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1. 1. 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 7o C, then it falls by 5o C, what is the final temperature of the room? (f) The temperature of Singaraja city is 32o C, while Bangli is 24o C. 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. 2. 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. 3. Mathematics for Grade VII Semester 1 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. 4. 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 – 2o C and it is forecasted that the temperature will drop by 3o C tomorrow morning. What will the temperature be tomorrow in Sydney? a. 5o C c. –5o C b. 1o C d. –1o C 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. 5. Mathematics for Grade VII Semester 1 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 -5o C is… a. 5o C below the freezing point of water b. 5o C above the freezing point of water c. -5o C below the freezing point of water d. -5o C 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. 6. 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. 7. Mathematics for Grade VII Semester 1 7 e. three-thirteen-hundredth = f. five-twelve-hundredths = 2. Write the following fraction in words a. 31 2 = b. 17 11 = c. 1300 7 6 = d. 150 3 7 = 3. What fraction describes how much of each figure is shaded a. b. c. 4. Reduce the following fraction to their simplest forms. a. 78 39 = b. 196 148 = c. 165 66 = d. 450 90 = e. 338 78 = f. 288 144 = 5. Insert an appropriate fraction between the following two fractions a. 4 1 , ……, 4 3 b. 8 3 , ……, 12 5 c. 3 2 , ……, 5 3 d. 7 6 , ……, 8 7 e. 7 3 , ……, 6 5 f. 2 1 , ……, 4 3 6. Write sign greater ‘>’ or less than ‘<’ on the following space a. 5 3 3 2 −− LL b. 7 3 8 5 LL c. 7 3 9 5 LL d. 5 3 3 2 −− LL e. 5 4 12 11 LL f. 5 2 18 13 LL g. 12 7 4 3 −− LL h. 11 5 9 2 LL i. 7 4 3 2 LL 7. Find the largest fraction of the following three fractions a. 14 4 , 21 9 , 28 4 (………….) b. 3 2 , 15 13 , 20 16 (………….)
8. 8. 8 c. 6 2 , 4 1 , 12 6 (………….) d. 6 5 , 30 21 , 15 12 (………….) e. 16 5 , 24 21 , 12 9 (………….) f. 18 10 , 9 6 , 15 4 (………….) 8. Arrange the following fraction in ascending order. a. 6 5 , 16 14 , 24 22 ….. , …... , ….. b. 9 6 , 5 4 , 15 9 ….. , …... , ….. c. 6 5 , 9 7 , 12 8 ….. , …... , ….. d. 21 10 , 7 4 , 6 3 ….. , …... , ….. e. 32 26 , 14 14 , 12 11 ….. , …... , ….. f. 3 2 , 6 5 , 11 9 ….. , …... , ….. 9. Arrange the following fractions in descending order. a. 3 2 , 6 5 , 8 6 , 12 7 ….,.....,….,….. b. 20 15 , 5 4 , 10 9 , 12 11 ….,.....,….,…. c. 6 5 , 3 2 , 18 16 , 36 33 ….,.....,….,….. d. 6 5 , 4 3 , 12 7 , 9 6 ….,.....,….,….. e. 6 5 . 18 15 , 9 6 , 12 7 ….,.....,….,….. f. 2 1 , 20 17 , 15 13 , 5 4 ….,.....,….,….. 10. Express each of the following fractions as a mixed or whole number a. 3 11 = ………. b. 5 16 = ………. c. 8 40 = ………. d. 40 263 = ………. e. 30 128 = ………. f. 7 82 = ………. g. 10 54 = ………. h. 25 430 = ………. i. 6 67 = ………. j. 14 325 = ………. k. 25 435 = ……… l. 24 476 = ………. 11. Express each of the following mixed numbers as improper fractions a. 3 2 5 = ………. b. 7 4 4 = ………. c. 13 11 12 = ………. d. 7 3 19 = ……….
