44 Asset and liability House Money Dic�onary Savings Jewellery Taxes Educa�on loan Car Installment House installment Learning Standard 3.1.1 Let’s Learn Asset What is owned su ch as cash and property. Dic�onary Asset LIABILITY Liability Financial commitments or loans. Dic�onary
45 Complete the bubble map below. Let’s Prac�se 3E jewellery house car loan educa�onal loan taxes savings house loan cash ASSET LIABILITY
46 Insurance and takaful INSURANCE TAKAFUL Buy and sell concept. Contribu�on concept. Risks are borne by the insurance company. Risks are borne by the par�cipants in groups. Insurance premiums are owned by the company. Contribu�ons are owned by takaful fund. The takaful operator only acts as the fund manager. Subject to government laws. Subject to Syariah laws and government laws. Non-syariah compliant. Syariah compliant. Learning Standard 3.2.1 Let’s Learn Did You Know Takaful is an Arabic term derived from the root word “Kafala”, which means to guarantee, protect, or look a�er. EXAMPLES OF THE USE OF INSURANCE AND TAKAFUL Road traffic accidents or damages Medical Travel Fire Borne Borne comes from the word bear which means to take responsibility. Dic�onary
47 Policy : ___________________________________ Func�ons : ___________________________________ ________________________________________________ ________________________________________________ Policy : ___________________________________ Func�ons : ___________________________________ ________________________________________________ ________________________________________________ Policy : ___________________________________ Func�ons : ___________________________________ ________________________________________________ ________________________________________________ Policy : ___________________________________ Func�ons : ___________________________________ ________________________________________________ ________________________________________________ State the types of policies and their func�ons. 1) 2) 3) 4) Let’s Prac�se 3F
48 Circle the correct financial term. 1. Something owned such as money, cash and possession. Dividend Asset 2. Deduc�on of a sum of money or par�al refund a�er purchase of goods. Rebate Invoice 3. A sum of money earned of savings in a bank. Interest Discount 4. Financial obliga�ons or debts. Liability Insurance 5. A piece of paper that qualifies the owner to get a cheaper price. Bill Voucher 6. A scheme for mutual guarantee or mutual assistance. Takaful Service tax Calculate the new price a�er rebate or discount is given. 1. Original price: RM79 Rebate: RM25 2. Original price: RM1 480 Rebate: RM139 3. Original price: RM542 Discount: 5% 4. Original price: RM3 682 Discount: 20% Let’s Prac�se 3G Let’s Prac�se 3H
49 Problem Solving Let’s Prac�se3 I Learning Standard 3.3.1 Solve the problem. 1) Nazri bought a house in 2016 for RM430 000. Five years later, he sold the house for RM650 000. Calculate the profit earned by Nazri. 2) The diagram shows the price of a vase. Maya bought 4 vases and got a discount of RM68.20. What is the price that Maya has to pay? 3) The cost price of a television of an old model was RM1 200. Shamil suffered a loss of RM375 when he sold the television. What was the selling price of the television? 4) A price of a refrigerator is RM3 650. Kamal got a discount of 10% when he bought it. Calculate the price of the refrigerator a�er the discount. 5) The diagram shows a receipt for the items bought by Lily. Lily had RM150. Then, she bought another 2 story books. How much did she have le�? KINDHEARTED BOOKSTORE NO. ITEM QUANTITY PRICE TOTAL 1. Story Books 3 RM15.90 RM47.70 2. Dic�onary 2 RM25.50 RM51.00 TOTAL RM98.70 THANK YOU – PLEASE COME AGAIN 6) The amount stated in Puan Shima’s phone bill is RM127, excluded of service tax of 6%. a) Calculate the value of the service tax. b) How much does Puan Shima need to pay? 7) Vinod invests RM35 000 at Costa Company. The company offered a dividend rate of 2% to him a�er a year. a) Calculate the value of dividend received by Vinod a�er a year. b) In the second year Vinod invests RM40 000 and the rate of dividend is 3.5%. What is the value of dividend obtained in that second year? 8) Mei Ling buys some clothes at Kita Supermarket. The total purchase of the clothes is RM374.50. She has 5 pieces of RM10 rebate coupons. How much money does she have to pay if she uses all the coupons? RM250
50 The �me in each country is different. For example, the �me in Malaysia is different from the �me in Australia. The whole world is divided into 24 �me zones. Each �me zone represents 1 hour for every 15°. There is a �me difference between countries because they are situated in different �me zones. Some countries such as Australia and Indonesia have more than one �me zone. Let’s Learn 4 TIME Learning Standard 4.1.1 Helpful Tips Earth rotates on its axis, area that receive sunlight experience day�me whereas the other area experience nigh�me. The clock shows 4:00 p.m. in Kuantan, Malaysia now. It is 6:00 p.m. in Canberra, Australia. 1 2 Time Zone 19 July 2023 19 July 2023
