ii Contents Must Know iii - x Chapter 1 Variation 1 – 11 NOTES 1 Paper 1 3 Paper 2 7 Chapter 2 Matrices 12 – 22 NOTES 12 Paper 1 14 Paper 2 18 Chapter 3 Consumer Mathematics: Insurance 23 – 30 NOTES 23 Paper 1 25 Paper 2 27 Chapter 4 Consumer Mathematics: Taxation 31 – 40 NOTES 31 Paper 1 33 Paper 2 36 Chapter 5 Congruency, Enlargement and Combined Transformations 41 – 56 NOTES 41 Paper 1 44 Paper 2 49 Chapter 6 Ratios and Graphs of Trigonometric Functions 57 – 73 NOTES 57 Paper 1 59 Paper 2 67 Chapter 7 Measures of Dispersion for Grouped Data 74 – 94 NOTES 74 Paper 1 76 Paper 2 82 Chapter 8 Mathematical Modeling 95 – 104 NOTES 95 Paper 1 97 Paper 2 99 SPM Assessment 105 – 117 Answers 118 – 134 Contents 1202BS Maths F5.indd 2 07/01/2022 3:35 PM
Important Definitions (Chapter 1) 1 @ Pan Asia Publications Sdn. Bhd. Important Definitions (Chapter 3) 7 @ Pan Asia Publications Sdn. Bhd. Important Definitions (Chapter 2) 3 @ Pan Asia Publications Sdn. Bhd. Important Definitions (Chapter 4) 9 @ Pan Asia Publications Sdn. Bhd. Important Definitions (Chapter 3) 5 @ Pan Asia Publications Sdn. Bhd. Important Definitions (Chapter 4) 11 @ Pan Asia Publications Sdn. Bhd. Principle of Indemnity, Policy and Premium Type of Matrices Risk and Insurance Taxation and Income Tax Road Tax, Property Assessment Tax and Quit Rent • Under the principle of indemnity, the insurance companies will pay compensation to policyholders in the occurrence of a loss insured for an amount not exceeding the loss incurred, subject to the sum insured. • Policy is a document that contains information on the scope of coverage, terms and conditions and exclusions in an insurance contract. • Premium is an amount of money payable by the policyholder to the insurance company. • A matrix is a set of numbers arranged in rows and columns to form a rectangular or a square array. • A row matrix has only one row. • A column matrix has only one column. • Matrix with m rows and n columns has the order m × n and is read as “matrix m by n”. • The matrices that are expressed in the form of equation is known as matrix equation. • Road tax is the tax levied on road user who owns vehicles including motorcycle and car. • Property assessment tax is the tax levied on all holdings or properties such as residential houses, industries, commercial buildings and vacant lands. • Quit rent is the tax levied on the owner of agricultural land, corporate land and land with building. • Taxation is a process of revenue(money) collection from individuals or companies, for use in the country’s development, by providing various facilities for the wellbeing of all citizens. • Income tax is a tax that imposed on the income earned by a salaried individual or the profit earned by a company operating in Malaysia. • Risk is the possibility of a disaster that cannot be avoided. • Insurance is a contract signed between the insurance company and the insurance owner. Under this contract, the insurance company promises to pay compensation for loss covered in the policy, in return for the premium paid by the policyholder. • Direct variation explains the relation between two variables, such that when variable y increases, then variable x also increases at the same rate and vice versa. This relation can be written as y varies directly as x. • In inverse variation, variable y increases when the variable x decreases at the same rate and vice versa. This relation can be written as y varies inversely as x. • Constant is a fixed or unchanged quantity value. Direct Variation, Inverse Variation and Constant MUST KNOW Important Definitions Must Know 1202BS Maths F5.indd 1 21/01/2022 4:16 PM
