|
|
Answer Key to Worksheet on Measures of Central Tendency
|
|
Unit II - Similar Triangles
Proportion and Similarity
Similarity Shortcuts: AA, SAS, and SSS Similarity in Right Triangles Proportions and Similar Triangles http://www.regentsprep.org/Regents/math/geometry/GP11/PracSim.htm
|
|
|
|
|
|
|
|
STUDY FOR LONG TEST 2:
INTERSECTION, UNION, COMPLEMENT OF A SET VENN DIAGRAM & APPLICATIONS EXERCISES 4 & 5 (FOUND IN WEEBLY & EDMODO)
|
|
key_to_exercises_on_venn_diagram.pdf | |
File Size: | 364 kb |
File Type: |
venn_diagram_exercise_4.pdf | |
File Size: | 240 kb |
File Type: |
Exercise 3 - Set Relations (Nov. 12)
|
|
Exercise 2 - Set Description (Nov. 9)
I. Find the cardinality of the following sets.
a. M = {m| m is a positive integer less than 25}
b. N = {n | n is a letter in the word ‘HELLO’}
c. P = {a, e, I, o, u}
d. Q = {q| q is a perfect square < 100}
e. R = {r| r is an integer, 1 < r < 10}
II. State whether the given set is finite or infinite.
a. the set of counting numbers whose numerals end in 4
b. the set of counting numbers whose numerals contain five digits
c. the set of odd counting numbers
d. the set of fractions between 0 and 1
e. the set of strands of hair in your head
f. the set of people watching the UAAP at the Araneta Coliseum
g. the set of daily commuters of the Light Rail Transit
h. the set of counting numbers less than 1
i. the set of words contained in your text book
j. the set of books in your library
k. the set of grains of sand in the world
III. Name and describe three sets that do not have members.
IV. Describe a set of which you are a member.
V. Describe at least 5 sets that you are NOT a member.
a. M = {m| m is a positive integer less than 25}
b. N = {n | n is a letter in the word ‘HELLO’}
c. P = {a, e, I, o, u}
d. Q = {q| q is a perfect square < 100}
e. R = {r| r is an integer, 1 < r < 10}
II. State whether the given set is finite or infinite.
a. the set of counting numbers whose numerals end in 4
b. the set of counting numbers whose numerals contain five digits
c. the set of odd counting numbers
d. the set of fractions between 0 and 1
e. the set of strands of hair in your head
f. the set of people watching the UAAP at the Araneta Coliseum
g. the set of daily commuters of the Light Rail Transit
h. the set of counting numbers less than 1
i. the set of words contained in your text book
j. the set of books in your library
k. the set of grains of sand in the world
III. Name and describe three sets that do not have members.
IV. Describe a set of which you are a member.
V. Describe at least 5 sets that you are NOT a member.
Exercise 1 - Set Definition & Set Notation (Nov. 8)
I. Classify the collection of objects as well-defined or not well-defined.
1. All gentlemen in your class.
2. All natural numbers greater than 1000.
3. All female students in the class.
4. All strong-legged animals.
5. Any two-digit number between 1 and 100.
6. All trees in Luneta Park.
7. All fragrant flowers in Cebu.
8. All state universities in the Philippines.
9. All beautiful people.
10. All ex-presidents of the Philippines.
II. Define the following sets using Roster Method.
1. The set of natural numbers greater than 9 but less than 15.
2. The set of pets in your house.
3. The set of subjects taken by H2 students.
4. The set of powers of 2 between 1 and 17.
5. The set of even natural numbers between 3 and 13.
I. Define the following sets using Rule Method.
1. The set of integers.
2. The set of high school teachers in Xavier School.
3. The set of Chinese schools in Manila.
4. The set of rational numbers greater than 1 but less than 2.
5. The set of natural numbers.
IV.Define the following sets using the appropriate method (Rule/Roster method).
