Mathematics V (Special Class)

Below is a set of exercises that you will submit when classes resume. Copy and paste the following questions in MS Word.

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Answer the following questions. Show complete solution. 

 

1.      Jack was given an end-of-year bonus.

         First, he gave half of his bonus plus P 40,000 to his parents.

         Next, he saved half of his remaining bonus plus P 30,000 in the bank.

         After that, he donated to charity half of his remaining bonus plus P 20,000.

         Finally, he spent half of his remaining bonus plus P 10,000 on some clothes.

         If he was left with P 100,000, how much was his bonus?

 2.     The number of students in a school doubled every year. If the school had its full intake in the year 2014 with 2400 students, in which year did the school have only 75 students?

3.     There are 40 students in a class. 25 of them like Science lessons. 18 of them like Math                 Olympiad lessons.     

      a.   How many students, at most, like both Science and Math Olympiad lessons?

      b.   How many students, at least, like both Science and Math Olympiad lessons?

4.        In the figure below, each box can be painted with only one color. How many different ways are there altogether to paint the two boxes using red, yellow, orange and blue?  

5.        Find the number represented by each letter. Each letter represents a different number

                                                                   M

                                                                 MA

                                                               MAT

                                                     x      MATH

                                                            4 8 0 0

6.        At a movie, the seat numbers of Anthony, Betty, Carol and Dolly are 20, 21, 22 and 23, but not in this order.

            Dolly’s seat number is bigger than Brannon’s

            Anthony and Betty are not sitting next to each other.

            Anthony’s seat number is bigger than that of Betty but smaller than Carol’s.

            What is Dolly seat number?

  

7.         Two overlapping squares, QTVU and SXYZ, are drawn inside the rectangle PQRS so that the    perimeters of the three shaded rectangles are equal.

         If the lengths of the sides of PQRS are 20 cm and 22 cm, what is the sum of the perimeters, in         centimeters, of the squares QTVU and SXYZ?

 8.         How many 4-digit numbers can be formed with the digits 0 to 6 so that the sum of the units,  tens and hundreds digits of such a 4-digit number is even? No digit is allowed to use twice in any such 4-digit number.

9.         A clerk her career with a monthly salary of P 6 000 and is promised an increase of P 900            per  month at the end of each year’s service. How many years does it take her to earn a total of 

   P 468 000? 

10.        Show that the number n – 1 and n + 15 are relatively prime for every even integer n, that   is,       their greatest common divisor is 1.

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Additionally, I have prepared two MTAP reviewers for you. Download these files and answer each question.

http://www16.zippyshare.com/v/25424395/file.html

http://www16.zippyshare.com/v/91844871/file.html

Prepared by:

Josel P. Jalon

joseljalon@yahoo.com

Grade3 Math Special Class

Math 3 Reviewer

Name:___________________________

Directions: Solve each problem and write your answer on the space provided before the number.

_____________1. Peter and John are each less than 30 years old. Peter is 9 years older than John. Each of their

                              ages is a composite number greater than 10 and do not have a common factor. How old is Peter?

_____________2. Rose noticed that the amount of money she saved doubled each month for 4 consecutive months.

                              She saved P360 in the fourth month. How much did she save during the four months?

_____________3. A piece of rope is cut into 3 pieces in the ratio 2 : 3 : 4. If the shortest piece is 12 m long, how

                              long is the whole rope?

_____________4. In a game, Joel score is 12 points more than Daniel’s. Charlse ‘s score is 9 points less than

                              Daniel’s. Together, the score of the three is 72. What is the score of Joel?

_____________5. One milk can has a radius of 10 cm and a height of 8 cm. A second milk can has a radius of

                              8 cm and a height of 10 cm. How much more milk does the bigger can hold?

_____________6. A circular lagoon has a radius of 28 m. If you walk around it five times, how many meters will

                              that be? ( π = 3.14 or 22/7 )

_____________7. What is the area of the lagoon in number 6?

_____________8. A rectangular lot has a perimeter of 156 m. If the width is 17 m longer than the length, find the

                              dimensions of the rectangle.

_____________9. A farmer began plowing his field at 5:15 A.M. He finished in 7 hours and 34 minutes. What time

                              did he finish?

_____________10. What is the supplement of an angle of 46⁰?

_____________11. What is 348.9 ÷ 1 000?

_____________12. In 5 days, Janice had a total of 15.5 hours of overtime. What was her average daily overtime?

_____________13. The ratio of boys to girls in a class of 32 pupils is 3 : 5. How many less boys than girls are

                                there?

