1 a b Circumference Radius Diameter WORKbook Consulting author Dr Ngo Hea Choon Singapore Maths Method Latest Indonesian Syllabus 21st Century Learning Skills ©Praxis Publishing Singapore Pte. Ltd.
IV Chapter 1 Equations and algebra..................... 1 Exercises.........................................3 Mastery Practice............................ 15 Chapter 2 Integers..........................................17 Exercises.......................................18 Mastery Practice............................ 29 Chapter 3 Combined operations .................... 31 Exercises.......................................31 Mastery Practice............................ 41 Chapter 4 Four operations with fractions ....... 44 Exercises.......................................47 Mastery Practice............................ 59 General Revision 1 ...................... 61 Chapter 5 Circles............................................73 Exercises ......................................74 Mastery Practice........................... 86 Chapter 6 Area and perimeter........................ 88 Exercises.......................................90 Mastery Practice............................ 97 Chapter 7 Surface area and volume of solids .......................................100 Exercises.....................................101 Mastery Practice.......................... 112 Chapter 8 Mean, median and mode............. 116 Exercises..................................... 118 Mastery Practice.......................... 131 Chapter 9 Probability................................... 133 Exercises.....................................133 Mastery Practice.......................... 139 General Revision 2 .................... 142 Contents ©Praxis Publishing Singapore Pte. Ltd.
Chapter 1 Equations and algebra 1 Chapter 1 Equations and algebra Equations 2 × 3 = 6 So, 2 × 3 = 6 is an equation. True equations and false equations 2 × 3 = 6 2 × 3 = 8 So, 2 × 3 = 6 is a So, 2 × 3 = 8 is a true equation. false equation. Equation with one unknown 2 × a = 10 a = 5 2 × 5 = 10 Solution True equation Properties of equality The same number can be added to or subtracted from both sides of an equation without making it false. Both sides of an equation can be multiplied by or divided by the same number without making it false. Unknown An expression on either side of equal sign Equal sign Equal Unequal ©Praxis Publishing Singapore Pte. Ltd.
9 Chapter 1 equations and algebra F Write your answers on the lines provided. 1. 4a + = 15a 2. 25m – = 9m 3. 7x + 3x – = 2x 4. 10 × b = 5 × 5. Find the value of 12p – 6, when p = 5. 6. Jenny was paid y rupiah for a week’s work. She worked five days in a week. How much was she paid for each day? 7. The length of a rectangle is 5r cm and the breadth is 2r cm. Write an algebraic expression for the perimeter of the rectangle. 8. The temperature in the morning was t °C. It had risen 3°C by midday and then it fell 1°C by sunset. What was the temperature at sunset? 14. 12r 6 + 98, when r = 11 ©Praxis Publishing Singapore Pte. Ltd.
10 Mathematics Grade 6 9. Square A has a length of 2q and Square B has a length of 7r. Square A is bigger than Square B. Write an algebraic expression for the difference in perimeter between the two squares. 10. Subtract 3x from the product of 10x and 8. 11. w books are shared equally among 18 children. How many books will each child receive? 12. A bag of rice is t kg. A bag of sugar is 2 kg less than a bag of rice. What is the total mass of three bags of rice and two bags of sugar? 13. Peggy is k years old. Her mother is twice as old as she. What is the sum of their ages in 5 years’ time? ©Praxis Publishing Singapore Pte. Ltd.
Chapter 2 Integers 17 Chapter 2 Integers Number lines A number line helps us to see the relationship between integers. –5 –4 –3 –2 –1 0 1 2 3 4 5 Negative numbers are less than 0. Positive numbers are more than 0. Zero is neither positive nor negative. On a vertical number line, • any number is less than a number above it. For example, 3 < 5, –2 < 1. • any number is greater than a number below it. For example, 4 > 3, –3 > –4. On a horizontal number line, • any number is less than a number to its right. For example, –1 < 2, –3 < –2. • any number is greater than a number to its left. For example, –4 > –5, 0 > –1. –5 –4 –3 –2 –1 0 1 2 3 4 5 ©Praxis Publishing Singapore Pte. Ltd.