9. 9. Mathematics for Grade VII Semester 1 9 e. 17 10 5 = ………. f. 17 7 9 = ………. g. 14 3 7 = ………. h. 21 8 4 = ………. i. 11 4 7 = ………. j. 7 5 3 = ………. k. 21 9 14 = ………. l. 10 7 9 = ………. 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. 5 3 5 6 3 3 −− = b. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −− 7 1 6 2 = c. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −+⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −− 4 1 5 2 1 = d. 3 2 6 4 3 2 − = e. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −− 3 5 1 6 1 2 = f. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −+− 5 3 1 9 5 4 = g. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −+⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −−− 18 8 4 6 5 3 3 5 3 = h. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −−+⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −− 7 5 3 5 2 1 4 3 4 = i. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −−+− 7 5 9 2 4 6 4 3 = j. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −−⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −−+⎟ ⎠ ⎞ ⎜ ⎝ ⎛ +− 8 5 6 5 4 1 3 2 5 1 = 14. Evaluate the following multiplications, write your answer in the simplest form a. 5 3 9 25 × = c. 5 24 8 1 × = e. 5 12 3 10 × =
10. 10. 10 b. 8 5 25 32 × = d. 30 28 7 6 × = f. 18 81 27 24 × = 15. Solve the following problems, write your answer in the simplest form a. 5 4 2 3 2 4 × = b. 7 4 1 9 8 6 × = c. 3 2 7 8 7 3 × = d. 2 1 6 3 2 4 × = e. 8 3 3 9 4 2 × = f. 5 2 5 3 2 7 × = 16. Evaluate the following problems, write your answer in the simplest form a. 4 3 4 5 4 5 3 2 ×× = b. 7 1 5 4 3 3 5 3 9 9 7 7 ××× = c. 9 5 3 7 4 3 5 2 2 ×× = d. 15 2 2 7 2 3 8 3 3 6 1 2 ××× = 17. Evaluate the following, express your answer in the simplest form a. 9 14 : 18 5 = b. 25 1 2: 5 3 1 = c. 28 15 1: 32 25 2 = d. 75 4 : 15 1 4 = 18. Evaluate the following, express your answer in the simplest form a. 15 2 3: 5 1 3 = b. 5 4 3: 6 3 2 =. c. 4 2 5: 4 3 2 = d. 3 2 5: 3 1 9 = e. 7 34 : 7 3 2 = f. 35 4 2: 7 1 2 = 19. Simplify the following expression, write your answer in the simplest form a. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −× 25 5 5 = b. ( ) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −÷− 5 4 16 =
11. 11. Mathematics for Grade VII Semester 1 11 c. ( )5 15 13 4 −× = d. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −×⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − 5 9 54 7 = e. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ×⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − 21 16 4 3 = f. ( )5 4 1 16 −÷ = g. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −÷⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − 12 35 16 25 = h. 3 4 1 7 4 7 ÷⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = i. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −÷ 18 7 12 9 = j. ( ) ( )12 12 1 12 −÷⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −×− = k. ( )12 6 5 5 4 2 −÷×⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = l. ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −×⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ×⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − 5 15 4 1 1 15 4 2 = 20. Express the following fractions as decimals a. 5 4 = b. 75 7 = c. 16 5 = d. 125 3 = e. 100 33 3 = f. 1000 25 = g. 100 131 = d. 5 24 = e. 100 83 2 = f. 200 12 6 = g. 500 35 5 = h. 100 3 56 = i. 200 5 = j. 3000 27 5 = k. 3000 33 10 = 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. 12. 