_____________14. If 13 : 7 = N : 63 , what is N?

_____________15. In a barangay, there are 56 children below 18 years of age for every 100 people. What is the

                                ratio of children to adults?

_____________16. Rounding me to the nearest hundred makes me 800. Rounding me to the nearest ten, makes me

                                850. If  the sum of my digits is 15, what number am I?

_____________17. There are 450 Grades 3 and 4 pupils in a school. If 42% of them are girls, how many are boys?

_____________18. If the rations for 24 scouts on a camp can last them for 12 days, how long will it last if 8 scouts

                                suddenly join them on the first day?

_____________19. What is the best metric unit to measure the height of a flagpole?     

_____________20. How many years are in 5  ½ decades?

_____________21. What is N in the pattern 165,  N,  125,  105?

_____________22. The result of dividing a number by 2  1/8 is 3  2/3. What is the number?

_____________23. The average weight of Larry and Martin is 50  2/3 kilos. If the weight of Larry is 54  ½ kilos,

                                find the weight of Martin.

_____________24. What fraction of 2 centuries are 2 decades?

_____________25. What is the biggest common divisor of 156 and 260?

_____________26. Write 1 148 as a product of its prime factors?

_____________27. Which of  111,  123,  183,  201,  239,  348 is a prime?

_____________28. The number 132 782 is not divisible by which of the numbers 2,  3,  4,  6,  7 and 8?

_____________29. I am thinking of a number greater than 70 but less than 80 than can be divided by 8 living a

                                remainder of 2. What is my number?

_____________30. What is the biggest possible remainder when a number is divided by 10?

_____________31. What number is four times the sum of the first five odd numbers?

_____________32. What is the remainder when 34 753 is divided by 34?

_____________33. Thrice my number plus 8 equals 53. What is my number?

_____________34. Write “forty-one and seventeen thousandths” in figures.

_____________35. Write 6 x 10⁶ + 3 x 10⁵ + 8 x 10³ + 5 x 10² + 2 x10 + 9 as one number.

_____________36. Write the smallest even number using all of 4,  9,  6,  0,  7 and 1.

_____________37. Round 247.864 to the nearest hundredth.

_____________38. How many ten thousands are there in 34 million?

_____________39. Round to the nearest hundred and estimate : 346 + 863 + 142 .

_____________40. Find two numbers whose difference is 24 and one number is four times the other.

_____________41. What digit can be placed in the blank in 45 __24 to make it divisible by 3 and 9?

_____________42. Express 2 , 435 as a product of its prime factors.

_____________43. Find the greatest common factor of 245 and 720.

_____________44. What is the smallest common multiple of 245 and 720?

_____________45. What is midway between 2 500 and 4 500?

_____________46. What is the multiple of 1 000 nearest to 35 734?

_____________47. 3  1/3 is equal to how many ninths?

_____________48. What two numbers have a sum of 18 and a product of 56?

_____________49. The product of two numbers is 36 and their sum is 13. What is their difference?

_____________50. The price of a candy is 75 ¢ . How many can I buy with my P15?

_____________51. Susan cut some pizza into 6ths. After serving 34 pieces, she had 8 pieces left. How many

                                pizzas did she cut?

_____________52. How many pieces of ribbon, each 12.5 cm long can be cut from a 100-m roll of ribbon?

_____________53. What is the ratio of 38 cm to 12 dm?

_____________54. Apples cost P12 each. How many can you buy with P150?

_____________55. Which is greater , 12/14 or 11/13?

_____________56. Loraine had 48 stamps. She gave 1/6 of them to Jane and 2/5 of the remainder to her sister.

                                How many stamps remained with Loraine?

_____________57. A movie is 2  1/5 hours long. If it ended at 7:40 p.m. , what time did it start?

_____________58. Joy’s garden is 16 m long and 14 m wide. If the fencing material costs P125.50 per meter,

                                how much did he spend in all?

_____________59. What is the area of Joy’s garden?

_____________60. A room is 6 m long, 8 m wide and 5 m high. How much air does it enclose?

_____________61. There are 960 pupils in a school. One stormy day, 25% of them were absent. How many were

                                present?

_____________62. Bryan has 24 fewer stamps than Mike. Together , they have 246 stamps. How many stamps

                                has Mike?

_____________63. Nica bought a pair of shoes and a bag. The pair of shoes costs P25 more than four times as

                                much as the bag. Together, the shoes and bag cost P565. How much did the pair of shoes cost?

_____________64. After reading a part of her book, Helen left the book open at a part where the sum of the page

                                numbers  on the two facing pages was 247. What was the page number on the left hand side?