Important Facts (Chapter 3) 8 @ Pan Asia Publications Sdn. Bhd. Important Facts (Chapter 1) 2 @ Pan Asia Publications Sdn. Bhd. Important Facts (Chapter 4) 10 @ Pan Asia Publications Sdn. Bhd. Important Facts (Chapter 2) 4 @ Pan Asia Publications Sdn. Bhd. Important Facts (Chapter 4) 12 @ Pan Asia Publications Sdn. Bhd. Important Facts (Chapter 3) 6 @ Pan Asia Publications Sdn. Bhd. Life Insurance and General Insurance Express the Relation in the Form of Equation Taxation Income tax, Property Assessment Tax and Quit Rent Addition and Subtraction of Matrices and Inverse Matrices Deductible and Co-insurance • The general steps in expressing the relation in the form of equation: (i) Write the relationship in the form of relation and equations with k as constant. (ii) Replace the value of x and the value of y with the given value. (iii) Find the value of constant k. (iv) Write the expression of y in terms of x. • y is varies directly as x, y fi x, y = kx where k is a constant. • y is varies inversely as x3 , y fi 1 x3 , y = k x3 . • y is varies directly as w and square root of x and varies inversely as cube of z, y fi w! x z3 , y = kw! x z3 . • All tax revenue collected is based on the acts passed in parliament and the collection of the revenue is used in the development of the country by providing various facilities for the well-being of all citizens. • Inland Revenue Board(IRB) and Royal Malaysian Customs Department are responsible for direct and indirect tax collection in Malaysia. The state government is responsible for the collection of revenue from mining, land and forests, revenue from the local authority and acquisition from the issuance of licenses except those collected by the Federal Government. • Deductible is an amount that must be borne by the policyholder before they can make a claim from the insurance company. • Co-insurance is the cost sharing of the loss between the insurance company and the policyholder. • Matrix M = Matrix N if and only if both the matrices have the same order and each corresponding element is equal. • Addition and subtraction of matrices can only be performed on the matrices with the same order. • If matrix A has an order of m × n and matrix B has an order of n × p, then the multiplication AB can be performed and the order of AB is m × p. • Given matrix A = [ a b ] c d , the inverse matrix, A–1 can be obtained using the formula as follow, A–1 = 1 ad – bc [ d –b ] –c a If the determinant ad – bc = 0, then the matrix does not has inverse matrix. • Chargeable income = Total annual income – tax exemption – tax relief. • Income tax payable = Income tax calculated based on the chargeable income – rebate – zakat payment • Property assessment tax = property assessment tax rate × annual value • Quit rent = quit rent rate per unit area × total land area. • Life insurance provides financial protection to the policyholder or his/her family members upon the death of the policyholder, suffering from critical illness and disability. • General insurance provides coverage against any loss or damage incurred, apart from the risks covered by life insurance. General insurance provides protection against any loss or damage to property incurred by the policyholder such as motor insurance, medical insurance, accident insurance and travel insurance. MUST KNOW Important Facts Must Know 1202BS Maths F5.indd 2 21/01/2022 4:16 PM