Mathematics Grade 6 18 A Write the correct answers on the lines. 1. Write in numerals. (a) Negative ten (b) Negative twenty-one (c) Negative thirty-four (d) Negative one hundred and one 2. Write in words. (a) – 7 (b) – 13 (c) – 85 (d) – 99 B Write the integer that is just before and just after each given integer. 1. 7 2. 0 3. – 2 4. – 9 5. – 16 6. – 28 7. – 69 8. – 100 Exercises ©Praxis Publishing Singapore Pte. Ltd.
27 Chapter 2 integers R Solve the following word problems. 1. In the sequence –7, –4, –1, x ..., what is the value of x? 2. The initial temperature of a freezer was –4°C. Two hours later, the temperature dropped by 3°C. When the freezer was switched off, the temperature rose by 8°C. What was the new temperature of the freezer? 3. In the morning, the temperature of a city was –3 °C. Its temperature then dropped by 5°C in the afternoon. At night, its temperature dropped by another 4°C. Find the temperature of the city at night. ©Praxis Publishing Singapore Pte. Ltd.
29 Chapter 2 integers 4. 9 5 x y –7 The figure shows a sequence of numbers. What are the values represented by x and y? A x = 1, y = – 3 B x = 1, y = – 2 C x = 2, y = – 5 D x = 3, y = –4 5. Which of the following is an integer? A – 2.1 C 0 B +0.5 D 1 2 6. How many integers are there between –4 and 2? A 4 C 6 B 5 D 7 7. –15–18 K L The figure shows a number line. What is the value of K and L? A K = –9, L = –3 B K = –9, L = – 6 C K = –11, L = –3 D K = –11, L = –6 8. Arrange –8, –10, 7, –2, 0 and 3 in increasing order. A 3, 7, 0, –2, –8, –10 B 0, – 2, 3, 7, –8, –10 C –2, – 8, –10, 0, 3, 7 D –10, –8, – 2, 0, 3, 7 Circle the correct answers. 1. –15 P Q 0 9 The figure shows a number line. What are the values of P and Q? P Q A –12 6 B –9 6 C –12 3 D –9 3 2. X Y –16 0 The figure shows a number line. What are the values represented by X and Y? A X = –20, Y = 12 B X = –19, Y = 9 C X = –18, Y = 8 D X = –17, Y = 6 3. Refrigerator Temperature (°C) T –2 U 1 V 7 W – 8 The table shows the temperature in four refrigerators. Which refrigerator is the coldest? A T C V B U D W Mastery Practice ©Praxis Publishing Singapore Pte. Ltd.
Chapter 3 Combined operations 31 Chapter 3 Combined operations Order of operations 123 + 68 × 40 – ( 108 ÷ 6 ) = 123 + 68 × 40 – 18 = 123 + 2720 – 18 = 2843 – 18 = 2825 Step 1: Carry out the operations in brackets first. Step 2: Carry out multiplication and division from left to right. Step 3: Carry out addition and subtraction from left to right. A Fill in the blanks with correct answers. 1. (72 + 89) – 123 = – 123 = 3. (264 + 396) – 325 = – 325 = 2. 9 × (56 + 36) = 9 × = 4. 312 ÷ (61 – 49) = 312 ÷ = Exercises Exercises ©Praxis Publishing Singapore Pte. Ltd.
32 Mathematics Grade 6 5. (46 + 162) × 4 = × 4 = 7. (508 – 493) × 6 = × 6 = 9. 6 × 6 + 72 ÷ 8 = + 9 = 11. 756 + 36 ÷ 9 = 13. 665 – 28 ÷ 4 = 15. 543 – (411 – 156) = 6. 9 × 11 + 866 = + 866 = 8. (762 – 671) ÷ 7 = ÷ 7 = 10. 12 + 56 – 63 ÷ 9 = – = 12. 8 × 6 + 892 = 14. 5 × 8 – 26 = 16. (42 ÷ 6) + 712 = ©Praxis Publishing Singapore Pte. Ltd.
