Integrated II Fall Final Review Materials 2015
Name: ______________
Period: _________
Please complete all work on separate paper.
Data and Surveys
1.
What type of sampling method is described below?
a. Surveying every student in your 3rd period class.
b. Placing a survey question on Edmodo asking students who is their favorite singer.
2.
Which of the following situations would result in a bias sample?
a. A family wants to gather information from other residents on their street about forming a
neighborhood watch. They survey every third house on both sides of the street.
b. For a class statistics project you survey students on Edmodo.
Will the following question result in a biased survey? Explain. “Should the government force
you to pay higher taxes?”
3.
4.
The box and whisker plot below represents the test scores for students in two different classes.
0
a.
b.
c.
10
20
30
40
50
60
70
80
90
100
What percent of the students scored higher than 81 in Class B?
What is the interquartile range for Class A?
Which statement is true?
i. The top 50% of Class A scored lower than then bottom 25% of Class B
ii. The range for Class A is less than the range of the bottom 25% of Class B
iii. No one in Class A scored better than the median score for Class B.
5.
What does the height of the bars represent in a histogram?
6.
What does the width of the bars represent in a histogram?
7.
Consider the data in the table below:
Hundreds of Acres Lost in Forest Fires
70
45
60
15
20
23
17
65
57
48
12
27
101
19
a. Why should this data be represented in a histogram and not with a bar chart?
b. What would be a reasonable interval width to represent the data in a histogram?
8.
Describe the following graphs using SOCS. What would be the appropriate measure of center and spread?
a.
b.
Probability
Mr. Moss uses cards to make up student groups. The cards are numbered from 5 to 23 inclusively. Every card
that has a number divisible by 4 is green.
9.
If Mr. Moss draws 1 card from his stack, what is the probability that he draws a green or even card?
10.
If Mr. Moss draws 2 cards without replacing the first card, what is the probability that he gets two odd
numbered cards?
11.
If Mr. Moss draws 2 cards but replaces the first card, what is the probability that he gets two evennumbered cards?
12
If Mr. Moss draws one card, what is the probability that he gets an even-numbered card or a card whose
number is greater than 13?
13.
For each figure, find the probability that a point shown at random is in the shaded area.
14.
What is the probability that a 16-year-old
student is a boy?
Boys
Girls
15.
Find p(15-year-old | girl)
16.
Change the numbers in the table so that p(girl
33
|16-year-old) = .
62
17.
15 years
31
37
16 years
23
29
If P(student takes algebra and geography) = .25; p(student takes algebra) = .72.
Find p(student takes geography | student takes algebra)
Writing Equations of Lines
18.
Write the equation of the line that passes through the point (5 , −8) with a slope of 1/2.
19.
Write the equation of the line passes through the point (−5, 2) with an undefined slope.
20.
Write the equation of the line in standard form that passes through the points (3 , 5) and (−4 , 19).
21.
Find the equation for the line that passes through (4, 1) and is parallel to the graph of
3𝑥 − 𝑦 = 12 .
22.
Find the equation for the line that passes through (−4, −1) and is perpendicular to the graph
of the linear equation 𝑦 − 4 = −2(𝑥 − 3) .
23. Find the equation for the line that passes through (−3, 4) and is perpendicular to the graph of the linear
1
equation = − 3 𝑥 + 5 .
Exponents
Simplify each expression.
25.  -4a12b7   12a4b
24.
27.



4 3
2x y 
9
36y
a
30. a
 3
28.  3r12 
r 
-3
5 63
5m n


-4 6
4mn p
2
31.



29. 36m-2 n-4
5
8
2
7
26.
 65
 5
y 
.
8
32. Write the given radical using rational exponents
3 11
7x y
Radicals
33. Evaluate
225
a.
3
b.
216
c.
196 - 169
34. Evaluate the following rational exponents
a.
125
2⁄
3
b. 32
2⁄
5
35. Simplify each expression
a.
350b7 d 8
b.
64
27k 6
d.
3 14 × 2 7
f.
2 3 27k 4 - k 3 64k
c.
3
e.
4 12x + 7 3x
g.
i.