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 = Multiple Choice Questions 1. The following fractions are equal to  7 2   except   a. 14 4       c.   49 14     b. 35 10       d.   54 18     2. The percent expression of  25 6  is   a. 0.24%      c.  42%    b. 2.4%      d.  24%    3. 15 14 ,1, 9 8  arranged in ascending order is   a. 9 8 , 15 14 ,1   c.  1, 15 14 , 9 8   b. 1, 9 8 , 15 14   d.  15 14 , 9 8 ,1     4. Which of the following sets of fractions are  arranged in ascending order?  a. 4 1 , 3 1 , 2 1   c.  4 1 , 8 3 , 8 5   b. 3 2 , 5 2 , 9 2   d.  8 1 , 4 3 , 2 1     5. 6 5 , 16 11 ,, 6 1 x  are arranged in ascending  order. The value of x is   a. 7 1       c.  12 5   b. 7 2       d.  18 7   6. What is the result of  1 3 7 2 2 8 ⎛ ⎞ − − −⎜ ⎟ ⎝ ⎠   a. ‐5 1 8        c. ‐9 1 8     b.  ‐5 7 8        d. ‐9 7 8
13. 13. Mathematics for Grade VII Semester 1 13 7. The following fractions are equal to  7 2   except   a. 14 4       c.   49 14     b. 35 10       d.   54 18     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. 14. 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. 15. Mathematics for Grade VII Semester 1 15 c. ( )232 2 qrp = d. ( )332 rqp = e. 2 2 2 2 3 ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ 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 xy yx − =− 3 2 , find x when y = -2, p = 3 and q = 4 10. If y qx x qp 2 3 3 2 + = − , find y when x = 3, p = -2 and q = 3 11. If zy x y x 1 3 32 =− + − , find x when y = 4 and z = 2 12. If 2 23 23 − + =+ z z yx , find z when x = 2 and y = -4 13. If y x zy zyx 2 2 3 322 = + −+ , find x when y = 4 and z = 1 14. If 4 3 47 53 = − + yx yx , find the value of y x
16. 16. 16 15. Find the HCF of the following: a. bcaabc 22 2and3 b. spqqrp 22 15and9 c. 222323 21and8 zyxzyx d. 232 21and14 abcba e. 3223 8and6,4 xyyxyx f. 22433 15and21,3 yxxyyx 16. Find the LCM of the following: a. 22232 21and8 zyxzxy b. 323 24and16 xyyx c. 5263 9and6 yxyx d. 32323 8and12,4 xyyxyx e. 23423 15and21,3 yxyxxy f. cabbca,cab 3232 6and104 17. Find the LCM and the GCF of the following expressions a. b. yzxzxy 222 12and8 c. 2223 3and9,6 accbba d. zxyyzxzyx 22322 21and8,6 e. ybaxyaybxa 2242333 2and6,3 18. Find the sum of the following a. xxxx 6-and75 22 −+−    =   b. xyxxyx 44and5 22 −+−   =
17. 17. Mathematics for Grade VII Semester 1 17 c. yxyxyxyx 333-and223 22 −++−   =   d. 357and357 +−−+ qpqqpq =   e. 2222 68and412 qpqpqpqp −+−+− =     19. Subtract a. 456from642 22 +−+− xxxx =     b. 23-from724 22 −+−+ xxxx =     c. 2222 46from2 yxyxyxyx ++−+ =     d. xxyxxxyx −−−−− 2323 43from643 =     e. xyxxxyxx 86from8 2323 +−−+   =     f. ( ) ( )8453from7534 −+−+ yxyx   =     g. ( ) ( )5674from8245 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. ab c cab a 5 12 3 15 3 4 × = j. abab c cab a 1 : 5 4 8 15 3 3 × = 21. Evaluate the following problems a. ( )2 2xy− = b. ( )32 2ab =
18. 18. 18 c. ( )22 4xyz− = d. ( )32 2xy− = e. ( )32 2 yx−− = f. ( )422 2 yx− = g. ( )432 3 yx−− = h. ( )3 32 qp −×− = i. ( )4 54 pqp ×− = j. ( )[ ]3232 2 qppq −×− =   Multiple Choice Questions 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. 19. Mathematics for Grade VII Semester 1 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% LLL LLLLLL LLLLLL LLLLLLLLLLLL LLLLLLLLLLLL == (b) selling price = Rp.210.000, profit = Rp.14.000; %=profit% LLL LLLLLL LLLLLL LLLLLLLLLLLL LLLLLLLLLLLL == (c) selling price = Rp.420.000, loss = Rp.140.000;