34 Mathematics Grade 6 C Find the results of the combined operations. Then, fill in the correct numbers in the puzzle. 1. 567 + 12 × 24 3. 153 ÷ 9 × (281 – 278) 4. 54 × 70 – 1237 × 3 6. 896 ÷ 4 ÷ (406 – 399) 8. (3605 – 3588) + (9201 – 9170) 9. (135 ÷ 5) × (208 ÷ 8) 1. 1085 ÷ 5 – 136 2. 300 – 4 × 61 3. 11 × 23 + 1740 ÷ 6 5. (144 ÷ 8) × (459 ÷ 9) 7. (2672 + 381) – (964 + 2062) 8. (550 – 536) × (792 – 789) 1 3 6 9 2 4 5 7 8 1 ACROSS DOWN ©Praxis Publishing Singapore Pte. Ltd.
38 Mathematics Grade 6 4. There are 106 female employees and 94 male employees in a company. They are divided equally among 4 departments. How many employees are there in each department? 5. A crate of oranges weighs 112 kilograms. If a crate of mangosteens is 28 kilograms lighter than the crate of oranges, what is the total mass of the crate of oranges and the crate of mangosteens? 6. In the first year, Company A sold 376 576 watches. In the second year, it sold 451 203 watches. In the third year, it sold 32 974 fewer watches than the previous year. How many watches did the company sell in the three years? ©Praxis Publishing Singapore Pte. Ltd.
41 Chapter 3 Combined operations Circle the correct answers. 1. 121 765 – 124 × 231 = A 93 121 B 93 211 C 680 781 D 28 099 071 2. 523 × 54 + 51 123 = A 37 965 B 79 365 C 1 854 571 D 26 765 571 3. 21 812 + 7368 ÷ 12 = A 2172 B 2712 C 22 426 D 24 226 4. 11 340 ÷ 20 – 13 = A 56 B 554 C 1386 D 2587 5. 160 + 73 × 10 + 14 = A 904 B 1912 C 2344 D 5592 Mastery Practice 6. 15 840 ÷ 9 + 158 × 12 = A 3656 B 4580 C 23 016 D 52 047 7. (121 765 – 119 124) × 231 = A 610 071 B 610 701 C 617 001 D 671 001 8. 32 × (514 − 484) × 12 = A 10 640 B 11 520 C 191 568 D 241 510 9. 134 258 + (17 480 – 385 × 24) = A 8280 B 97 418 C 142 498 D 544 538 10. 48 125 − 10 835 ÷ 11 = A 566 B 7468 C 8466 D 47 140 ©Praxis Publishing Singapore Pte. Ltd.
Mathematics Grade 6 44 Chapter 4 Four operations with fractions Converted into improper fraction form Converted back into mixed number form Converted into equivalent fraction with the same denominator as 3 8 Addition of fractions Example: 1 2 + 3 8 = 1 2 × 4 × 4 + 3 8 = 4 8 + 3 8 = 7 8 2 1 5 + 7 10 = 11 5 + 7 10 = 22 10 + 7 10 = 29 10 = 2 9 10 Addition of three fractions Example: 3 4 5 + 1 1 5 + 2 3 5 = (3 + 1 + 2) + 1 4 5 + 1 5 + 3 5 2 = 6 + 8 5 = 6 + 1 3 5 = 7 3 5 1 1 6 + 3 2 3 + 2 1 2 = (1 + 3 + 2) + 1 1 6 + 2 3 × 2 × 2 + 1 2 × 3 × 32 = 6 + 1 1 6 + 4 6 + 3 6 2 = 6 + 8 6 = 6 + 1 2 6 1 3 = 6 + 1 1 3 = 7 1 3 ©Praxis Publishing Singapore Pte. Ltd.
Mathematics Grade 6 46 Multiplication of fractions Example: 2 × 3 7 = 2 × 3 7 = 6 7 5 6 × 7 9 = 5 × 7 6 × 9 = 35 54 Division of fractions Example: 3 —4 ÷ 1 —2 = 3 —4 × 2 —1 = 6 —4 = 1 1 —2 1 —3 ÷ 4 = 1 —3 × 1 —4 = 1 —–12 Reciprocal of —1 2 3 2 ©Praxis Publishing Singapore Pte. Ltd.
