EXPLORING THE WORLD OF MATHEMATICS 6 … · EXPLORING THE WORLD OF MATHEMATICS 6 ST. MATTHEW'S PUBLISHING CORPORATION First RVC Building, 92 Anonas, Cr. K-6th Streets, East Kamias,

Authors: Federico C. Castillo Ed. D. Emilia C. Maglonzo, BSEEd, MT2

EXPLORING THE WORLD OF MATHEMATICS 6

ST. MATTHEW'S PUBLISHING CORPORATIONFirst RVC Building, 92 Anonas, Cr. K-6th Streets,

East Kamias, Quezon CityTel. Nos: 426-5611 433-5385 926-7956

Telefax No.: 426-1274 Email: [email protected]

Website: www.stmatthews.ph

Copyright St. Matthew's Publishing Corporation ©

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ISBN:


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cannot be sold, transferred, or distributed in any manner without the prior written consent of St.

Matthew's Publishing Corporation.

First RVC Building, 92 Anonas, Cr. K-6th Streets,

East Kamias, Quezon City

Tel. Nos: 426-5611 | 433-5385 | 926-7956

Telefax No.: 426-1274

Email: [email protected]

Website: www.stmatthews.ph

1Copyright St. Matthew's Publishing Corporation ©For the sole and exclusive use of the clients of the St. Matthew's Publishing Corporation. Not for sale and distribution


Name: _________________________________ Date: ____________

Chapter 1Fractions

I. Choose the letter of the best answer.

1. What is the equivalent of in lowest term?

A. B. C. D.

2. Which is the simplest form for 5 ?

A. B. C. D.

3. Which fraction has a value of 1?

A. B. C. D.

4. How do you write 4 as improper fraction?

A. B. C. D.

5. Which is the least common denominator of and ?

A. 6 B. 9 C. 12 D. 18

6. Which is the multiplicative inverse of ?

A. B. C. D.

7. Which is the reciprocal of 1 ?

A. 1 B. C. D.

8. What is the product of and its reciprocal?

A. 4 B. 3 C. 2 D. 1

9. What is the resulting answer if 5 is divided by ?

A. 30 B. 25 C. 15 D. 5

912

69

103

55

176

124

31

34

153

43

206

13

4345

23

173

32

246

12

34

36

193

56

296

824

23

23

56

56

23

412

15

13

2For the sole and exclusive use of the clients of the St. Matthew's Publishing Corporation. Not for sale and distribution

Copyright St. Matthew's Publishing Corporation ©EXPLORING THE WORLD OF MATHEMATICS 6

10. How many 's are there in 2 ?

A. 8 B. 8 C. 5 D. 1

B. Choose the letter of the correct answer from the right to make the sentence complete.

11.

12.

13. 4

14. 7

15. 14

16. 12

C. Perform the indicated operation. Simplify the answers if needed.

13

23

13

23

89

310

620

1320+ + =

1718

518

418+ + =

42058

7937

58

91891438

A.

B.

C. 4

D. 6

E. 6

F. 7

G. 7

H. 6

29

39

29+ + =

414

314

214+ + =

58

14- = 8

47- = 6 2

7 + 57

481234

+

n

17. 3523615

+

n

18. 20. 91234

-

n

15

6

7834

-

n

19. 45

2

3Copyright St. Matthew's Publishing Corporation ©EXPLORING THE WORLD OF MATHEMATICS 6

For the sole and exclusive use of the clients of the St. Matthew's Publishing Corporation. Not for sale and distribution

21.14- 7 = n 2

3 + 139 22. = n 2

3x56 1

24. = n 37÷6

723. = n 15 x 3

43 1

27.15÷ = n 4

5 x 34

25. = n ÷ 559 26. = n 1

2÷14 15

II. Read and analyze each problem then solve.

A. Rollie weighs 82 kg. After a month of work-out, his weight was reduced to 76 kg. How much was the decrease in weight? 1. What operation will be used to solve the problem? 2. What is the answer to the problem?

B. Mang Ysmael, a fruit vendor has 28 boxes of lanzones to sell. This morning he sold of it. How many boxes of lanzones were sold? 1. What operation will be used? 2. What is the answer to the problem?

C. Mrs. Marquez has a sari-sari store. She has still 10 kg of sugar to be repacked in small plastic bags. How many small plastic bags does she need if each bag contains kg? 1. What is asked in the problem? 2. What is the answer to the problem?

D. Mrs. Mariano bought 2 and 1 kg of chicken. She used of it for cooking adobo. How many kg of meat was left? 1. How many operations are needed to solve the problem? 2. The answer to the problem is .

