Spotlight A+1 Mathematics Form 1

iv Learning Area: Numbers and Operations Chapter 1 Rational Numbers 1.1 Integers .......................................................... 1 1.2 Basic Arithmetic Operations Involving Integers .......................................................... 3 1.3 Positive and Negative Fractions .................... 9 1.4 Positive and Negative Decimals .................. 12 1.5 Rational Numbers ........................................ 13 Mastery Challenge 1 ............................................. 15 Chapter 2 Factors and Multiples 2.1 Factors, Prime Factors and Highest Common Factor (HCF) ................................................ 19 2.2 Multiples, Common Multiples and Lowest Common Multiple (LCM).............................. 21 Mastery Challenge 2 ............................................. 23 Chapter 3 Squares, Square Roots, Cubes and Cube Roots 3.1 Squares and Square Roots ......................... 26 3.2 Cubes and Cube Roots ............................... 29 Mastery Challenge 3 ............................................. 33 Learning Area: Relationship and Algebra Chapter 4 Ratios, Rates and Proportions 4.1 Ratios ........................................................... 37 4.2 Rates ............................................................ 39 4.3 Proportions ................................................... 40 4.4 Ratios, Rates and Proportions..................... 42 4.5 Relationship between Ratios, Rates and Proportions with Percentages, Fractions and Decimals....................................................... 44 Mastery Challenge 4 ............................................. 46 Chapter 5 Algebraic Expressions 5.1 Variables and Algebraic Expressions........... 48 5.2 Algebraic Expressions Involving Basic Arithmetic Operations................................... 51 Mastery Challenge 5 ............................................. 56 Chapter 6 Linear Equations 6.1 Linear Equations in One Variable ................ 59 6.2 Linear Equations in Two Variables............... 63 6.3 Simultaneous Linear Equations in Two Variables....................................................... 66 Mastery Challenge 6 ............................................. 72 Chapter 7 Linear Inequalities 7.1 Inequalities ................................................... 74 7.2 Linear Inequalities in One Variable.............. 76 Mastery Challenge 7 ............................................. 80 Learning Area: Measurement and Geometry Chapter 8 Lines and Angles 8.1 Lines and Angles.......................................... 82 8.2 Angles Related to Intersecting Lines ........... 90 8.3 Angles Related to Parallel Lines and Transversals ................................................. 92 Mastery Challenge 8 ............................................. 97 Chapter 9 Basic Polygons 9.1 Polygons..................................................... 100 9.2 Properties of Triangles and the Interior and Exterior Angles of Triangles ....................... 101 9.3 Properties of Quadrilaterals and the Interior and Exterior Angles of Quadrilaterals ........ 104 Mastery Challenge 9 ........................................... 107 Chapter 10 Perimeter and Area 10.1 Perimeter.....................................................110 10.2 Area of Triangles, Parallelograms, Kites and Trapeziums...........................................111 10.3 Relationship between Perimeter and Area .113 Mastery Challenge 10 ..........................................114 Learning Area: Discrete Mathematics Chapter 11 Introduction to Set 11.1 Set ...............................................................118 11.2 Venn Diagrams, Universal Sets, Complement of a Set and Subsets ................................. 120 Mastery Challenge 11 ......................................... 124 Learning Area: Statistics and Probability Chapter 12 Data Handling 12.1 Data Collection, Organization and Representation Process, and Interpretation of Data Representation .................................. 126 Mastery Challenge 12 ......................................... 134 Learning Area: Measurement and Geometry Chapter 13 The Pythagoras’ Theorem 13.1 The Pythagoras’ Theorem.......................... 139 13.2 The Converse of Pythagoras’ Theorem..... 141 Mastery Challenge 13 ......................................... 142 Pentaksiran Sumatif Ujian Akhir Sesi Akademik (UASA)......................................................................................146 Answers ..................................................................................157 CONTENTS Contents Spot A+1 Maths F1.indd 4 04/04/2023 12:30 PM

1 1.1 Integers 1.1.1 Recognise positive and negative numbers based on real-life situations 1. Positive numbers are the numbers written with the positive sign (+) on the left and their value is greater than zero (0). However, positive sign are usually ignored. For example, +3, 4, +0.6, 7.42, 1 2 . +3 is read as ‘positive three’ or ‘three’. 2. Negative numbers are the numbers written with the negative sign (–) on the left and their value is smaller than zero (0). For example, -12, -0.6, -1.2, – 3 4 . -12 is read as ‘negative twelve’. 3. Positive numbers and negative numbers can be used to represent two opposite changes. For example, –120 m +200 m +100 m –50 m helicopter is 100 m above sea level, is represented as ‘+100’. submarine is 50 m below sea level, is represented as ‘–50’. cargo ship is 200 m on the right of the lighthouse, is represented by ‘+200’. cruise ship is 120 m on the left of the lighthouse, is represented by ‘–120’. Example 1 Write in the form of positive number and negative number based on the following situations. (a) The temperature in the desert is 49.7°C. (b) The car reverses about 0.75 km. (c) Irfan moves 1 2 m to the left. Solution: (a) +49.7 (b) –0.75 (c) – 1 2 ➡ Diagnostic Test 1.1: Question 1 Example 2 Identify the numbers below are positive numbers or negative numbers. -0.24, 3 8 , +6.17, -1, 4.81, – 4 7 Solution: Positive numbers : 3 8 , +6.17, 4.81 Negative numbers : -0.24, -1, – 4 7 ➡ Diagnostic Test 1.1: Question 2 1.1.2 Recognise and describe integers Integers are groups of numbers which include positive and negative whole numbers as well as zero. Negative integers Zero Positive integers Integers ..., –4, –3, –2, –1 0 1, 2, 3, 4, ... TIPS Corner 1. Zero (0) is an integer but not a positive integer or negative integer. 2. Fractions and decimals are not integer. 1 Rational Numbers CHAPTER 1 01 Spot A+1 Maths F1.indd 1 19/04/2023 12:57 PM

