Student WorkBook Math Grade-7

Mathematics for Grade VII Semester 1

1

Chapter 1 Whole numbers

Student Activities

1. When the weather forecasters said ’Today will be raining in the city with a minimum temperature of 2°C below zero and a maximum temperature of 16°C. How would you express all information above in whole numbers

2. A temperature of 14° C (Celsius) is decreased by 18 degrees Celsius. What is the resulting temperature?

3. Write down the result of the following statements (a) all the natural numbers less than 4 :

(b) all the even numbers between 18 and 39 :

(c) all the odd numbers between 15 and 25 :

(d) The temperature drops by 3 unit from zero :

(e) If the initial temperature of a room is 7oC, then it falls by 5oC, what is the final temperature of the room?

(f) The temperature of Singaraja city is 32oC, while Bangli is 24oC. What is the temperature difference of the two cities?

4. Draw a number line to represent the whole numbers (a). 1, 3, 5 and 7;

(b) greater than 3 but less than 13

5. Find the sum of each of the following. (a) 26574 + 24938 =

(b) 23 453 + 96 875 =

2

(c) 54613 + 4042 + 1793 + 248039 =

(d) 29359 + 9632 + 82175 + 184938 =

6. Calculate the following mentally. (a) 14 × 5 + 14 × 3 =

(b) 16 × 4 + 16 × 6 =

(c) 19 ×13 – 19 × 7 =

(d) 18 × 17 – 28 × 17 =

7. The populations of Semarapura, Singaraja, Amlapura are 309 346, 204 188, and 306 470 respectively. What is the total population of the three towns?

8. A farmer were able to produce 24 679 kg of rice in 2004, 467 248 kg of rice in 2005 and 56 350 kg of rice in 2006. How many kilograms of rice did the farmer produce in the three years?

9. a. Find the difference between 964 239 and 685 136.

b. Subtract 29 604 from 57 814

10. The price of a new car is Rp.120 500 490 whereas the price of a used car is Rp.85 900.000 less than the price of the new car. What is the price of the used car?

11. The length of a road is 440 530 meters and another road 280 320 meters long. Find the difference in length between the two roads.

12. Ani is 12 years older than Tuti and 5 years younger than Sri. If Sri is 30 years old, how old is Tuti?

13. In a class of 28 students, 12 are boys. One day, 8 new students enroll in the class and 5 of them are boys. Calculate the number of girls in the class now.


3

14. A can of fruit juice costs Rp.7500 and a packet of sweets costs Rp.6000. Mrs. Sudani bought 3 cans of fruit juice and 4 packets of sweets. Calculate the total amount of money that Mrs. Sudani paid.

15. A box contains 100 apples. Budi bought 8 boxes of apples and distributed them equally to 25 poor families. Calculate the number of apples each family received.

16. Putu buys a magazine costing Rp.15 000, a dictionary costing Rp.25 000 and a scientific calculator costing Rp.40 000. Find the total amount of money he pays.

17. An electronics supply house has 432 resistors of a certain type. If 36 are sold during the first week, 72 during the second week, 29 during the third week, and 58 during the fourth week, how many are left at the end of the month?

18. Rudi has Rp.230 000 in his savings account. If he spends Rp.150 000 to buy a game, how

much is left in his savings account?

19. Putu has Rp.440 000 in his savings account. He wishes to buy a tennis racquet for Rp.210 000. How much is left in his savings account?

20. The temperature was –15° at 6a.m. but by noon the temperature has risen to 23°. How many degrees did it rise from 6 am to noon?

21. The temperature dropped 22° from –7° at midnight to just before daybreak at 7 am. What was the temperature at 7 am.?

22. Erni was born in 1986. How old will she be in the year 2010?

4

23. A chemist has 100 ml of acid and she needs 368 ml of the acid. How much more is needed?

24. If a person has Rp.780 000 after paying off a debt of Rp.230 000, how much money did he have before paying off the debt? Write a statement involving the operation of subtraction of integers to show your answer.

25. A piece of wood 24 meters long is cut into three pieces so that two of the pieces measure 8 meters and 10 meters. What is the length of the third piece?

26. Amy has Rp.450 000 in assets and she wants to borrow enough money to buy a stereo system

for Rp.695 000. How much will she owe?

27. The top of Mt. Everest in Asia is 8100 meters above sea level and the top of Mt. McKinley in Alaska is 6 320 meters above sea level. How much higher is the top of Mt. Everest than the top of Mt. McKinley?

Multiple Choice Questions

1. The temperature in Sydney tonight is –

2oC and it is forecasted that the temperature will drop by 3oC tomorrow morning. What will the temperature be tomorrow in Sydney? a. 5oC c. –5oC b. 1oC d. –1oC

2. Which of the following is not a common

multiple of 4 and 6?

a. 12 c. 48 b. 32 d. 72

3. x, 29, 31, 37, y are prime numbers arranged in a certain order. The value of y – x is a. 16 c. 20 b. 18 d. 64


5

4. 23, w, x, y, z, 43 are prime numbers arranged in increasing order. Which of the following is the number 37? a. w c. y b. x d. z

5. The lowest common multiple of 3, 4 and 8 is 1. 24 c. 48 2. 32 d. 60

6. The definition of -5oC is…

a. 5oC below the freezing point of water b. 5oC above the freezing point of water c. -5oC below the freezing point of water d. -5oC above the freezing point of water

7. Which of the following number lines

shows the equation -5 + 3?

a.

b.

c.

d.

8. The identity of addition operation in a whole number is… a. 0 c. -1 b. 2 d.

9. is equivalent to…

a. c.

b. d.

