Download x - Sonoma Valley High School

Spring Final Study Guide
In addition to reviewing previous tests, quizzes, homework, and notes, you should review the following topics: Ø Check a solution (linear, inequality) Ø Classify Sequence as geometric or arithmetic and write equation Ø Factor (what if a term is missing?) Ø Find a vertex of a parabola Ø Find an equation between two points (exponential, linear) Ø Find an equation from graph (exponential, linear) Ø Find generator (arithmetic/geometric/percent increase) Ø Find x-­‐ and y-­‐intercepts Ø Find x-­‐intercepts of parabola from equation (Zero Product Property) Ø Fraction Busters Ø Functions (Input/Output) Ø GCF (Greatest Common Factor) Ø Graph given an equation (linear/exponential/quadratic) Mixed Review
1. Factor: x 2 + 2 x − 24
Ø Investigate a parabola (intercepts, vertex) Ø Investigate Exponential and Linear Growth (write equations, make a table) Ø Multiply Polynomial (Generic Rectangle, FOIL, or Distributive) Ø Quadratic Formula (exact and approximate) Ø Scatterplots, Line of best Fit, and Association Ø Scientific Notation Ø Simplifying Exponents Ø Solve for x (what about fractional coefficients?) Ø Solve System of Equations Ø Solving Equations with Absolute Value Ø Solving Proportions Ø Water Balloon Contest (farthest toss/highest toss) Ø Y-­‐form 2. Factor: 2 x 2 + 5 x + 3
4) 3. Factor: m 2 − 36
5) n 0 1 2 3 4 t(n) 4 1 -­‐2 equation: _______________________________ 6. Set up a proportion and solve:
The sophomore class can wash 3 cars in
14 minutes. How long will it take them to
wash 27 cars?
n 0 1 2 3 4 t(n) 6 7.2 8.64 equation: _______________________________ 7. Use the similar triangles to find the
missing value for x.
6 15 20 x It will take ____________ minutes.
x = _____________
8. Solve:
3(2x – 1) + 12 = 4x – 3
9. Solve:
x = ___________________
x = ___________________
x = ___________________
11. Find the point of
intersection:
12. Find the equation of
the sequence with: a1 = 17, a3 = 3 explicit equation: ______________________________ 13. Simplify:
2 3𝑥 !
3𝑥 !!
𝑥 + 2𝑦 = 17
𝑥−𝑦 =2
10. Solve:
4x(x – 2) = (2x + 1)(2x – 3)
x + 2 x −1
=
3
2
14. The sum of two numbers is 20. The
first number is three times the second
number. Find each number.
15. Graph the system to find the point of
intersection:
# y = 2x + 4
$
% y = −x +1
€
Solution:
(
,
16. Use the generic rectangle to multiply:
(x – 2y)(x + 2y)
)
17. Determine if the following sequences are arithmetic, geometric, or neither. a)
-­‐7, -­‐3, 1, 5, 9, … b)
-­‐64, -­‐16, -­‐4, -­‐1, … sum: ______________________
18. Create multiple representations of the line described below.
!
A line with slope ! that passes through the point (6, 7).
x y equation: _______________________________ 19. If nine of Mr. Hunter’s 172 students want to
try out for the wrestling team, how many students
in the entire school (1548 total) would you expect
to be at tryouts?
21. Use the quadratic formula to
solve:
2x2 – 6x + 9 = 0
20. Factor:
3x2 – 12x
22. Sonoma’s population is 20,000 and is
increasing at a rate of 15% per year. Write a
function to model the growth and complete
the table.
What will be the population after 5 years?
x = _______________________
23. An association (relationship) between two numerical variables can be
described by its form, direction, strength, and outliers. Describe the association of
each graph:
24. Solve the system using the equal values method and graph the lines to confirm
the point of intersection.
y = 3x + 2
and
solution: (
,
y = −2x − 3
)
25. Simplify by combining like terms:
(x
2
)
(
+ 8x + 17 + (x 2 + x + 3) − 2x 2 − 3x + 10
)
26. Find the slope of the line through the
points:
(49, 40) and ( 33, 72 )
slope = __________________
27. Factor and use the zero product
property to solve:
2x2 + 7x + 3 = 0
28. Solve the system:
# 4 x + 3y = 7
$
%2x − 9y = 35
€
x = __________
29. Solve:
5− x 2
=
9
3
or
x = __________
solution: (
30. Solve for m:
)
31. Solve:
4 p = 4 + 2(m − p)
x = _______________
32. The sum of two numbers is 16.
The first number is three times the
second number. Find each number.