Chapter 4 Four operations with fractions 47 A Add. 1. 1 1 10 + 2 3 10 + 4 7 10 2. 3 1 4 + 1 3 4 + 5 1 4 = = 3. 2 1 7 + 1 3 7 + 3 2 7 4. 4 1 5 + 2 2 5 + 1 3 5 = = 5. 4 2 7 + 3 1 7 + 1 3 7 6. 5 1 9 + 1 4 9 + 2 5 9 = = Exercises ©Praxis Publishing Singapore Pte. Ltd.
51 Chapter 4 Four operations with fractions E Multiply. 1. 5 × 2 7 2. 4 9 × 15 = = 3. 7 10 × 4 9 4. 5 6 × 9 20 = = 5. 4 × 2 1 3 6. 3 3 8 × 6 = = 7. 2 3 5 × 120 8. 1 4 5 × 2 8 9 = = ©Praxis Publishing Singapore Pte. Ltd.
56 Mathematics Grade 6 5. Mrs Ng bought 10 kg of flour. She used 5 1 4 kg to bake cakes and 2 1 2 kg biscuits. How much flour is left? 6. The total volume of three containers is 7 1 3 l. If two of the containers have volume of 4 1 6 l and 1 3 4 l respectively, calculate the volume of the third container. ©Praxis Publishing Singapore Pte. Ltd.
59 Chapter 4 Four operations with fractions Circle the correct answers. 1. 2 4 5 + 1 3 10 + 3 1 2 = A 6 3 5 C 7 3 5 B 6 3 10 D 7 3 10 2. 7 1 3 – 2 5 6 – 1 1 4 = A 3 1 4 C 4 1 4 B 3 1 12 D 4 1 12 3. 2 1 3 × 27 = A 9 C 27 B 21 D 63 4. 4 1 4 × 248 = A 540 C 1054 B 992 D 4216 5. 1 5 ÷ 4 = A 1 20 C 1 1 4 B 4 5 D 20 6. 5 6 ÷ 2 3 = A 5 9 C 1 1 2 B 1 1 4 D 2 4 9 Mastery Practice 7. 3 1 2 ÷ 8 = A 7 16 C 8 B 1 7 16 D 28 8. 2 3 8 ÷ 1 4 = A 2 19 C 4 1 4 B 4 19 D 9 1 2 9. Jenny had 4 1 2 m of ribbon. She used 2 1 4 m of it and gave 1 1 8 m to her friend. How many metres of ribbon did she have left? A 1 1 8 m C 6 3 4 m B 2 1 4 m D 7 7 8 m 10. On a day, Kalu took 2 1 2 hours to clean his room, 1 3 4 hours to practice his guitar and 1 1 4 hours to exercise. How many hours did Kalu take to do all the work? A 2 3 4 h C 4 1 4 h B 3 3 4 h D 5 1 2 h ©Praxis Publishing Singapore Pte. Ltd.
General Revision 1 61 A Choose the correct answer and write its number in the brackets provided. 1. Simplify 17 + 8a – 12 – 5a. (1) 5 – 3a (2) 5 + 3a (3) 29 + 3a (4) 29 + 13a ( ) 2. Find the value of 12p – 3 + 3p when p = 2. (1) 15 (2) 18 (3) 24 (4) 27 ( ) 3. The breadth of a rectangle is x cm and its length is 5 cm longer. Find the perimeter of the rectangle in terms of x. (1) (2x + 5) cm (2) (2x + 10) cm (3) (4x + 10) cm (4) (4x + 20) cm ( ) 4. The average of 4 numbers is y. What is the sum of the 4 numbers? (1) 4 + y (2) y – 4 (3) 4y (4) y 4 ( ) 5. p adults attended a concert with their children. The total number of children was 18 more than adults. How many people attended the concert? (1) p + 18 (2) 2p – 18 (3) 2p + 18 (4) 2p + 36 ( ) 6. In the sequence – 7, – 4, – 1, x, …, the value of x is (1) – 2 (2) – 4 (3) 2 (4) 4 ( ) General Revision 1 ©Praxis Publishing Singapore Pte. Ltd.
