–1
–1
–2
–3
B.)
g (x)
y
3
–3
9.
f (6)
g (2)
3
–2
A.)
b)
–3
C.)
1
2
3 x
Objective 21: Solve systems of equations by graphing.
10.
11.
3x  y  10

4 x  4 y  8
When solving a system of equations by graphing the solution is
a) The vertex
b) The shaded region
c) The point of intersection
d) The y-intercept
12. If the system of equations graphs parallel lines then how many solutions does it have?
13. What will the graph of a system of equations look like if the solution is “many solutions?”
14. If two lines intersect, how many solutions does the system of equations have?
Objective 22: Solve systems of equations algebraically.
x  3 y  9
15. 
3x  9 y  27
25.
3x  y  8

x  y  4
26. Miss McClain buys milk and donuts for her top scoring class after their six week tests. The first time she
buys 4 dozen donuts and 2 gallons of milk for $20.92. The second six weeks she buys 3 dozen donuts and
1 gallon of milk for $14.35. How much do the donuts and milk cost?
27. The Village Inn offers two special packages. For two nights and three meals the cost is $158. For two
nights and five meals the cost is $181. Write and solve a system of linear equations to find the costs per
night and per meal.
Objective 24: Solve systems of linear inequalities.
28. Solve the system of inequalities by graphing.
 y  2x  1