,
€
2x −1 4 x
=
3
5
x = ___________________
3
33. Graph y = − x + 1
2
34. Simplify:
| 7 – 4(4) | + 3(2)2 = ____________
35. At the soccer match, Hot Dogs are sold
for $3 each and Colas are sold for $2 each.
There were 3 times as many colas sold as hot
dogs. If a total of $72 was collected, how
many of each item were sold?
12 – 3(-5) – (3)3 + 2|15 – 6| = ______
36. Consider the line 2x − 4y = 16
x-intercept (
,
)
y-intercept (
,
)
37. Factor:
4x2 + 16x
Does the point ( 3, − 5 ) lie on the line? Explain
your reasoning. _______________________________________
_______________________________________________________
38. Use the quadratic formula to solve:
5x2 + 6x – 9 = 0
39. The sum of the numbers is -18. The
first number is three less than twice the
second number. Find the two numbers.
x = _______________________
40. Solve for x:
41. Simplify:
7x – 2(x – 3) + x – 5 = 7
-3(2x + 4y) + 3(x – y)
x = _______________
42. Factor and use the zero product
property to solve:
5x2 – 8x – 4 = 0
x = ____________
or
x = _____________
43. Write the equation of the line that has
a slope of 3 and passes through the point
(2, 0).
44. Joe’s water balloon follows the parabola given by the rule:
y = -x2 + 8x – 12
a) Complete the table for Joe’s water balloon.
x
y
1
2
3
4
4
5
6
7
b) Plot the appropriate points on the graph.
c) How high did the balloon go? _______________
d) How far did the balloon go? ________________
45. Create a table and graph the rule
x
y
-3
-2
-1
0
1
x-intercepts: (
,
)
(
,
)
y-intercept: (
,
2
y = x2 – 1
3
4
5
)
46. Solve the quadratic equation using
any method:
2x2 + 10x + 8 = 0
47. Solve:
x 1
− =2
2 4
LCD = _____________
€
x = _____________ or
48. Solve 2x + 3 = 5
x = ______________
solution: ____________________________
49. Does the point (2, 3) lie on the
parabola y = x2 – 1? Explain.
€
x = _______________
50. Write the equations for the following sequences: a)
51. Simplify:
|2(-3) – 4| + 2(-5)2 = _____________
-­‐7, -­‐3, 1, 5, 9, … 12 – 42 + 4(-9) = _____________
b)
-­‐64, -­‐16, -­‐4, -­‐1, … 53. Factor:
52. Multiply:
(2x – 2)(x + 4) =
2x2 + 3x – 20
3x2 + 4x + 1
(3x + 2)(x + 6) =
54.
½(6 – 2)2 – 4 • 3
55.
3[2(1 + 5) + 8 – 32]
56.
(8 + 12) ÷ 4 – 6
57. Fill in the table and write the equation
rule:
x
-3 -2 -1 0
1
2
y
-1 1
5
58. Fill in the table and write the
equation rule:
x
-2 -1 0
1
2
3
y
1
5
rule: __________________________
rule: __________________________
59. Use the function machine to find the
missing values:
f(2) = __________
f(-2) = _________
input x = f(9) = __________
f(-5) = _________
f( ______ ) = 8
output 56.
–x(3 – 1)
60. Evaluate
57.
-4x2 + 8
f( ______ ) = -7
-4(x – 1)
58.
x(y – z)
for x = 5
61. Evaluate
59.
a(b – c)
-2x2 – 3x + 4
for x = 1
63. Simplify:
62. Simplify:
(5x2y4)2(2x)2 = _____________
7|6(-3) – 4| – 2(-5)2 = _____________
(-2y3)3 = _______________
12 – 3(3 + 5) – 42 = _____________
65. Factor:
64. Multiply:
(x – 2)(5x – 4) =
3x2 + 9x – 12
(3x + 2)(3x – 2) =
5x2 + 4x – 1
66. Write the expression using positive
67. Simplify:
exponents:
(6x
3x −4 y 7
15x −9 y −3
−6
y6)
2
= ____________
2x −4 y 6
18x −3 y 9 = ____________
€
€
68. Find the slope between
(-2, 3) and (4, 3).
69. Solve
2x +1 = 5
€
70. Solve:
0 = (2x – 5)(x + 3)
€
m = ____________________
x = ______________
x = ________
71.
72.
73.