Common Mistakes (Chapter 1) 25 @ Pan Asia Publications Sdn. Bhd. Common Mistakes (Chapter 3) 31 @ Pan Asia Publications Sdn. Bhd. Common Mistakes (Chapter 1) 27 @ Pan Asia Publications Sdn. Bhd. Common Mistakes (Chapter 3) 33 @ Pan Asia Publications Sdn. Bhd. Common Mistakes (Chapter 2) 29 @ Pan Asia Publications Sdn. Bhd. Common Mistakes (Chapter 4) 35 @ Pan Asia Publications Sdn. Bhd. Combined Variation Medical Insurance Graph of Inverse Variation Multiplication of Matrices Motor Insurance Zakat Correct Wrong Insurance company only pay medical costs that have deducted deductible and coinsurance. Assuming that after having medical insurance, all medical costs will be paid by the insurance company. Correct Wrong Graph y is varies inversely as x. y 0 1 – x Graph y is varies inversely as x. y 1 – 0 x Correct Wrong Zakat payment is deducted from income tax payable. Zakat payment is treated as donation and included in tax exemption. Correct Wrong Third party policy do not cover loss and damage to one’s own vehicle due to theft and accident. The presumption that a third party policy for motor insurance provides protection against loss and damage to one’s own vehicle due to theft and accident. Correct Wrong Correct multiplication of matrices [ 3 6 ] 2 4 [ 9 0 ] 5 7 = [ 3(9) + 6(5) 3(0) + 6(7)] 2(9) + 4(5) 2(0) + 4(7) = [ 57 42 ] 38 28 Wrong multiplication of matrices [ 3 6 ] 2 4 [ 9 0 ] 5 7 = [ 3(9) 6(0)] 2(5) 4(7) = [ 27 0 ] 10 27 Correct Wrong y is varies inversely as x and z. y fi 1 xz y is varies inversely as x and z. y fi x z MUST KNOW Common Mistakes Must Know 1202BS Maths F5.indd 5 21/01/2022 4:16 PM
Important Diagrams (Chapter 3) 32 @ Pan Asia Publications Sdn. Bhd. Important Diagrams (Chapter 1) 26 @ Pan Asia Publications Sdn. Bhd. Important Diagrams (Chapter 3) 34 @ Pan Asia Publications Sdn. Bhd. Important Diagrams (Chapter 1) 28 @ Pan Asia Publications Sdn. Bhd. Important Diagrams (Chapter 4) 36 @ Pan Asia Publications Sdn. Bhd. Important Diagrams (Chapter 2) 30 @ Pan Asia Publications Sdn. Bhd. Insurance Graph of Direct Variation Motor insurance Calculate the Income Tax Payable Graph of Inverse Variation Solving Simultaneous Linear Equations y 0 x2 y α x2 Policy Coverage Act Third Party Third party, fire & theft Comprehensive Liability to third party due to injury and death. Yes Yes Yes Yes Loss of property suffered by third party. No Yes Yes Yes Loss to own vehicle due to accidental, fire or theft. No No Yes Yes Loss and damage to own vehicle due to accident. No No No Yes Simultaneous Linear Equation ax + by = p cx + dy = q Matrix form AX = B [ a b ] c d [ x ] y = [ p ] q [ x ] y = 1 ad – bc [ d –b ] –c a [ p ] q (i) y 0 1 – x (ii) y x 0 Calculate the Chargeable Income Calculate the Income Tax Deduct Tax Rebate Income Tax Payable pays a premium Policyholder Insurance Company pays compensation for any loss incurred MUST KNOW Important Diagrams Must Know 1202BS Maths F5.indd 6 21/01/2022 4:16 PM
1 Chapter 1 Variation 1.1 Direct Variation 1. If y varies directly as x, then y fi x y = kx or y x = k where k is the constant of variation. Example: Given that y varies directly as x and y = 20 when x = 5. Then, y fix y = kx 20 = k(5) k = 20 5 = 4 Therefore, y = 4x 2. Other cases of direct variation are y fi x2 , y fi x3 , y fi x 1 2 or y fi ! x which can be written as y = kx2 , y = kx3 , y = kx 1 2 or y = k! x . Example: Given that E varies directly as the square root of F and E = 9 when F = 36. Calculate the value of E when F = 16. METHOD 1 (Find the value of k) E fi !F E = k!F 9 = k! 36 9 = k(6) k = 9 6 = 3 2 Hence, E = 3 2 !F When F = 16 E = 3 2 × ! 16 = 3 2 × 4 = 6 METHOD 2 (Make k as the subject of equation) E fi !F E = k!F k = E !F Hence, E1 !F1 = E2 !F2 When 9 ! 36 = E2 ! 16 E2 = 9 ! 36 × ! 16 = 9 6 × 4 = 6 1.2 Inverse Variation 1. If y varies inversely as x, then y fi 1 x that is y = k( 1 x ) y = k x or xy = k where k is the constant of variation. Example: Given that y varies inversely as x and y = 9 when x = 6. Then, y fi 1 x y = k x k = xy k = 6 × 9 = 54 Therefore, y = 54 x 2. Other cases of inverse variation are y fi 1 x2 , y fi 1 x3 , y = 1 ! x which can be written as y = k x2 , y = k x3 , y = k ! x . Example: Given that w varies inversely as the square of v and w = 5 when v = 3. Then, w fi 1 v2 w = k v2 5 = k 32 k = 5 × 32 = 45 Therefore, w = 45 v2 NOTes C01 1202BS Maths F5.indd 1 25/07/2022 5:13 PM