10. The inverse of addition of –12 is… a.

c.

b. d. –12

11. If , and , the value of is… a. –1 c. –7 b. 1 d. –21

12. Which of the following statements

correctly describes the figure below?

a. 4 + (-2) c. 4 + (-6) b. -4 + 6 d. -4 + (-6)

13.

a. c. b. 14 d.

14. a. – 120 c. 120 b. 110 d. – 110

15. The inverse of 7 is…

a. c.

b. 7 d.

16. If , and , the result of is… a. 1 c. 7 b. −1 d. −7

17. If 63 = −21, then is…

a. −3 c. −5 b. 3 d. 5

18.

6

a. – 37 c. - 55 b. 73 d. 91

19.

a. 3 c. – 20 b. – 3 d. – 25

20.

a. – 15 c. – 20 b. 15 d. 20

21. If and , then

a. 105 c. 115 b. 36 d. 120

22. If and , then

a. 35 c. 37 b. 36 d. 38

23.

a. − 243 c. – 54 b. − 243 d. 54

24. Which of the following is the lowest

common multiple of 3, 5 and 8? a. 240 c. 120 b. 60 d. 30

25. The first three prime numbers which are greater than 18 are a. 19,21,23 b. 19, 23, 27 c. 19, 23, 29 d. 23, 29. 31

26. 96 is a common multiple of 8 and x.

Which of the following is not a value of x? a. 16 c. 24 b. 32 d. 46

27. 2 and 3 are the prime factors of 126.

Another prime factor of 126 is a. 5 c. 6 b. 7 d. 11

28. 3 is a factor of p. p is a factor of 63. The

possible value of p is a. 6 b. 9 b. 12 b. 15

29. The prime factors of 132 are

a. 2,3, and 6 b. 2,3, and 11 c. 2,4, and 11 d. 3,7, and 11

Chapter 2 Fractional Numbers

Student Activities

1. Write the following fractions in numeral

a. one-fifth = b. three-seventh =

c. seven-nineteenth = d. eleven-hundredths =


7

e. three-thirteen-hundredth = f. five-twelve-hundredths =

2. Write the following fraction in words

a. 312 = b.

1711 =

c. 1300

76 = d. 150

37 =

3. What fraction describes how much of each figure is shaded

a. b. c.

4. Reduce the following fraction to their simplest forms.

a. 7839 = b.

196148 = c.

16566 =

d. 45090 = e.

33878 = f.

288144 =

5. Insert an appropriate fraction between the following two fractions

a. 41 , ……,

43 b.

83 , ……,

125 c.

32 , ……,

53

d. 76 , ……,

87 e.

73 , ……,

65 f.

21 , ……,

43

6. Write sign greater ‘>’ or less than ‘<’ on the following space

a. 53

32

−− LL b. 73

85

LL c. 73

95

LL

d. 53

32

−− LL e. 54

1211

LL f. 52

1813

LL

g. 127

43

−− LL h. 115

92

LL i. 74

32

LL

7. Find the largest fraction of the following three fractions

a. 144,

219,

284 (………….) b.

32,

1513,

2016 (………….)

8

c. 62,

41,

126 (………….) d.

65,

3021,

1512 (………….)

e. 165,

2421,

129 (………….) f.

1810,

96,

154 (………….)

8. Arrange the following fraction in ascending order.

a. 65,

1614,

2422 ….. , …... , ….. b.

96,

54,

159 ….. , …... , …..

c. 65,

97,

128 ….. , …... , ….. d.

2110,

74,

63 ….. , …... , …..

e. 3226,

1414,

1211 ….. , …... , ….. f.

32,

65,

119 ….. , …... , …..

9. Arrange the following fractions in descending order.

a. 32,

65,

86,

127 ….,.....,….,….. b.

2015,

54,

109,

1211 ….,.....,….,….

c. 65,

32,

1816,

3633 ….,.....,….,….. d.

65,

43,

127,

96 ….,.....,….,…..

e. 65.

1815,

96,

127 ….,.....,….,….. f.

21,

2017,

1513,

54 ….,.....,….,…..

10. Express each of the following fractions as a mixed or whole number

a. 3

11 = ………. b. 5

16 = ………. c. 840 = ……….

d. 40263 = ………. e.

30128 = ………. f.

782 = ……….

g. 1054 = ………. h.

25430 = ………. i.

667 = ……….

j. 14325 = ………. k.

25435 = ……… l.

24476 = ……….

11. Express each of the following mixed numbers as improper fractions

a. 325 = ………. b.

744 = ………. c.

131112 = ………. d.

7319 = ……….


9

e. 17105 = ………. f.

1779 = ………. g.

1437 = ………. h.

2184 = ……….

i. 1147 = ………. j.

753 = ………. k.

21914 = ………. l.

1079 = ……….

12. Determine the values of the following statements

a. five twelfth of Rp.1.200.000 :

b. a third of an hour (in minute) :

c. three seventh of an area of a semicircle of radius 14 cm :

d. a fifth of a 10-gram apple

e. one-eighth of a three-dozen

13. Simplify the following expressions:

a. 535

633 −− = b. ⎟

⎠⎞

⎜⎝⎛−−

71

62 =

c. ⎟⎠⎞

⎜⎝⎛−+⎟

⎠⎞

⎜⎝⎛−−

41

521 = d.

326

432 − =

e. ⎟⎠⎞

⎜⎝⎛−−

351

612 = f. ⎟

⎠⎞

⎜⎝⎛−+−

531

954 =

g. ⎟⎠⎞

⎜⎝⎛−+⎟

⎠⎞

⎜⎝⎛−−−

1884

653

353 = h. ⎟

⎠⎞

⎜⎝⎛−−+⎟

⎠⎞

⎜⎝⎛−−

753

521

434 =

i. ⎟⎠⎞

⎜⎝⎛−−+−

75

924

643 = j. ⎟

⎠⎞

⎜⎝⎛−−⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−−+⎟

⎠⎞

⎜⎝⎛ +−

85

65

41

32

51 =

14. Evaluate the following multiplications, write your answer in the simplest form

a. 53

925

× = c. 524

81× = e.

