Download 1st Sem Rev - Moore Public Schools

Name: _____________________________
Date: __________
Hour: _____
ALGEBRA II – 1st Semester Test Review
Objective 8: Manipulate basic algebraic expressions using order of operations and properties of real numbers.
1.
Evaluate: -2x² - 3x + 6, if x = -3.
2.
x  3  y   y 2 ; x  4, y  1
3. When using the order of operations on the following problem what would be your first step?
3  2  7   2  15
2
Objective 9: Review multi-step linear equations.
4.
Solve: 4x + 3(x + 2) – 4 = 6(x – 1) + 3
5.
6(x – 0.8) – 0.2(5x – 4) = 6
Objective 11: Define and distinguish between relations and functions.
6.
Sketch a picture of a graph that is a function. Sketch another that is not a function.
7.
Does the following relation represent a function? Explain why or why not. {(2, -3), (4, 6), (3, -3)}
8.
A function is a relation in which…
a) no two different ordered pairs have the same y coordinate
b) no two different ordered pairs have the same x coordinate
c) no two different ordered pairs have the same x or y coordinate
d) it does not pass the horizontal line test
9.
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.
10. For f(x) = -6x + 5 and g(x) = 3x – 2, find:
a) f(-4) + g(3)
b)
f (6)
g (2)
d) f  g
c) f  g
11. State the domain and range of the function {(2, -3), (4, 6), (3, -3)}.
12. Find the domain and range and determine whether it is a function.
y
–3
–2
y
3
3
2
2
2
1
1
1
–1
–1
1
2
3
x
–3
–2
–2
–1
–1
1
2
3 x
–3
–2
–3
A.)
y
3
–1
–1
–2
–3
B.)
–2
–3
C.)
1
2
3 x
Objective 16: Graph linear equations and write equations of lines.
13. Graph the equation: 6x – 5y = 30.
14. Write an equation of a line in slope intercept form thru (-1, -4) with m = 2.
15. Write an equation of the line (below).
y
7
6
5
4
3
2
1
–7 –6 –5 –4 –3 –2 –1
–1
1
2
3
4
5
6
7
x
–2
–3
–4
–5
–6
–7
Objective 17: Determine slope when given an equation, graph or two points.
16. Find the slope of the line through the points
 5,3 and  4, 7  .
Objective 15: Write linear equations that model real world data.
17. The graph below represents Alan’s trip on his bike. If x represents time and y represents miles.
Write the equation of the line. What is the slope of the line and what does it represent?
y
40
30
20
10
2
4
6
x
8
Objective 13: Display data involving two variables on a scatter plot and find the best fit linear or quadratic equation and interpret results.
The data in the table shows the number of minutes spent studying for a math test and the score that the
student earned. Make a scatter plot and decide if a linear model is reasonable. Does the data have a positive
correlation or a negative correlation? Draw the trend line and write its equation. (Hint: use a calculator and do a
linear regression)
18.
1
20
60
2
65
85
3
30
70
4
90
100
5
45
88
6
30
77
7
80
90
8
50
82
9
35
80
Test Score
Student
Study time (in Minutes)
Test score
Objective 21: Solve systems of equations by graphing.
19.
20.
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
21. If the system of equations graphs parallel lines then how many solutions does it have?
22. What will the graph of a system of equations look like if the solution is “many solutions?”
23. If two lines intersect, how many solutions does the system of equations have?
Objective 22: Solve systems of equations algebraically.
x  3 y  9
24. 
3x  9 y  27
25.
3 x  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. Identify the quadratic, linear, and constant terms. y = (3 – x)(2x + 1)
31. Does the graph of y  8  7x2  3x open up or down?
32. Write the quadratic equation given the solutions of 2 and –5.
33. Use vertex form to write the equation
of the parabola.
y
6
4
2
–6 –4 –2 O
–2
2
4
6
–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.
34.
f ( x)  3( x  4) 2  6 V(_____, _____)
35. Graph y = -3x² + 6x + 5.
Does the function have a maximum or minimum
value? What is the value of the maximum or
minimum value? What is the y intercept?
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?
x
37. Identify the vertex and the y-intercept of the graph of the function. Then graph.
y = -3(x + 2)² + 2.
38. Suppose that you are throwing a water balloon to a friend on the third floor. After t seconds, the height of
the water balloon in feet is given by h  16t  38.4t  .96 . Your friend catches the balloon just as it
reaches its highest point. How long does it take the balloon to reach your friend and at what height does
your friend catch it?
2