51 The �me zone is measured from Greenwich Meridian (GMT 0) as shown in the map. 1. Complete the table with the informa�on given below. Japan Time difference: 1 hour Germany Time difference: 7 hours Mexico Time difference: 13 hours New Zealand Time difference: 4 hours Posi�on West Malaysia East Country Time difference 2. Mark (√ ) for the correct loca�on of Kuala Lumpur. Kuala Lumpur is in the east of Berlin. Kuala Lumpur is in the west of Berlin. Let’s Prac�se 4A Puan Nisa takes a flight from Kuala Lumpur to Berlin. The flight departs at local �me 10:15 a.m.. Berlin is 7 hours behind Kuala Lumpur. West East North Greenwich Meridien (GMT 0)
52 Determine the �me difference between two ci�es located in different �me zones Time becomes earlier for places situated on the right side (East). Time becomes later for places situated on the le� side (West). 1. Riyadh is situated on the west of Malaysia. The �me in Riyadh is on Wednesday, 4:00 p.m. while the �me in Kuala Lumpur is 9:00 p.m. on the same day. Calculate the �me difference between Riyadh and Kuala Lumpur. The �me difference between Riyadh and Kuala Lumpur is 5 hours. hours minutes 9 00 - 4 00 5 00 Learning Standard 4.1.2 How to find �me difference between two countries? Determine the posi�on of the country in a map (whether to the east or to the west) Get the �me difference between the two countries. Determine the opera�on. West side of the country being referred: Subtrac�on East side of the country being referred: Addi�on Kingdom Centre, Riyadh, Saudi Arabia 4:00 p.m., Wednesday. Petronas Twin Tower, Kuala Lumpur, Malaysia 9:00 p.m., Wednesday. Riyadh Kuala Lumpur 4:00 p.m. 9:00 p.m. Time difference? Let’s Learn
53 2. The following diagram shows the �me in two ci�es. What is the �me difference between these two cites? Time difference = 14 hours + 1 hour = 15 hours 1. Calculate the �me difference between Melaka and Sydney. 2. Lyon, France is situated in the west of Malaysia. The �me there on Monday, 10 July 2023 is 9 p.m. while the �me in Malaysia on Tuesday, 11 July 2023 is 3 a.m.. Calculate the �me difference between Lyon, France and Malaysia. Vancouver 10 July 2023 1054 hours Kajang 11 July 2023 0154 hours 2454 hours 14 hours 1 hour Let’s Prac�se 4B 1:54 a.m. 10:54 a.m. Vancouver, Canada Monday 10 July 2023 Kajang, Malaysia Tuesday 11 July 2023 Melaka, Malaysia 10 February 2023 Sydney, Australia 10 February 2023 0930 hours Tips find the �me difference, you can convert the �me in a 12-hour system to a 24- hour system. 0730 hours 0930 hours
54 Solve Time difference: hours minutes 7 00 - 2 00 5 00 Helpful Tips The 5- Time in Saudi Arabia hours minutes 15 00 - 5 00 10 00 Time in Saudi Arabia is 10:00 a.m.. Kota Bahru, 3:00 p.m. Convert the �me to 24-hour system before doing the calcula�on. Kota Bahru, 7:00 a.m. Let’s Learn Solve the problems involving �me zone. 1. On the same day, the �me in Kota Bahru shows 7:00 a.m. while the �me in Saudi Arabia is 2:00 a.m.. What is the �me in Saudi Arabia if the �me in Kota Bahru shows 3:00 p.m. ? Given Asked for Kota Bahru, 7:00 a.m. Time in Saudi Arabia Saudi Arabia, 2:00 a.m. Learning Standard 4.2.1 hour �me difference is because the �me in Kota Bahru is ahead of the �me in Saudi Arabia.
55 1. Mr. Selva was sent for a seminar in Poland by his company. Poland is situated in the west of Kuala Lumpur with the �me difference of 6 hours. Mr. Selva departed from Kuala Lumpur at 0440 hours, 20 July 2023 and the flight to Poland took 11 hours and 48 minutes. Determine the expected �me of Mr. Selva to arrive according to Poland �me. 2. The table below shows the �me in two towns at the same �me. a. State the posi�on of Plymouth from Kuala Lumpur. b. Find the �me difference between the two ci�es. 3. The �me difference between Singapore and Tokyo is 1 hour. Japan located to the east of Singapore. What is the �me in Japan if the �me in Singapore is 2103 hours? 4. The �me in Johannesburg, South Africa is 6 hours behind the �me in Jakarta. Find the �me in Johannesburg when the �me in Jakarta is 2:57 p.m.. 5. A basketball match is broadcast live from Brasilia, Brazil on Thursday, 1500 hours. Brandon stays in Sydney, Australia. The �me in Sydney is 13 hours ahead of the �me in Brasilia. At what �me can Brandon watch the live broadcast? 6. Faridah returns to Ohio to con�nue her studies. As soon as she arrives in Ohio at 7:15 a.m., she calls her mother who is in Seremban . The �me in Seremban is 12 hours ahead of the �me in Ohio. State the �me in Seremban at that moment. Plymouth, England Kuala Lumpur, Malaysia 2205 hours 22 March 2023 0505 hours 23 March 2023 Singapore 2103 hours Let’s Prac�se 4C
56 Let’s Learn 5 MEASUREMENT Length and volume of liquid The diagram below shows the distance between three towns. Encik Yap’s car uses 1 litre of petrol for every 16 km. Calculate the volume of petrol needed, in ℓ, by Encik Yap to travel from Town P to Town R through Town Q. Solu�on 1 litre of petrol is used for every 16 km. Total distance from Town P to Town R : 20 + 48 = 68 km. How many litres of petrol needed if the total distance travelled is 68 km? 16 km 1 ℓ 68 km = 4.25 ℓ Solve Understand the problem 1 Learning Standard 5.1.1 (ii) Town P Town Q Town R 20 km 48 km