a. 
1
 y   3 x  4
b.
3x  4 y  12

5 x  4 y  28
5
29. Which point is a solution to the system of inequalities?
a)
b)
c)
d)
(2, 0)
(3, -2)
(-1, -1)
(0, 2)
-5
5
-5
Objective 25: Identify characteristics of graphs based on general equations. (y=ax 2 + bx + c)
30. Does the graph of y  8  7x2  3x open up or down?
31. Write the quadratic equation given the solutions of 2 and –5.
32. Use vertex form to write the equation
of the parabola. y = a (x – h)2 + k
y
6
4
2
–6 –4 –2 O
–2
2
–4
–6
Objective 26:, Graph a quadratic function and identify the x- and y-intercepts and maximum or minimum value,
using various methods and tools, which may include a graphing calculator.
33.
f ( x)  3( x  4) 2  6 V(_____, _____)
34. Graph y = -3x² + 6x + 5.
35.
Does the function have a maximum or minimum
value?
What is the value of the maximum or minimum
value?
What is the y intercept?
4
6
x
36. A manufacturer determines that the number of drills it can sell is given by the formula
a.
, where p is the price of the drills in dollars.
At what price will the manufacturer sell the maximum number of drills?
b.
What is the maximum number of drills that can be sold?
37. Identify the vertex and the y-intercept of the graph of the function. y = -3(x + 2)² + 2.
38. A ball is kicked in the air. The flight of the ball is represented by the function h(t) = -16t2 + 24t , where h
is the height in feet t seconds after it is kicked.
a.) Determine mathematically using correct units, how long the ball is in the air before it hits the ground.
b.) State the meaning of your answer in Part A in a complete sentence.
c.) How long does it take to reach the maximum height? Justify mathematically, using correct units.
d.) What was the maximum height reached by the ball? Justify mathematically, using correct units.
Objective 28: Factor quadratic equations.
39. Factor the following:
x 2  4 x  21
a.
d. -25x² - 15x
b.
x 2  9 x  20
e. 4x² - 29x -63
c.
x 2  2 x  48
f. 25x² - 4
Objective 64: Solve quadratic equations by factoring and graphing.
40. Solve for x.
a.
12 x 2  5x  3  0
b. 3x² + 25x – 18 = 0
Objective 30: Simplify, add, subtract, and multiply complex numbers.
43. –6 –
44.
45.
46.
Objective 32: Solve quadratic equations by completing the square.
47. What value will make the expression a perfect square trinomial?
x2  6 x  ___
x2 
2
x  ___
3
Objective 33: Solve quadratic equations by using the quadratic formula or by square rooting, including complex solutions.
Solve
48.
x2  3x  28 =0
50.
2 x2  2 x  1
51.
9 x2  6 x  7
52. 25x² + 81 = 0
53.
 5x  2
2
 10  2
Objective 35: Write a polynomial in standard form and classify by degree and number of terms.
54.
x
2
 2 x  5  2 x  3
55.
 2x
4
 2 x 2    x 4  2 x3  x 2  x  2 
Objective 65: Sketch a graph of a polynomial function..
56. Determine the end behaviors of y = x – x4 + 5. (Do the ends rise or fall?)
57. Graph the polynomial
f ( x)   x 3  4 x  2
Objective 36: Given the graph a polynomial, identify the x – and y – intercepts, relative maximums and relative minimums,
58. Use the graph to answer the following questions.
y
a) What are the x-intercepts?
8
b) What is the y-intercept?
6
c) Are intercepts numbers or points?
4
d) What are the zeros of the function?
2
e) Which is a relative maximum function value?
–4
–3
–2
f) Name the relative minimum.
–1
–2
1
2
3
4
x
–4
g) State the domain and range of the function.
–6
–8
59. What do the right and left ends of the function do?
f ( x)  3x3  x 2  2 x  4
60. What is the maximum possible number of x-intercepts for the function?
***Objective 37: Divide polynomial expressions using long division and synthetic division.
61. a. Divide using synthetic division
(3x4  2 x2  x  1)  ( x  5)
62. Solve. x3  3x2  13x  15  0
f ( x)  3x3  x 2  2 x  4
63. Use synthetic division to find P(-1) if P(x) = x2  5x  7
64. Determine which binomial is a factor of
a.
x+5
b.
.
x + 20
c.
x – 24
d.
x–5
Objective 66: Solve polynomial equations by factoring to include sum and difference of two cubes..
65. Solve
64x3 + 8 = 0
for x.
Objective 31: Find rational zeros and the connection of zeros, factors, and solutions of polynomial equations.
66. When finding the solutions of a polynomial equation that is set equal to zero by looking at the graph,
what part of the graph should you look at?
67. a. What are the real zeros for the polynomial that is graphed?
y
50
b.
If there are roots with multiplicity, state where they occur.
40
30
Justify your answer.
20
10
c.
What are the factors of the function?
–5
d.
–4
–3
–2
–1
–10
1
2
3
4
5
–20
If the function is in standard form, is the sign of the leading
–30
Coefficient positive or negative? Justify answer.
–40
–50
e.
Is the degree even or odd? Justify your answer.
Objective 31: Find rational zeros and the connection of zeros, factors, and solutions of polynomial equations.
68. Write the equation in both factored and standard form of a polynomial with the zeros 4, -2, and 1.
69. If the factors are (x – 3),(x + 2) and (x -5), what are the zeros?
70. Find the zeros of 2x3 + 10 x2 + 12x = 0.
Objective 41: Simplify radical expressions
71.
Simplify the expression
225x10 y 4
Objective 67: Multiply and Divide Rational Expressions
73.
74.
3 y  4 xy 4  6 x 5 y 2
(3x 4 )3 (2 x2 )2
72.
Simplify the expression
Simplify the Expressions
4
64x9 y16 z 23
x
Objective 68: Add and Subtract radical expressions and multiply and divide binomial radical expressions
to include rationalizing fractions that contain complex numbers
Simplify the Expressions
75.
3
18 + 2 72
76.
6

24  2 6
Objective 42: Convert expressions from radical notation to rational exponents and vice versa.
Add, subtract, multiply, divide, and simplify expressions containing rational exponents.
77.
Write the exponential expression in radical form.
Simplify the Expressions
78.
8ab  8ab 
79.
 64 3
1
2 2
2
1
2
2
Objective 37: Solve radical equations.
2
80.
 x  2 3  4  5
2x
3
4