CHAPTER 1 Rational Numbers 1 Example 6 Arrange 3, –2, 0, 4, –1 in ascending order and descending order. Hence, state the smallest integer and the largest integer. Solution: –2 –1 0 1 2 3 4 Ascending order : -2, -1, 0, 3, 4 Descending order : 4, 3, 0, -1, -2 The smallest integer : -2 The largest integer : 4 TIPS Corner The number line can be used to arrange integers orderly. Then, the largest and smallest integers can be identified from the arrangement. ➡ Diagnostic Test 1.1: Question 8 Diagnostic Test 1.1 1. Write in the form of positive number and negative number based on the situations below. (a) Haizan takes the lift to go down two levels below the ground floors. (b) Nurin heats the soup up to 90°C. (c) Mustaqim deposits RM1 000 into his account in a bank. 2. Identify the numbers below are positive numbers or negative numbers. -0.3, – 1 10, +6, –2.34, 0.95, 2 9 3. Classify the following numbers into positive integers, negative integers or non-integer. – 2 3 4.9 72 8 –11 –21 4. Represent integers from –4 to 2 on a horizontal number line. 5. Fill in the blanks with the symbol “” or “”. (a) 6 –6 (b) -3 3 6. Compare the values of –1 and –7 by using a number line. 7. Is the statement “–2 is less than –12” true or false? Explain it. HOTS Evaluating 8. Arrange the integers 6, –1, 4, 1, –7 in ascending order and descending order. Hence, state the smallest integer and the largest integer. 1.2 Basic Arithmetic Operations Involving Integers 1.2.1 Add and subtract integers using number lines or other appropriate methods. Hence, make generalisation about addition and subtraction of integers 1. Addition of integers is the process of finding the total of positive integers or negative integers. 2. On a number line, (a) when adding a positive integer +a to an integer x, the integer x moves a units to the right in the positive direction. x x + (+a) + (+a) (b) when adding a negative integer –a to an integer x, the integer x moves a units to the left in the negative direction. 3 01 Spot A+1 Maths F1.indd 3 19/04/2023 12:57 PM

Learning Area: Numbers and Operations 1 x + (–a) x + (–a) Example 7 Solve each of the following. (a) (+2) + (+4) (b) (-3) + (–5) (c) (+1) + (+4) + (-3) Solution: (a) 1 2 3 4 5 6 7 Start from 2, move 4 units to the right. (+4) (+2) + (+4) = 6 Alternative Method (Coloured chips) (+2) + + (+4) + + + + For addition of positive integers, calculate the number of positive chips. (b) –9 –8 –7 –6 –5 –4 –3 –2 Start from –3, move 5 units to the left. (–5) (–3) + (–5) = –8 Alternative Method (Coloured chips) (–3) – – – (–5) – – – – – For addition of negative integers, calculate the number of negative chips. (c) 0 1 2 3 4 5 6 Start from 1, move 4 units to the right. Follow by 3 units to the left (+4) (–3)   (+1) + (+4) + (–3) = (+5) + (–3) = 2 Alternative Method (Coloured chips) (+1) + (+4) + + + + (–3) – – – A pair of positive and negative chips represents zero. Calculate the number of remaining chips after grouped by pair. Calculator Press (a) 2 + 4 = 6 (b) (–) 3 + (–) 5 = –8 ➡ Diagnostic Test 1.2: Question 1 3. Look at Example 7(a) and 7(b), we found that: (a) (+2) + (+4) = 2 + 4 = 6 (b) (-3) + (–5) = -3 – 5 = –8 Therefore, we can generalise that: x + (+a) = x + a x + (-a) = x – a 4. Subtraction of integers is the process of finding the difference between two integers. 5. Subtraction is the inverse process of addition, therefore on a number line, (a) when subtracting a positive integer +a from an integer x, the integer x moves a units to the left. x – (+a) x – (+a) 4 01 Spot A+1 Maths F1.indd 4 19/04/2023 12:57 PM

CHAPTER 1 Rational Numbers Diagnostic Test 1.5 1 1. Determine whether each of the following is rational number. Explain it. (a) –6 (b) – 7 0 (c) 0.125 (d) 1 10 2. Solve each of the following. (a) 9 – (-0.25) + 3 5 (b) –1 3 4 ÷ 2 – 1 8  (c) –6 3 7 + – 5 2  – 2 (d) 2 5 6 – (–4) × 1 2 3. Haikal has 450 stamps. He gave 1 5 of the stamps to Arif and 1 3 of the remaining stamps to Danial. Calculate the number of stamps that are still with Haikal. HOTS Analysing 1. Which of the following is not an integer? A –4 B 0 C 2.5 D 36 2. Which of the following temperature is higher than –5°C? A −1°C B –6°C C –7°C D –9°C 3. City E is located at 3.18 km to the west of City F, while City G is located at 4.56 km to the east of City F. Find the distance, in km, from City E to City G which passes through City F. A 7.74 B 1.38 C −1.38 D –7.74 4. –5 – (−1) = A −3 B –4 C –5 D –6 5. –12 + 3 × (–2) 6 – (–30) = A 1 2 B 5 6 C – 1 2 D – 2 3 6. Which of the following is not true? A −3 × 4 = −12 B 8 ÷ (−2) = 4 C –9 × 1 = –9 D –6 ÷ (−2) = 3 7. −21, −16, −11, ... The diagram above shows a number pattern. What is the eighth number? A −11 B −1 C 9 D 14 8. Solve –4.5 + (−0.62) × 0.5. A −2.56 B −3.88 C –4.81 D –5.12 MASTERY CHALLENGE 1 15 01 Spot A+1 Maths F1.indd 15 19/04/2023 12:57 PM