3  4 6 + 2 15
3 3
7



h.
3
192m7
2
8
j.
4 3



6 +2 3



2 × KE
, where
m
m is the mass and v is the velocity in meters per second. Assume a wheel with mass 12 kilograms has KE 150
Joules. Find the velocity of the wheel.
36. Kinetic energy (KE) results from a body in motion. It can be expressed in the equation v =
Pythagorean Theorem, Distance Formula, Midpoint Formula, and Coordinate Proofs
37. A 25.5 foot ladder rests against the side of a house at a point 24.1 feet above the ground. The foot of the
ladder is x feet from the house. Find the value of x to one decimal place.
38. If EFGH is a rectangle, what is FH?
39. a) Find the distance between the pair of points given below.
b) Find the midpoint between the points.
,
40. The vertices of the triangle LMN are
two, or no sides of equal length.
Determine whether the triangle has three,
41 The coordinates of the vertices of a quadrilateral are A (1, -1) , B (6, 1), C (-5, -10) and D (-3, -5)
a.
How long is each side of the quadrilateral? Show your work.
b.
What are the slopes of each side of the quadrilateral? Show your work.
c. What type of quadrilateral is it? Explain your reasoning.
42. A student proves that every right triangle is isosceles by assigning coordinates as shown and by using the
distance formula to show that
𝑃𝐶 = 𝑎 and 𝐵𝐶 = 𝑎 . Which of the following best explains the student’s error?
A.
B.
C.
D.
The proof is not correct because the assigned
coordinates do not result in a general right
triangle.
The proof is correct because the assigned
coordinates result in a general right triangle.
The proof is not correct because the assigned
coordinates result in a rectangle.
The proof is not correct because the assigned
coordinates do not result in a right triangle.
B(a, a)
P(0 , 0)
C(a, 0)
43. a. Draw a general right isosceles triangle on a coordinate plane.
b. Prove that your diagram is an isosceles right triangle.
c. Prove that the median from the right angle is perpendicular bisector to the hypotenuse
Geometric Transformations
44. Describe the transformations below.
45. Point A(-4, 2) is reflected over the x-axis. Find A’.
46. Point A(-5, 9) is rotated 270 degrees counter clockwise about the origin. Find A’.
47. Point A(2, -7) is translated using the vector <-2, 5>. Find A’
48. What are the coordinates for the image of GHK after a 90 degrees clockwise rotation about the origin and
a translation of (x,y)→ (𝑥 + 3, 𝑦 + 2)
.
49. Reflect point C across the line AB to form point C’. List what you know about the relationship between C
and C’, line CC’ and line AB, and name one other relationship that you have found.
Triangle Congruence and Proof
50. List the six congruence statements that are known from ABC  JKL .
51. Draw pictures of two triangles that represent the different ways to prove triangles congruent. Make sure you
are marking your diagrams.
52. How can you prove the following triangles congruent, if possible? List the information needed to prove the
triangles congruent and write the congruence statement.
53. What other piece of information is needed
to prove the triangles congruent? State the
congruence statement and theorem used.
54. In the figure, ABC  DEF . Find the value of x and y.
E
F
6y-4
B
80
3x-y
18.8
10
D
30
A
70
19.7
C
55. Write a proof.
Given: W is the midpoint of XY and VZ ; XV  YZ
Prove: XVW  YZW
X
V
W
Z
Y
56. Write a proof.
Given: PQ  PS ; QR  SR
Prove: Q  S
Q
P
R
S
57. Write a proof.
Given: MPN is isosceles with vertex P ; PQ bisects ∠𝑀𝑃𝑁
Prove: ∆𝑀𝑄𝑃 ≅ ∆𝑁𝑄𝑃
M
Q
P
N