2 1.3 Combined Variation 1. Joint variation is a relation between three or more variables. The relation can be (a) two direct variation Example: p varies directly as s and t. p fi s and p fi t that is, p fi st p = kst where k is a constant. (b) two inverse variation Example: y varies inversely as the cube of x and the square of z. y fi 1 x3 and y fi 1 x2 that is, y fi 1 x3 x2 y = k x3 x2 where k is a constant. (c) One direct variation and one inverse variation Example: u varies directly as m and inversely as the square root of n. u fi m and u fi 1 ! n that is, u fi m ! n u = km ! n where k is a constant. 2. Solving problem in joint variation Example: Given that p varies directly as ! r and inversely as s. p = 6 when r = 4 and s = 3. Find the value of r when p = 18 and s = 2. METHOD 1 p fi ! r s p = k! r s 6 = k! 4 3 k = 6 × 3 !4 = 9 Therefore, p = 9! r s When p = 18 and s = 2 18 = 9! r 2 ! r = 18 × 2 9 ! r = 4 (! r ) 2 = 42 r = 16 METHOD 2 p = 9! r s k = ps ! r Hence, p1 s1 ! r1 = p2 s2 ! r2 6(3) ! 4 = 18(2) ! r2 ! r2 = 36 × ! 4 18 ! r2 = 4 r2 = 42 = 16 3. Distance, s travelled by a bike is varies directly as the square of the speed, v, and varies inversely as acceleration, a. Given that s = 120 m, v = 6 m s–1, and a = 0.5 m s–2. Calculate the value of a when s = 360 m and v = 9 m s–1. Solution: s fi v2 a s = kv2 a 120 = k(6)2 0.5 k = 120 × 0.5 36 = 5 3 360 = ( 5 3 )(9)2 a a = 135 360 = 0.375 m s−2 C01 1202BS Maths F5.indd 2 25/07/2022 5:13 PM
3SOS TIP PAPER 1 1. Given that t varies directly as the square root of s and t = 24 when s = 9. Express t in terms of s. A t = 8! s B t = 3s C t = 24 9 s2 D t = 24s 2. Given that p fi 1 q and p = 3 when q = 2. Find the value of p when q = –5. A –5 B –6 C 5 D – 6 5 3. The table shows some values of the variables E and F where E varies directly as the cube of F. E 24 y F 2 3 Calculate the value of y. A 27 B 81 C 9 D 1 4. The table shows the relation between the variables H and K as direct variation. H 30 42 K 5 7 Which of the following is true? A H = K2 B H = 6!K C H = 6K D H = K 6 5. Given that p is directly proportional to q2 and p = 20 when q = 2, express p in terms of q. A p = 10q2 B p = q2 C p = 5q2 D p = q 6 6. If h varies directly as the square root of k, the relation between h and k is A h fi k2 C h fi k B h fi k 1 2 D h fi 1 ! k 7. P varies inversely as the square of Q and Q = 2 when P = 2. Find the value of P when Q = 4. A –5 C 1 2 B 1 32 D 1 8 8. Given that m fi 1 ! n and m = 12 when n = 1 4 , calculate the value of m when n = 4. A 1 3 C 12 B 3 D 24 9. R varies inversely as the cube of S and R = 32 when S = 1 4 . Calculate the value of S when R = 1 2 . A R = 1 2 B 1 4 C 1 D R = 2S2 10. Given that h fi k3 and h = 64 when k = 2. Determine the constant of variation. A 1 8 C 32 B 16 D 8 11. The table shows some values of the variables p and q where q varies inversely as the square root of p. p 4 64 q 8 2 Find the relation between p and q. A q = 16 ! p C q = 16!p B q = 4p2 D q = 4 ! p CLONE SPM Question 3: The relation is varies directly, E fi F3 . E = kF3 , find the value of constant k. Question 9: The relation is varies inversely, R fi 1 S3 . R = k S3 , find the value of constant k. Every question has 4 answer options A, B, C and D. Choose one answer for every question. C01 1202BS Maths F5.indd 3 25/07/2022 5:13 PM