1. The set of colors found in the rainbow.
2. The set of all mathematical operations used among numbers.
3. The set of national holidays in the Philippines.
4. The set of Jesuits in Xavier School.
5. The set of odd natural numbers.
6. The set of integers greater than -3 but less than 1.
7. The set of months in a year starting with the letter B.
8. The set of natural numbers greater than 4.
9. The set of letters in the Greek alphabet.
10. The set of books in the National Library.
1. All gentlemen in your class.
2. All natural numbers greater than 1000.
3. All female students in the class.
4. All strong-legged animals.
5. Any two-digit number between 1 and 100.
6. All trees in Luneta Park.
7. All fragrant flowers in Cebu.
8. All state universities in the Philippines.
9. All beautiful people.
10. All ex-presidents of the Philippines.
II. Define the following sets using Roster Method.
1. The set of natural numbers greater than 9 but less than 15.
2. The set of pets in your house.
3. The set of subjects taken by H2 students.
4. The set of powers of 2 between 1 and 17.
5. The set of even natural numbers between 3 and 13.
I. Define the following sets using Rule Method.
1. The set of integers.
2. The set of high school teachers in Xavier School.
3. The set of Chinese schools in Manila.
4. The set of rational numbers greater than 1 but less than 2.
5. The set of natural numbers.
IV.Define the following sets using the appropriate method (Rule/Roster method).
1. The set of colors found in the rainbow.
2. The set of all mathematical operations used among numbers.
3. The set of national holidays in the Philippines.
4. The set of Jesuits in Xavier School.
5. The set of odd natural numbers.
6. The set of integers greater than -3 but less than 1.
7. The set of months in a year starting with the letter B.
8. The set of natural numbers greater than 4.
9. The set of letters in the Greek alphabet.
10. The set of books in the National Library.
Textbook Exercise 10a
Answer Exercise 10a numbers 3, 4, 5, and 6 only. NSM Book 2 page 292. Write your answers in your math notebooks.
Exit Ticket
Use the rule method to specify the sets described in the following, and tell why the roster method is difficult or impossible.
1. The counting numbers greater than 100
2. The students in your school who have been abroad
3. The Filipino citizens who have read the Constitution
4. The books in the LRC
5. The set of triangles whose area is less than 3
6. Give an example of a set which has just two elements; one element; no elements; an infinite number of elements.
1. The counting numbers greater than 100
2. The students in your school who have been abroad
3. The Filipino citizens who have read the Constitution
4. The books in the LRC
5. The set of triangles whose area is less than 3
6. Give an example of a set which has just two elements; one element; no elements; an infinite number of elements.
"Home computers are being called upon to perform many new functions, including the consumption of homework formerly eaten by the dog."
- Doug Larson
PRACTICE: Match the inequalities with their graphs.
Homework # 9
Answer Exercise 3b NSM Book 3 page 61
Numbers 2, 6, 8, 12, and 14
Solve, graph, and write solutions in interval form and set-builder notation.
Write solutions on short bond paper. Submit tomorrow, Oct. 4 before 7:30 A.M.
Numbers 2, 6, 8, 12, and 14
Solve, graph, and write solutions in interval form and set-builder notation.
Write solutions on short bond paper. Submit tomorrow, Oct. 4 before 7:30 A.M.
solutions_to_practice_test_word_problems.pdf | |
File Size: | 67 kb |
File Type: |
Practice Test - Applications
Solve completely.
1. An airplane flying with the wind can cover a certain distance in 2 hours. The return trip against the wind takes 2.5 hours. How fast is the plane and what is the speed of the air, if the one-way distance is 600 miles?
2. An exam worth 145 points contains 50 questions. Some of the questions are worth two points and some are worth five points. How many two-point questions are on the test? How many five-point questions are on the test?
3. How many gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 9 gallons of 30% alcohol solution?
4. Two small pitchers and one large pitcher can hold 8 cups of water. One large pitcher minus one small pitcher constitutes 2 cups of water. How many cups of water can each pitcher hold?
5. The perimeter of a rectangle is 54. If the width is half the length, how long is the rectangle?
6. The sum of the digits of a two-digit number is 11. If we interchange the digits then the new number formed is 45 less than the original. Find the original number.
7. The sum of three numbers is 14. The largest is 4 times the smallest, while the sum of the smallest and twice the largest is 18. Find the numbers.
8. Emma is 10 years older than half Olivia’s age. If the sum of their ages is 31, how old is Olivia?
1. An airplane flying with the wind can cover a certain distance in 2 hours. The return trip against the wind takes 2.5 hours. How fast is the plane and what is the speed of the air, if the one-way distance is 600 miles?