Learning Area: Numbers and Operations 1 9. Which of the following fraction is between –1 3 8 and 2 1 5 ? A –1 3 4 C 2 1 8 B –1 2 5 D 2 3 10 10. –0.49 –0.25 M The diagram above shows a number line. Determine the value of M. A 0.37 B 0.11 C −0.01 D −0.13 11. 1 2 3 × 2 1 4 – 1 2  = A 1 5 12 B 211 12 C 3 3 4 D 4 1 6 12. Which of the following is not a rational number? A 3.25 B 2 C 2 D –4 13. Given P 7.5 = – 6 Q = −0.6, find the value of P – Q. A −14.5 B –5.5 C 5.5 D 14.5 14. There are 35 oranges in each box. Haikal bought 9 boxes of oranges and distributed all the oranges to 63 orphans equally. Calculate the number of oranges received by every orphan. A 4 B 5 C 6 D 7 15. 1 kg of dried fish costs RM32.65 and 1 kg of red onions costs RM15.70. Imran bought 1.6 kg of dried fish and 2.4 kg of red onions. Calculate the total amount of money that Imran has to pay. A RM37.68 B RM52.24 C RM88.82 D RM89.92 16. (a) Determine the values of P, Q and R. P –1 Q 0 R 1 1 1 3 (b) (i) Circle the correct calculation step. 4.5 ÷ 3 4 × 7(–6 + 21) = I 4.5 × 4 3 × (–42 + 21) II 4.5 × 3 4 × 105 III 6 × 105 IV 6 × 7(–15) (ii) A factory keeps the produced piano in 4 warehouses. There are 32 pianos in each warehouse. All the pianos with another 40 new pianos will be distributed to 6 musical instrument shops equally. (a) Write the above statement into a number sentence. (b) How many pianos will each of the musical instrument shop receive? 16 01 Spot A+1 Maths F1.indd 16 19/04/2023 12:57 PM

CHAPTER 1 Rational Numbers 1 17. (a) Fill in the box below with the symbol “” or “”. –4 –9 (b) Rearrange all the integers below in ascending order. –3, –9, –6, 1, –8, 4 18. Find the total value of the answers for the following three questions. Show your workings. (a) –27 – (59 + 21) = (b) The original mass of a packet of flour is 8 kg. Calculate the mass of flour taken out if only 1 kg of flour is left. (c) The price of share of a company in the morning is RM0.44. In the evening, the price of share became RM0.39. What is the change in the price of share? 19. The table below shows the vertical distance from the sea level for some objects. Object Vertical distance from the sea level (m) Shark –24 Submarine –33 Helicopter 23 Aeroplane 47 Based on the table above, (a) state the object which is the farthest from the sea level, (b) find the vertical distance between the helicopter and the shark, (c) state the object whose distance from the sea level is more than the distance of shark from the sea level. 20. (a) Solve 0.5 + (-1.2) × 6. (b) Is the value of 5.8 – (25 × 0.5) same as the value in (a)? Prove it. 21. (a) Calculate -12.5 + (–6.8). (b) Multiply 0.7 with the answer in (a). State the answer in two decimal places. 22. The reading of a thermometer in a room is –8°C. (a) Find the temperature reading on the thermometer if the temperature increased by 3°C and then decreased by 4°C. (b) What is the difference of temperature between –8°C and 4°C? 23. Arif owed RM250 from Haikal. He borrowed another RM620 from Haikal. (a) What is the total amount of his debt? Write the answer in the form of a positive integer or a negative integer. (b) Arif paid back RM500 to Haikal. Is his debt settled? Explain your answer. 24. Farhan’s savings in a bank is RM8 500. He issues RM400 each month from January to June to pay for television instalment. (a) Calculate the balance of Farhan’s savings at the end of June. (b) He saved another RM2 300 in July. Calculate Farhan’s total savings at the end of July. 17 01 Spot A+1 Maths F1.indd 17 19/04/2023 12:57 PM

Learning Area: Numbers and Operations 1 25. When –2 3 4 is divided by a certain number, the quotient is equal to 142 multiplied by 1 2 . State the number with the proof of your calculations. HOTS Analysing 26. The length of a plank is 3 m. Haikal has 3 pieces of planks in equal size. He uses 1 1 5 m of each plank to do a project. Calculate in fraction, the length of the remaining planks. 27. A furniture store is conducting a grand sale. The original price of a cupboard in the furniture store is RM478. (a) Calculate the selling price of the cupboard if the original price is reduced by 3 10. (b) Alia wants to share money equally with her 3 siblings to buy the cupboard, what is the amount to be paid by each of them? HOTS Applying 28. Isma walked from his house to a leisure area for a distance of 964.7 m. He took 22 minutes to reach the place. (a) Calculate the distance travelled by him every 1 minute. (b) There is a retail shop nearby the leisure area. If Isma needs to take 4 minutes to reach the retail shop, what is the distance from Isma’s house to the retail shop? HOTS Analysing 18 01 Spot A+1 Maths F1.indd 18 19/04/2023 12:57 PM