7SOS TIP Question 4: Change the subject of the relation to h. Based on the new relation, substitute all the given values of unknowns to find the value of h. PAPER 2 1. Table below shows some values of the variables p and q. p 1 x 1 5 q 4 108 y It is given that q varies inversely as the cube of p. (a) Write an equation which relates p and q. [2 marks] (b) Find the values of x and of y. [2 marks] Answer: (a) (b) 3. L varies directly as the square root of m and inversely as the square of n. Given that L = 4 5 when m = 64 and n = 5. (a) Express L in terms of m and n. [2 marks] (b) Find the value of L when m = 81 and n = 3 [1 mark] (c) Find the value of m when L = 15 8 and n = 4. [1 mark] Answer: (a) (b) (c) 2. It is given that w varies directly as the cube of x and inversely as the square root of y. Given that w = 27 when x = 3 and y = 4. (a) Write an equation which relates w, x and y. [2 marks] (b) Find the value of w when x = 4 and y = 16. [2 marks] Answer: (a) (b) 4. The volume of a cone, V with base radius r and height h is V = 1 3 r2 h. (a) What is the relation between h and r? (Using symbol fi and h as the subject.) [1 mark] (b) Given that the height is 5 cm when its base radius is 4 cm. Calculate its height when the base radius is 2 cm. [2 marks] Answer: (a) (b) Section A C01 1202BS Maths F5.indd 7 25/07/2022 5:13 PM
9SOS TIP Question 9: Find the value of constant which relates the m and y. Replace y with 3x – 1 and form a new equation of the relationship between m and x. Enter the given value of y and find the value of m. 9. Given m varies inversely as y in which y = 3x – 1. Given x = 5 when m = 2. (a) Express m in terms of y. [2 marks] (b) Express m in terms of x. [1 mark] (c) Calculate the value of x when m = 4. [1 mark] Answer: (a) (b) (c) 11. Table shows some of the values of three variables X, Y and Z such that X fi 1 Y and X fi Z2 . X 8 25 Y 3 h Z 4 10 (a) Express X in terms of Y and Z. [2 marks] (b) Calculate the value of h. [1 mark] Answer: (a) (b) 10. It is given p varies directly as q and r3 . Given p = 108 when q = 2 and r = 3. (a) Express p in terms of q and r. [2 marks] (b) Calculate the value of p when q = 3 4 and r = 4. [1 mark] (c) Find the value of q when p = 6 and r = 1 3 . [1 mark] Answer: (a) (b) (c) 12. It is given that M varies directly as !N and inversely as G3 . Given N = 4 when G = 2 and M = 1 1 2 . (a) Express M in terms of N and G. [2 marks] (b) Calculate the value of M when N = 9 and G = 3. [1 mark] (c) Calculate the value of N when M = 3 4 and G = 4. [1 mark] Answer: (a) (b) (c) Section B C01 1202BS Maths F5.indd 9 25/07/2022 5:13 PM
11SOS TIP 15. Encik Aman wants to install rectangular tiles for his new house floor. The number of tiles needed, T, varies inversely as the length, L m and width, W m, of the tiles used. Encik Aman needs 580 pieces of tiles if the tile is 0.5 m in length and 0.3 m in width. (a) Calculate the number of tiles needed if the length is 0.4 m and the width is 0.3 m.[2 marks] (b) If the tiles he ordered are in square shape and the length of the square tile is 0.5 m. The price of one unit of the tile is RM1.90. How much Encik Aman has to pay for the tiles installation? [2 marks] (c) If the area of the tile decreases, what is the change in the number of tiles needed for the installation? HOTS Analysing [1 mark] Answer: (a) (b) 16. Amran needs some money to expand his business. He decided to borrow money from a bank. It is given that the interest charge on the loan, C, varies directly as the amount of loan, L, and the period in year, T for repaying the loan. Amran has to pay total