123

4

34

34

34

12

23

14



Name: _________________________________ Date: ____________

Chapter 2Decimals


1. What is the sum of 1.001 + 0.75 + 0.8?

A. 255.1 B. 25.51 C. 2.551 D. 0.2551

2. How much lesser is 5.09 than 5.9?

A. 0.081 B. 0.81 C. 1.099 D. 10.99

3. Which addends give the sum of 9.0263?

A. 5.804 and 3.2223 C. 5.840 and 32.23 B. 58.04 and 3.223 D. 5.804 and 3.2233

4. Which are the factors of 3.06?

A. 100 and .036 C. 10 and 0.306 B. 10 and 30.6 D. 0.01 and 30.6

5. Which has a diff erence of 0.4398?

A. 0.7004 - 0.2066 C. 7.004 - 2.606 B. 0.7004 - 0.2606 D. 7.004 - 0.2606

6. What number will be multiplied by 2.6 that will give a product of 0.026?

A. 100 B. 10 C. 0.01 D. 0.001

7. How many decimal places are there in the product of 0.358 x 0.9?

A. 5 B. 4 C. 3 D. 2

8. How many zeroes are there in the quotient of 54 ÷ 0.9?

A. 1 B. 2 C. 3 D. 4

9. If 348 ÷ 100 is 3.48, what is 0.348 ÷ 0.01?

A. 0.348 B. 3.48 C. 34.8 D. 348



10. Which of the following has a repeating decimal quotient?

A. 3 ÷ 8 B. 6 ÷ 7 C. 4 ÷ 5 D. 4 ÷ 9

11. Which of the following has a terminating decimal quotient?

A. 315 ÷ 20 B. 612 ÷ 23 C. 420 ÷ 17 D. 568 ÷ 36

12. What is the dividend if the divisor is 100 and the quotient is 0.3?

A. 3 B. 30 C. 300 D. 3 000

13. What is the resulting answer if the sum of 3.29 and 12.017 is subtracted from 24.8?

A. 0.09493 B. 9.493 C. 94.93 D. 949.3

14. If the product of 3.5 and 2.4 is divided by 0.01, what is the resulting answer?

A. 840 B. 84 C. 8.40 D. 0.84

15. What is the resulting answer if the quotient of 48.9 and 15 is multiplied by 100?

A. 3.06 B. 3.26 C. 32.6 D. 326

B. Perform the indicated operation.

16. 0.8205 0.265 2.3102 0.0008

+

n

17. 7.0348 0.0801 3.915 2.63

+

n

18. 0.526 - 0.029 = n

19. 4.8 - 0.2137 = n

20. 6.7 3.6

x

n

21. 24.45 0.29

22. 0.3214 ÷ 0.001 = n

23. 456 ÷ 0.15 = n

24. 151.58 ÷ 5.3 = n

x

n



II. Read and analyze each problem carefully then solve. (2 points each)

1. Cherry wants to put a yellow piping around a triangular piece of cloth. How long is the cloth piping if one side measure 63.5 cm and each of the two other sides measures 47.75 cm?

2. Each of the ten pupils was able to solicit ₱2 585.75 for the MTAP convention in Baguio. How much did they solicit in all?

3. A liter of gasoline cost ₱32.50. If Patrick paid the amount of ₱503.75, how many liters of gasoline was loaded to his motorbike?



Name: _________________________________ Date: ____________

Chapter 3Ratio, Proportion and Percent


1. What is the ratio of 35 km to 5 liters of gasoline?

A. 7:1 B. 1:7 C. 5:5 D. 3:5

2. Which equation shows equal ratio?

A. 3:2 : 6:8 C. 3:5 : 6:15 B. 4:3 : 12:9 D. 4:6 : 10:12

3. Which is the value of the missing term in 9:7 : 27:n?

A. 28 B. 24 C. 21 D. 15

4. Which value of n solves the proportion of 6:n ÷ 2:18?

A. 72 B. 54 C. 48 D. 16

5. What is the equivalent of 78% in decimals?

A. 0.87 B. 0.78% C. 0.78 D. 0.67 6. How is 1.25 written in percent?

A. 1.25% B. 12.5% C. 120% D. 125%

7. What is 15% of 235?

A. 35.25 B. 235 C. 352 D. 425

8. Which is the missing term in 23:3 :: n:9?

A. 119 B. 109 C. 79 D. 69

9. Which two numbers has a sum of 75 and are in the ratio of 2:3?

A. 15 and 60 C. 35 and 40 B. 20 and 55 D. 30 and 45



10. Three numbers are in the ratio of 2:3:4. What is the largest number if the sum is 342?

A. 76 B. 114 C. 152 D. 164

B. Solve the missing term to form the proportion, Write your answer in the blank.

11. 4:5 :: n:35 14.12. 18:17 :: n:9 13. n:45 :: 3:5 15.

C. Replace the blank with the correct rate, base or percentage.

16. 30 is % is 120 17. 10% of 160 = 18. 50 is 100% of 19. 90% of 270 = 20. 60% of = 90

II. Solve the problem (2 points each).

1. Three men can fi nish the work in 10 days. How long can two men fi nish the work at the same rate?

2. The original price of a branded pair of slippers is ₱3 100 is now sold at 20% discount. How much is the discount?

3. A book is now sold for ₱210, previously sold at ₱350. What was the rate of decrease?

4. Mrs. Magpayo receives 23% commission from selling books and magazines. How much commission will she receive from her total sales of ₱28 350?

5. Mrs Alviar deposited ₱50 000 in the bank. It earns a simple interest of 6% per annum. How much will her money be after a year?

2025

4n=

n8

64=



Name: _________________________________ Date: ____________

Chapter 4Order of Numbers and Integers


1. Which is the exponential notation for 4 x 4 x 4 x 4 x 4?

A. 54 B. 46 C. 45 D. 44

2. Which has a greater value? 25 or 52?

A. 25 B. 52 C. 10 D. 25

3. What does 35 mean?

A. 5 x 5 x 5 C. 3 x 3 x 3 x 3 B. 5 x 5 x 5 x 5 D. 3 x 3 x 3 x 3 x 3

4. How is "15% decreases in price" represents in integer?

A. -16 B. +15 C. -15 D. 15

5. Which si the order of operations in (12 - 5) + 23 x 6 ÷ 2 using GEMDAS?

A. MDAS B. GEMD C. GMDE D. GEDM 6. Which symbol will replace the blank to make the sentence complete in -6 __ 2?

A. = B. > C. < D. ≠

7. Which has the least value - or ?

A. B. C. D.

8. Which integers are arranged in ascending order?

A. -20 , -12 , -9 , -2 , 1 C. 20 , -16 , -15 , 7 , 3 B. -12 , 9 , -4 , -10 , -2 D. 16 , 4 , -9 , -12 , -20

35

25

55

25

35

35- -



9. Which is the absolute value of -12?

A. 100 B. 12 C. 0 D. –12

10. Using the numberline below, which is the opposite of 4 units to to the left of -5?

A. 1 B. 2 C. 0 D. -12

II. Perform the indicated operation.

A.1. 36 + (-16) = n2. -25 + 25 = n3. -27 - (-15) = n4. 9 - (-17) = n5. -20 x (-4) = n

6. 9 x (-3) = n7. 34 x 6 = n8. -24 ÷ (-6) = n9. 54 ÷ (-9) = n

10. -72 ÷ (8) = n

B. Solve the equation below.11. 42 ÷ 6 + 7 x 4 ÷ 212. 64 - 20 ÷ 4 x 7 + 25

13. 24 - (5 x 4) ÷ 2 + 614. [15 + (9 ÷ 3 )] x 43 ÷ 8

III. Analyze and solve the problems.

A. Mrs. Soriano bought 3 kilograms of banana for ₱45 per kilogram and a dozen of lemon fruits for ₱120. How much did Mrs. Soriano pay for all the fruits? 1. What is the number sentence for the problem? 2. What is the answer to the problem?