57 1.2 ℓ of petrol is used to travel a distance of 10 km. The distance between Janna’s house and her office is 45 km. Each week she works 5 days and fills 63 ℓ of petrol. Is the quan�ty of the petrol enough for her to travel to and fro between her house and her office for a week? Prove your answer. Solu�on 1.2 ℓ of petrol is used to travel a distance of 10 km. Distance from Janna’s house to her office is 45 km. Distance of a round trip per day : 45 × 2 = ___ km. To prove whether 63 ℓ of petrol is enough for Janna to travel to and fro between her house and her office for a week. The distance of a round trip per day : 45 × 2 = 90 km. Total distance travelled in 5 days : 90 × 5 = 450 km. Conclusion : A distance of 450 km only uses 54 ℓ of petrol. Hence 63 ℓ of petrol is enough for Janna to travel to and fro between her house and her office for a week. Given Asked for Solve 2
58 Let’s Learn Mass and volume of liq uid The diagram below shows the ingredients needed to make watermelon juice. Innarah bought 3.75 kg of watermelon. Calculate the volume of water needed to make watermelon juice using all the watermelon that she bought. Solu�on 1.5 kg of watermelon needs 2 ℓ of water. How many litres of water are needed if 3.75 kg of watermelon is used? Understand the problem Solve Method 1 1.5 kg 2 ℓ 3.75 kg = 5 ℓ of water Method 2 = 2.5 serving of juice 3.75 kg of watermelon can make 2.5 serving of juice. 1 serving of juice 2 ℓ of water 2.5 serving of juice __ ℓ of water 2.5 × 2 ℓ of water = 5 ℓ of water 1 Learning Standard 5.1.1 (iii)
59 The diagram below shows a part of a recipe to bake a cake. Puan Rossidah has 400 mℓ of fresh milk. If Puan Rossidah wants to bake a cake using all the fresh milk, what is the mass, in g, of bu�er needed? Solu�on 250 mℓ of fresh milk needs 115 g of bu�er. What is the mass of bu�er needed if 400 mℓ of fresh milk is used? Understand the problem Solve Method 1 250 mℓ 115 g 400 g = 184 g of bu�er Method 2 = 1.6 cake 400 mℓ of fresh milk can make 1.6 cake. 1 cake 115 g of bu�er 1.6 cake __ g of bu�er 1.6 × 115 g of bu�er = 184 g of bu�er 2
60 Let’s Learn Length and mass A rectangular cake with mass of 4 860 g is cut into three different sizes as shown in the diagram below. P Q R 15 cm 7cm 5cm The width and height of each piece is the same. Calculate the mass, in g, of the cake labelled P. Solu�on A 4 860 g cake is cut into three parts, P, Q and R. Total mass of a cake: 4 860 g. Total length of a cake: 15 cm + 7 cm + 5 cm = 27 cm. Given Calculate Step 1 27 cm 4 860 g 1 cm 4 860 ÷ 27 = 180 g Step 2 The longest part, 15 cm is cake P. The mass of cake P is 15 × 180 g = 2 700 g. 1 Learning Standard 5.1.1 (i)
61 Let’s Prac�se 5A A piece of aluminium with the length of m has a mass of 18 kg. A contractor wants to put the aluminium on the wall of a restaurant kitchen. The length of the restaurant kitchen wall is 3.5 m. Calculate the total mass of aluminium, in kg, needed to cover the wall. Solu�on A piece of m (or 1.5 m) aluminium has a mass of 18 kg. The aluminium length needed is 3.5 m. 1) The diagram below shows the height of water level in a container. The volume of water in the container is 1200 mℓ. The height of the container is 18 cm. What is the volume, in mℓ, of addi�onal water needed to fill the container un�l full? Given Calculate Step 1 1.5 m 18 kg 1 m 18 ÷ 1.5 = 12 kg Step 2 The length of the restaurant kitchen wall is 3.5 m. The total mass of aluminium is 12 kg × 3.5 m = 42 kg. 2
62 The quan�ty of petrol in Encik Kumar’s car tank is 7.6 ℓ. He filled another 10.4 ℓ of petrol. Using the petrol, what is the distance, in km, that Encik Kumar’s car can travel before he needs to fill petrol again? 3) The table below shows the recipe to make 12 muffins. Ingredient Quan�ty Flour 250 g Brown Sugar 120 g Milk 160 mℓ Chocolate powder 75 g Hayfa has 500 g of flour. She wants to use all the flour to make muffins. Calculate the volume of milk needed, in mℓ, by Hayfa to make muffins. 4) A container contains 1 200 g of sugar. Sofea used 800 g of the sugar to make 12 ℓ of orange juice. (a) Calculate the mass, in g, of sugar needed to make 4 ℓ of orange juice. (b) If Sofea intends to make another 10 ℓ of orange juice, is the sugar in the container enough? Prove your answer. 5) 300 g of sugar is needed to make 10 ℓ of syrup drinks. If Hajar wants to make 20 ℓ of syrup drinks, what is the mass of sugar, in g, that she needs? 6) The diagram below shows a water tank. The water tank is filled with 27 ℓ of water. If the full capacity of water in the tank is 72 ℓ, calculate the height of water, in cm, when the tank is filled full with water. 2) The diagram below shows the consump�on of petrol and the distance that can be travelled using the petrol.