512

310

× =

10

b. 85

2532

× = d. 3028

76× = f.

1881

2724

× =

15. Solve the following problems, write your answer in the simplest form

a. 542

324 × = b.

741

986 × = c.

327

873 × =

d. 216

324 × = e.

833

942 × = f.

525

327 × =

16. Evaluate the following problems, write your answer in the simplest form

a. 434

54

532 ×× = b.

715

433

539

977 ××× =

c. 953

743

522 ×× = d.

1522

723

833

612 ××× =

17. Evaluate the following, express your answer in the simplest form

a. 9

14:185 = b.

2512:

531 =

c. 28151:

32252 = d.

754:

1514 =

18. Evaluate the following, express your answer in the simplest form

a. 1523:

513 = b.

543:

632 =. c.

425:

432 =

d. 325:

319 = e.

734:

732 = f.

3542:

712 =

19. Simplify the following expression, write your answer in the simplest form

a. ⎟⎠⎞

⎜⎝⎛−×

2555 = b. ( ) ⎟

⎠⎞

⎜⎝⎛−÷−

5416 =


11

c. ( )515134 −× = d. ⎟

⎠⎞

⎜⎝⎛−×⎟

⎠⎞

⎜⎝⎛−

59

547 =

e. ⎟⎠⎞

⎜⎝⎛×⎟

⎠⎞

⎜⎝⎛−

2116

43 = f. ( )5

4116 −÷ =

g. ⎟⎠⎞

⎜⎝⎛−÷⎟

⎠⎞

⎜⎝⎛−

1235

1625 = h.

341

747 ÷⎟⎠⎞

⎜⎝⎛− =

i. ⎟⎠⎞

⎜⎝⎛−÷

187

129 = j. ( ) ( )12

12112 −÷⎟⎠⎞

⎜⎝⎛−×− =

k. ( )1265

542 −÷×⎟⎠⎞

⎜⎝⎛ = l. ⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−×⎟

⎠⎞

⎜⎝⎛×⎟

⎠⎞

⎜⎝⎛−

515

411

1542 =

20. Express the following fractions as decimals

a. 54 = b.

757 = c.

165 =

d. 125

3 = e. 100333 = f.

100025 =

g. 100131 = d.

524 = e.

100832 =

f. 200126 = g.

500355 = h.

100356 =

i. 2005 = j.

3000275 = k.

30003310 =

21. Express the following as fractions in their lowest terms:

a. 0.075 = b. 0.360 = c. 0.0125 = d. 0.0064 =

e. 10.205 = f. 0.1250 = g. 5.625 = h. 6.0625 =

12

22. Round off to the nearest whole number!

a. 44.75 = b. 0.089 = c. 4.934 =

d. 0.1568 = e. 0.2419 = f. 4.7569 =

g. 16.0069 = h. 319.87839 = i. 649.75689 =

23. Write down the following numbers in the standard form

a. 6000000 b. 2.37000000000000

c. 10.0000000130 d. 34.000045000

24. Write down the following standard forms into the general form

a. 1.0123 × 10-3 = b. 1.4500 × 10-6 =

c. 12.3030 × 10-9 = d. 4.03 × 10-6 =

e. 17.3040 × 10-6 = f. 2.3030 × 10-5 =


1. The following fractions are equal to 72

except

a. 144 c.

4914

b. 3510

d. 5418

2. The percent expression of 256

is

a. 0.24% c. 42% b. 2.4% d. 24%

3. 1514,1,

98

arranged in ascending order is

a. 98,

1514,1 c. 1,

1514,

98

b. 1,98,

1514

d. 1514,

98,1

4. Which of the following sets of fractions are arranged in ascending order?

a. 41,

31,

21

c. 41,

83,

85

b. 32,

52,

92

d. 81,

43,

21

5. 65,

1611,,

61 x are arranged in ascending

order. The value of x is

a. 71 c.

125

b. 72 d.

187

6. What is the result of 1 37 22 8

⎛ ⎞− − −⎜ ⎟⎝ ⎠

a. ‐518 c. ‐9

18

b. ‐578 d. ‐9

78


13


except

a. 144 c.

4914

b. 3510

d. 5418

1. The standard form of 12,564,000 with rounding off up to 2 decimal is… a.

c. b.

d.

2. The decimal form of is… a. 0.0637 b. 0.00637 c. 0.000637 d. 0.0000637

3. If +10 minutes means that Andi arrives at school 10 minutes before the bell rings, what does – 12 minutes mean? a. Andi goes

home 12 minutes before the bell rings b. Andi goes

home 12 minutes after the bell c. Andi is late

12 minutes before the morning bell d. Andi arrives

school 12 minutes before the bell

4. a. 15 c. 49 b. -15 d. -49

5. The decimal form of with rounding

off up to 2 decimal point is… a. 3.26 c. 3.27

b. 3.28 d. 3.29

6.

a. 1.4 c. 1.8 b. 1.6 d. 2.0

7. Two cubes have lengths of 4 cm and 6

cm, respectively. The ratio of the volume of both cubes is… a. 1 : 3 c. 8 : 9 b. 2 : 3 d. 8 :

27

1.

a. c.

b. d.

2.

a. c.

b. d.