interest RM4 800 to settle his loan of RM20 000 over three years. (a) Calculate the period for Amran to repay the loan of RM30 000 if he has to pay total interest RM7 200 to the bank. [3 marks] (b) Amran pay total interest RM7 200 to repay the loan. If Amran able to repay the loan within 5 year’s time. Find the amount of money that he borrowed from the bank. Does he increase or decrease the amount of money he borrowed from the bank? Explain your answer. HOTS Analysing [4 marks] Answer: (a) (b) (c) Question 15: Form an equation to relates T, L and W. T = k LW , substitute the value of T, L and W then find the value of constant k. Substitute the new values of L and W, then find the number of tiles, T. Section C C01 1202BS Maths F5.indd 11 25/07/2022 5:13 PM
105 1. Diagram 1 shows a triangle PQR. 2x + 6 P R Q h Diagram 1 It is given that the area of the triangle is (4x2 – 36) cm2 . Express h in terms of x. A x – 3 C 4x – 12 B 2x – 9 D 3x + 12 2. Which of the following graph represents the quadratic equation of y = (2 – x) (3 + x)? A C –3 2 6 y x –2 3 6 y x B D –3 2 6 y x –2 3 –6 y x 3. Diagram 2 shows a piece of land PQRS which is a trapezium belong to Encik Tan. 2k m (3k + 4) m (4k + 3) m 13 m W Z Y X Diagram 2 Find the value of k. A k = 3 C k = 5 B k = 6 D k = 12 4. It is given that ξ = {x : 27 , x , 38}, M = {x : x is a multiple of 4}, N = {x : x is a whole number and the remainder is 1 after divided by 3} State the members of (M N). A {28, 32, 36} C {29, 30, 33, 35} B {28, 31, 34, 37} D {28, 31, 32, 34, 36, 37} 5. Table 1 shows the equivalent value of the number in base eight and base five. Base 8 Base 5 001 1 011 K 100 224 101 G Table 1 Find the value of K + G as a number in base 5. A 10015 C 745 B 1445 D 2445 6. Given that x8 = 83 + (2 × 8) + (4 × 80 ), find the value of x. A 324 C 6 464 B 1 201 D 1 024 7. Diagram 3 shows an archery target board consists of five concentric circles with the same width The radius of the target board is 100 cm. I II III IV V Diagram 3 An arrow is released to hit the archery target board. Find the probability of the arrow hit the region III. A 1 5 C 3 25 B 1 25 D 7 25 PAPER 1 Time: 1 hour 30 minutes This paper has 40 questions. Answer all questions. SPM Assessment MPaper 1202BS Maths F5.indd 105 25/07/2022 5:19 PM
106 8. A total of 270 candidates pass the interview for the job of medical assistant, nurse, and pharmacy assistant. A total of 72 candidates are appointed as medical assistants. The probability to choose a nurse from the group of candidates is 3 5 . Calculate the number of pharmacy assistants. A 54 B 36 C 216 D 198 9. Given that W8 = 3437 , find the value of W. A 250 B 110 C 262 D 178 10. Diagram 4 shows the Venn diagram that shows the relation between set P, set Q and set R. ● 9 ξ ● 8 ● 5 ● 6 ● 7 ● 3 ● 4 ● 2 ● 1 P Q R Diagram 4 Which of the following is true? A (P Q)´ = {2, 4, 9} B P R = {2, 4, 5, 8} C P Q R = {6} D (Q R) P = {2, 4, 5, 6, 8} 11. Diagram 5 shows a graph with multiple edges and loops. P Q R S T Diagram 5 Which of the following is true? A d(P) = 2 C d(Q) = 4 B d(R) = 3 D ∑d(v) = 18 12. Diagram 6 shows a graph. Diagram 6 Which of the following is not the tree drawn from the graph above? A B C D 13. Diagram 7 shows a graph with loops and multiple edges. Diagram 7 Based on the graph above, which of the following is true? A n(V) = 4, n(E) = 8, ∑d(v) = 18 B n(V) = 5, n(E) = 7, ∑d(v) = 14 C n(V) = 4, n(E) = 8, ∑d(v) = 16 D n(V) = 6, n(E) = 6, ∑d(v) = 16 14. Diagram 8 shows a graph of the relation between three linear inequalities. y y = x + 3 y = 3x – 9 x + y = 3 x O A B C D 3 3 –9 –3 Diagram 8 Which of the region A, B, C or D, satisfied the linear inequalities system of y < x + 3, y > 3x – 9 and x + y > 3? 15. Diagram below shows a straight line graph of y = 3x – 5. y = 3x – 5 y x –5 Diagram 9 Which of the following point satisfied the inequality of y . 3x – 5? A (3, –2) C (–1, 3) B (0, –5) D (5, 0) MPaper 1202BS Maths F5.indd 106 25/07/2022 5:19 PM
