Download Algebra II, MP3 - Long Branch Public Schools

Name: ___________________________
Based on the results of your chapter 10 and 12
assessment, the following skills and concepts
need to be remediated by completing the
attached worksheets.
Worksheet
#
1
2
3
4
5
6
7
8
Worksheets
to be
completed
Skills
Grade on
worksheet
out of 10
Basic Probability
Geometric
Probability
Permutations,
Combinations, and
Counting Principle
Probability of
Multiple Events
Venn Diagrams
Special Right
Triangles
Trigonometry
Trig Extension
Average: ______
This will be put in as a formative assessment
grade.
Basic Probability
1. Convert each percentage into a fraction and decimal
a. 100%
b. 90%
c. 99.9%
d. 9%
e. .09%
f. 0%
2. Convert each decimal into a percentage and fraction
a. .85
b. .6768
c. 1
d. 0
e. .005
f. .1
g. .01
h. 4
3. Convert each fraction into a decimal and percentage
a. 20/100
b. 15/40
c. 1/100
d. 100/100
e. 0/100
f. 35/95 (decimal rounded to the nearest thousandth)
4. If there is a 30% chance of rain, what is the chance of no rain?
5. If there is a 5/8 chance of winning, what is the chance of not winning?
6. If there is a .734 chance of picking blue, what is the chance of not picking blue?
7. There are 20 pieces of paper in a hat numbered 1 – 20.
a. What is the probability it is a factor of 20?
b. What is the probability it is a factor of 4?
c. What is the probability it is a multiple of 3?
d. What is the probability it is a multiple of 11?
e. What is the probability it is a perfect square?
f. What is the probability it is a composite number?
g. What is the probability it is a prime number?
h. Are the probabilities theoretical or experimental?
8. There are 8 green, 9 red and 3 yellow marbles.
a. What is the probability of picking a red marble out of the hat?
b. What is the probability of picking a purple marble out of the hat?
c. What is the probability of picking a green or red marble out of the hat?
d. What is the probability of picking a green, red, or yellow marble out of the hat?
e. Are the probabilities theoretical or experimental?
9. A bag has green, blue, and yellow marbles in it. I went in the bag 90 times and grabbed
a yellow marble 12 times.
a. What is the probability of picking a yellow marble?
b. Is this experimental or theoretical probability?
10. What is the probability of spinning a wheel (circle) and landing on the spot that has an
angle of 60º? (hint: there are 360º on a circle)
11. The big rectangle dimensions are 10 by 6 and the small one is 8 by 5.
a. What is the probability of a coin landing in the unshaded region?
b. What is the probability of a coin landing in the shaded region?
c. Are the probabilities theoretical or experimental?
Geometric Probability
For each problem:
a. Find the probability that a randomly chosen point will land in the shaded region.
b. If 500 points were plotted, find the number of points that would land in the
nonshaded region.
Permutation, Combination, and Counting Principle
1. You have 4 shirts, 5 pants, 4 hats and 2 shoes. If you will wear one of each item, how
many possible combinations are there?
2. How many possible 4 digit numbers can be made if the thousands place is a 2 and units
place is either a 4 or a 7. For Ana’s SAT teacher!
3. You are making a five digit code. It can consist of letters and digits. How many
possibilities are there?
4. You are making a four digit code each. It can consist of letters and digits but they can not
repeat. How many possibilities are there?
5. You are in a class of 20 and four people are going on a class trip. How many possible
groups of 4 can be made?
6. There are 250 boys in the school. One girl had eight valentines. How many different
possibilities are there?
7. You are in a class of 20. One student is winning a free trip to Great Adventure, another
student is winning a no homework pass and one student is winning a marker. How many
different ways are possible?
8. If I arrange 5 colored pencils, how many orders are possible?
Probability of Multiple Events
A bag contains three red blocks, six blue blocks, and two yellow blocks.
1. Suppose you draw a block at random, return it to the bag, and then draw another block.
i. Are the events independent or dependent?
ii.
Draw a tree diagram
iii.
P(2 reds)
iv. P(red and then blue)
v. P(red and blue in any order)
vi. P(at least 1 yellow)
vii. P(1 yellow)
viii. P(both not yellow)
.2. Suppose you draw a block at random, do not return it to the bag, and then draw another
block.)
i.
Are the events independent or dependent?
ii.
Draw a tree diagram
iii. P(red and red)
iv. P(red and then blue)
v. P(red and blue in any order)
vi. P(at least 1 yellow)
vii. P(1 yellow)
viii. P(both not yellow)
Venn Diagrams
In a group of 35 children, 10 have blonde hair, 14 have brown eyes, and 4 have both blonde hair and
brown eyes.
1. Draw a Venn Diagram of this situation and answer the questions below.
2. If a child is selected at random, find the probability that:
a. the child has blonde hair or brown eyes.
b. the child has only blonde hair
c. the child does not have brown eyes.
d. the child has neither brown eyes nor blonde hair.
e. the child has brown eyes given that the child has blonde hair.
Trigonometry
1. Draw the triangle and solve for the side x.
5
sin( 30) 
x
2. Draw the triangle and solve for the angle theta.
3
cos(θ) =
11
3. Find the value of the missing sides and angles.
8
K
14
L
j
4.
Find the measure of the missing sides and angles
e
F
7
32
d
5. Bob locked himself out of the house. A ladder is needed to climb through a window that is
20 feet above the ground. The ladder is 30 feet long and rests at the base of the window.
What is the measure of the angle that the ladder makes with the ground? Draw the triangle,
then solve.
6. Bob is in his green car. The green car and a yellow car are at the same intersection. The
yellow car drives south for an unknown distance and green car drives west 50 feet. Bob gets
out of his green car and looks directly at the yellow car. The angle measure between the
street the green car drove on and Bob’s line sight is 32°. What is the distance between Bob’s
green car and the yellow car? Draw the triangle, then solve.
Special Right Triangles
Complete the charts. Leave answers in simplest form.
a
b
1
3
c
3
4
1/2
5
5 2
1
10
2
8 6
3
5 3
24
6
7
8
14
9
7
8
5 3
6 2
c
a
b
2
4
6 2
5
6
12
15
7 3
2 2
Trigonometry Extension
So far, we have dealt with finding sides and angles only right triangles.
Trigonometry can be used to find the measure of sides and angles of non-right
triangles as well.
Part 1: Law of Sines
For any triangle with angles A, B, and C, and sides of lengths a, b, and c. I(a is opposite of
Angle A, b is opposite of Angle B, and c is opposite of Angle C)
sin A sin B
sin B sin C
sin A sin C


or
or

a
b
b
c
a
c
Use this law to solve the following triangles. Note: Neither of these are right triangles.
40
Part 2: Law of Cosines
For any triangle with angles A, B, and C, and sides of lengths a, b, and c. I(a is
opposite of Angle A, b is opposite of Angle B, and c is opposite of Angle C)
c2 = a2 + b2 – 2abcosC
or b2 = c2 + a2 – 2cacosB or a2 = c2 + b2 – 2cbcosA
Use this law to solve the following triangles. You will have to use law of cosines at first and
then use the law of sines to solve the rest.