Chapter 5 Circles 73 Chapter 5 Circles Parts of a circle O is the centre of the circle. OJ is the radius of the circle. OL is the radius of the circle. OK is the radius of the circle. OJ, OL, OK are the radii of the circle. Semicircle Quadrant J K L O JOK is the diameter of the circle. Diameter = 2 × Radius Circumference is the perimeter of a circle. Circumference = π × Diameter or Circumference = 2πr Area of circle = π × Radius × Radius π is read as pi. We usually take its value as 3.14 or 22 7 . ©Praxis Publishing Singapore Pte. Ltd.
Mathematics Grade 6 74 A Complete the table below. Circle Centre Radius Diameter 1. O P C A B 2. M Q Z K Y X 3. E H J I G F R Exercises ©Praxis Publishing Singapore Pte. Ltd.
75 Chapter 5 Circles B Fill in the correct answers. Centre of circle : Radius of circle : Diameter of circle : Centre of circle : Radius of circle : Diameter of circle : 1. 2. C D A L G J B H V Y R M S L P C Use a ruler and a pair of compasses, draw the following circles. 1. A circle with the following line as its radius. Q P 2. A circle with centre X and a diameter of 2.4 cm. 3. Draw CD that is 2 cm long. Draw Circle C and Circle D by using the length of CD as the radius. ©Praxis Publishing Singapore Pte. Ltd.
77 Chapter 5 Circles E Find the perimeter of each figure shown below. (Take π = 22 7 ) 1. 21 cm 2. 7 cm F Find the area of each of the following figures. (Take π = 3.14) 1. 6 m 6 m 2. 5 cm 5 cm ©Praxis Publishing Singapore Pte. Ltd.
79 Chapter 5 Circles 2. The figure is made up of two quadrants. Find the area of the figure. (Take π = 22 7 ) 14 cm 7 cm 3. The figure is made up of a rectangle and two semicircles. Find the area of the figure. Give your answer correct to 1 decimal place. (Take π = 3.14) 10 cm 28 cm ©Praxis Publishing Singapore Pte. Ltd.
80 Mathematics Grade 6 H Find the circumference of each circle with the given measurement. (Take π = 3.14) 1. Radius = 10 mm 2. Radius = 15 m 3. Diameter = 27 cm 4. Diameter = 40 m I Find the circumference of each circle given below and show the workings. (Take π = 22 7 ) 1. 14 mm 2. 3.5 cm ©Praxis Publishing Singapore Pte. Ltd.
84 Mathematics Grade 6 4. The figure shows a clock face with a minute hand of length 7 cm. Calculate the distance covered by the point P and the tip of the minute hand after 2 hours. (Use π = 22 7 ) 5. The wheel of a bicycle has a radius of 56 cm. (Use π = 22 7 ) (a) How far has the bicycle travelled, in m, after the wheel has made 10 complete revolutions? (b) How far has the bicycle travelled, in m, after the wheel has made 125 complete revolutions? 12 6 11 1 10 2 9 3 8 4 7 5 7 cm P ©Praxis Publishing Singapore Pte. Ltd.
85 Chapter 5 Circles 6. Given that PQR is a semicircle, calculate the perimeter of the figure. (Use π = 22 7 ) 7. The figure shows two circles with a common centre O. Find the area of the shaded region. (Use π = 22 7 ) P Q T R S 10 cm 6.6 cm 18.2 cm 16.8 cm O ©Praxis Publishing Singapore Pte. Ltd.
Mathematics Grade 6 88 Chapter 6 Area and perimeter Perimeter The perimeter of a shape is the total length around all sides of it. Circumference is the perimeter of circle. Perimeter of rectangle = Length + Breadth + Length + Breadth = 2 × (Length + Breadth) Perimeter of square = 4 × Length of side Perimeter of triangle = Length of side + Length of side + Length of side Circumference of circle = π × Diameter or 2πr Area The area of a shape is the amount of surface it covers. Area of square = Length of side × Length of side Area of rectangle = Length × Breadth Area of triangle = 1 2 × Base × Height Area of circle = π × Radius × Radius Example: Figure ABCDEFGH is made up of a rectangle and two identical squares. (a) Find the length of ED. (b) Find the perimeter and area of the figure. A 30 cm B CDG 14 cm F E H 28 cm ©Praxis Publishing Singapore Pte. Ltd.