B. An elevator went up to 36th fl oor. Then it went down 10 fl oors and another 7 fl oors. At what fl oor is the elevator now? 1. What operation will be used to solve the problem? 2. What is the answer to the problem?

C. The ACHES football team won by 3 points during fi rst round, lost by 4 points on the second round, and won by 6 points on the last round. Did they win in the game? 1. What is the number sentence for the problem? 2. By how many points did the team win?



Chapter 5Geometry, Patterns and Algebra


1. What kind of fi gure has three dimensions that occupy space and have volume?

A. plane fi gure C. circular fi gure B. space fi gure D. polygonal fi gure

2. Which solid fi gure has a polygonal base and triangular faces that meets at a common vertex?

A. pyramid C. cube B. cone D. rectangular prism

3. Which of the following fi gures have curved and fl at surfaces?

A. cylinder solid C. cone B. sphere D. pyramid

4. Which solid fi gure has a curved surface in which all points have equal distances from the center?

A. cone C. circle B. sphere D. cube

5. It is a closed fi gure that lies on the same plane.

A. solid fi gure C. space fi gure B. plane fi gure D. cone

6. Which plane fi gures are associated with cylinder?

A. square and circle C. rectangle and circle B. triangle and circle D. square and rectangle

7. What do you call the pattern of a three-dimensional fi gure?

A. pattern B. set C. net D. nest

Name: _________________________________ Date: ____________



8. Which of the following forms a net of a solid fi gure?

A. B. C. D.

9. Find the next term in the sequence, 7, 13, 25, 49, .

A. 86 B. 87 C. 96 D. 97

10. Which is the 5th term in the sequence of 3, 7, 15, , .

A. 63 B. 64 C. 65 D. 66

11. What do you call the combination of numbers and valuables joined by operation symbols?

A. expression C. solution B. equation D. variable

12. Which number sentence forms an equation?

A. 9 x n B. =5 C. 12(7 - 3) D. 5a + 6

13. How is twenty less than the product of eight and three is nine written in symbols?

A. 9 x 3 - 8 = 20 C. 8 x 3 - 20 = 9 B. 8 + 3 - 9 = 20 D. 20 - 8 x 3 = 9

14. Write thirty fi ve less than thrice of fi fteen is ten in symbols.

A. 3 x 15 - 30 = 10 C. 35 - 3 + 15 = 10 B. 3 x 10 - 15 = 30 D. 10 x 3 - 15 = 30

15. What do you call the algebraic expression or equation that represents the unknown number using letters or symbols?

A. symbols C. variable B. term D. notation

16. Which is the variable in a - ?

A. 6 B. - C. 24 D. a

32 - 75

246



17. Express the product of fi ve and the number is equal to the sum of twelve and eight in symbols.

A. 5 + n = 12 + 8 C. 5 x n = 12 + 8 B. 12 - 5 = 8 - n D. 5 - n = 12 + 8

Express each situation in algebraic form.

18. A certain school received 500 chairs from the NGO. The school head distributed them to x rooms. Find the number of chairs for each room in terms of B chairs.

A. = B C. 500+ x = B B. 500– x = B D. (500) x = B

19. Arnel is 3 times as old as his brother Aris. If Aris is n years old, how old are the two boys in terms of x as their total age.

A. 3 x 3 + n = x C. (3 ÷ n) + n = x B. (3 x n) + n = x D. (3 + n) n = x

II. Solve each problem (2 points each).

1. Jazhtine is 11 years old. Her mother is 3 times as old as she is. How old will her mother be after 5 years?

A. 33 B. 38 C. 48 D. 53

2. Lourdes has 5 more pocketbooks than Aleli. How many pocketbooks does Lourdes have if Aleli has 2 less than a dozen?

A. 5 B. 8 C. 10 D. 15

3. JessiLyn together with her cousins went to their favorite coff ee shop. They agreed to share the payment for their bill of ₱700 but one if her cousin does not have money. How much will each share for their cousin?