_____________65. Find the perimeter of the figure at the right.                                            36 cm

                                                                                                                                                              

_____________66. What is the area of the figure?                                                                   

                                                                  

                                                                                                                                                                                                                                        20 cm

                                                                                                   14 cm                            

                                                                                                                             

                                                                                                                                                                                                 50 cm

_____________67. Elizabeth wrote her name fifty times on a long piece of tape without any space between her

                                written name. What letter was the 100^th space?

_____________68. The product of two whole numbers is 10 000. Neither of the two numbers contains a zero last

                                 digit. What are the two numbers?

_____________69. What is 24 less than the product of the first two multiples of 7?

_____________70. In 63 763 192, how many times as great is the underlined 3 than the 3 that is not underlined?

_____________71. Write 4 x 100 000 + 5 x 1 000 + 3 x 100 + 7 x 10 as a single number.

_____________72. What is the smallest digit that can be placed in the blank in 23 47__ to make it divisible by 6?

_____________73. What is the sum of the smallest odd prime number and the largest prime number less than 100?

_____________74. Divide three times 20 by the product of 6 and 5.

_____________75. What is the value of 3⁴ – 2³ + 6²?

_____________76. If 2.345 x 794.5 = N x 79.45, what is the value of N?

_____________77. On a number line , what fraction is midway between 0.25 and 0.80?

_____________78. What is the ratio, in lowest terms, of 14 hours to 2 days?

_____________79. A man drove for 4 hours at a speed of 40 km/h and for 3 hours at 60 km/h. What was his

                                average speed for the journey?

_____________80.If 4 : N = N : 36, what is N?

_____________81. What comes next in 729 , 243 , 81 , ___ ?

_____________82. What is 24 more than the twice the sum of 13 and 14?

_____________83. Estimate 356 + 873 + 924 using the rounding off method.

_____________84. Use the rounding method to estimate the product of 76 x 435.

_____________85. Mike  baked 267 cookies. He sold 30 dozens in their store. How many cookies remained?

_____________86. If 3 x 150 = N x 75 , what is N?

_____________87. Change 17 / 25 to a decimal.

_____________88. Two sides of a triangle are 14.5 cm and 11.7 cm. If the perimeter is 34.7 cm, what is the length

                                of the third side?

_____________89. Change 67 / 9 to a decimal to the nearest tenth.

_____________90. Mr. Fernando has 45-hectare field. He sold 2/5 of it. How many hectares remained with him?

_____________91. Rose had 204 stamps. She gave 1/3 of them to her sister and 1/6 of them to her friend. How

                                many stamps did Rose give away?

_____________92. The length of a rectangle is 5 cm longer than the width. If the perimeter is 74 cm, find the

                                length?

_____________93. The scale of a map is 1 cm to 3 km. How far apart are the two towns which are 10.5 cm on

                                 the map?

_____________94. How many posts 2 m apart are needed for the fence of a yard that is 12 m by 20 m?

_____________95. The perimeter of an isosceles triangle is 72 cm. The base is 4 cm shorter than the sum of the

                                legs. Find the length of the base.

  

COMPUTER GRADE 6

COMPUTER GRADE 6

COVERAGE FOR SECOND GRADING

ICT AND SOCIETY

Lesson 4 – Applying ICT Today

Lesson 5 – Using Graph

Lesson 7 – IPR Issues in ICT

Lesson 8 – Ethical Behavior in ICT

Lesson 9 – Software and Hardware Issues in ICT

*** Lesson 4 and 5 were already discussed so handout regarding these lessons will be posted later.***

Lesson 7 - IPR Issues in ICT

The biggest issues surrounding ICT concerns the violation of Intellectual Property Right. It means knowingly or unknowingly stealing other people’s works and ideas.

Three Branches of Intellectual Property Law

a. Patent – a right given to the individual or company that invents something

b. Trademark – a law intended to protect the franchise brands, designs, symbols, and logos that companies use to develop unique images and preconceptions as well as to misidentification with the products of other companies.

c. Copyright – the exclusive right to use, lease, distribute and copy a creative work; (which includes literary and artistic material, music, films, and recordings and software material)

IPL – Intellectual Property Law
- Summarizes the rights of people to own creative works and ideas.
- It has to be applied for and granted to the applicant by the proper authorities.

Royalty – payment made to the owner of a patent, copyright, design, trademark or idea.

Common Offenses Surrounding ICT

a. Piracy – process of plundering or theft concerns illegal copying, distribution and sale of copyrighted material without the permission of the owner.

b. Invasion of Privacy

c. Undesirable Propaganda

d. Electronic Crimes

    * hacker – They are computer programmers who use their technical skills to break into secure internal computer systems of companies and organizations like banks.