Mathematics Grade 6 90 A Solve the following questions. 1. ABCD is a rectangle. DE is 1 2 of CE. (a) Find the area of the shaded part. (b) What fraction of the figure is shaded? 2. Find the area of the shaded part. 16 cm 5 cm 10 cm 12 cm 16 cm 6 cm D A C E B Exercises ©Praxis Publishing Singapore Pte. Ltd.
Mathematics Grade 6 94 9. The figure below shows two identical quadrants and a semicircle enclosed in a rectangle. Find the perimeter of the shaded part. (Take π = 22 7 ) 10. The figure shows 3 identical triangles in an equilateral triangle. Find the perimeter of the shaded part. 16 cm 16 cm 2 cm 7 cm 7 cm 14 cm ©Praxis Publishing Singapore Pte. Ltd.
Mathematics Grade 6 100 Chapter 7 Surface area and volume of solids Nets of solids The net of a solid is the shape produced on a plane when all the surfaces of the solid are unfolded on the plane. Example: Cube Cuboid Triangular prism Square pyramid Cone Cylinder ©Praxis Publishing Singapore Pte. Ltd.
101 Chapter 7 Surface Area and Volume of Solids A Match each object with the correct name of its solid. 1. • • Sphere 2. • • Cylinder 3. • • Pyramid 4. • • Prism 5. • • Cone Exercises ©Praxis Publishing Singapore Pte. Ltd.
103 Chapter 7 Surface Area and Volume of Solids 5. The solid shown is a . It has faces. The faces are . 6. The solid shown is a . It has faces. faces are and faces are . 7. The solid shown is a . It has faces. faces are and faces are . 8. The solid shown is a . It has faces. faces are and face is a . ©Praxis Publishing Singapore Pte. Ltd.
Mathematics Grade 6 104 C Name the solid formed by each net. 1. 2. 3. 4. 5. 6. 7. 8. ©Praxis Publishing Singapore Pte. Ltd.
Chapter 7 Surface Area and Volume of Solids 111 4. 5. 11 cm 7 cm 16 cm 12 cm 42 cm 20 cm 18 cm 26 cm 95 cm ©Praxis Publishing Singapore Pte. Ltd.
Mathematics Grade 6 116 Chapter 8 Mean, median and mode Average = Total number or amount Number of items Example: Find the average mass of the parcels. 5.3 kg 8.8 kg 6.8 kg 9.4 kg Total mass of parcels = 5.3 kg + 6.8 kg + 8.8 kg + 9.4 kg = 30.3 kg Total number of parcels = 4 Average mass of parcels = 30.3 4 = 7.575 kg The average mass of the parcels is 7.575 kg. ©Praxis Publishing Singapore Pte. Ltd.
Mathematics Grade 6 118 A Write the correct answers in the spaces provided. 1. 35 kg, 27 kg, 42 kg, 37 kg, 24 kg (a) What is the total mass? Total mass = kg + kg + kg + kg + kg = kg (b) Find the average mass. Average mass = kg ÷ = kg 2. 163 cm, 147 cm, 180 cm, 154 cm (a) What is the total length? Total length= cm + cm + cm + cm = cm (b) What is the average length? Average length = cm ÷ = cm Exercises ©Praxis Publishing Singapore Pte. Ltd.
Chapter 8 Mean, Median and Mode 121 D Solve the following word problems. 1. The height of 4 pupils are shown in the table below. Pupil Ben Lynn Evan Suria Height (m) 1.62 1.53 ? 1.68 The average height of the pupils is 1.635 m. What is Evan’s height? 2. The table below shows the masses of 4 parcels. Parcel P Q R S Mass (g) 852 607 ? 915 The average mass of the parcel is 0.78 kg. What is the mass of Parcel R? ©Praxis Publishing Singapore Pte. Ltd.