4 37 4.1.1 Represent the relation between three quantities in the form of a : b : c 1. Ratio for three quantities is a comparison among these quantities with the same units. 2. Ratio for these three quantities can be written as a : b : c such that a, b and c are non-zero integers. We read them as “a to b to c”. 3. Ratio is written without units. Example 1 Write RM100 to RM63 in ratio form a : b or a b . Solution: 100 : 63 or 100 63 . ➡ Diagnostic Test 4.1: Question 1 Example 2 Write 30 cm, 41 cm and 62 cm in ratio form a : b : c. Solution: 30 cm : 41 cm : 62 cm = 30 : 41 : 62 ➡ Diagnostic Test 4.1: Question 2 4.1.2 Identify and determine the equivalent ratios in numerical, geometrical or daily situation contexts If a b can be expanded or simplified into c d , then a b and c d are equivalent ratios. Make sure the units for all quantities are the same. Example 3 Determine whether the following pairs of ratios are equivalent ratios or not. (a) 12 : 24 : 48 and 1 : 2 : 4 (b) 3 : 5 : 8 and 15 : 24 : 40 Solution: (a) 1 : 2 : 4 = 1 × 12 : 2 × 12 : 4 × 12 = 12 : 24 : 48 Thus, they are equivalent ratios. Alternative Method 12 : 24 : 48 = 12 12 : 24 12 : 48 12 = 1 : 2 : 4 (b) 3 : 5 : 8 = 3 × 5 : 5 × 5 : 8 × 5 = 15 : 25 : 40 Since one of the numbers is not the same after multiplied by 5, thus they are not equivalent to each other. ➡ Diagnostic Test 4.1: Question 3 Example 4 A pen costs RM8. What is the total cost of 5 similar pens? Solution: 1 5 = RM8 RM( ) 1 × 8 5 × 8 = RM8 RM(40) Hence, the total cost for 5 pens is RM40. ➡ Diagnostic Test 4.1: Questions 4 – 6 Every number needs to be multiplied or divided by the same number. 4.1 Ratios 4 Ratios, Rates and Proportions CHAPTER 04 Spot A+1 Maths F1.indd 37 19/04/2023 1:47 PM

Learning Area: Relationship and Algebra 4 38 Example 5 A C B P R Q The diagram shows two similar triangles, ABC and PQR. Given that the lengths AB : BC : CA ß PQ : QR : RP. If AB : BC : CA = 4 : 3 : 5 and PQ is 12 cm, find the lengths of QR and RP. Solution: From the ratio AB : BC : CA, the equivalent ratio = 4 × 3 : 3 × 3 : 5 × 3 = 12 : 9 : 15 Then, QR = 9 cm and RP = 15 cm. ➡ Diagnostic Test 4.1: Questions 7 and 8 4.1.3 Express ratios of two and three quantities in simplest form A ratio can be simplified by either multiplying or dividing each number by their common factors other than 1. Example 6 Express the following ratios in their simplest forms. (a) 2 3 : 6 21 (b) 1.5 : 4.5 : 2 Solution: (a) 2 3 : 6 21 = 2 3 ÷ 6 21 a : b = a b = a ÷ b = 2 3 × 21 6 = 7 3 = 7 : 3 (b) 1.5 : 4.5 : 2 = 1.5 × 10 : 4.5 × 10 : 2 × 10 = 15 : 45 : 20 = 15 5 : 45 5 : 20 5 The highest common factor is 5. = 3 : 9 : 4 Calculator Press (a) 2 3 ➤ ÷ 6 2 1 = 7 3 ➡ Diagnostic Test 4.1: Question 9 1. Express the following ratios in their simplest forms. 25 minutes : 1.5 hours ✓ ✗ 25 minutes : 1.5 hours = 25 minutes : 90 minutes = 5 : 18 25 minutes : 1.5 hours = 25 : 1.5 = 5 : 0.3 = 50 : 3 2. If x : y = 1 : 4 and y : z = 6 : 5, find x : y : z. ✓ ✗ x : y = 1 × 3 : 4 × 3 = 3 : 12 y : z = 6 × 2 : 5 × 2 = 12 : 10 Therefore, x : y : z = 3 : 12 : 10. x : y = 1 + 2 : 4 + 2 = 3 : 6 Therefore, x : y : z = 3 : 6 : 5 Learn it right Diagnostic Test 4.1 1. Write each of the following in ratio form a : b or a b . (a) 21 cm and 30 cm (b) 1 hour and 1 hour 12 minutes (c) 1.4 kg and 490 g Change the decimal number into whole number. 04 Spot A+1 Maths F1.indd 38 19/04/2023 1:47 PM