*Spyware – programs that enter a computer connected to the Internet, it gathers data about your surfing habits and other information like e-mail addresses and country of origin.

* Computer Virus – These are computer programs that can break and wreak computer systems all over the world.

e. False or Unsolicited Advertising

     *spam – also known as junk mail, the term for unsolicited e-mail that is often commercial in nature

Agencies concern about Intellectual Property

a. MTRCB – Movie and Television Review and Classification Board

b. OMB – Optical Media Board

c. NBI – National Bureau of Investigation

d. NITC – National Information and Technology Council – effectively enforces the existing laws.

    * Electronic Commerce Act – known as Republic Act No. 8792 enacted in June 2002. The CA applies to “any kind of electronic data message or electronic document used in the context commercial and noncommercial activities”

Lesson 8 – Ethical Behavior in ICT

ICT has such a strong hold and influence on us because of the integration of the computer and other associated devices into our lives.

Personal computer – one of the convergence machine.

VoIP – Voice Over Internet Protocol - use for calling abroad

IRC – Internet Relay Chat – allows us to talk to people in real time

Some Effects of ICT on Human Values

a. Erosion of Traditions (example, the mail order bride business)

b. Depersonalization (the tendency to disregard actual face to face interaction)

c. Union of Home and Office (conducting business and facilitate transactions with someone without the need for them to meet in person)

    

*Telecommuting or Teleworking – working on a job from a location that is distance from the physical office or workplace

    

* Electronic Cottage – state or situational capability of doing business or work using computers and other communication devices without leaving the home.

    

*webcast – a kind of online presentation similar to a television broadcast, electronic pulses that are translated from and into data readable and presentable by a computer.

d. Strengthening of Family Bonds

e. Reduction of Pollution

Proper behavior When Using ICT

Phonetics - standard or guidelines of proper behavior in using cellular phones for people to follow.

Netiquette  - is the etiquette over the virtual world of the Internet. It is basic respect when interacting with other people online. These rules were formulated as the Internet became more popular for communicating.

List of Netiquette

1. Do not use all-capital letter when e-mailing.

2. Use emoticons when necessary.

3. Keep messages short.

4. Do not reveal secret.

5. Avoid spamming.

6. Use text abbreviations when needed.

Online – state of being connected to the Internet

Flaming – is the offense to a person because of an e-mail message.

Emoticons – are little faces that you can make by using keystrokes.

Sample of Abbreviation

BRB – Be right back

BTW – By the way

IMHO – In my humble opinion

LOL – laughs out loud

ROTFL – Rolling on the floor laughing

Lesson 9 – Software and Hardware Issues in ICT

Freeware – are programs that have been copyrighted by their authors and are available for downloading, copying, distribution and usage under certain terms and conditions.

Association of Shareware Professionals (ASP) – adheres to the idea that shareware is a marketing method rather than just products themselves. Their products include games, accounting solutions, inventory managers and other office utilities.

Famous Product and Companies Affiliated with ASP

1. WinZip (WinZip Computing, Inc.)

2. Paint Shop Pro (Jasc Software , Inc.)

*Beta Testers – These are people who paid to try out programs before they are released commercially.

*bugs – errors in the programs.

Abandonware – is use for software programs that are still available commercially but from which support and development have been stopped by the makers.

Warez – software programs that are illegally sold or distributed for profit.

The Groups which attempts the distribution of abandonware

a. Entertainment Software Association (ESA)

b. Software and Information Industry association (SIIA)

Measures to prevent the illegal copying and distribution of software

1. requiring information like serial number

2. on-disk protection

3. use of dongles or dangling

*dongle – is a piece of hardware that is attached to a computer before a program can be run.

*Leet or Leetspeak – comes from the word “elite”. This is a way of writing ad even speaking in cipher. Its main characteristic is the use of non-alphabet characters in place of letters have a reasonable resemblance to them.

Open Source – A freeware with executable file and source code which is makes it open to modification.

Sample:

1. Linux Operating system – developed by Linus Torvalds

2. Java

3. GNU Image Manipulation Program

4. AbiWord and OpenOffice.org.

Advantages of Open Source Software

1. Cost – they are free

2. Security – Faults are easily detected and corrected by the community using the software.

3. Reliability – They are upgraded by those who knows want they want from the software.

4. Freedom – Users are not compelled to use any particular software.

Richard Stallman, founder of the free software movement and free software designer, has given the following reasons why restrictions on copying, changing and building on existing software and hardware are harmful:

1. Fewer people will be able to use the programs and hardware.

2. The users will not be able to adapt or to fix software and hardware problems.

3. Other developers cannot learn from the program or hardware or base new work on it.