A. ₱35 B. ₱55 C. ₱100 D. ₱140

500x



Name: _________________________________ Date: ____________

Chapter 6Measurements


1. How does the speed measure?

A. kph B. kwh C. km D. kmd

2. Which of the following is the formula for calculating the speed?

A. S = B. S = d x t C. S = d + t D. S = d + t

3. What unit of measure is used for fi nding the surface area?

A. l C. cubic unit B. m D. square unit

4. Which formula shows the area of a triangle?

A. A = b x h B. A = C. A = D. πr2

5. Which of the following fi gures has one circular base and a curved surface with a vertex?

A. cone C. pyramid B. sphere D. cube

6. It is the sum of all the areas of the surface of a solid fi gure.

A. surfaces C. surface area B. volume D. area

7. What is the surface area of the stack of cubes shown below if the sides of each cube measures 1 cm?

A. 25 cm² B. 75 cm² C. 125 cm² D. 130 cm²

dt

b x h2

l x w2



8. What is the least amount of wrapper that can be used to cover a box with an edge of 15 cm?

A. 45 cm² B. 225 cm² C. 1350 cm² D. 3375 cm²

9. What is the surface area of a rectangular box with a length of 20 cm, a width of 15 cm and a height of 10 cm?

A. 650 cm² B. 1300 cm² C. 1300 cm² D. 3000 cm²

10. What part of a prism is the pyramid?

A. B. C. D.

11. Which fi gure has a formula of V = ?

A. cone C. cube B. sphere D. pyramid

12. Which formula is used to fi nd the volume of a cylinder?

A. V = bh B. V = πr2 C. V = πr2h D. V = πr2h

13. How is volume measured?

A. cubic units C. units B. square unite D. square

14. What is the volume of a cylindrical tank that has a radius of 5 dm and a height of 8 dm?

A. 25.12 dm³ C. 125.6 dm² B. 75.6 dm³ D. 125.6 dm³

15. A ball has a radius of 6 cm. How much air was enclosed by the ball?

A. 2712.96 cm³ C. 904.32 cm³ B. 1912.54 cm³ D. 704.32 cm³

16. What is used to determine the amount of electricity consumed by the consumer?

A. water meter C. gas meter B. electric meter D. hydrometer

13

13

12

14

15

16

πr2h3



17. What operation is used to calculate the usage of electricity and water?

A. Division C. Subtraction B. Multiplication D. Addition

18. How many kwh was consumed if the previous electricity meter reading was 3876 and the present reading is 4524 kwh?

A. 4524 kwh C. 1648 kwh B. 3876 kwh D. 648 kwh

19. The previous water meter reading was 0054326 and the present is 00725211. How many cubic meters of water was consumed?

A. 18 m³ B. 19 m³ C. 20 m³ D. 21 m³

20. Based on the dials below, what was the previous reading if the latest consumption is 254 kwh?

A. 8675 B. 8421 C. 8167 D. 8067

21. The Rivera family consumed 23 m3 of water last month. If a cubic meter of water costs ₱15.51, how much did the family pay the basic charge?

A. ₱356.73 B. ₱486.75 C. ₱556.73 D. ₱602.17

22. An electric bill shows a previous reading of 5092 kwh and a present reading of 5140 kwh. How much will they pay for the generation charge if it cost ₱5.35 per kilowatt?

A. 267.50 B. 256.80 C. 256.50 D. 246.80

23. A cylindrical can of juice has a radius of 5 cm and a height of 12 cm. How much juice can it hold if it was filled up tp the brim?

A. 980 cm³ B. 2975 cm³ C. 942 cm³ D. 840 cm³



24. An aquarium is 40 cm long, 20 cm wide and 30 cm high. How much water can it hold if it is full?

A. 22 500 cm³ C. 19 000 cm³ B. 22 000 cm³ D. 18 000 cm³

25. Mr. Ramos would like to paint a piece of rectangular wood 10 dm long, 6 dm wide and 0.2 thick. What is the total area of the surface he is going to paint?

A. 63.2 dm2 C. 52.3 dm2 B. 53.6 dm2 D. 48.7 dm2

13



15

12

12

12

14

13

13

13

13

14

14

14

12

16

15

15

Name: _________________________________ Date: ____________

Chapter 7Statistics and Probability


1. How many possible outcomes when a coin is tossed 3 times?

A. 2 B. 4 C. 6 D. 8

2. What is the probability of a number more than 3 when a dice is rolled up?

A. B. C. D.

3. How many sample space in the experiment of drawing a card from the pile of diamonds, hearts, clubs and spades?

A. 4 B. 6 C. 8 D. 10

4. What is the probability of chance that the fl ight to Cebu will be cancelled due to thunderstorm?

A. unlikely C. certain B. likely D. even chance

5. A coin is toss 10 times in an experiment to fi nd the probability that it will land on heads or tails. How many trials will be made?

A. 12 B. 10 C. 8 D. 6

6. What is the probability of getting even numbers after tossing a die once?

A. B. C. D.

7. What is the probability of picking yellow and red marbles in a box with 3 yellow marbles, 4 blue marbles, 6 white and 2 red marbles?

A. B. C. D.

8. What is the probability of picking composite numbers in a box with digits 2 , 3 , 5 , 7 , 9?

A. B. C. D.



9. Twelve out of 40 children choose to become policemen someday. How many degree does it represent in a pie graph?

A. 120˚ B. 118˚ C. 108˚ D. 100˚

10. How many percent does the answer in no. 9 question represent in the pie graph?

A. 20% B. 30% C. 35% D. 40%

II. A.1 Listed below is the list of television shows that 25 people prefer to watch. Make a frequency table showing the data.

dramaentertainment

actionentertainment

dramaactiondramaaction

educational

entertainmentaction

entertainmentdramaaction

entertainmententertainmenteducational

dramaeducationaleducational

actiondrama

entertainmententertainment

action

FREQUENCY TABLE

Television Show Tally Frequency

Drama

Action

Educational

Entertainment

1.

2.

3.

4.

A.2 Which is the most viewed show?



B. The table below shows the survey on the profession the children want to become someday. Find the number of degrees each profession represents in the pie graph.

7. What profession do children like the most? 8. What is the least profession they like to become?

C. Use the data in the graph to answer the questions below.

Profession No. of Pupils Degrees

TeacherPolicemen

NurseDoctor

EngineerArchitect

10144462

1. 2. 3. 4. 5. 6.

Total 40

Food 35%

Electricity15%

Education 25%House Rental

12%

Savings 5%

Water 3% Tran

spor

tatio

n 5%

Alonzo Family budget - ₱35 000 1. What percent of their budget gets for Education?

2. Which have the same amount of expenses?

3. How much is spent for electricity and water?

4. How much more was he budget for food than education?

5. What expenses has the least amount?

6. How much is allotted for food?

7. How much does the family save?



Chapter 1 FRACTIONS

A. 1. B 2. C 3. A 4. D 5. A 6. A 7. C 8. D 9. B10. A

B.11. A12. D13. C14. G15. H16. D

C.

17. 1

18. 8

19. 4

20. 9

21. 2

22. 1

1. 5

2. 2

3.

4. 3

5. 3

II.

A.

1. Subtraction

2. 5 kg

B.1. Multiplication2. 21 boxes

C.1. Number of small plastic bags2. 43 plastic bags

D.