63 Regular polygons are shapes withequal sides and equal interior angles. Polygon Number of sides Number of angles Interior angle Sum of interior angles 1 Equilateral triangle 3 3 60° 180° 2 Square 4 4 90° 360° 3 Pentagon 5 5 108° 540° 4 Hexagon 6 6 120° 720° 5 Heptagon 7 7 128.5° 900° 6 Octagon 8 8 135° 1080° 6 SPACE Draw regular polygons up to eight sides and measure the interior angles formed 6.1.1 1 Learning Standard Let’s Learn Measure the interior angles
64 How to draw polygon? 1. Equilateral Triangle – using triangle grid paper Mark point A. Count 4 units on the triangle grid to the right. Mark point B at the end of the line. Join points A and B. Count 4 units on the triangle. grid from point A upwards. Mark it as point C. Label it as 4 units. Join point C with point B. Label it as 4 units too. Place the centre of the protractor on point A. The baseline of the protractor must overlap line AB. Read the value of angle of line AC and label it as 60°. Repeat the same method to measure angles B and C. Remember The three sides of an equilateral triangle must be of equal length
65 2. Regular Pentagon-Using A Blank Paper And A Ruler Remember Each interior angle of the pentagon is 108° Draw a 5 cm straight line. Label it as point A and B Construct angle A, 108°. Draw a long straight line. Construct angle B, 108°. Draw a long straight line too. Measure 5 cm from B along the straight line drawn and label it as C. Measure 5 cm from A along the straight line drawn and label it as E. Construct angle C, 108°. Draw a long straight line. Erase extended lines at points C, D and E Label the angles and the length of the sides. A B Construct angle E, 108°. Draw a long straight line. Label it as D at the intersec�on point of line DE and line CD.
66 1. Draw and measure the interior angles of the following polygons on a blank paper. a. equilateral triangle. b. hexagon. 2. Draw a square on the given grid. 3. Name the polygons and measure angle K for each of the diagram below. a. b. K 4. Complete the table. Polygon Number of sides Heptagon 8 Polygon Interior angle Polygon Interior angle Let’s Prac�se 6A K
67 Let’s Learn Form angles based on given degrees How to form angle? 50° angle 1. Draw a line that forms the given angle star�ng from the line PQ in the diagram below. a. 90° b. 120° Draw a straight line. Mark point A and B. ______________ A B Place the baseline of the protractor exactly on line AB. Ensure that the centre of the protractor is exactly on point B. Measure angle 50° (read from protractor). Mark and label it as C. Then draw a straight line joining B to C. The angle B formed is 50°. C 50° A B Learning Standard 6.1.2 Let’s Prac�se 6B Helpful Tips An angle is formed when two lines meet. A B C P Q P Q
68 Let’s Learn 2. By using a ruler and a protractor, construct an angle of 56° at point S. Recognise centre, diameter and radius of a circle. Learning Standard 6.2.1 Centre Radius Diameter The point located in the middle of a circle The centre of a circle is labelled as ‘O’. A straight line that goes through the centre of a circle from one end of the circumference to the other end. A straight line from the centre of the circle to any point on the circumference of the circle. Circumference The closed curve that forms the boundary of the circle. O circumference of the circle centre of the circle diameter radius Helpful Tips The length of the radius from the centre of a circle to any point on the circumferences is always the same. S
69 1. Fill in the blanks correctly. 2. Name the parts of the circle. a. O b. WOX c. OY d. WZXY Let’s Prac�se 6C radius centre circumference b. c. a. O Y X W Z
70 Let’s Learn Draw a circle based on given radius then label centre, radius and diameter 1. Draw a circle using round-shaped objects 1. Draw circles according to the given informa�on. a. b. 1 2 Step-by-step: 1. Draw a circle using the circumference of a small plas�c cup. 2. Cut out the circle. 3. Fold the circle into half. 4. Make another fold to make four parts of equal size. 5. Unfold it. Observe the folded intersec�on in the middle. 6. Mark the centre of a circle. Then, label the centre of the circle and the diameter. Learning Standard 6.2.2 3 4 5 6 Let’s Prac�se 6D My radius is 2 cm. My diameter is 5 cm.