110 PAPER 2 Time: 2 hours 30 minutes Section A [40 marks] Answer all questions in this section. 1. (a) Determine whether the statement is true or false. 11 2 = 5.5 or 23 = 6 [1 mark] (b) State whether the statement below is a statement or not a statement. x + 3 – p [1 mark] (c) Make a general conclusion by induction for the sequence of numbers 9, 27, 57, 99 which follows the following pattern: 9 = 6 (1) + 3 27 = 6 (4) + 3 57 = 6 (9) + 3 99 = 6 (16) + 3 [2 marks] Answer: (a) (b) (c) 2. Diagram 1 shows a distance-time graph for the journey of a train from Seremban to Kajang. Distance (km) (Seremban) 0 (Mantin) 25 (Kajang) 70 Time (min) 20 25 t Diagram 1 (a) It is given that the speed of the train travel from Mantin to Kajang is 1.5 km min–1. Find the value of t. [2 marks] (b) How long, in minutes, the time taken by the train reached Kajang from Mantin? [1 mark] (c) Calculate the average speed, in km h–1, for the whole journey. [1 mark] Answer: (a) (b) (c) 3. Table 1 shows the name of three male students and two female students in a school. They are assigned to clean the class during recess. Male Female Ahmad Borhan Chong Devi Eliana Table 1 Three students are chosen at random to clean the class. (a) List all the possible outcomes of the event for this sample space. You may use the capital letter such as A for Ahmad and so on. [2 marks] (b) Find the probability that (i) The two students chosen are female. (ii) Borhan and Chong are not assigned together. [2 marks] Answer: (a) (b) (i) (ii) MPaper 1202BS Maths F5.indd 110 25/07/2022 5:19 PM
113 11. A furniture shop sells two types of chairs, type A and type B. The profit from the sale of a unit of chair of type A is RM8 and a unit of chair of type B is RM5. The shop sells x unit of type A chair and y unit of type B chair. The maximum number of chairs sold is 160. The number of chair of type B sold is at least 2 3 of the number of chair of type A. The total profit from the selling of chairs is at least RM400. (a) Based on the given situation, state three linear inequalities, other than x > 0 and y > 0. [3 marks] (b) Using a scale of 2 cm to 20 chairs on both axes, draw and shade the region which satisfies the system of linear inequalities in (a). [3 marks] (c) From the graph in (b), determine the minimum number of chair of type A if 40 of the chair of type B are sold. [1 mark] (d) It is given that the shop managed to sell 80 chairs of type A. Calculate the maximum total profit obtained by the company from the sales of the two types of chairs. [2 marks] Answer: (a) (b) (c) (d) 12. Table 3 shows the individual income tax assessment form for Encik Yusof. Item Tax assessment (RM) Employment income RM95 560 RELIEF Individual 9 000 Lifestyle (limited to 2 500) Child whose age is below 18 years old 2 000 Life insurance and EPF (limited to 7 000) Education and Medical insurance (limited to 3 000) TAX SUMMARY Total income RM95 560 Total tax relief W CHARGEABLE INCOME X Tax on the first (50 000 or 70 000) Y Tax on the next balance (× 14% or × 21%) Z Table 3 In the assessment year, Encik Yusof spent RM2 890 for lifestyle, RM5 680 for life insurance and RM3 150 for medical insurance. Encik Yusof also paid zakat amounting to RM500. Table 4 shows the income tax rate: Chargeable Income (RM) Calculation (RM) Rate (%) Tax (RM) 50 001 – 70 000 On the first 50 000 Next 20 000 14 1 800 2 800 