3 + 3(6 – 2)2 – 4 • 3
-3[2(13 – 5) + 8 – 32]
x = ________
2(8 + 32) ÷ 4 – 6
74. Use the quadratic formula to solve:
x2 + 7x + 5 = 0
75. Use the quadratic formula to solve:
6x2 + 1 = 8x
x = ____________
x = ____________
or x = ______________
or x = ______________
76. Graph the parabola and find the important values.
y = x2 – 2x – 8
x
y
x-intercepts: (
,
y-intercept: (
vertex: (
)
,
,
(
,
)
)
)
77. Does the point (-5, 2) lie on the
parabola y = 2x2 + 3x – 1? Explain.
78. Solve:
x + 2 x −1
=
3
2
x = _____________
79. Solve the system:
80. Multiply:
#2x − y = 18
$
%y = 4 x − 8
(2x – 1)(2x + 1)
(3x – 9)(2x2 + 3x – 1)
€
Solution: (
,
)
81. Pearl has started a new diet. Seven weeks into the diet she weighs 135 pounds, but when she started she weighed 156 pounds. Assuming that she is losing the same amount each week, complete the table, graph, and write an equation to model her weight loss. x y She weighed __________ pounds at the start of her diet. She lost ___________ pounds per week. In __________ weeks she will weigh 126 pounds. equation: __________________________ 82. Find the slope between the points:
83. Evaluate for x = -2:
(-2, 1) and (0, 5)
-6x2 – 3x + 4
(0, 6) and (-6, 6)
-x2 – 3x
(-3, 7) and (-3, 8)
3 – 5x
84. Solve:
x 1
− =7
2 3
85. Use the quadratic formula to solve:
2x2 – 4 = 7x
LCD = _____________
€
solution: ____________________________
86. Find the intercepts of
the line: 3x – 4y = -24
x-int: (
y-int: (
,
87. Simplify:
2
7 − 5 ⋅ 4 − ( −2 )
or x = ______________
88. Factor completely:
6x2 - 600
)
,
)
89. Solve the system:
90. Factor and use the zero product
property to solve:
x + y = 12
3x2 + 7x + 2 = 0
2 x + 5 y = 27
Solution: (
x = ____________
,
)
91. Graph the following equation: 3 x + 2 y = −6 x-­‐int: ( , ) y-­‐int: ( , ) x = ____________
or x = ______________
92. Write the equation of the graph below:
93. Find the intercepts of
the line: 6x – 4y = -24
x-int: (
y-int: (
,
,
94. Simplify:
2
7 − 5 ⋅ 4 − ( −2 )
95. Factor completely:
9x2 – 16
)
)
96. Solve:
x 2x
+
=5
6 3
97. Factor and use the zero product
property to solve:
LCD = _____________
3x2 + 2x – 5 = 0
solution: ____________________________
x = ____________
98. Solve:
2
2 ( x − 2) = 8
99. Simplify:
3 4
( 2x y )
2
x = ______________ or
x = _____________
( 2x
−2
or x = ______________
y −3 z )
−2
100. The graduation dance
has sold 200 tickets,
earning $1225. Advance
tickets cost $5 and tickets
at the door cost $8. How
many of each type of ticket
were sold?
101. I have 42 coins in my
pocket, all dimes and
nickels. The total value is
$3.45. How many of each
coin do I have?
102. Paul spent $20.25 to
buy a dozen flowers for his
wife. The bouquet
contained roses @ $2.00
each and daises @ $0.75
each. How many of each
type of flower did Paul buy?
103. Simplify:
104. Write the expression
105. Find the slope
through the points (-3, 12)
and
(-6, 9).
using positive exponents:
(3x2y4)(2x)2 = _____________
3x −4 y 4
5x 2 y −3
(5y3)3 = _______________
slope = __________________
€
106. Complete the generic rectangle and
write as a product and a sum.
107. Simplify using the distributive
property:
– 4 -3(2x + 1) = _____________________
2x 3x +8 sum: __________________________________
2 – 3(5x + 2) = ______________________
product:_______________________________
108. |x + 3| = 12 x = _____________ x = ____________
110. Solve:
111. Solve:
3 − 2 ( x + 3) + 4x = 9
x = ___________________
113. Solve the system:
# x + 4 y = 10
$
% 3x − 4 y = 6
,
112.
1 5
1 + =
4 8
3
x− x=4
5
€ x = ___________________
€
x = ___________________
114. State the x- and yintercepts of the line:
115. Simplify:
7 + 5x – 3x + 2(x – 4) – x
2x – 5y = 20
€
Solution: (
109. 2|x + 3| + 4 = 12 x = _____________ x = ____________
)
x-intercept: (
,
)
y-intercept: (
,
)
116. Write the equation of the line shown
in the graph
117. Write the equation of the line that is
through the points (1, -1) and (2, -9).
Equation: ______________________________