71 Let’s Learn Solve daily rou�ne problems involving space 1. Su Lin wants to sell a round shaped mini pizza with a radius of 5 cm. What is the suitable diameter of the pizza board to be used? Give your reason. Given Asked for Radius of 5 cm Suitable diameter of pizza board Solve or, Pizza board - circular in shape with a diameter of 11 cm. Reason – the size of pizza board must be larger than the size of the pizza itself. radius 5 cm diameter 10 cm Helpful TipsHelpful The diameter is two �mes the radius. To Learning Standard 6.3.1 radius 5 cm diameter 10 cm Pizza diameter 10 cm
72 1. Lydia wants to make a plan of a garden in her school. She plans to combine two shapes, a regular octagon and a square in her plan. Suggest to Lydia by drawing the composite shape. 2. Fida wants to cut a circle from the manila card. Diagram below shows a square manila card with the sides of 40cm and a straight line OA. a. Draw a circle with OA as a radius. b. one smaller circle with OA as the diameter. 3. Zaki wants to make a frame with eight equal sides. The perimeter of the frame is 480 cm. a. Name the shape of the frame. b. Calculate the length, in mm, of each side of the picture frame. Let’s Prac�se 6E A 40 cm 20 cm 73
Coordinates COORDINATES, RATION AND PROPORTION Distance between two coordinates ► Coordinates are numbers that determine the posi�on of a point or object in two dimensions. ► Coordinates are used to determine the distance between two loca�ons. ► Actual horizontal distance and ver�cal distance between two loca�ons can be determined based on a scale given in the first quadrant on a Cartesian plane. a) What is the horizontal distance and ver�cal distance of point Q from point P, in km? Unit km Horizontal distance (unit) 6 – 1 = 5 5 × 1 km = 5 km Ver�cal distance (unit) 7 – 3 = 4 4 × 1 km = 4 km b) The actual horizontal distance of point R to point S is . c) The actual ver�cal distance of point P to point R is . d) The actual horizontal distance of point S to point Q, in km, is . Meanwhile, the ver�cal distance is . Let’s Learn 7 Learning Standard 7.1.1 5 km 73
74 O Fill in the blanks. 1. The Cartesian plane shows the loca�on of four houses. a) The actual horizontal distance of Indra’s house from Joanne’s is_______ . b) The actual ver�cal distance of Salmi’s house from Danish’s house is _______ . c) The actual horizontal distance of Joanne’s house from Salmi’s house is ________ . d) The actual distance of Danish’s house from Indra’s house is ________ horizontally and ________ ver�cally. 2. The Cartesian plane shows the loca�on of three factories. Scale: 1: 100 000 a) The actual horizontal distance from ______________ to Factory T is 6 km. b) The actual ver�cal distance from _______________ to Factory R is 4 km. c) The total distance from Factory T to ________________ is 8 km. Let’s Prac�se 7A 1 cm 1 cm Scale: 1 cm represents 1 km Salmi’s house Joanne ’s house Indra’s house Danish’s house 1 cm 1 cm Factory R Factory S Factory T d) Factory S is _______ km from the origin. O
75 Ra�o Ra�o between two quan��es ► Ra�o is a comparison in the simplest form of size or value between two objects. ► Ra�o is used to compare two quan��es of the same type and measured in the same unit. ► The ra�o of a to b can be wri�en in the form a : b. a) The ra�o of the number of black circles to the number of the white circles = 2 : 6 = 1 : 3 wri�en in the simplest form. b) Aimi has RM10. Hasya has RM20. Write the ra�o of Aimi’s money to Hasya’s money. = 10 : 20 = 1 : 2 wri�en without the unit and in the simplest form. c) There are 4 of water in jug A and 6 000 m of water in jug B. What is the ra�o of water in jug A to the water in jug B? Jug A Jug B 4 6 000 m convert units to 4 6 The ra�o of jug A to jug B: Let’s Learn Learning Standard 7.2.1 Helpful Tips The ra�o 1 : 2 is read asthe ra�o of one to two. It can also be wri�en as a frac�on . = 4 : 6 = 2 : 3 wri�en without the unit and in the simplest form
76 1 State the ra�o between two quan��es in the simplest form. a. 2 : 8 = b. 3 : 15 = c. 4 : 10 = d. 25 : 5 = e. 6 : 10 = f. 56 : 21 = 2 Write each of the following in the term of a ra�o. a. 4 red apples to the 20 green apples. b. 3 metres of red ribbons to 9 metres of white ribbons c. 12 girls to 8 boys d. 16 kg of sugar to 20 kg of salt. e. 25 km to 100 km f. RM20 to 1 400 sen g. 800 m to 1 Let’s Prac�se 7B h. 5 minutes to 45 minutes i. 4 hours to 180 minutes j. 20 red balloons to 30 blue balloons
77 Proportion Determine the proportionate quantity ► The propor�onate quan�ty can be determined based on a given ra�o. Examples: a) The ra�o of the number of yellow marbles to the number of white marbles is 2 : 5. There are 8 yellow marbles altogether. Number of yellow marbles in one part = 8 ÷ 2 = 4 Number of white marbles = 5 × 4 = 20 b) The ra�o of Jennie’s age to Lisa’s age is 4 : 5. If Lisa is 15 years old, how old is Jennie? 15 5 parts 15 years old 1 parts 15 ÷ 5 = 3 years old 4 parts 4 × 3 years = 12 years old Therefore, Jennie is 12 years old. Learning Standard 7.3.1 Helpful Tips Use the unitary method. Find the value of a unit first. Lisa Jennie Let’s Learn
78 c) The ra�o of the number of girls to the number of boys in 6 Crea�ve is 3 : 4. There are 24 girls in the classroom. i) Calculate the number of boys in the classroom. Girls Boys 3 : 4 8 8 24 32 So, the number of boys is 32. ii) Calculate the total number of pupils in the classroom. 24 (girls) + 32 (boys) 56
79 Calculate the following. 1. K : M = 2 : 5 Calculate the value of M if K is 68 kg. 2. P : Q = 5 : 8 Calculate the value of P if Q is RM160. Let’s Prac�se 7C 3. T : V = 7 : 9 Calculate the value of T if V is 135 m. 4. Y : Z = 8 : 3 Calculate the value of Z if Y is 72 hours.