1. 2

2. 1 kg

Grade 6 - Key to Corrections

34

35

34

512

2318

34

12

19

718



Chapter 2 DECIMALS

I.A. 1. C 2. B 3. A 4. C 5. B 6. C 7. B 8. A 9. C10. D11. A12. B13. B14. A15. D

B.16. 3.396517. 13.659918. 0.49719. 4.586320. 24.1221. 7.090522. 321.423. 28.624. 3040

II. (2 points each)1. 159 cm2. ₱25 857.503. 15.5 liters

Chapter 3 RATIO, PROPORTIONS, DECIMALSI.A. 1. A 2. B 3. C 4. B 5. C 6. D 7. A 8. D 9. D10. C

B.11. 2012. 613. 2714. 515. 1216. 25%17. 1618. 5019. 24320. 150

II. (2 points each)1. 15 days2. ₱6203. 40%4. ₱6 520.505. ₱53 000.00



Chapter 5 GEOMETRY, PATTERN AND ALGEBRA

1. B 2. A 3. A 4. B 5. B 6. C 7. C 8. C 9. D10. A

11. A12. B13. C14. A15. C16. D17. C18. A19. B20. B

21. B22. D23. D24. A25. A

Chapter 6 MEASUREMENTS

1. A 2. A 3. D 4. B 5. A 6. C 7. C 8. C 9. B10. A

11. A12. C13. A14. D15. C16. B17. C18. D19. A20. C

21. A22. B23. C24. D25. A

Chapter 4 ORDER OF OPERATIONS & INTEGERS

I. 1. C 2. A 3. D 4. C 5. B 6. C 7. D 8. A 9. B10. A

II.A. 1. 10 2. 0 3. 42 4. -8 5. 80 6. -27 7. 204 8. -4 9. 610. 9

B.1. 212. 543. 404. 39

III.A. 1. 3 X 45 + 120 = n 2. ₱210

B. 3. Addition and Subtraction 4. 19th floor

C. 1. 3 - 4 + 6 = n 2. 5 points



Chapter 7

I. 1. D 2. D 3. A 4. C 5. B 6. A 7. B 8. D 9. C10. B

II.A.1. llll - l 62. llll - l 63. llll 44. llll - llll 95. Entertainment Show

B.1. 90˚2. 126˚3. 36˚4. 36˚5. 54˚6. 18˚7. Policeman8. Architect

C.1. 25%2. Transportation and Savings3. ₱6 300.004. ₱3 500.005. water6. ₱12 250.007. ₱1 750.00




Name: _________________________________ Date: ____________

First Quarter Test


1. Which is the least common denominator of , , and ?

A. 6 B. 15 C. 18 D. 30

2. How much greater is from ?

A. B. C. D.

3. What is in simplest form?

A. B. C. D.

4. What number will be subtracted to 23 that will give a diff erence of 14 ?

A. 8 B. 8 C. 7 D. 6

5. What is 4 added to the diff erence of 32 and 29 ?

A. 9 B. 9 C. 8 D. 7

6. What is the diff erence if the sum of and is subtracted from 2 ?

A. 1 B. 1 C. 2 D. 2

7. If 5 is multiplied by , what is the product?

A. 3 B. 3 C. 4 D. 5

8. How many meter can be cut from a bolt of 50 m?

A. 120 B. 100 C. 75 D. 50

56

25

13

67

34

12

17

13

328

35

528

23

34

47

815

23

23

12

34

12

1315

77

14

16

115

67

14

1315

67

14

16

1315

57

12

16

1315

815

37

810

310-



9. Which is the multiplicative inverse of expressed in lowest form?

A. 3 B. 2 C. D.

10. Which is the quotient in 8 ÷ ?

A. 5 B. 8 C. 8 D. 12

11. If 67 x 358 = 23 986, which number will be multiplied by 0.358 to get the product of 2.3936?

A. 358 B. 67 C. 6.7 D. 0.67

12. What is seventy eight hundredths divided by one hundredth?

A. 78 B. 7.8 C. 0.78 D. 0.078

13. Which is the diff erence if you take away 0.158 from 21.6?

A. 21.542 B. 21.442 C. 214.42 D. 21 442

14. What is the quotient in 429 ÷ 1000?

A. 0.429 B. 4.29 C. 42.9 D. 429

15. Which has a repeating decimal quotient?

A. 4 ÷ 9 B. 6 ÷ 7 C. 12 ÷ 25 D. 9 ÷ 16

II.A. Perform the indicated operations.

1718A. 17

1718C. 15

12D. 15

B. 16

815A.

415C. 1

15D. 1

B. 1115

518718618

+

1. 12

3

4153513

+

2.

34

23x

58

12

45

13

45



49A. 25

49C. 24

19D. 23

B. 24 89

79A. 5

79

49

C. 6

19D. 7

B. 6

A. 35

12C.

D. 1

23B.

79A.

2027C.

2427D.

89B.

A. 2

316A.

1415

315

A. 2

38C. 1

14C.

C. 3

1025C. 1

45A. 1

14D. 1

38D.

D. 3

13D. 2

1125B. 1

B. 1 58

B. 516

B. 3 815

13

2379

+3. 15

9

1359

-5. 12

6

5814

-4. 8

7

68

12x6.

1215

34x7.

59

34÷9.

23

415x8. 3

25

23÷ 110. 2



B. Do what you are told to do.

III. Read and analyze each problem. Answer the questions that follow.

A. A bakeshop has 26 kg of sugar. Three fi fths of it was used for baking cakes. How many kg of sugar were used in baking? 1. What part of the sugar was used in baking? 2. What information were given to solve the problem? 3. What operation will be used to solve the problem?

B. Jonjon's luggage weighs 17.75 kg while John Lery's luggage weighs 21.50 kg. Twice the diff erence of the weight of the two luggages is the weight of their mother's hand carry bag. How heavy is the hand carry bag? 1. What information were given to solve the problem? 2. What is the hidden question? 3. What operations are needed to solve the problem? 4. What is the answer to the problem?

Add:

1. 0.3421 0.0153 0.130 0.4014

2. 6.314 0.023 1.537 4.26

Subtract:

3. 0.548 0.219

4. 7.23 5.187

Multiply:

5. 68.07 0.32

6. 3.74 26.4

7. 46.38 0.001

Divide:

8. 462 ÷ .03 9. 46.74 ÷ 3.8 10. 80.55 ÷ 45

- -

x x x

14





IV. Solve the problems (2 points each)

1. Nikko spent ₱1 286.25 for 35 liters of gasoline fuel to fill his tank for a trip. How much is the price of gasoline fuel per liter?