139 13.1 The Pythagoras’ Theorem 13.1.1 Identify and define the hypotenuse of a right-angled triangle Hypotenuse is the longest side of a right-angled triangle and it is opposite to the right angle. A B C Hypotenuse In the diagram above, AB is the hypotenuse. Example 1 Name the hypotenuse of the right-angled triangle below. L J K Solution: LK ➡ Diagnostic Test 13.1: Question 1 13.1.2 Determine the relationship between the sides of right-angled triangle According to the Pythagoras’ theorem, in a rightangled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. B C c b a A Proof of Pythagoras’ theorem using water demonstration. https://www.youtube.com/watch?v=CAkMUdeB06o Spotlight Portal Spotlight Portal TIPS Corner Right angle is 90°. Example 2 State the relationship between the sides of the right-angled triangle below. B C A Solution: AC2 + CB2 = AB2 ➡ Diagnostic Test 13.1: Question 2 13.1.3(i) Determine the length of the unknown side of a right-angled triangle According to the Pythagoras’ theorem, the length of the unknown side of a right-angled triangle can be determined if the length of the other two sides are known. Example 3 Find the value of x for each of the following rightangled triangles. (a) 12 m x m 13 m (b) 8 cm 15 cm x cm Solution: (a) 132 = 122 + x2 (b) x2 = 152 + 82 x2 = 169 – 144 = 225 + 64 = 25 = 289 x =  25 x = 289 = 5 = 17 Calculator (b) Press  1 5 x2 + 8 x2 = 17 ➡ Diagnostic Test 13.1: Question 3 Pythagoras’ theorem: a2 + b2 = c2 or c2 – a2 = b2 or c2 – b2 = a2 13 13 The Pythagoras’ Theorem CHAPTER 13 Spot A+1 Maths F1.indd 139 19/04/2023 2:25 PM

PENTAKSIRAN SUMATIF 146 PENTAKSIRAN SUMATIF UJIAN AKHIR SESI AKADEMIK (UASA) 1. Which of the following is an integer? A 3.7 B 1 5 C –2.4 D –9 2. Diagram 1 shows a calculation process. 4 × 6 + 4 × 10 + 4 × (-3) = 4 × (6 + 10 – 3) = 4 × 13 = 52 Diagram 1 Which of the following arithmetic law of operations is used in the computation above? A Identity Law B Distributive Law C Commutative Law D Associative Law 3. Simplify 20m5 n2 ÷ 4m2 n3 A 4m3 n B 5m3 n C 4m3 n D 5m3 n 4. The lowest common multiple (LCM) of 2, 3 and m is 12. What is the smallest value of m? A 4 B 5 C 6 D 7 5. The sum of all prime factors of 72 is A 2 B 3 C 5 D 7 6. 2 1 4 + 1.53 = A 1.5 B 2.14 C 3.375 D 4.875 7. It is given that h : k = 2 : 5, find the ratio of 2k + h : 4k 2 . A 1 : 2 B 2 : 5 C 5 : 6 D 6 : 5 SECTION A [20 marks] Answer all questions. 8. Given that 4x + y = 5 and –2x – 6y = 14. Find the value of y. A 3 B 2 C -2 D -3 9. Which of the following represents the solution of the simultaneous linear inequalities of –4  5 – x and 5 – x  3? A 2 9 B 2 9 C 2 9 D 2 9 10. In Diagram 2, POQ and ROS are straight lines. R Q O S T 2x x P 57° Diagram 2 Find the value of x. A 40° B 41° C 42° D 43° 11. The highest common factor (HCF) of 18 and 24 is 3k. Find the value of k. A 1 B 2 C 3 D 4 12. Diagram 3 shows a polygon. Diagram 3 Calculate the number of diagonals for the polygon. A 5 B 6 C 8 D 9 P.Sumatif Spot A+1 Maths F1.indd 146 19/04/2023 2:26 PM

PENTAKSIRAN SUMATIF 148 Pentaksiran Sumatif SECTION B [20 marks] Answer all questions. 21. (a) Mark (✓) for numbers that are integers. [2 marks] Answer: 9 1 4 –120 7.3 (b) Write the factors of the given number in the empty space. [2 marks] Answer: 18 22. (a) Complete the steps of the operation below. [2 marks] Answer: 2 1 4 × 1 100 = 4 × 1 100 =  = (b) Circle the common multiple of the following numbers. [2 marks] Answer: Number Common Multiple 3 and 4 3 4 12 24 23. (a) Express each of the following ratios in the simplest form. [2 marks] Answer: Ratio Equivalent ratio 16 : 24 30 : 75 45 : 95 as as  P.Sumatif Spot A+1 Maths F1.indd 148 19/04/2023 2:26 PM

PENTAKSIRAN SUMATIF 150 Pentaksiran Sumatif SECTION C [60 marks] Answer all questions. 26. (a) Diagram 1 shows two containers, P and Q containing the same number of pens. P: x + 8 Q: 2x – 4 Diagram 1 Based on Diagram 1, (i) write a linear equation. [1 mark] (ii) find the total number of pens in the two containers. [2 marks] Answer: (i) (ii) (b) At the reading corner of Class 1 Pintar, the ratio of the number of storybooks to the number of magazines is 1 : 3 while the ratio of the number of magazines to the number of reference books is 2 : 7. Find the ratio of the number of storybooks to the number of magazines to the number of reference books. [3 marks] Answer: (c) (i) Solve: [2 marks] 2(x + 4) = 3x (ii) Diagram 2 shows an incomplete number line. –1.5 0 1.5 Diagram 2 State the positive integers and negative integers of the number line. [2 marks] Answer: (i) (ii) P.Sumatif Spot A+1 Maths F1.indd 150 19/04/2023 2:27 PM