Chapter 3 Algebraic Expression

14

Student Activities

1. Translate the following statement into an algebraic expression

a. The sum of a number and three is 200.

b. The difference of fifteen and a number is −3.

c. Three more than five times a number is twelve.

d. Thirty percent of a number is forty.

e. Three more than twice the reciprocal of a number is

f. Five times the difference of twice a number and six equals twenty.

g. Seventeen times x plus 13 times y.

h. Four times the square of x minus twice the cube of y.

i. Three quarter x cubed plus two y squared.

j. Five times a plus b multiplied by the square root of c.

k. Twice x2 minus 4 times the cube root of y.

l. The cost of x articles at two thousands Rupiah each.

m. The cost of y apples which are sold at 3 for five thousands.

n. The total distance moved by a body in x hours at a speed of k km per hour.

o. Nine times the product of x and 3h minus the quotient when k is divided by 2y.

p. The cube of the sum of x and y minus the square root of the sum of 5x and 3y.

2. Simplify each of the following

a. x − 4x−- 3x = b. 3x – 12 + (2x − 6) =

c. 2x − 3(x + 1) = d. 8x2 − 3x2 + l + 3x − 4 =

e. x2 + 5x 2– 2x − (2x2 + l) = f. 3(2x – 7) – 4x(2x - 4) =

g. (2x2 − 3x2 + x) − 2(x2 + 2x +11) = h. (x2 + 3x – 3x2) – 2x (x – 2) =

3. What must be added to 6x2– 4y2 to give 3y2– 2x2?

4. If p = −2, q = 2, r = −3, the value of the following expressions

a. prprqp 433 32 −+ =

b. ( )32 33 rqp +− =


15

c. ( )2322 qrp =

d. ( )332 rqp =

e. 2

2

2

23

⎟⎟⎠

⎞⎜⎜⎝

⎛r

qp =

f. 2222 43 rpqrpq −+ = g. 233 32 rqp −+ = h. prqbqp 243 342 −+ =

5. If 2543 2 =+− xyxy , find x when y = 2

6. If 622 2 +=+ ptqqp , find t when p = -2 and q = -3

7. If 1452 23 =+ yxx , find y when x = -1

8. If qrqp 453 =− , find p when q = -2 and r = -1

9. If qp

xyyx−

=−32 , find x when y = -2, p = 3 and q = 4

10. If y

qxx

qp2

33

2 +=

− , find y when x = 3, p = -2 and q = 3

11. If zy

xyx 1

332

=−+− , find x when y = 4 and z = 2

12. If 2

2323−+

=+z

zyx , find z when x = 2 and y = -4

13. If yx

zyzyx

22

3322

=+

−+ , find x when y = 4 and z = 1

14. If 43

4753

=−+

yxyx , find the value of

yx

16

15. Find the HCF of the following:

a. bcaabc 22 2 and 3

b. spqqrp 22 15 and 9

c. 222323 21 and 8 zyxzyx

d. 232 21 and 14 abcba

e. 3223 8 and 6 ,4 xyyxyx

f. 22433 15 and 21 ,3 yxxyyx

16. Find the LCM of the following:

a. 22232 21 and 8 zyxzxy

b. 323 24 and 16 xyyx

c. 5263 9 and 6 yxyx

d. 32323 8 and 12 ,4 xyyxyx

e. 23423 15 and 21 ,3 yxyxxy

f. cab bc a, cab 3232 6and104

17. Find the LCM and the GCF of the following expressions

a.

b. yzxzxy 222 12 and 8

c. 2223 3 and 9 ,6 accbba

d. zxyyzxzyx 22322 21 and 8 ,6

e. ybaxyaybxa 2242333 2 and 6 ,3

18. Find the sum of the following

a. xxxx 6- and 75 22 −+− =

b. xyxxyx 44 and 5 22 −+− =


17

c. yxyxyxyx 333- and 223 22 −++− =

d. 357 and 357 +−−+ qpqqpq =

e. 2222 68 and 412 qpqpqpqp −+−+− =

19. Subtract

a. 456 from 642 22 +−+− xxxx =

b. 23- from 724 22 −+−+ xxxx =

c. 2222 46 from 2 yxyxyxyx ++−+ =

d. xxyxxxyx −−−−− 2323 43 from 643 =

e. xyxxxyxx 86 from 8 2323 +−−+ =

f. ( ) ( )8453 from 7534 −+−+ yxyx =

g. ( ) ( )5674 from 8245 22 −++−− yyyy =

20. Carry out multiplication on the following problems

a. ( )baa 83 + = b. ( )abaa 524 − =

c. ( )qpp 472 2 +− = d. ( )qpp 365 2 −− =

e. ( )abbaa 7452 +− = f. ( )22 4563 babab −+− =

g. ( ) 232 6:824 ababa × = h. ( ) 32245 3:9 baacba × =

i. abc

caba

512

315

3

4

× = j. abab

ccab

a 1:54

815

3

3

× =

21. Evaluate the following problems

a. ( )22xy− = b. ( )322ab =

18

c. ( )224xyz− = d. ( )322xy− =

e. ( )322 yx−− = f. ( )4222 yx− =

g. ( )4323 yx−− = h. ( )332 qp −×− =

i. ( )454 pqp ×− = j. ( )[ ]32322 qppq −×− =


1. The simplified form of

is… a. b. c.

d.

2.

a.

b.

c.

d.

3.

a.

b.

c. d.

4. The simplified form of is…

a.

b.

c.

d.

5. The simplified form of

is… a. c.

b. d.

6.

a.

b.

c.

d.

7.

a. c.

b. d.


19

8.

a. c.

b. d.

9.

a.

b.

c.

d.

10.

a.

b.

c.

d.

11. Which of the followings is a pair of like

terms? a.

b. c. d.