2. Manuel traveled at the average speed of 80 km/hr for 1 hours. Going back, he travelled for 2 at the speed of 55 km/hr. What is the total distance that Manuel covered?

3. Mrs. Manansala bought a refrigerator for ₱16 250.75. She gave ₱5 000 to the cashier as down payment and promised to pay the remaining balance for 6 months. How much will be her monthly payment?

4. Mrs. Madrid receives a net salary of ₱34 775.25. She gave her 5 children ₱1 500 each for their allowance and allotted ₱6 000 for their food. How much was left for other expenses?

121

4



Name: _________________________________ Date: ____________

Second Quarter Test


1. Which forms a ratio of 15 colored pencils to 3 coloring books?

A. 5:1 B. 3:5 C. 3:15 D. 1:5

2. Which does not form the ratio of 48 months to 4 years?

A. 48:4 B. 12:1 C. 1:12 D. 24:2

3. Which is as much as the value of ?

A. B. C. D.

4. Which shows the proportion for the situation below? Three kg of banana cost ₱135, how many kg of banana for ₱225?

A. 135:3 : : n:225 C. 3:135 : : 225:n B. 3:225 : : n:135 D. 3:135 : : n:225

5. Which is the missing term in 12:72 :: 3:N?

A. 16 B. 17 C. 18 D. 19

6. How is 125% written in decimals?

A. 125 B. 12.5 C. 1.25 D. 0.125

7. What is the value of 53?

A. 243 B. 125 C. 75 D. 15

8. Which has the least value, 43 , 34 , 52, , or 25?

A. 43 B. 52 C. 34 D. 25

9. Which is the right symbol to compare 26 __ 82?

A. = B. > C. < D. ≠

58

1016

85

1012

68



10. Which integer represents "won ₱50 000 in the raffl e draw"?

A. 5 000 B. -5 000 C. -50 000 D. 50 000

11. Which has the greatest value 1 – 4 – 3 – 2?

A. -4 B. -3 C. 1 D. -2

12. Which set of integers are arranged in descending order?

A. -4 , -2 , 0 , -5 , 1 C. 2 , 0 , -4 , -6 , -12 B. -8 , -7 , -6 , -5 , -4 D. 5 , 4 , -3 , 0 , -1

13. Which is 12% of ₱3 500?

A. ₱420 B. ₱450 C. ₱480 D. ₱520

14. Which is the correct order of operations following GEMDAS in 12 - (5 x 2) + 23 + 6 x 4?

A. SGEAM B. GEMSA C. GSAME D. GEMAS

15. Which operation is described in

A. Division C. Subtraction B. Multiplication D. Addition

16. Which is simplifi ed form of ratio for 27:54:63?

A. 1:2:3 C. 3:6:9 B. 3:2:6 D. 3:6:7

17. Which is the biggest number if 242 is divided in a ratio of 1:3:4?

A. 121 B. 120 C. 90.75 D. 88

18. What is the value of n in n% of 90 = 72?

A. 90% B. 80% C. 75% D. 70%

+ + + + - -- - - - - -

=



19. What is 15% of 120?

A. 18 B. 19 C. 21 D. 26

20. Using the numberline below which point described 6 units to the right of -4?

A. X B. Y C. Z D. W

II.A. Find the missing term to form a proportion.

21. 9:n = 27:21

A. 9 C. 7 B. 8 D. 6

22. n:24 = 6:16

A. 15 C. 10 B. 12 D. 9

B. Solve.

25. 15 is 25% of what number?

A. 60 B. 72 C. 78 D. 80

26. 25% of n is equal to 13.5

A. 54 B. 48 C. 44 D. 27

27. What is 35% of 120?

A. 60 B. 45 C. 30 D. 42

A

-8

B

-7

C

-6

D

-5

E

-4

F

-3

G

-2

H

-1

X

0

Y

1

Z

2

W

3

P

4

Q

5

R

6

S

7

T

8

23. 7:12 = 21:n

A. 42 C. 24 B. 36 D. 18

24. 16:5 = n:25

A. 25 C. 80 B. 75 D. 85



28. What percent of 64 is 8?

A. 15% B. 12.5% C. 12% D. 8%

29. What is 10% of 200?

A. 25 B. 22 C. 20 D. 2

C. Evaluate the following.

30. 5 x 4 - 12 ÷ 4 = n

31. 4 + 3 x 7 + 12 ÷ 3 x 2 = n

32. (16 - 4) + 8 x 52 ÷ 5 = n

33. (7 + 8) 3 ÷ 5 - 7 = n

34. 15 + 4 (4³ - 24) ÷ 5 x 3 = n

III. Read and analyze the problem. Answer the questions that follow.

A. Susan received ₱1 200.00 commission for selling beauty products which was 25% of her total sales. How much did she sell in all? 1. What is asked in the problem? 2. What operation will be used to solve the problem?

B. Josh and Dave bought a gift for their grandmother. They shared the amount of ₱1 500 in a ratio of 2:3. How much is the share of each? 1. What kind of proportion is involve in the problem? 2. Who has a bigger share?

IV. Solve each problem (2 points each)

1. A man working 8 hours a day could fi nish the work in 15 days. How many days could he fi nish the same work if he works in 10 hours a day?

2. Jonjon got 80% of the 50 item test in English. How many question did he answer correctly?



3. A sum of money was shared among Joy, Karen and Kris in a ratio of 3:4:5. What percentage of money will Joy receive?

4. Two cars left the town in opposite directions at 40 and 50 km per hour respectively. In how many hours are they 270 km apart?

5. Sam spent 20% of his money on books and 15% of remainder on his project in Livelihood Education. What percentage of his money had he used?