2. An exam worth 145 points contains 50 questions. Some of the questions are worth two points and some are worth five points. How many two-point questions are on the test? How many five-point questions are on the test?
3. How many gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 9 gallons of 30% alcohol solution?
4. Two small pitchers and one large pitcher can hold 8 cups of water. One large pitcher minus one small pitcher constitutes 2 cups of water. How many cups of water can each pitcher hold?
5. The perimeter of a rectangle is 54. If the width is half the length, how long is the rectangle?
6. The sum of the digits of a two-digit number is 11. If we interchange the digits then the new number formed is 45 less than the original. Find the original number.
7. The sum of three numbers is 14. The largest is 4 times the smallest, while the sum of the smallest and twice the largest is 18. Find the numbers.
8. Emma is 10 years older than half Olivia’s age. If the sum of their ages is 31, how old is Olivia?
HOMEWORK # 8
1) A two-digit number is three less than seven times the sum of its digits. If the digits are reversed, the new number is 18 less than the original number. What is the original number?
2) If 18 is added to a two-digit number, the digits are reversed. The sum of the digits is 8. What is the original number?
3) The sum of the digits of a two-digit number is 9. The number is 6 times the units digit. Find the number.
4) The sum of the digits of a two-digit number is 6. When the digits are reversed, the resulting number is 6 more than 3 time the original number. Find the original number.
5) The sum of the digits of a two-digit number is 12. The number is 13 times the ten’s digit. Find the number.
6) The sum of the digits of a two-digit number is 11. When the number with the digits reversed is subtracted from this number, the difference is 9. What is the number?
7) Twice the tens digit of a number increased by the units digit is 22. If the digits are reversed, the new number is 45 less than the original. What is the number?
*8) The hundreds digit is the sum of the tens and units digit. The units digit is twice the tens digit. The difference between the number and the new number with reversed digits is 297. What is the original number?
1) A two-digit number is three less than seven times the sum of its digits. If the digits are reversed, the new number is 18 less than the original number. What is the original number?
2) If 18 is added to a two-digit number, the digits are reversed. The sum of the digits is 8. What is the original number?
3) The sum of the digits of a two-digit number is 9. The number is 6 times the units digit. Find the number.
4) The sum of the digits of a two-digit number is 6. When the digits are reversed, the resulting number is 6 more than 3 time the original number. Find the original number.
5) The sum of the digits of a two-digit number is 12. The number is 13 times the ten’s digit. Find the number.
6) The sum of the digits of a two-digit number is 11. When the number with the digits reversed is subtracted from this number, the difference is 9. What is the number?
7) Twice the tens digit of a number increased by the units digit is 22. If the digits are reversed, the new number is 45 less than the original. What is the number?
*8) The hundreds digit is the sum of the tens and units digit. The units digit is twice the tens digit. The difference between the number and the new number with reversed digits is 297. What is the original number?
HOMEWORK # 7 (SOLVE IN YOUR NOTEBOOKS. MAKING A TABLE WILL HELP.)
1) It took the pilot an hour and a half to make a flight of 240 miles when flying against a headwind. If the return trip took an hour and twelve minutes (the wind had not shifted nor changed its speed), what was the speed of the wind?
2) A skater crossed a frozen river 1 mile wide in 5 minutes with the wind behind him. It took him 15 minutes on his return trip where he skated into the wind. What was the speed of the wind?
3) A speedboat travels 60 miles in three hours with the current. The return trip against the current takes 4 hours. What is the rate of the speedboat in still water and what is the rate of the current?
4) Traveling against the wind, a plane flies 2,100 miles from Chicago to San Diego in 4 hours and 40 minutes. The return trip, flying with a wind that is blowing twice as fast, takes four hours. Find the rate of the plane in still air.
5) A ship on the Pasig River travels 24 miles upstream in 3 hours. The return trip takes the ship only two hours. Find the rate of the ship in still water.
6) Gertrude rows her boat 24 miles downstream in 4 hours. In order to make the return trip upstream in the same amount of time, the rate of the boat in still water was doubled. Find the rate of the current and the rate that Gertrude was rowing downstream.
7) When flying with a tailwind, a pilot required 18 minutes to make a flight of 90 miles. The return trip took 24 minutes. There was no change in the direction or speed of the wind. What was the speed of the wind?