12. What is the coefficient of respectively on terms:

, a. 2, -4, -13 b. -1, 2, -13 c. -13, -2, 1 d. -13, 2, -1

Chapter 4 Social Arithmetic

Student Activities

1. Find the profit or loss percent in the following cases:

(a) cost price = Rp.280.000, profit = Rp35.000;

% =profit % LLLLLLLLL

LLLLLL

LLLLLLLLLLLL

LLLLLLLLLLLL==

(b) selling price = Rp.210.000, profit = Rp.14.000;


LLLLLL

LLLLLLLLLLLL

LLLLLLLLLLLL==

(c) selling price = Rp.420.000, loss = Rp.140.000;

20

% = loss % LLLLLLLLL

LLLLLL

LLLLLLLLLLLL

LLLLLLLLLLLL==

(d) cost price = Rp.1.625.000, selling price =Rp.1.850.000


LLLLLL

LLLLLLLLLLLL

LLLLLLLLLLLL==

2. A second-hand bicycle is sold for Rp.635.000 at a profit of 27%. Find the profit.

3. By selling a book for Rp.16.500, a bookseller loses 12%. What is the cost price of the book?

4. Budi bought an antique chest for Rp.600.0000 and was forced to sell it for Rp.500.000. Find the percentage loss.

5. If Susan sells her car at a loss of 6%, what is her selling price when she paid Rp.180.400.000 for it?

6. To make a profit of Rp.500,000 a bicycle must be sold for Rp.2,400,000. What is the cost price of the bicycle?

7. The profit on a certain refrigerator is 30% of the cost price. If the profit is Rp.2.700.0000 find

(a) the cost price

(b) the selling price of the refrigerator,


21

8. The retail price of a television set is Rp.8,400,000 If this is 140% of the wholesale price, find the wholesale price.

9. A man buys a dozen cameras for Rp.18,000,000. He sells them at a profit of Rp.360,000 each. Find his profit percentage.

10. A florist bought 360 roses at Rp.10 000 per dozen. If he sold them at Rp.1100 each, what is his percentage profit?

11. Mr. Gunawan buys 200 identical articles at a total cost of Rp.1,500,000. He fixes the selling price of each article at 20% above the cost price and sells 160 articles at this price. As for the remaining articles, he sells them at 50% of the selling price. What is Mr. Gunawan’s total profit?

12. Tuti lent Asih Rp.4,800,000 for 7 months. At the end of this period Asih has to pay Tuti an interest of Rp.119,000. What is the rate of simple interest per annum?

22

13. Find (a) the discount, (b) the money paid, in the following cases. a. The list price of a watch is Rp.198,000 but if you buy now, the dealer will give a 15%-

discount to the purchaser.

i. The discount =

ii. The money paid =

b. A shoe which has a catalogue price of Rp.595,000 but is sold at a discount of 20% during a sale.

i. The discount =


c. A printer which has a marked price of Rp.1,400,000 but is sold at a discount of 8% to a customer who pays for it in cash.

i. The discount =


d. A small sofa-bed priced at Rp.500,000 but is sold at a discount of 16% to a customer who arranges for its delivery. i. The discount =



23

14. A sales promotion girl (SPG) will receive a commission of 20% of monthly sales amounting to Rp.7,800,000. Find the SPG’s monthly commission.

15. A door-to-door salesman is paid a basic salary of Rp.520,000 per month plus a commission of 25% of total sales made during the month. If he sells Rp.5,264,000 worth of goods in a particular month, find his total income for that month.

16. In a certain place, the sales tax is 6%. If Jimmy pays Rp.54,000 in sales tax for his refrigerator, what is its price?

17. In a certain city, the sales tax is 8%. Find the amount of tax that has to be paid on the purchase of a television set which costs Rp.950,000

18. In a certain town, the property tax is 3% of the assessed valuation of the property. What is the assessed value of a piece of property which pays Rp.7,200,000 in taxes a year?


1. A retailer purchased a car from a

manufacturer and received a 30% trade discount. The original price was

Rp.124,000,000 What price did the retailer pay? a. Rp.37,200,000 b. Rp.61,200,000

24

c. Rp.86,800,000 d. Rp.124,000,000

2. A sales promotion girl (SPG) will

receive a commission of 20% of monthly sales amounting to Rp.7 800 000. Find the SPG’s monthly commission. a. Rp.1,560,000,000 b. Rp.6,240,000,000 c. Rp.7,800,000,000 d. Rp.9,360,000,000

3. Budi saved his money of Rp.2,500,000

on a bank. He was given a simple interest rate of 6% per annum. How long will it take for the amount to add up to Rp.3,400,000? a. 12 years c. 6 years b. 4 years d. 8 years

4. A manager of a shop borrowed

Rp.6,600,000 from a bank at 8% simple interest per annum. Find the debt he had to pay to the bank at the end of 11 months? a. Rp.7,084,000 b. Rp.7,128,000 c. Rp.6,072,000 d. Rp.7,128,000

5. The sum of three consecutive odd

numbers is 243. Find the three numbers. a. 77,79,81 c. 79, 81, 83 b. 81,83,85 d. 77, 81, 85

6. Santhi earns Rp.2 800 000 a month. She

spends 15% of her monthly income on food, 5% on rent, 8% on clothes. 35% on others and saves the rest. How much does she save a month? a. Rp.1 036 000 c. Rp.920 000 b. Rp.960 000 d. Rp.880 000

7. In a school, 54% of the students are girls.

The number of girls in the school is 567. Calculate the number of boys in the school. a. 448 c. 476 b. 465 d. 483

Chapter 5 Linear Equations and Linear Inequality with One Variable

Student Activities

1. Solve the following problems

a. yy =+ 52 b. 42 −= mm


25

c. 1045 −= pp d. 5879 +=+ tt

e. 7273 +=− zz f. 5223 +=− xx

g. 3

33

29

12 −

=+

+−−

nnn h. aa

−=− 108

75

i. 02

512

3=

−−

+ xx j. 2

534

32

−=−

+− bb

k. ( )431

526

552 xx −

=−+ l. ( )

431

526

552 xx −

=−+

m. ( ) ( ) 041249 =++− xx n. ( ) ( ) 045234 =−−−+ xxx

o. ( ) ( ) 312323 −=+−− yyy p. ( ) ( ) 616104254 =−−++ yyy

q. ( ) ( )10326235 −=−− yyy r. ( ) ( )yy −=++ 46143

s. ( ) ( ) 9463223 +−=−− yyy

2. Solve the following equations

26

a. ( ) ( )135351

−=+−− xxx b.. ( ) 04

33

12=+

− xx

c. ( ) ( )4152

326

51

=−−+ xx d. 43

727

16=

−−

+ xx

e. ( ) ( ) 0143123

2114 =−−−−+ xxx f.

