Download Integrated Algebra Midterm Study Guide

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Integrated Algebra Midterm Study Guide
Rational/Irrational Numbers
1.
Which of the following is irrational?
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a)
b) .132
c) .621479…
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Scientific Notation
2.
Express 9.25  10 4 in decimal notation
3.
Express 9.25  10 3 in decimal notation
4.
Express .625 in scientific notation
5.
Express 3,276 in scientific notation
6.
(8  10 3 )(5  10 9 )
(2  10 4 )
Absolute Value
7.
 7   10 
Evaluate Expressions
8.
Find the value of 3 x 2  4 x  2 when x= -3
d) .3
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Set Theory
Set Notation: Represent all real numbers greater than 0 and less than or equal to 4 using
the following notations:
9.
Set-builder notation:
10. Interval
Notation:
11. Graph:
Set Operations: Describe each of the terms below
12. Intersection:
13. Union:
14. Complement:
Properties
15. Commutative
16. Associative
17. Distributive
18. Additive
identity
19. Additive Inverse
20. Multiplicative identity
21. Multiplicative
inverse
a+b=b+a
(a + b) + c = a + (b + c)
a(b + c) = ab + ac
a+0=a
a + (-a) = 0
ax1=a
1
ax
=1
a
Verbal expressions
22.
23.
10 more than 3 times a number
6 less than 2 times a number is the product of 3 and the number
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Radicals
24. Simplify
25.Addition
2 48
25.Subtraction 6 5  10 45
27. Division
26. Multiplication
27  4 12  3
3 6 6 6
6 48
3 16
Polynomials
28. Simplify
x 2  x  6  2x 2  4
29. Simplify
( x 2  2 x  3)  (4 x 2  2 x  3)
30. Simplify
(4 x 2  3x  2)  (3x 2  7 x  6)
31. Simplify
( x  6) 2 Remember: This means (x – 6)(x – 6)! You must double distribute!
32. Simplify
6 x 2  18 x  3
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Solve Equations
33.
3( x  2)  4  47  4 x
34.
0.2x  8  1.7x 10
35. Solve for x: ax – 2b = b + q
Inequalities
36. -3x + 6 > 18
37.
 4  2x  2  10
38. Your local garden shop has plants on sale for $1.50 each. You are planning a vegetable
garden. You have $20 to spend on tomato plants.
a. Write an inequality to find the greatest number of plants (p) you can buy.
b. What is the greatest number of plants you can buy?
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Word Problems
39. Coin Problems:
Dominick has twice as many nickels as pennies and 5 times as many dimes as pennies in his
talking cow bank. He has total of $ 1.22. How many of each kind does he have?
Types of
coin
Quantity
Value
(cents)
Total
Total
40. Age Problems:
A man is now 6 times as old as his son. In 6 years, the father will be 3 times as old as the
son will be then. Find their present ages.
Present age
Future age
41. Motion Problems:
Two planes started at the same time from the same airport and flew in opposite directions.
One flew 60 miles per hour faster than the other. In 5 hours, they were 5,300 miles
apart. Find the rate of each plane.
Rate
(Mph)
Total
Time
(Hr)
Distance
(mi)
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42. Consecutive Integer Problems
Let x = 1st
Let x+1 = 2nd
Let x+2 = 3rd
Find three consecutive integers whose sum is 93
43. Consecutive even/consecutive odd
Let x = 1st
Let x+2 = 2nd
Let x+4 = 3rd
The length of the sides of a triangle are consecutive odd numbers. What is the length
of the longest side if the perimeter is 45?
Percent
44. I made 105 gingerbread cookies for Christmas 2005. For Christmas 2006, I made 160
cookies. What was the percent increase to the nearest tenth?
45. 12 of 20 girls went to the movies. What percent did not got to the movies?
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Probability
Single event:
46. A bag contains 4 red marbles, 16 yellow marbles, 5 purple marbles, 16 blue marbles, and
10 green marbles. What is the probability of pulling out a red or a green marble?
47. A dice cube has 6 sides that are numbered 1 to 6. If the cube is thrown once, what is
the probability of rolling an odd number?