20. 20. 20 %=loss% LLL LLLLLL LLLLLL LLLLLLLLLLLL LLLLLLLLLLLL == (d) cost price = Rp.1.625.000, selling price =Rp.1.850.000 %=profit% LLL LLLLLL 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. 21. Mathematics for Grade VII Semester 1 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. 22. 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 = ii. The money paid = 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 = ii. The money paid = 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 = ii. The money paid =
23. 23. Mathematics for Grade VII Semester 1 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? Multiple Choice Questions   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. 24. 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. 25. Mathematics for Grade VII Semester 1 25 c. 1045 −= pp d. 5879 +=+ tt e. 7273 +=− zz f. 5223 +=− xx g. 3 3 3 2 9 1 2 − = + + − − nnn h. a a −=− 10 8 7 5 i. 0 2 5 12 3 = − − + xx j. 2 5 34 3 2 −= − + − bb k. ( ) 4 31 5 26 5 52 xx − =− + l. ( ) 4 31 5 26 5 52 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. 26. 26 a. ( ) ( )1353 5 1 −=+−− xxx b.. ( ) 0 4 3 3 12 =+ − xx c. ( ) ( ) 4 1 52 3 2 6 5 1 =−−+ xx d. 4 3 72 7 16 = − − + xx e. ( ) ( ) 014 3 1 23 2 1 14 =−−−−+ xxx f. 12 3 6 1 9 2 + = − − xxx g. 2 3 2 5 3 = − − xx h. 5 12 4 3 3 14 + = − − − xxx i. 24 72 8 32 6 43 − = + − − xxx j. ( ) ( ) 4 32 2 9 2 12 2 1 − =−−− x xx k. ( )34 4 1 4 1 3 3 1 2 1 2 2 1 −+⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −=⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − xxx l. ( ) ( )43 15 1 2 5 1 3 5 1 2 +=+−⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − xxx 3. Solve the following equation. Give your answers correct to 2 decimal places where necessary. a. ( ) 3.1235.215.0 =−+ xx b. 6.0 10 12 4 + + = xx
27. 27. Mathematics for Grade VII Semester 1 27 c. 5.1 5 3 7 25 ++ − = + x xx d. 6 1 4 1 3 1 4 1 25.0 −+ − +=+ x x x e. 6 34 5.0 12 7 25.25.0 − ++=− xx x f. ( ) ( )1 3 1 3 1 3 2 1 50 +=⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −++ xx.x 4. Solve the following problems 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. 28. 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 6 1 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. 29. Mathematics for Grade VII Semester 1 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. 30. 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 2 1 1 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. 31. Mathematics for Grade VII Semester 1 31 g. 425 <− x h. 42732 +≤−p i. 11745 −>− pp . 6. Solve the following problems a. 105 3 1 >−x g. 7 2 1 4 1 ≤+y b. 2 5 1 4 3 >− yy h. 10 72 −≤ pp c. 6 1 32 ppp − >− i. ( ) 4 1 554 2 1 +<− qq d. ( ) ( ) 01 2 1 3 4 3 >−++ xx j. ( ) ( ) 4 1 1 3 1 4 2 1 ≤+−− nn
32. 32. 32 e. ( ) 2 1 4 3 3 2 4 4 3 <⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −−+ nn k. 4 36 2 12 3 24 + ≤ + − + xxx f. 0 5 31 4 21 3 1 < − + − − − xxx l. xx 28 3 4 1 1 7 5 2 +≥+ Multiple Choice Questions   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 ( ) ( ) 22 2 1 32 4 3 ≤−−+ xx is c. 4 5 −≤x c. 5 1 ≥x d. 1≤x d. 1≥x 3. The solution of ( ) ( ) 11 3 1 1 2 1 ≥+−− 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 12 8 32 6 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 xx 14 3 2 1 1 7 5 5.0 +≥+ a. 4 11 −≥x c. 4 11 ≥x b. 2 3 −≤x d. 11 4 ≤x 7. For what value of x does the following inequality is correct ( ) ( ) 6 32 2 9 2 12 2 1 − ≤−−− x xx a. 5.8−≥x c. 5.6−≥x b. 5.8−≤x d. 5.4≤x
33. 33. Mathematics for Grade VII Semester 1 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. 34. 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. 35. Mathematics for Grade VII Semester 1 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. Multiple Choice Questions 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.