123

61

92 +

=−

−xxx

g. 23

25

3=

−−

xx h. 5

124

3314 +

=−

−− xxx

i. 24

728

326

43 −=

+−

− xxx j. ( ) ( )4

3229212

21 −

=−−−xxx

k. ( )3441

413

31

212

21

−+⎟⎠⎞

⎜⎝⎛ −=⎟

⎠⎞

⎜⎝⎛ − xxx l. ( ) ( )43

1512

513

512 +=+−⎟

⎠⎞

⎜⎝⎛ − xxx

3. Solve the following equation. Give your answers correct to 2 decimal places where necessary.

a. ( ) 3.1235.215.0 =−+ xx b. 6.010

124

++

=xx


27

c. 5.15

37

25++

−=

+ xxx d. 61

41

31

4125.0 −+

−+=+ xxx

e. 6

345.012725.25.0 −

++=−xxx f. ( ) ( )1

31

313

2150 +=⎟

⎠⎞

⎜⎝⎛ −++ xx.x


a. A number exceeds another by 4 and their sum is 32. Find the two numbers.

b. When a number is doubled and 5 is subtracted from the result, the answer is 37. What is the number?

c. The sum of two numbers is 120. If the larger number is four times the smaller number, what are the two numbers?

d. The sum of three consecutive numbers is 93. Find the smallest of these numbers.

e. The sum of three consecutive even numbers is 210. Find the largest of these numbers.

f. The sum of three consecutive odd numbers is 243. Find the three numbers.

g. The sum of four consecutive numbers is 210. Find the four numbers.

h. The sum of five consecutive even numbers is 220. Find the smallest of these numbers.

28

i. Find two consecutive odd numbers such that when the smaller number is subtracted from three times the bigger number, the result is 56.

j. When 42 is added to twice a number, the result is 346. Find the number.

k. When a number is divided by 4 and has 12 subtracted from it, the result is 61 of the number.

What is the Number?

l. The larger of two integers is seven more than the smaller integer. Their sum is 49. Find the integers.

m. The larger of two integers is one more than twice the smaller integer. Their sum is 43. Find the integers.

n. The larger of two integers is two more than three tunes the smaller integer. Their sum is 70. Find the integers.

o. The larger of two integers is one less than four times the smaller integer. Their sum is 74. Find the integers.

p. When a number is multiplied by 5, it gives the same result as when 48 is added to twice the number. Find the number.

q. Ahmad is twice as old as Bobby. John is 7 years younger than Ahmad. If the sum of their ages is 38, how old are the three boys?


29

r. Janet is three times as old as her daughter, Mary. Five years ago, Janet was 4 times as old as Mary. How old is Janet now? How old will Mary be in 7 years’ time?

s. A man was 26 years old when his son was born. Now, he is three times as old as his son. How old is the son now?

t. A father is four times as old as his son. The difference in their ages is 36. Find the sum of their ages in 5 years’ time.

u. Ben is three times as old as Carl now. In two years’ time, Ben will be twice as old as Carl. How old is Carl now?

v. Ali is 8 years older than Fatimah. Six years ago, Ali was 5 times as old as Fatimah. How old is Fatimah? How old will Au be in 8 years’ time?

w. Budi is 50 years old. His son, Hendra is 24 years old. How many years ago was Budi three times as old as Hendra?

x. The sum of the ages of two brothers is 24. In three years’ time, the elder brother will be twice as old as the younger brother. How old are the brothers?

30

y. Adam is 5 times as old as Charles. In 8 years’ time, the sum of their ages will be equal to twice Adam’s present age. Find their present ages.

z. Tom is twice as old as Harry. In 9 years’ time, their combined ages will be five times Harry’s present age. How old is Tom now? How old will Harry be in 9 years’ time?

aa. A, B and C shared Rp.1540,000. A received three times as much money as B and C’s share is half that of A’s. How much money did C receive?

bb. A librarian bought 50 books for a library. Each hard cover book is 211 times as expensive

as each paperback which costs Rp.40,000 each. How many hard cover books did the librarian buy if he spent a total of Rp.2,560,000 on the books?

5. Solve the following problems and draw the solution in a number line.

a. mm 45 <+ b. 2462 −<+ mm c. mm 2575 −>−−

d. xx +−<+ 113 e. 2613 −≤+ xx f. xx 274 >−


31

g. 425 <− x h. 42732 +≤−p i. 11745 −>− pp

.


a. 10531

>−x g. 721

41

≤+y

b. 251

43

>− yy h. 1072−≤

pp

c. 6

132

ppp −>− i. ( )

41554

21

+<− qq

d. ( ) ( ) 01213

43

>−++ xx j. ( ) ( )411

314

21

≤+−− nn

32

e. ( )21

43

324

43

<⎟⎠⎞

⎜⎝⎛ −−+ nn k.