48. If one letter is chosen at random from the word “refuse”, what is the probability that
the letter chosen will be an "e"?
Multiple Events:

With Replacement
49. I have a jar full of jelly beans that I picked through to get my 2 favorite flavors:
licorice and cherry. So I have 3 black and 5 red jelly beans. I choose a jelly bean, then I
put it back into the jar, (hard to believe, but I just started a diet!) choose another one.
P (black, red) =
P (red, black) =
P (black, black) =
P (red, red) =
P (same color) =
P (different colors) =
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50. Without Replacement!
Now, when you pick a card, or choose a lollipop, you will not replace it in the group before you
pick again. You have five lollipops in a bag 2 grape and 3 cherry. Without looking, you pick one
lollipop and then pick another for your friend.
P (grape, cherry) =
P (cherry, grape) =
P (both cherry) =
P (both grape) =
P (different flavors)=
Permutations
51. How many permutations are there of the letters in each word?
a) JUMP
b) PIE
52. How many permutations are there of the letters in each word?
a) MISSISSIPPI
b) GEOMETRY
53. In how many ways can you arrange 4 letters of the word NORTH?
54. In how many ways can 5 different mathematics texts be arranged on a shelf that has
only 3 spaces?
55. How many ways can we arrange 5 vases (red, crystal, silver, blue, black) on a shelf if the
blue one must always be the first one on the left?
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56. How many ways can you arrange a license plate if it has 3 letters followed by 3 digits,
with no repeats? With repeats?
Statistics
57. The weekly salaries of six employees at McDonalds are $140, $220, $90, $180, $140,
$200. For these six salaries, find:
(a) the mean
(b) the median
(c) the mode
(d) the range
58. Andy has grades of 84, 65, and 76 on three math tests. What grade must he obtain on
the next test to have an average of exactly 78 for the four tests?
59. The scores for a class of 20 students are as follows:
93, 84, 97, 98, 100, 78, 86, 100, 85, 92, 72, 55, 91, 90, 75, 94, 83, 60, 81, 95
a) Copy and complete the table shown at the left.
Test
Scores
91-100
Frequency
b) Find the modal interval. (The "modal interval" is the interval
containing the greatest frequency. It is not the mode.)
81-90
71-80
61-70
51-60
c) Find the interval that contains the median.
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60. The table below shows a cumulative frequency distribution of runners' ages.
Work backwards!
a) According to the table, what is the total number of
runners?
b) According to the table, what is the range of the
ages of the runners?
c) According to the table, how many runners are in their forties?
d) According to the table, what interval does the upper quartile fall into?
e) According to the table, what percentage of the runners is greater than or equal to
50 years old to the nearest percent?
f)
61. Bowling scores for 25 women: 128, 130, 120, 125, 128, 130, 150, 130, 132, 134, 130, 130,
135, 148, 140, 156, 155, 140, 163, 160, 158, 133, 150, 145, 165.
a. Create a stem and leaf plot to organize all your data!
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62. Using the bowling scores above:
a) List the 5 Statistical Summary Values:
b) Create a box and Whisker Plot:
Using the same bowling scores for 25 women: 128, 130, 120, 125, 128, 130, 150, 130, 132, 134,
130, 130, 135, 148, 140, 156, 155, 140, 163, 160, 158, 133, 150, 145, 165.
63. Create a frequency table and a cumulative frequency table for the data.
Interval
Frequency
Interval
Cumulative
Frequency
64. Using your table in # 2, create a frequency histogram and cumulative frequency
histogram.
Histogram
Cumulative Histogram
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Vocabulary
65. Jed's new horse is 15.2 hands high,1250 pounds, costs $2,200, and is 3 years, 4 months.
Is this quantitative or qualitative data?
66. The tree has rough brown bark, red berries, wandering branches, and small, sharply
edged leaves. Is this quantitative or qualitative data?
67. In a study that was conducted to determine whether office workers have high blood
pressure, when the participants in the study were friends of the researcher who shared
the same doctor, biased or unbiased?.