133 Chapter 9 Probability Chapter 9 Probability Probability line Impossible Unlikely Equally likely Likely Less likely More likely Certain No chance Poor chance Even chance Good chance Certain Theoretical probability Theoretical probability of an event = Number of desired outcomes Total number of possible outcomes A Describe each of the following events. 1. Fill in the blanks with “certain” or “impossible”. (a) The sun will rise. (b) You will walk on the moon this evening. (c) Fish will grow legs and walk on the ground. (d) June will come after May. (e) Sea water will be salty. Exercises ©Praxis Publishing Singapore Pte. Ltd.
Mathematics Grade 6 134 (f) You will live to be 300 years old. (g) There will be 7 days a week. (h) You will blink your eyes today. There are 13 months in a year. An odd number multiply by 2 becomes an even number. To get a number when a dice is thrown. Today is Monday. Tomorrow is Sunday. A newborn baby rides a bicycle. There are 60 seconds in a minute. 70 can be divided by 3 without any remainder. Sugar tastes sweet. 2. Classify the following event either it is the possibility of the event “certain” or “no chance”. Event Certain No chance a b c d e f g h ©Praxis Publishing Singapore Pte. Ltd.
Chapter 9 Probability 135 3. Match the definitions with the following terms. 4. Colour the likelihood for each of the events. (a) This year Alia’s age is 12 years old and Daniel’s age is 10 years old. Next year, both Alia and Daniel’s age will be the same. Impossible Less likely More likely (b) Maria and Tanvi each goes on vacation to Bali. Both of them might meet. Impossible Less likely More likely (c) Salma is a Year 6 pupil who always get A’s in all subjects when the results are out. She will get all A’s in the final exam. Impossible Less likely More likely (d) There are 5 red marbles and 5 green marbles in a box. Peter took out a red marble and a green marble. Impossible Less likely More likely (e) Nina rolls two dice simultaneously and gets a pair of sixes in a single roll. Impossible Less likely More likely Impossible The event might or might not happen. Less likely The event will never happen. Equally likely The event has a low possibility of happening. More likely The event will surely happen. Certain The event has a high possibility of happening. ©Praxis Publishing Singapore Pte. Ltd.
Mathematics Grade 6 136 B Fill in the blanks with “certain”, “likely”, “equally likely”, “unlikely” or “impossible”. 1. Look at the picture below. Describe the probability of each of the event. (a) It is to pick a shape with corners. (b) It is to pick a pentagon. (c) It is to pick a triangle. (d) It is to pick a shape in grey colour. (e) It is as to pick a circle as it is to pick a square. 2. A box contains 1 white ball, 7 yellow balls and 2 black balls. What is the likelihood of (a) picking a yellow ball from the box? (b) picking a white ball from the box? (c) picking a red ball from the box? (d) picking a ball from the box? C Describe the probability of each of the event with “certain”, “good chance”, “even chance”, “poor chance” or “no chance”. 1. A digit is randomly selected from the 5 535 595. (a) What are the chances of selecting a 9? (b) What are the chance of selecting a 5? (c) What are the chances of selecting an odd number? (d) What are the chances of selecting an even number? ©Praxis Publishing Singapore Pte. Ltd.
General Revision 1 61 A Choose the correct answer and write its number in the brackets provided. 1. Simplify 17 + 8a – 12 – 5a. (1) 5 – 3a (2) 5 + 3a (3) 29 + 3a (4) 29 + 13a ( ) 2. Find the value of 12p – 3 + 3p when p = 2. (1) 15 (2) 18 (3) 24 (4) 27 ( ) 3. The breadth of a rectangle is x cm and its length is 5 cm longer. Find the perimeter of the rectangle in terms of x. (1) (2x + 5) cm (2) (2x + 10) cm (3) (4x + 10) cm (4) (4x + 20) cm ( ) 4. The average of 4 numbers is y. What is the sum of the 4 numbers? (1) 4 + y (2) y – 4 (3) 4y (4) y 4 ( ) 5. p adults attended a concert with their children. The total number of children was 18 more than adults. How many people attended the concert? (1) p + 18 (2) 2p – 18 (3) 2p + 18 (4) 2p + 36 ( ) 6. In the sequence – 7, – 4, – 1, x, …, the value of x is (1) – 2 (2) – 4 (3) 2 (4) 4 ( ) General Revision 1 ©Praxis Publishing Singapore Pte. Ltd.