436

212

324 +

≤+

−+ xxx

f. 0531

421

31

<−

+−

−− xxx l. xx

283

411

752 +≥+


1. Which of the following expressions is a linear equation with one variable a. b. 7p + 3 = 14 c. 4k – 3 = 17 – 2m d. 6 – 3u = 18

2. The solution of ( ) ( ) 222132

43

≤−−+ xx

is

c. 45

−≤x c. 51

≥x

d. 1≤x d. 1≥x

3. The solution of ( ) ( ) 11311

21

≥+−− nn is

a. 1−≥n c. 1≤n b. 5−≥n d. 5≤n

4. The solution set of

where is a. b. c. d.

5. The solution of 24

128

326

43 +≥

+−

− xxx

is a. 6≥x c. 6−≥x b. 4−≤x d. 4≤x

6. Which of the following values of x satisfying the inequality

xx143

211

755.0 +≥+

a. 4

11−≥x c.

411

≥x

b. 23

−≤x d. 114

≤x

7. For what value of x does the following inequality is correct

( ) ( )6

3229212

21 −

≤−−−xxx

a. 5.8−≥x c. 5.6−≥x b. 5.8−≤x d. 5.4≤x


33

Chapter 6 Ratio and Proportion

Student Activities

1. A map is drawn to a scale of 1: 50 000. a) What is the actual distance represented by

(i) 2 cm, (ii) 7.5 cm, (iii) 0.6 cm,

b) What length on the map represents the actual distance of (i) 4km, (ii) 15 km. (iii) 250 m,

2. A map is drawn to a scale of 1 cm : 2 km. a) What is the actual distance represented by

(i) 3 cm, (ii) 4.5 cm, (iii) 1 m,

b) What length represents the actual distance of (i) 5 km. (ii) 500 m. (iii) 9 km.

3. The distance between Amlapura and Gilimanuk is 225 km. On a map with a scale of 1 cm : 50 km. how far apart would the towns be?

4. The scale of a map is 1 : 20,000. Find the distance in km of a road represented by 5.5 cm on the map.

34

5. Given that 1 cm on a map represents 2 km on the ground, calculate the area of a park on the map if the actual area of the park is 10 km2.

6. The scale of a map is 1 cm: 8 km. What area on the map would represent (a) 64 km2. (b) 128 km2,

(c) 320 km2, (d) 1 600 km2

7. On a scale of 1 cm : 2 km, the plan of the field measures 5 cm by 3.5 cm on the map. Find the actual area of the field.

8. In the given figure below, ABC is a triangle of height 4 cm and base 7 cm, drawn to a scale of 1 cm : 3 km. Find the actual area of the triangle.

A B

C

7 cm

4 cm

9. The figure below is a rectangle, drawn to a scale of 1 cm: 200 m. Given that AB = 6 cm and BC = 4 cm, find the actual a) length and breadth of the rectangle;

b) area of the rectangle in km2.

A B

D C

6 cm

4 cm

10. The scale of a map is 1 : 20 000. Find the area on the map which represents 124 km2.


35

11. A map is drawn to a scale of 1: 50 000. a) Calculate the actual distance, in kilometers, represented by 4 cm on the map.

b) Two towns are 28 km apart. Calculate, in centimeters, their distance apart on the map.

c) On the map, a forest has an area of 12 cm2. Calculate, in square kilometers, the actual area

of the forest.

12. A school librarian has enough money to order 8 paperback books at Rp.55,000 each. If the librarian decides instead to order books with hard covers at Rp.88,000 each, how many books can the librarian buy?

13. Thirty-five workers build a house in 16 days. How many days will 28 workers working at the same rate take to build the same house’?

14. A contractor estimates that he would need 56 workers to complete a job in 21 days. If he is asked to complete the job in 14 days, find the additional number of workers he has to employ.


1. The scale of a map is 1: 20 000. What is the distance in km of a road represented by 51 cm on the map? a. 1020000 c. 102000 b. 1020 d. 102

2. In the given figure below, ABC is a triangle of height 4 cm and base 7 cm,

drawn to a scale of 1 cm : 3 km. Find the actual area of the triangle.

36

A B

C

7 cm

4 cm

a. 94 km2 c.126 km2 b. 63 km2 d. 21 km2

3. Thirty-five workers build a house in 16 days. How many days will 28 workers working at the same rate take to build the same house’? a. 10 workers c. 7 worker b. 20 workers d. 25 workers

4. A contractor estimates that he would need 56 workers to complete a job in 21 days. If he is asked to complete the job in 14 days, find the additional number of workers he has to employ. a. 84 workers c. 28 workers b. 14 workers d. 7 workers

5. 800 cookies are divided among Sita, Joni

and Komang in the ratio 3 : 8 : 9. Which of the following statements below is not true? a. Joni received 320 cookies. b. Joni received 200 more cookies than

Sita. c. Joni received 40 fewer cookies than

Komang d. Joni received 150 fewer cookies than

what Komang and Sita received.

6. The number of stamps owned by Sumer, Nisan and Jalal is in the ratio 5 : 6 : 7. The total number of stamps is 540. Nisan gives 50 of his stamps to Sumer and 40 stamps to Jalal. The new ratio of Sumer’s, Nisan’s and Jack’s stamps is a. 30 : 16 : 23 b. 9 : 2 : 7 c. 20 : 9 : 25 d. 15 : 11 : 20

7. The value of donations collected by Marni, Joyce and Siti for a ‘Panti

Asuhan’ is in the ratio 5 : 7 : 8. The difference in donations between Marni and Joyce is Rp.64 000. Calculate how much Siti collected. a. Rp.640 000 c. Rp.256 000 b. Rp.268 000 d. Rp.224 000.