80 Problem Solving Let’s Prac�se 7D Learning Standard 7.4.13.3 1 The Cartesian plane below shows the posi�ons of a museum and a library. a) Calculate the horizontal distance, in km, between the museum and the library. b) The total distance, in m, of the museum and the library is 10 000 m. Prove it. 2 RM8 RM36 RM48 a) The ra�o of the price of the shoes to the price of the blouse is _________. b) The ra�o of the price of the book to the price of the blouse is _________. c) The ra�o of the price of the shoes to the different price of the blouse and the book is ________ . 3 Drinks Volume Carrot juice 6 Orange juice 5 Lemon juice 3 more than carrot juice A seller prepared a few types of drinks for his customers. State the ra�o of the volume of carrot juice to the total volume of orange juice and the lemon juice. Scale: 1 cm represents 1 km 1 cm 1 cm library museum
81 O 4 The diagram below shows the distance between three loca�ons. X Y Z The ra�o of the distance of XY to the distance of YZ is 5 : 3. Calculate the distance, in km, of YZ if the total of XY and YZ is 56 km. 5 The following Cartesian plane shows the loca�on of Fendy’s car and the shop. Fendy drove the car to the shop. Each unit represents 2 km. What is the total distance that Fendy travelled? 6 The ra�o of Amani’s pocket money to Arissa’s pocket money is 6 : 5. The pocket money Amani receives is RM18 per day. What is the total of Arissa pocket money in a week? 7 There are 330 adults and some children in a shopping mall. The ra�o of the number of the adults to the number of the children is 3 : 5. Calculate the total number of visitors in the shopping mall. Fendy’s car shop Scale: 1 cm represents 2 km
82 8 The incomplete table shows Maya’s and Andy’s score in an online quiz. Name Marks Maya Andy 48 The ra�o of Maya’s score to Andy’s score is 7 : 4. Calculate the difference between their marks. 9 The ra�o of Encik Jamil’s mass to his bother’s mass is 5 : 9. Calculate the mass of Encik Jamil if their total mass is 168 kg. 10 The table shows the Mathema�cs marks for class 6 Cerdik. Marks 95 85 80 75 60 Number of pupils 12 6 5 10 7 What is the ra�o of the number of pupils who gets the highest mark to the total number of pupils?
83 Pie Charts Let’s Learn DATA HANDLING AND LIKELIHOOD Complete pie chart and interpret data. Complete the pie chart based on the informa�on in the table. Vehicle Value of angle Percentages Walk 45 12.5% Motorcycle 90 25% Car 180 50% School bus 45 12.5% Step 1 : Divide the circle to 8 equal parts. Step2 : Relate the frac�ons with angles. 1 8 Learning Standard 8.1.1 180 90 45 45 180 90 = 25% 45 = 12.5% Tips The total value of angle for the whole pie chart is 360 . 1 = 360 100% = 360 The total percentage for the whole pie chart is 100%. 1 = 100% Therefore 100% = 360 use rela�onship between frac�ons and percentages: If So
84 The pie chart below showsthe number of pupilsin 6 DLP class and their hobbies. Hobbies of the pupils of Class 6 DLP Step1 : Relate the pie chart with frac�ons and angles to complete the table. The table shows the number of pupils and their hobbies. Hobbies Number of pupils Frac�ons Angles Percentages Dancing 16 180 50% Swimming 4 45 12.5% Reading 4 45 12.5% Playing Badminton 8 90 25% Step 3: Interpret the data from the pie chart and table. (a) The frac�on of dancing is and is represented by 180 . (b) The frac�on of playing badminton is and is represented by 90 . (c) The frac�on of reading is and is represented by 45 . Dancing 16 Swimming 4 Playing Badminton Reading 8 4 Step 2: Transfer the informa�on from the pie chart into a table. 2 Dancing Playing Badminton Swimming Reading Dancing 180 Swimming 45 Playing Badminton 90 Reading 45 (d) The frac�on of swimming is and is represented by 45 . (e) The mode is dancing with the highest number of pupils, which is 16.