8) Ben’s motorboat can cover 21 miles upstream in 3 hours. He travels 22 miles downstream in 2 hours. Find the speed of Ben’s motorboat and the speed of the current.
1) It took the pilot an hour and a half to make a flight of 240 miles when flying against a headwind. If the return trip took an hour and twelve minutes (the wind had not shifted nor changed its speed), what was the speed of the wind?
2) A skater crossed a frozen river 1 mile wide in 5 minutes with the wind behind him. It took him 15 minutes on his return trip where he skated into the wind. What was the speed of the wind?
3) A speedboat travels 60 miles in three hours with the current. The return trip against the current takes 4 hours. What is the rate of the speedboat in still water and what is the rate of the current?
4) Traveling against the wind, a plane flies 2,100 miles from Chicago to San Diego in 4 hours and 40 minutes. The return trip, flying with a wind that is blowing twice as fast, takes four hours. Find the rate of the plane in still air.
5) A ship on the Pasig River travels 24 miles upstream in 3 hours. The return trip takes the ship only two hours. Find the rate of the ship in still water.
6) Gertrude rows her boat 24 miles downstream in 4 hours. In order to make the return trip upstream in the same amount of time, the rate of the boat in still water was doubled. Find the rate of the current and the rate that Gertrude was rowing downstream.
7) When flying with a tailwind, a pilot required 18 minutes to make a flight of 90 miles. The return trip took 24 minutes. There was no change in the direction or speed of the wind. What was the speed of the wind?
8) Ben’s motorboat can cover 21 miles upstream in 3 hours. He travels 22 miles downstream in 2 hours. Find the speed of Ben’s motorboat and the speed of the current.
HOMEWORK # 6
Answer the following in your notebooks. BE PREPARED. I will call on anyone to discuss the solutions in front.
1) A mixture of peanuts and corn sells for P40 a kilo. The peanuts sell for P42 a kilo while the corn sells for P36 a kilo. How many kilos of each kind are used in 12 kilos of the mixture?
2) A group of 26 H-2 boys decided to check out the new wakepark at Nuvali. Each of the 5 chaperones will drive a van or a sedan. The vans can seat 7 people, and the sedans can seat 5 people. How many of each type of vehicle could transport everyone to Republic Wakepark in one trip?
3) In basketball, a free throw is1 point and a field goal is either 2 points or 3 points. In the 2000-2001 season, Kobe Bryant scored a total of 1938 points. The total number of 2-point field goals and 3-point field goals was 701. he made 475 of the 557 free throws that he attempted. What was Kobe Bryant's 2-pt. and 3-pt. field goals that season?
Answer the following in your notebooks. BE PREPARED. I will call on anyone to discuss the solutions in front.
1) A mixture of peanuts and corn sells for P40 a kilo. The peanuts sell for P42 a kilo while the corn sells for P36 a kilo. How many kilos of each kind are used in 12 kilos of the mixture?
2) A group of 26 H-2 boys decided to check out the new wakepark at Nuvali. Each of the 5 chaperones will drive a van or a sedan. The vans can seat 7 people, and the sedans can seat 5 people. How many of each type of vehicle could transport everyone to Republic Wakepark in one trip?
3) In basketball, a free throw is1 point and a field goal is either 2 points or 3 points. In the 2000-2001 season, Kobe Bryant scored a total of 1938 points. The total number of 2-point field goals and 3-point field goals was 701. he made 475 of the 557 free throws that he attempted. What was Kobe Bryant's 2-pt. and 3-pt. field goals that season?
Homework # 1 - Answer Graphing Equations Worksheet (Sept. 6)
Homework # 2 - Solve all even-numbered problems NSM Bk 2 page 253 (Sept. 7)
Homework # 3 -Exercise 5C page 163, number 1 f-j (Sept. 11)
Homework # 4 - Exercise 5c page 163, number 2 (Sept. 12)
Homework # 5 - Answer the rest of the numbers in the Practice Test. Write solutions with checking on short bond paper. (Due: Sept. 15)
substitutionhw.pdf | |
File Size: | 101 kb |
File Type: |
answer_key_to_practice_test_2_elim_substi.pdf | |
File Size: | 269 kb |
File Type: |