Name: _________________________________ Date: ____________

Third Quarter Test


1. Which solid fi gure is represented by a die?

A. cone B. pyramid C. cube D. cone

2. Which solid fi gure can roll in all directions?

A. B. C. D.

3. Which net can form a cylinder?

A. B. C. D.

4. Which shows an expression?

A. 3 x 4 - y = 4 C. 6 x n + 4 = 16 B. 3 x y = 15 - 8 D. 4x3

5. Which is the algebraic equation for "three times a number is six more than twice the number" ?

A. 3 x n = 6 + 2 x n C. 3 x n = 6 + 2 - n B. 3 + n = 6 + 2 D. 3 x 2n

6. Which is the 7th term in the sequence of 5 , 11 , 23 , 47 , 95 , 191 , ____?

A. 131 B. 283 C. 363 D. 383

7. How many surfaces are there in a pyramid?

A. 7 B. 6 C. 5 D. 4

8. Which solid fi gure resembles the object usually near by the children during the party?

A. B. C. D.



9. Which is not a polyhedron?

A. B. C. D.

10. Which is 25th term in a rule of n x 3 - 1?

A. 78 B. 76 C. 75 D. 74

11. A car travels in a speed of 60 kph. How far is the car if it travels for 5 hours?

A. 400 km B. 350 km C. 300 km D. 250 km

12. Mang Jose had 30 pieces of balloon to sell. At the end of the day, he had 8 pieces left. Which is the expression for the situation in terms of x balloon?

A. 30 - x = 8 C. 30 - 8 = x B. 30 + x = 8 D. 30 ÷ 8 = x

13. Which is the sum of all edges, faces and vertices of a pyramid?

A. 24 B. 22 C. 18 D. 15

14. Which solid fi gure can roll in one direction only?

A. cylinder B. cone C. cube D. cylinder

15. Which gives the area of a triangle?

A. s x s B. C. l x w D. ( )h

16. A triangle is drawn inside a circle whose diameter is 12 cm as shown below. What is the area of the triangle?

17. What is the area of the shaded fi gure?

Y A. 18 cm2 C. 72 m2B. 36 cm2 D. 144 m2

A. 4 cm2 C. 12B. 8 cm2 D. 16 cm2

8 cm

2 cm

b x h2

b1 + b22



18. What is the formula to fi nd the area of the base if the four lateral faces of a prism are congruent?

A. C. ( )h

B. s x s D. l x w x h

19. Which is the toal area of the surfaces of the net shown below.

20. Which is the least amount of wrapper that can cover a box with a length of 10 cm, a width of 15 cm and a height of 8 cm?

A. 150 cm2 B. 240 cm2 C. 280 cm² D. 340 cm²

II. Which formula matches the fi gure at the left. Write the letter of the correct answer.

1.

2.

3.

4.

5.

A. 54 cm3 C. 18 cm2B. 48 cm2 D. 9 cm2

b1 + b22

b x h2

3cm

A. S2 x 6

B. s2 + 2 (s x l )

C. (l + w + l x h + w x h) 2

D. πr2 + πrl

E. πr2 + 2 πr2h

F. 4 πr2



III. Find the surface area of the fi gures below.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

IV. Analyze the problem. Answer the questions that follow.

A. A box of chocolate has two congruent triangle and three rectangular faces. What is the surface area of the box if it measures 20 cm long, a base of 4 cm and a slant height of 4 cm? 1. What is asked in the problem? 2. What information are given? 3. What solid fi gure represents the chocolate box?

B. A cylindrical can is 14 cm tall and has a diameter of 10 cm? What is the total surface area of the can? 1. What is the formula in fi nding the surface area of a cylindrical can? 2. What unit of measure is used in surface area?

6 cm

5 cm

4 dm

10 dm

r = 8 cm

r = 12 cm

3 cm

10 cm

5 cm

3 cm10 cm

15 cm

12 cm

10 cm

4 cm3 cm

S = 5 cm

7 cm

8



12

V. Solve each problem. (2 points each)

1. Mr. Fernandez drives at 40 km/hr and reaches the school after 1 hrs. How far is his place from school?

2. Miguel reached his destination after driving for 4 hours and covering a distance of 280 km. What was the rate of speed?

3. Matteo drove 320 km with a constant speed of 80 kph. How many hours did he drive?

4. A van travels 120 km with a constant speed of 60 km/hr, and another 130 km with a constant speed of 65 km/hr. How long did the van travel?

5. Antonio left home and drove at the rate of 45 kph for 2 hours. He stepped at the drive-through for lunch then he drove 3 hours at the rate of 55 kmh to reach his destination. How many km did he drive?



Name: _________________________________ Date: ____________

Fourth Quarter Test


1. What part of the volume of a cylinder is the volume of a sphere?

A. B. C. D.

2. The volume of a sphere can be determined by the volume of what solid fi gures?

A. cone C. cylinder B. pyramid D. cube

3. Which solid fi gure will use the formula of V = ?

A. pyramid C. sphere B. cylinder D. cone

4. Which measures the amount of water consumed by the user?

A. hydrometer C. water meter B. electricity meter D. kilometer

5. How is water usage measured?

A. cubic units C. units B. square units D. meters

6. A pie graph is in a shape of circle. How many degress does it have?

A. 480˚ B. 360˚ C. 240˚ D. 180˚

7. Using the probability line, what is the probability of an event that is impossible to happen?

A. 0 B. C. D. 1

8. How many sample space in the equipment of tossing a coin once?

A. 6 B. 5 C. 4 D. 2

13

12

14

23

12

43

πr2h3



9. Which is the probability that a coin will land to tail up?

A. unlikely C. likely B. even chance D. certain

10. Which is the probability of seeing the birds fl ying when the sun shines?

A. certain C. unlikely B. likely D. impossible

11. How much water was consumed if the previous water meter reading was 0038271 and the present reading is 0065432?

A. 27161 cu units C. 272 cubic units B. 1716 cu units D. 27 cubic units

12. The Magdangal family consumed 368 kwh for this month. What is the present reading if the previous electric meter reading was 4978?

A. 5346 C. 4610 B. 5246 D. 4346

13. Which is the correct water meter reading?

14. Based on the dials below, how many kwh was consumed if the present electric reading is 3926?

A. 3752 B. 3852 C. 3762 D. 3852

15. A cylindrical water tank has a radius of 1.5 meters and height of 2 meters. How much water can it hold?

A. 14.15 m3 B. 14.13 m3 C. 9.42 m3 D. 6.28 m3

A. 52962 C. 52B. 5262 D. 530052962



For items 16-22, Refer to the table below. Choose the letter of the correct answer. from column B.