PENTAKSIRAN SUMATIF 151 Pentaksiran Sumatif 27. (a) In an experiment, a type of liquid has an initial temperature of 25°C. The liquid is cooled by 1.2°C for every minute. It is given that the freezing point of the liquid is –10°C. Does the liquid freeze after half an hour? Explain. [3 marks] Answer: (b) (i) Diagram 3 shows several number cards. 11 –6 0 –4 –1 –8 –2.3 Diagram 3 Calculate the product of the largest integer and the smallest integer. [2 marks] (ii) Calculate the value of 9 4 5 ÷  3 4 – – 1 8 . Express the answer in the simplest fraction form. [2 marks] Answer: (i) (ii) (c) (i) List all the factors of 42. [1 mark] (ii) Find the difference between the lowest common multiple (LCM) and the highest common factor (HCF) of 6, 18 and 42. [2 marks] Answer: (i) (ii) P.Sumatif Spot A+1 Maths F1.indd 151 19/04/2023 2:27 PM

157 ANSWERS Chapter 1 Diagnostic Test 1.1 1. (a) –2 (b) +90 (c) +1 000 2. Positive numbers: +6, 0.95, 2 9 Negative numbers: –0.3, – 1 10 , –2.34 3. Positive integers: 72, 8 Negative integers: –11, –21 Non-integers: – 2 3 , 4.9 4. –4 –3 –2 –1 0 1 2 5. (a)  (b)  6. –7 –6 –5 –4 –3 –2 –1 –7 is smaller than –1 because –7 is at the left of –1. 7. The statement is false because –2 lies at the right of –12. 8. Ascending order: –7, –1, 1, 4, 6 Descending order: 6, 4, 1, -1, –7 Value of the smallest integer: –7 Value of the largest integer: 6 Diagnostic Test 1.2 1. (a) 12 (b) –16 (c) 3 2. (a) –7 (b) 3 (c) 8 3. (a) 30 (b) –8 (c) –21 (d) 16 4. (a) 4 (b) –4 (c) 4 (d) –4 5. (a) –11 (b) –7 (c) 12 6. (a) –0.75 (b) 0 (c) 63 (d) 0 (e) 1 7. (a) 478 292 (b) 5 875 000 8. (a) 92 982 (b) 170 800 9. (a) 105 750 (b) 7 056 10. 70 marks Diagnostic Test 1.3 1. –1 3 9 – 10 15 0 2 3 16 12 2. – 1 2 – 1 4 0 1 6 2 3 Descending order: 2 3 , 1 6 , – 1 4 , – 1 2 3. (a) 2 (b) – 1 4 (c) 4 8 9 (d) –5 17 20 4. 3 9 20 kg Diagnostic Test 1.4 1. –1.2 –0.7 0 0.1 0.5 2. (a) Ascending order: –5.5, –4.5, –3.5, 0.5 (b) Descending order: 0.5, 0.3, -0.4, -0.6 3. (a) 7.6 (b) 19.3 (c) –6 (d) -0.76 (e) -19.9 (f) 36.4 4. RM163.75 5. 93.75 cm / 0.9375 m Diagnostic Test 1.5 1. (a) –6 is a rational number because –6 is an integer that can be expressed in fractional form, that is –6 1 . (b) – 7 0 is not a rational number because the denominator is 0. (c) 0.125 is a rational number because 0.125 can be expressed in fractional form, that is 1 8 . (d) 1 10 is a rational number because 1 10 is in fractional form. 2. (a) 9 17 20 (b) – 14 15 (c) –10 13 14 (d) 4 5 6 3. 240 stamps Mastery Challenge 1 1. C 2. A 3. A 4. B 5. C 6. B 7. D 8. C 9. C 10. D 11. B 12. C 13. A 14. B 15. D ANSWERS Answer SPotlight A+1 Maths F1.indd 157 19/04/2023 2:29 PM

158 ANSWERS 16. (a) P = –1 2 3 , Q = – 1 3 , R = 2 3 (b) (i) III (ii) (a) [(4 × 32) + 40] ÷ 6 (b) 28 pianos 17. (a)  (b) –9, –8, –6, –3, 1, 4 18. (a) –27 – (59 + 21) = –27 – 80 = –107 (b) 1 kg – 8 kg = –7 kg (c) RM0.39 – RM0.44 = –RM0.05 Total value = –107 + (–7) + (–0.05) = –107 – 7 – 0.05 = –114.05 19. (a) Aeroplane (b) 47 m (c) Submarine and aeroplane 20. (a) –6.7 (b) 5.8 – (25 × 0.5) = 5.8 – 12.5 = –6.7 Yes, the values are same. 21. (a) –19.3 (b) –13.51 22. (a) –9°C (b) 12°C 23. (a) –870 (b) Arif’s debt is not settled because he still owes RM370 from Haikal. 24. (a) RM6 100 (b) RM8 400 25. – 11 284 26. 5 2 5 m 27. (a) RM334.60 (b) RM83.65 28. (a) 43.85 m (b) 1 140.1 m Chapter 2 Diagnostic Test 2.1 1. (a) Yes (b) No (c) Yes 2. (a) 1, 2, 4, 5, 10, 20 (b) 1, 2, 3, 4, 6, 9, 12, 18, 36 (c) 1, 2, 3, 6, 7, 14, 21, 42 3. (a) Yes (b) No (c) Yes 4. (a) 2 (b) 3 and 17 (c) 7 and 13 5. (a) 2 × 3 × 5 (b) 3 × 3 × 5 (c) 2 × 2 × 2 × 3 × 3 6. (a) No (b) Yes (c) Yes (d) No 7. (a) 1 and 2 (b) 1 and 3 (c) 1 and 2 (d) 1, 3, 5, 15 8. (a) 4 (b) 14 (c) 6 (d) 15 9. (a) 18 cm (b) 9 10. 40 squares Diagnostic Test 2.2 1. (a) 6, 12, 18, 24 (b) 7, 14, 21, 28, 35 (c) 8, 16, 24, 32, 40, 48 (d) 9, 18, 27, 36, 45, 54 (e) 12, 24, 36, 48, 60 2. (a) 15 and 30 (b) 30 (c) 36 (d) 12, 24, 36 3. (a) 28 (b) 105 (c) 36 (d) 48 4. Impossible. They will meet on every 36 days. 5. 10:45 morning. Mastery Challenge 2 1. A 2. D 3. B 4. C 5. B 6. A 7. C 8. C 9. B 10. A 11. C 12. B 13. D 14. B 15. C 16. 78 2 × 39 2 × 3 × 13 17. 41, 61, 71 18. 1, 2, 3, 6, 9, 18, 27, 54 19. 56 20. 4; 13; 26 21. 3; 7; 21; 49 22. 12, 24, 48 23. 24 24. 12 25. (a) 15 (b) 3 26. 48 gift parcels 27. m = 4 28. y = 84 29. k = 47 30. 48 seconds 31. (a) 39 (b) 49 Chapter 3 Diagnostic Test 3.1 1. 22 2. 32 = 3 × 3 3. 4 = 2 × 2 = 22 Answer SPotlight A+1 Maths F1.indd 158 19/04/2023 2:29 PM