Objective 27: Identify the parent graph of the function y  x 2 and predict the effects of transformations on the parent graph
and find domain and range.
39. Use the graph of y = (x – 3)² + 5.
a. If you translate the parabola to the right 4 units and down 6 units, what is the equation of the
new parabola in vertex form?
b.
If you translate the original parabola to the left 3 units and up 7 units, what is the equation of the
new parabola in vertex form?
c.
How could you translate the new parabola in part (a) to get the new parabola in part (b)?
Objective 28: Factor quadratic equations.
40. Factor the following:
a. x  4 x  21
b. x  9 x  20
c. x  2 x  48
d. -25x² - 15x
e. 4x² - 29x -63
f. 25x² - 4
2
2
2
Objective 64: Solve quadratic equations by factoring and graphing.
41. Solve for x.
a. 12 x  5 x  3  0
2
b. 3x² + 25x – 18 = 0
Objective 30: Simplify, add, subtract, and multiply complex numbers.
42. (3+8i)²
43. –6 –
44.
45.
46.
Objective 32: Solve quadratic equations by completing the square.
47. What value will complete the square?
x 2  6 x  ___
x2 
2
x  ___
3
48. Solve by completing the square.
x 2  10 x  6  0
x 2  4 x  25
Objective 33: Solve quadratic equations by using the quadratic formula or by square rooting, including complex solutions.
x 2  3x  28 =0
49.
50. 2 x  2 x  1
51. 9 x  6 x  7
2
2
53.  5 x  2   10  2
2
52. 25x² + 81 = 0
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 13: Display data involving two variables on a scatter plot and find the best fit linear or quadratic equation and interpret results.
56. Mrs. Kay’s bakery showed increasing profits until June and then her profits began to decrease. The
information is shown in the table below (profits in thousands of dollars). Find a quadratic model,
determine which pair(s) of values would best complete the table.
FEB
APR
JUNE
AUG
OCT
2.5
3.1
3.25
3.0
2.4
a)
( March, 3.25)
b) (July, 3.5)
c)
(July, 3.15)
Objective 65: Sketch a graph of a polynomial function..
57. Determine the end behavior of y = x – x³ + 5.
58. 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,
using various methods and tools which may include a graphing calculator.
59. Use the graph to answer the following questions.
y
8
a) What are the x-intercepts?
6
b) What is the y-intercept?
4
c) Are intercepts numbers or points?
2
d) What are the zeros of the function?
e) Which is a relative maximum function value?
f) Name the relative minimum.
–4
–3
–2
–1
–2
–4
–6
g) State the domain and range of the function.
–8
1
2
3
4
x
60. What do the right and left ends of the function do?
f ( x)  3x3  x 2  2 x  4
61. What is the maximum possible number of x-intercepts for the function?
f ( x)  3x3  x 2  2 x  4
***Objective 37: Divide polynomial expressions using long division and synthetic division.
62. a. Divide using long division.
b. Divide using synthetic division.
(3x  2 x  x  1)  (4 x  2)
4
2
(3x 4  2 x 2  x  1)  ( x  5)
2
63. Solve. x 3  3x 2  13x  15  0
64. Use synthetic division to find P(-1) if P(x) = x 2  5x  7
65. 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..
66. Solve 64x3 + 8 = 0 for x.
67. Solve. x3 – 7x + 6x = 0 for x.
Objective 31: Find rational zeros and the connection of zeros, factors, and solutions of polynomial equations.
68. 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?
y
50
40
69. What are the zeros for the polynomial that is graphed?
30
20
70. What are the linear factors of the polynomial?
10
–5
–4
–3
–2
71. What is the equation of the graph in both factored and
standard form?
–1
–10
1
2
3
–20
–30
–40
–50
Objective 31: Find rational zeros and the connection of zeros, factors, and solutions of polynomial equations.
72. List all the possible solutions to the function? 3x3 + 4x2 - 3x – 18 = 0
73. Solve x4+7x2-18=0 for x
74. Given that one of the roots is 4, find the other 2 roots. P(x) = x 3 -6x2 + 5x + 12
75. Write the equation in both factored and standard form of a polynomial with the zeros 4, -2, and 1.
4
5
x
76. If the factors are (x – 3),(x + 2) and (x -5), what are the zeros?
77. Find the zeros of 2x3 + 10 x2 + 12x = 0.
Objective 41:
78.
Simplify radical expressions
Simplify the expression
225x10 y 4
Objective 67: Multiply and Divide Rational Expressions
3
80.
640w 3 z 8
3
81.
79.
Simplify the expression
3 y  4 xy 4  6 x 5 y 2
(3x 4 )3 (2 x2 ) 2
82.
5wz 4
Simplify the Expressions
to include rationalizing fractions that contain complex numbers
18 + 2 72
3
85.
84.
3  2 5 1  3 15 
86.
3  2 5 
1  3 15 
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.
3
2x 4
87.
Write the exponential expression in radical form.
88.
Write the radical expression in exponential form and simplify.
5
256x2
Simplify the Expressions
 2 1  1 1 
89.  s 5 t 3  s 2 t 2 






90.
8ab  8ab 
92.
 64 3
1
2 2
Simplify the Expressions
91.
1
3
1
2

3
4
1
2
x y
x y
2
Objective 37: Solve radical equations.
2
93.
64x 9 y16 z 23
Simplify the Expressions
Objective 68: Add and Subtract radical expressions and multiply and divide binomial radical expressions
83.
4
 x  2 3  4  5
95. Graph and describe the translation of the
following function.
y = -2│x +3│- 4
94.
x 3  x 5
2
1
2