End of semester Test

1. There are 268 pens in a box. 64 of them are red pens, 49 are blue pens and the rest are black pens. How many black pens are there in the box? a. 76 c. 84 b. 110 d. 155

2. The total mass of Agung, Candra,

and Suwi is 156 kg. Candra weighs 48 kg. If Suwi 4 kg lighter than Candra, find Agung’s mass in kg a. 58 c. 64 b. 65 d. 67

3. If ,3−=x 4=y , and 2z and −= then the value of yzx 23 − is … a. −43 c. −11 b. −25 d. 7

4. If x =−2 and y = −1, the value of

xyx +− 32 is a. −14 c. 18 b. −18 d. 20


except

a. 144 c.

4914

b. 3510 d.

5418

6. The percent expression of 256 is

a. 0.24% c. 42% b. 2.4% d. 24%


37

7. 1514,1,

98 arranged in ascending order is

a. 98,

1514,1 c. 1,

1514,

98

b. 1,98,

1514 d.

1514,

98,1

8. Which of the following sets of fractions are arranged in ascending order?

a. 41,

31,

21 c.

41,

83,

85

b. 32,

52,

92 d.

81,

43,

21

9. 65,

1611,,

61 x are arranged in ascending

order. The value of x is

a. 71 c.

125

b. 72 d.

187

10. 1 892 437 when written in words is a. One million eight hundred and

ninety-two four hundred and thirty-seven

b. One million thousand eight hundred and ninety-two four hundred and thirty-seven

c. One million eight thousand ninety-two four hundred and thirty-seven

d. One million eight hundred and ninety-two thousand four hundred and thirty-seven

11. The least common factors of 2310 rqp and 4218 rqp is…

a. 290 pqr c. 2180 pqr b. 43290 rqp d. 432190 rqp

12. The least common multiple (LCM) of yxyx 223 8 and 12 is

a. 2312 yx c. 2324 yx

b. 2248 yx d. 2224 yx

13. What is the result of 1 37 22 8

⎛ ⎞− − −⎜ ⎟⎝ ⎠

a. -5 18

c. -9 18

b. -5 78

d. -9 78

14. The standard form of 0.02756 with a rounding off up to one decimal is... a. 2.7 × 10-3 c. 2.7 × 10-2 b. 2.8 × 10-2 d. 2.8 × 10-3

15. The lowest common multiple of 6, 8 and 16 is a. 16 c. 24 b. 32 d. 48

16. Which of the following is the highest common factor of 36 and 60 a. 12 c. 14 b. 18 d. 20

17. Subtract 432 from 647 22 +++− xxxx a. 25 2 −−− xx b. 25 2 −−− xx c. 25 2 +− xx d. 275 2 −+− xx

18. A school bought 25 packs of books with a price of Rp.375.000 (1 pack contains 40 books). If the school sells those books and expects a profit of 20%, then the selling price of the book is…. a. Rp.300 c. Rp.400 b. Rp.450 d. Rp.475

19. The cost of a dozen shirts is Rp.96.000. If

the shirt is sold at Rp.10.000 for one shirt, the percent of the profit is… a. 20% c. 25% b. 35% d. 40%

20. A sporting store purchases 50 tennis

racquets for Rp.5,500,000. They sell each

38

racquet for Rp.175,000 What is the percentage of total profit? a. 59% c. 30% b. 40% d. 29%

21. An egg seller sold 150 eggs for Rp.700

per egg. Since some of the eggs are broken, he got lost Rp.7.500. What is the buying price? a. Rp.97 500 c. Rp.112 500 b. Rp.105 000 d. Rp.115 500

22. Rudy gets a bonus 10% of his salary once

every three months. If his salary per month is Rp.200.000. What is the total bonus he gets for 2 years? a. Rp.40 000 c. Rp.120 000 b. Rp.160 000 d. Rp.480 000

23. What is the % discount given when

Rp.637,500 is paid for products costing Rp.750.000? a. 15% c. 20% b. 25% d. 30%

24. A retailer purchased a car from a

manufacturer and received a 30% trade discount. The original (list) price was Rp.124.000.000. What price did the retailer pay? a. Rp.37,200,000 c. 161,200,000 b. Rp.86,800,000 d. 124,000,000

25. How much has a customer to pay for an

article costing Rp.240.000 with a 3% Value Added Tax (VAT) imposed on it? a. Rp.247 200 c. Rp.232 800 b. Rp.243 000 d. Rp.237 000

26. The sum of three consecutive odd

numbers is 243. Find the three numbers. a. 77,79,81 c. 79, 81, 83 b. 81,83,85 d. 79, 83, 85

27. When a number is multiplied by 5, it gives the same result as when 48 is added to twice the number. What is the number a. 12 c. 16 b. 18 d. 14

28. Which of the following graphs represents the set { }Rxxx ∈≤≤− ,34 ?

3-4

-4 3

-4 3

3-4

a.

b.

c.

d.

29. The solution of ( ) ( ) 02213

43

≤−++ xx is

a. 2≥x c. 51

≥x

b. 1≤x d. 1>x

30. The solution of ( ) ( )211

314

21

≥+−− nn is

a. 56

−≥n c. 56

≤n

b. 65

−≥n d. 65

≤n

Reference: 1. Sudjatmiko, Pontjo. Mathematika Kreatif. Konsep dan Terapannya,1A. PT. Tiga Serangkai

Pustaka Mandiri.

2. Cholik, M. and Sugiono. Matematika untuk SMP Kelas VII. 1A. Penerbit Erlangga


39

3. Song T.K and L.C. Keong. New Syllabus Mathematics 1. Shinglee Publisher. Singapore

4. Mc. Seveny, A. et al. Signpost Mathematics 9, Advance Course. Longman

5. Tim Studi Grup SMP. Soal-soal Uji Kompetensi Matematika SMP. Penerbit Pustaka Setia

Bandung

Documents

Student WorkBook Math Grade-7