Record of Electrical Consumption of Each Family for the Month of January

Meter Reading Column BFamily

A. Barrameda

B. Rivera

C. Elizalde

D. Dela Predia

Previous

2516

3312

1802

2837

Present

2594

3457

1938

2994

kwh used

(16)

(17)

(18)

(19)

A. 136

B. 157

C. 173

D. 78

E. 145

20. Which family consumed the least amount of electricty?21. Which family consumed more electricity?22. How many kwh did the Dela Predia family consumed?

For items 23-28, Refer to the graph.

23. Where does the greatest amount of their income go?

A. Education C. Home Rental B. Food D. Miscellaneous

Food40%

20%Education

Home Rental15%

15%

10%

Wat

er & El

ectric

ity

Miscellaneous

Cantiveros Family BudgetMonthly Income - ₱ 45 000



24. How many percent goes to water and electricity?

A. 20% B. 15% C. 10% D. 5%

25. How much is spent for food?

A. ₱15 000 C. ₱8 000 B. ₱10 000 D. ₱5 000

26. How much more is allotted to Education than the home rental expenses?

A. ₱5 000 C. ₱3 500 B. ₱4 500 D. ₱2 250

27. Which expenses have the same budget?

A. Water and Electricity and House Rental B. Miscellaneous and House Rental C. Education and Food D. Education and House Rental 28. How much is the family budget for the month?

A. ₱54 000 C. ₱45 000 B. ₱48 000 D. ₱35 000

29. A cylindrical can has diameter of 8 cm and a height of 12 cm. What is the volume of the can?

A. 2 449.2 cm³ C. 602.88 cm³ B. 802.88 cm³ D. 402.88 cm³

30. A ball has a radius of 6 cm. How much air can it hold?

A. 150.72 cm³ C. 678.24 cm³ B. 604.32 cm³ D. 904.32 cm³



II. Write the formula then fi nd the volume of each fi gure.

III. Study the tree diagram below, then answer the questions that follow. Express the answer in percent.

4 cm

9 cm

a.

3 cm

6 cm

b.

r = 3cmd.

5 dm

20 dm

e.

S = 4 cm

h = 12 cm

c.

V =

V =

V =

V =

V =

(1) (7)

(3) (9)

(5)

(2) (8)

(4) (10)

(6)

HeadHead

HeadTail

Tail

Tail

12

12

1212

12

12

1. What is the chance of having two heads from two tosses?

2. What is the probability of getting at least one head from two tosses?

3. What is the chance of having two tails from the experiment?

4. How many possible outcomes in the experiment of tossing a coin two times?



IV. Solve each problem (2 points each)

1. There are 100 boxes of noodles in the warehouse. If each box measures 40 cm long, 40 cm wide and 30 cm high, how many cubic meter of space is occupied by the boxes of noodles? (1 cm3 = 0.000001 m3)

2. A spherical water tank has a radiuus of 12 dm. How many liters of water does it contain? (1 dm3 = 1 liter)

3. A dental clinic had 24 patients for that particular day. Thirteen of them had the prophylaxes treatment. What is the the probability that the next patient will have the same treatment?



Quarter Test Grade 6 Key to Correction

First Quarter TestI.1. D2. C3. A4. B5. D6. A7. C8. B

9. B10. D11. C12. A13. B14. A15. A

II.A.1. B2. D3. A4. C5. A

6. D 7. A 8. A 9. C10. B

B.0.888812.1340.3292.04321.7824

98.7360.0463815 40012.31.79

III.A.

1.

2. 26 ;

3. Multiplication

B.1. 17.75 kg , 21.50 kg ; 22. The total weight of the 2 luggages3. Addition, Subtraction, Multiplication4. 7.5 kg

IV.

1. ₱36.75

2. 243 km

3. ₱1875

4. ₱21 275.25

35

14

35

34



Second Quarter TestI. 1. A 2. C 3. A 4. D 5. C 6. C 7. B 8. B 9. A10. D

11. C12. C13. A14. B15. C16. D17. A18. B19. A20. C

II.A.21. C22. D23. B24. C

B.25. A26. A27. D28. B29. C

C.30. 1731. 3332. 52

33. 234. 39

III.A.1. Total sales or amount of total sales2. Division

B.1. Partitive Proportion2. Dave

IV. 2 points each1. 12 days2. 453. 25%4. 3 hours5. 32%



Third Quarter TestI. 1. C 2. D 3. C 4. D 5. A 6. D 7. C 8. D 9. A10. D

11. C12. A13. C14. D15. B16. A17. D18. B19. A20. D

II.1. E2. D3. F4. B5. C

III. 1. 1 350 cm2 2. 1 808.64 cm2 3. 1 055.04 dm2 4. 190 cm2 5. 452.16 cm2 6. 95 cm2 7. 164 cm2 8. 94.2 cm2 9. 864 cm210. 803.84 cm2

IV.A.1. surface area of the box2. l = 20 cm , b = 4 cm , sl = 4 cm3. triangular prism

B.1. SA = πr2 + 2 πr2h2. square units

V.1. 60 km2. 70 km/hr3. 4 hours4. 4 hours5. 255 km



Fourth Quarter TestI. 1. C 2. A 3. D 4. C 5. A 6. B 7. A 8. D 9. B10. A11. D12. A13. C14. A15. B

16. D17. E18. A19. B20. A21. D22. 157 kwh23. B24. B25. B26. D27. A28. C29. C30. D

II.

1. V =

2. 150.72 cm3

3. V = πr2h

4. 169.56 cm3

5. V = Bh or

6. 64 cm3

7. V = πr3

8. 113.04 cm3

9. V = πr2h

10. 1 570 dm3

III.1. 25%2. 75%3. 25%4. 8 possible outcomes

IV.1. 4.8 m3

2. 7 234.56 liters3. It is likely to happen

πr2h3

13

43

Bh3

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