85 1. Complete the following pie chart based on the informa�on in the table below. Type of Recycled Materials Frac�on Value of angle Plas�c 180 Aluminium cans 45 Old books 90 Others 45 Title: ____________________________________________ 1. The pie chart below shows the number of books read by 160 pupils according to the type of book in a library. Number of books read by 160 pupils. Storybook 180 Encyclopedia 45 History 90 Magazine 45 Let’s Prac�se 8A
86 Let’s Learn (a) Complete the table based on the given pie chart and interpret the data. Type of book Value of angle Frac�on Percentage Number of book Encyclopedia 12.5 % 20 Storybook History Magazine (b) The frac�on of storybook is __________ and is represented by ______ (c) The frac�on of history is __________ and is represented by _____ (d) The frac�on of magazine is __________ and is represented by _____ (e) The frac�on of encyclopedia is __________ and is represented by _____ State whether the event is likely or unlikely to occur. Recognise the 5 likelihood of events. Likely to occur Unlikely to occur February has 29 days. 11 divided by 3, its remainder is 1. It will be raining today. There are 8 days in a week. A rainbow can be seen a�er the rain. A dragon can be found on Malaysian beaches. Likelihood Learning Standard 8.2.1 1 Unlikely means there's no chance that an event will happen. Likely means there is a chance that an event will happen. Likelihood Impossible Less likely Equally likely More likely Certain 2
87 1 Determine whether the following events are likely or unlikely to occur. Event Likely or unlikely to occur (a) A month has 30 days. Reason : ________________________________ (b) An even number can be divided by 3 without any remainder. Reason : ___________________________________________ (c) It will rain a�er a thunderstorm. Reason : ___________________________________________ (d) A giraffe has spots on its body. Reason : ___________________________________________ (e) is less than . Reason : ___________________________________________ (f) Tigers are carnivores. Reason : ___________________________________________ (g) An odd number is a prime number. Reason : ___________________________________________ (h) There are sharks in Pahang River. Reason : ___________________________________________ (i) A hexagon has five straight sides. Reason : ___________________________________________ (j) The maximum sum of numbers obtained when two dice are tossed is 13. Reason : ___________________________________________ Let’s Prac�se 8B
88 Let’s Learn 2 State the likelihood (Impossible, Less likely, More likely, Equal likely or Certain) for each of the following events. (a) There are 28 days in February. (b) Malaysia has 4 seasons. (c) Plants need water and sunlight for photosynthesis. (d) Ge�ng tails a�er tossing a coin. (e) Floods will occur when it rains heavily for a week. The pie chart shows the masses of Year 6 pupils. Mass of Year 6 pupils (a) What is the value of angle that represents the largest part? The largest part is 35 kg which is half of the pie chart. Therefore, the value of angle for half of the pie chart is 180 Problem Solving Learning Standard 8.3.1 1 35 kg 37 kg 90 40 kg 45 38 kg
89 Let’s Prac�se 8C (b) If the number of pupils who have a mass of 38 kg is 4, what is the total number of pupils? The por�on for the pupils with the mass of 38 kg = which is equal to 4. Each of part is equal to 4 pupils. Therefore, the total number of pupils is 32. Total number of pupils = 4 × 8 parts. = 32 pupils. 1. The pie chart shows the favourite colour of pupils in 6 Mawar. 10 pupils like red colour. (a) What colour represents the angle of 180°? 4 4 4 4 4 4 4 4
90 (b) What is the number of pupils who like blue? (c) Calculate the total pupils in 6 Mawar. 2. The pie chart shows the mass of vegetables bought by Puan Ain. The total mass of vegetables bought is 10 kg. (a) What is the mass of cabbage bought?
91 (b) What is vegetable represents 90°? (c) Calculate the total mass of carrot, cabbage and brinjal.
