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5 
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
12. Intersection:
13. Union:
14. Complement:
Properties
Provide an example
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
26.Subtraction 6 5  10 45
27. Multiplication
6 48
28.Division
3 16
Polynomials
29. Simplify
30.Addition
x 2  x  6  2x 2  4
( x 2  2 x  3)  (4 x 2  2 x  3)
30. Subtraction
(4 x 2  3x  2)  (3x 2  7 x  6)
31. Multiplication
( x  6) 2
32. Division
6 x 2  18 x  3
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27  4 12  3
3 6 6 6
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Solve Equations
33.
3( x  2)  4  47  4 x
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34. 6
x  8  23 x  10
35. Solve for x: ax – 2b = b + q
Inequalities
36. -3x + 6 > 18
37. -14 < 4x + 2 < 8
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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39. consecutive integers
Find three consecutive integers whose sum is 93
40. Consecutive even/consecutive odd
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
41. I made 105 gingerbread cookies for Christmas 2005. For Christmas 2006, I made 160
cookies. What was the percent increase to the nearest tenth?
42. 12 of 20 girls went to the movies. What percent did not got to the movies?
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Factoring
43. Factor GCF: 2 x 3  4 xy
44. Factor Difference of Perfect Squares:
9  4x 2
45. Factor Trinomial: x 2  6 x  16
46. Factor Completely: 4 x 2  16
Probability
Single event:
47. 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?
48. 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?
49. If one letter is chosen at random from the word “refuse”, what is the probability that
the letter chosen will be an "e"?
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Multiple Events:

With Replacement
50. 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) =
51. 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
52.
How many permutations are there of the letters in each word?
a) apple
b) strawberries
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53. How many ways can you make an ID code if each code has 3 letters followed by 3
digits, with no repeats?
What about with repeats?
Statistics
54. 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
55. 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 80 for the four tests?
56. 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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57. The table below shows a cumulative frequency distribution of runners' ages.
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 ?
58. Bowling scores for 25 women: 120,125, 128, 128 130, 130, 132, 133, 134, 135,139, 141,
148, 148, 150, 155, 156, 160, 160, 163,168, 170, 174,178,185
a. Create a stem and leaf plot to organize all your data!
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59. Using the bowling scores above:
a) List the 5 Statistical Summary Values:
b) Create a box and Whisker Plot:
60. Using the same bowling scores for 25 women: 120,125, 128, 128 130, 130, 132, 133,
134, 135,139, 141, 148, 148, 150, 155, 156, 160, 160, 163,168, 170, 174,178,185
Create a frequency table and a cumulative frequency table for the data.
Interval
Frequency
Interval
Cumulative
Frequency
Vocabulary
61. 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?
62. The tree has rough brown bark, red berries, wandering branches, and small, sharply
edged leaves. Is this quantitative or qualitative data?
63. Would the following result in biased or unbiased data, and why? Researchers want to
know what the population of students in a school think about the lunch served at the
cafeteria, so they ask students “ On a scale of 1 – 10, how was the food today” as they
are cleaning up their trays on one random Friday.
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