169 ANSWERS (ii) 1 2 3 4 5 Pocket money (RM) 12. (a) (i) Stem Leaf 1 8 2 0 8 9 3 2 4 6 7 4 1 3 Key: 2 | 8 means 2.8 (ii) Between 3.2 m until 3.7 m. (b) (i) 5 gold medals (ii) 4 medals 13. (a) (i) Score Midpoint Frequency 21 – 25 23 6 26 – 30 28 5 31 – 35 33 8 36 – 40 38 9 41 – 45 43 6 46 – 50 48 4 51 – 55 53 2 (ii) Frequency 23 2 0 28 33 38 Score 18 43 4 6 8 10 48 53 58 (iii) 21 students (b) (i) 120 residents (ii) 41 2 3 % (iii) (23 – 27) years old 14. (a) 72° (b) (i) 50 0 Monday 100 150 200 250 Number of visitors Day Tuesday Wednesday Adult Thursday Friday Children (ii) 46.3% (iii) Wednesday, Thursday and Friday Chapter 13 Diagnostic Test 13.1 1. (a) c (b) a (c) b 2. (a) r 2 = p2 + q2 (b) q2 = p2 + r2 3. (a) x = 5 (b) x = 5 4. x = 4 5. 4.47 m Diagnostic Test 13.2 1. Right-angled triangle. 2. LN = 15 cm, ∠LNP = 90〫 Mastery Challenge 13 1. D 2. D 3. C 4. B 5. A 6. B 7. A 8. C 9. Yes. r = 25 cm 10. (a) iii (b) i (c) ii 11. BE =  162 cm, FE = 5 cm, FB = 13 cm No 12. The length of AC = 20x2 + 5y2 = 5 units, the area of triangle ABC = 4x2 + 3xy – y2 = 6 unit2 13. (a) 40 km2 (b) RM600 000 000 14. (a) 12 cm (b) Yes 15. No 16. (a)  75 cm (b) (15 + 53) cm 17. (a) 42 m (b) No 18. (a) 86 cm (b) 492 cm2 19. (a) 96.95 m (b) 534.375 m2 20. (a) 26 cm (b) 128 cm 21. (a) 48 cm2 (b) 52.11 cm 22. Yes Pentaksiran Sumatif Ujian Akhir Sesi Akademik (UASA) Section A 1. An integer is a group of numbers that are positive whole numbers and negative whole numbers including zero. Answer: D 2. Addition and subtraction are said to obey the Distributive Law if and only if a × (b + c) = a × b + a × c a × (b – c) = a × b – a × c Answer: B  Answer SPotlight A+1 Maths F1.indd 169 19/04/2023 2:31 PM

170 ANSWERS 3. 20m5 n2 ÷ 4m2 n3 = 5 1 20m5 n2 4m2 n3 = 5m5–2n2–3 = 5m3 n–1 = 5m3 n Answer: D 4. Method of listing the common multiples Multiples of 2: 2, 4, 6, 8, 10, 12, 14, ... Multiples of 3: 3, 6, 9, 12, 15, ... Multiples of 4: 4, 8, 12, 16, ... ✓ Multiples of 6: 6, 12, ... ˜ The smallest value of m is 4. Answer: A 5. Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 123 Prime numbers º The prime factors of 72 are 2 and 3. ˜ 2 + 3 = 5 Answer: C 6.  2 1 4 + 1.53 = 9 4 + 1.53 = 3 2 + 3.375 = 1.5 + 3.375 = 4.875 Answer: D 7. 2k + h : 4k 2 2(5) + 2 : 4(5) 2 12 : 10 6 : 5 Answer: D 8. 4x + y = 5 ...  –2x – 6y = 14 ...   × 2, –4x – 12y = 28 ... c  + c, –11y = 33 y = –3 Answer: D 9. –4  5 – x x  5 + 4 x  9 5 – x  3 –x  3 – 5 –x  –2 x  2 ˜ 2  x  9 Answer: A 10. 2x + x = 180° – 57° 3x = 123° x = 123° ÷ 3 x = 41° Answer: B 11. Factors of 18: 1, 2, 3, 6, 9, 18 Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Therefore, the highest common factor of 18 and 24 is 6. 3k = 6 k = 2 Answer: B 12. Number of diagonals = n(n – 3) 2 = 6(6 – 3) 2 = 9 Answer: D 13. h = 64° + 75° h = 139° Answer: B 14. There are 8 elements in set P. Answer: D 15. –3 + (–7) = –3 – 7 = –10 Answer: B 16. 48 cm ÷ 4 = 12 cm Area of square = 12 cm × 12 cm = 144 cm2 Area of triangle = 1 2 × 12 cm × 12 cm = 72 cm2 144 cm2 + 72 cm2 = 216 cm2 Answer: C 17. RM800 – RM600 = RM200 Answer: B 18. Length of the diagonal = 52 + 122 =  169 = 13 Answer: B 19. y2 = ( 109)2 – 102 = 109 – 100 = 9 y = 3 Answer: C 20. 20 50 × 100% = 40% Answer: C  Answer SPotlight A+1 Maths F1.indd 170 19/04/2023 2:31 PM