Mathematics Grade 6 62 7. – 12 – (– 14) – 4 + 9 = (1) 1 (2) 3 (3) 7 (4) 11 ( ) 8. Which of the following sets of numbers is arranged in ascending order? (1) –3, –6, –5, 2, 4, 8 (2) –9, –1, 0, 6, 4, 2 (3) –2, 2, –3, 3, 4 (4) –7, –4, 3, 6, 10 ( ) 9. The initial temperature of a solution is –20˚C. The solution is heated so that its temperature rises 4˚C every minute. Find the temperature of the solution after 7 minutes. (1) 8˚C (2) 48˚C (3) – 8˚C (4) –48˚C ( ) 10. What is the missing number in the box? 40 + 8 ÷ 4 × 5 – 15 = (1) 45 (2) 37 (3) 120 (4) 35 ( ) 11. 3.26 × 24 ÷ 6 = (1) 84.24 (2) 78.24 (3) 13.04 (4) 9.78 ( ) 12. Find the value of 36 + 6 ÷ 3 × 4 – 11. (1) 33 (2) 45 (3) 44 (4) 108 ( ) 13. (6500 – 2879) × _____ = 50 694 What number must be written on the line? (1) 140 (2) 1.4 (3) 14 (4) 0.14 ( ) ©Praxis Publishing Singapore Pte. Ltd.
Mathematics Grade 6 64 20. The number of girls was twice the number of boys in Class 6A. 1 8 of the girls brought muffins for the class party. What fraction of the pupils in the class brought muffins? (1) 1 24 (2) 1 16 (3) 1 12 (4) 1 6 ( ) B Write your answers on the lines provided. 1. State the algebraic expression for the following. Multiply p by 9 and add it to 10 2. Find the value of 27 + 3x 6 when x = 7. 3. There are q children in the nursery. 15 of them are girls. How many of them are boys? Give your answer in terms of q. 4. Anthony paid Rp m for 8 packets of noodles. How much was one packet of noodles? Give your answer in terms of m. 5. 18a = 6 × . What is the missing value? ©Praxis Publishing Singapore Pte. Ltd.
Mathematics Grade 6 142 General Revision 2 A Choose the correct answer and write its number in the brackets provided. 1. The figure is made up of a rectangle, a semicircle and a quadrant. What is its perimeter? (Take π = 22 7 ) 37 cm 14 cm (1) 90 cm (2) 93 cm (3) 100 cm (4) 104 cm ( ) 2. The figure shows a quadrant and a semicircle. Find the ratio of area of A to the total area of A and B. B A (1) 1 : 2 (2) 1 : 3 (3) 2 : 3 (4) 3 : 4 ( ) 3. The figure shows a quadrant and a triangle enclosed in a square. Find the area of the shaded part. (Take π = 3.14) 20 cm (1) 43 cm2 (2) 86 cm2 (3) 243 cm2 (4) 314 cm2 ( ) ©Praxis Publishing Singapore Pte. Ltd.
Mathematics Grade 6 146 13. Which of the following figures is not the net of a cuboid? (1) (2) (3) (4) ( ) 14. C A F Which of the following figures can be used to form the dice as shown above? (1) E F B D C A (2) (3) E F B D C A (4) E F B D C A ( ) E F B D C A ©Praxis Publishing Singapore Pte. Ltd.
Mathematics Grade 6 152 11. The figure below three circles with centres P, Q and R. The smallest circle has a radius of 3 cm. Find the length of wire needed to form these circles. Give your answer in terms of π. 12. A wheel with a diameter of 15 cm made 6 complete turns along a straight line from Point A to Point B. Find the distance between Point A and Point B. Give your answer in metres and correct it to 1 decimal place. (Take π = 3.14) 15 cm Point A Point B P Q R ©Praxis Publishing Singapore Pte. Ltd.