92 ANSWERS UNIT 1: WHOLE NUMBERS AND BASIC OPERATIONS Let’s Practise 1A 1.(a) three million six hundred ten thousand two hundred and ninety (b) three million six hundred ten thousand two hundred and nine (c) three million six hundred one thousand and twenty nine 2. (a) 350 264 (b) 1 370 519 (c) 4 000 816 Let’s Practise 1B 1 (a) The number pattern is in ascending order by tens (b) The number pattern is multiply previous number by five (c) The number pattern is in descending order divided by twos (d) The number pattern is in descending order by millions Let’s Practise 1C 1 (a) seven-tenths of a million (b) zero point five six million (c) eight point three four million (d) two and three fourths of a million (e) two point zero seven five million 2 (a) million (b) 5 million (c) 0.3 million (d) 6.012 million Let’s Practise 1D 1 (a) 700 000 (b) 190 000 (c) 1 800 000 (d) 3 050 000 (e) 43 000 (f) 8 021 000 2. (a) 300 000 (b) 400 000 (c) 750 000 (d) 5 250 000 (e) 7 500 000 (f) 9 875 000 Let’s Practise 1E 1 (a) 0.125 million (b) 0.6 million (c) 0.875 million (d) 1.3 million (e) 5.7 million (f) 8 .4 million 2. (a) million (b) million (c) million (d) 2 million (e) 7 million (f) 8 million Let’s Practise 1F 1 (a) 1 million / 1 000 000 (b) 1.9 million / 1 900 000 (c) 4.5 million / 4 million (d) 7.875 million / 7 875 000 2 (a) 5 153 500 b 1.2 million Let’s Practise 1G (a) 90 000 (b) 2.8 million / 2 800 000 (c) 0.715 million/ 750 000 (d) 2.23 million / 2 230 000 (e) 2.23 million / 2 230 000 Let’s Practise 1H 1. (a) 1.1 million (b)5.5 million (c) 9 million 2. (a) 3 220 000 (b) 1 512 000 (c) 7 200 000 (d) 5 250 000 Let’s Practise 1I 1 (a) 2 360 000 (b) 780 000 / 0.78 million 2. (a) 3 020 000 (b) 575 000 (c) 235 000 Let’s Practise 1J 1 (a) 4 750 000 (b)2 425 000 (c) 2 320 000 . Let’s Practise 1K 1 (a) 120 000 (b)480 000 (c) 1 124 000 (d)120 000 Let’s Practise 1L 1 (a) 3.18 million / 3 180 000 (b) 0.478 million / 478 000 (c) 5.98 million / 5 980 000 (d) 3.06 million / 3 060 000 (e) 4.1 million / 4 100 000 (f) 1.315 million / 1 315 000 Let’s Practise 1M 1 (a) 2.24 million (b)1.43 million (c) 0.45 million (d) 0.68 million Let’s Practise 1N (a)0.83 million (b) 6 million
93 (c) 1.008 million (d) 1.75 million (e) 0.245 million (f) 153 000 (g) 0.625 million (h) 3.47 million (i) 0.335 million (j) 1.91 million Let’s Practise 1O 1 i) 41,43,47 ii) 42,44,45,46,48,49.50 2. 27,57,77,87 3. 13,7 dan 3 ,17 4. (a) 41,43,47,53,59 (b) 5 Let’s Practise 1P (a) 0.99 million (b) i. 1 350 000 ii 2.712 million (c) i. 21,22,24,25,26,27,28,30,32,33,34 ii. 5 (d) 5350 , No UNIT 2: FRACTIONS, DECIMALS AND PERCENTAGES Let’s Practise 2A 1 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) 2 (a) 3 (b) (c) (d) Let’s Practise 2B 1 (a) 1.359 (b) 5.796 (c) 29.16 (d) 45.695 (e) 16.875 2 (a) 3 (b) 2.4 (c) 9 (d) 49.375 (e) 1.34 Let’s Practise 2C 1 (a) 6% (b) 70% (c) 19% (d) 108% (e) 830% (f) 456% 2 (a) 0.05 (b) 0.2 (c) 0.13 (d) 2.05 (e) 6.2 (f) 9.95 Let’s Practise 2D 1 (a) 7% (b) 21% (c) 60% (d) 27% (e) 36% (f) 92% 2 (a) 13% (b) 11% (c) 8% (d) 35% (e) 41% (f) 34% Let’s Practise 2E 1 (a) 1.26 (b) 28.2 (c) 9.075 (d) 83.76 (e) 8.125 (f) 31.35 (g) 0.99 (h) 14.72 (i) 107.5 2 (a) 60% (b) 60% (c) 300% (d) 240% (e) 450% (f) 250% (g) 300% (h) 60% (i) 150% Let’s Practise 2F 1 2.83 2 8.78 3 6.85 4 4.31 5 11.855 6 14.335 7 2.025 8 5.6 9 5.25 10 30.375 11 5.36 12 13.5 13 6.16 14 8.946 15 7.866 16 1.928 17 0.21 18 5.67 19 6.8 20 73.79 21 6.375 22 88.55 23 10.68 24 12.34 Let’s Practise 2G 1 56% 2 3 kg 4 (i) 1.35m (ii) 2.1m 5 75 containers 6 7 46 plates 8 131.75 9 (i) 108.6 kg (ii) 18.1 kg 10 (i) 18 roses (ii) 3m UNIT 3: MONEY Let’s Practice 3A 1) i) RM105 ii) RM237 iii) RM509 iv) RM582 2) i) profit/RM16 ii) loss/RM24 iii) profit/RM582 iv) loss/RM571 Let’s Practice 3B 1) RM41 2) RM437 3) RM1 929 4) RM413 5) RM53.30 6) 1 free cupcake Let’s Practice 3C 1) Total RM37, Service tax RM1.85, Total payment RM38.85 2) Total RM140, Service tax RM5.60, Total payment RM145.60 3) Total RM680, Service tax RM40.80, Total payment RM720.80 Lets’s Practice 3D 1) RM140 2) RM875 3) RM2 856 4) RM1 260 5) RM2 870 6) RM8 455 Let’s Practice 3E Asset : jewellery, house, savings, cash Liability: educational loan, house loan, car loan, taxes Lets’s Practice 3F 1) Policy : Accident Functions : Claim compensation for car repair and injury due to accident. 2) Policy : Fire Functions : Receive compensation due to house destruction. 3) Policy : Medical Function : Covering medical expenses. 4) Policy : Travel Function : Coverage during travel such as loss of assets or life. Let’s Practice 3G 1) Asset 2) Rebate 3) Interest 4) Liability 5) Voucher 6) Takaful