171 ANSWERS Section B 21. (a) 9, –120 (b) 1, 2, 3, 6, 9, 18 22. (a)  2 1 4 × 1 100 = 9 4 × 1 100 = 9 400 = 3 20 (b) 12, 24 23. (a) 2 : 3, 2 : 5, 9 : 19 (b) (i) Yes (ii) No 24. (a) (i) ✓ (ii) ✗ (b) (i) h and k (ii) g and m 25. (a) (i) –1  x  9 (ii) –1  x  9 (b) (i) ✗ (ii) ✓ Section C 26. (a) (i) x + 8 = 2x – 4 (ii) x + 8 = 2x – 4 2x – x = 8 + 4 x = 12 P = 12 + 8 P = 20 Q = 2(12) – 4 Q = 24 – 4 Q = 20 Total = 20 + 20 = 40 pens (b) Let x = number of storybooks (b) y = number of magazines (b) z = number of reference books x : y = 1 : 3 y : z = 2 : 7 x : y = 2 : 6 y : z = 6 : 21 Therefore, x : y : z = 2 : 6 : 21 (c) (i) 2(x + 4) = 3x 2x + 8 = 3x 3x – 2x = 8 x = 8 (ii) Positive integer = 1, negative integer = –1 27. (a) The temperature of liquid after half an hour = 25°C + (–1.2°C × 30) = 25°C – 36°C = –11°C Because the liquid reaches freezing point (–11°C  –10°C), then the liquid freezes after half an hour.  (b) (i) Largest integer = 11 Smallest integer = –8 11 × (–8) = –88 (ii) 9 4 5 ÷  3 4 – – 1 8  = 9 4 5 ÷  3 4 + 1 8  = 49 5 ÷ 7 8 = 49 5 × 8 7 = 11 1 5 (c) (i) 1, 2, 3, 6, 7, 14, 21, 42 (ii) LCM: Method of repeated division 3 6, 18, 42 2 2, 6, 14 3 1, 3, 7 7 1, 1, 7 1, 1, 1 Therefore, the LCM of 6, 18 and 42 is 3 × 2 × 3 × 7 = 126. HCF: Method of repeated division 3 6, 18, 42 2 2, 6, 14 1, 3, 7 Therefore, the HCF of 6, 18 and 42 is 3 × 2 = 6. Difference between LCM and HCF = 126 – 6 = 120 28. (a) (i) 3  8.1 ≈ 3 8 ≈ 2 (ii)  65 ≈  64 ≈ 8 (iii) 3 –123 ≈ 3 –125 ≈ –5 (b) Perimeter = 2(y + 7) cm + 2(5y – 25) cm = (2y + 14) cm + (10y – 50) cm = (2y + 14 + 10y – 50) cm = (12y – 36) cm (c) (i) 4h  RM50 (ii) h  RM50 4 h  12.5 Amin has bought 12 boxes of mango juice. Divide the given numbers until all the quotients become 1. Divide the given numbers by a common factor repeatedly.   Answer SPotlight A+1 Maths F1.indd 171 19/04/2023 2:31 PM

172 ANSWERS 29. (a) 18(3) + 10x = 104 54 + 10x = 104 10x = 104 – 54 10x = 50 x = 50 10 x = 5 (b) (i) 4 + 5x 2  7 4 + 5x  14 5x  10 x  2 (ii) 3 7 k – 9  6 3 7 k  15 k  15 × 7 3 k  35 (c) (i) HK (ii) x = 90° – 34° x = 56° 30. (a) (i) x = 180° – 60° x = 120° (ii) y = 180° – 120° – 38° y = 22° (iii) x – y = 120° – 22° x – y = 98° (b) Side = 76 cm ÷ 4 (b) = 19 cm Area = 19 cm × 19 cm = 361 cm2 (c) (i) Pʹ = {1, 3, 6} (ii) Q ⊂ P 31. (a) (i) Number of days took by a group of students to complete a geography case study Stem Leaf 1 0 1 2 3 4 6 9 2 0 0 0 1 1 1 1 3 4 4 4 3 0 0 Key: 1  0 means 10 days (ii) 10 20 × 100% = 50% (b) (i) 5 students (ii) 9 – 1 = 8 books (c) (i) EG = 202 + 132 =  569 = 23.85 cm GK = 112 + 72 =  170 = 13.04 cm EK = 23.852 + 13.042 = 738.86 = 27.18 cm (ii) Perimeter = 27.18 cm + 20 cm + 13 cm + 11 cm + 7 cm = 78.18 cm     Answer SPotlight A+1 Maths F1.indd 172 19/04/2023 2:31 PM