70 001 – 100 000 On the first 70 000 Next 30 000 21 4 600 6 300 Table 4 You are advised to complete the space for the tax assessment related to tax relief in the table above before answer the following questions. (a) Find the value of W, X, Y and Z. [4 marks] (b) Calculate the income tax payable imposed on Encik Yusof for the assessment year. [2 marks] (c) If Encik Yusof join the Monthly Tax Deduction (PCB) system and RM250 is deducted from his salary every month. Does Encik Aman need to pay any more income tax to the Inland Revenue Board (IRB)? [3 marks] Section B [45 marks] Answer all questions in this section. MPaper 1202BS Maths F5.indd 113 25/07/2022 5:19 PM
115 15. Cik Rita wants to buy a house worth RM350 000. She needs to pay the preliminary money amounting to 12% of the original price of the house. But she only has money amounting to M. She decided to save her money M in the bank as fix deposits account. The bank offered interest rate of r% per annum for the fix deposits account and compounded every year. She will receive the new total saving, S, after t years of saving which followed the mathematical model S(t) = 28 000(1.06)t . (a) What is the saving principal, M of Cik Rita and the annual interest rate offered by the bank? [2 marks] (b) Calculate the total saving in the fix deposits account of Cik Rita after 6 years of saving. [2 marks] (c) How many year does Cik Rita needs to save her money M in fix deposits account to enable her to pay for the preliminary money to buy the house? [3 marks] (d) Refining the mathematical model if the interest rate for the fix deposits account offered by the bank is compounded every three months. [2 marks] Answer: (a) (b) (c) (d) Section C [15 marks] Answer any one of the question from this section. 16. Diagram 6 shows a histogram which represents the mark obtained by a group of students in a mathematics test. 0 19.5 24.5 29.5 34.5 39.5 44.5 49.5 54.5 1 2 3 4 5 6 7 8 9 10 11 Frequency Marks Diagram 6 (a) Based on the information in the histogram, complete the table in the answer space provided. [3 marks] (b) Based on the data in the table, (i) State the modal class. [1 mark] (ii) Find the mean mark of the mathematics test. [3 marks] (iii) Calculate the standard deviation for the mark of the mathematics test. [3 marks] (c) Using a scale of 2 cm to 5 marks on the horizontal axis and 2 cm to 5 students on the vertical axis, draw an ogive for the data. [3 marks] (d) Based on the ogive drawn in (c), calculate the interquartile range of the data. [2 marks] MPaper 1202BS Maths F5.indd 115 25/07/2022 5:19 PM
116 Answer: Class interval (Mark) Frequency, f Midpoint, x 20 – 24 (b) (i) (ii) (iii) (c) (d) 17. (a) Diagram 7 shows point W on a Cartesian plane. 1 y x O –1 –4 –3 –2 –1 1 2 3 4 5 6 –2 –3 –4 W 2 3 6 5 4 Diagram 7 Transformation G is a translation ( 4 ) 2 . Transformation H is a rotation of 90° anticlockwise about the centre (1, 1). State the coordinates of the image of point W under each of the following transformations: (i) H2 (ii) HG [4 marks] (b) Diagram 8 shows three pentagons ABCDE, FGHIJ and FGRSJ, drawn on a Cartesian plane. y x 2 O –2 –10 –8 –6 –4 –2 2 4 6 8 10 –4 –6 –8 –10 4 6 12 10 8 A B C R G F H I J S D E Diagram 8 (i) Pentagon FGRSJ is the image of ABCDE under the combined transformation XY. Describe, in full, the transformation: (a) Y, (b) X [4 marks] (ii) It is given that pentagon FGRSJ represents a region of area 315 m2 . Calculate the area, in m2 , of the shaded region. [5 marks] (iii) Draw the image of FGHIJ under a reflection at the line y = 4 on the Cartesian plane. [2 marks] MPaper 1202BS Maths F5.indd 116 25/07/2022 5:19 PM
118 CHAPTER 1 Paper 1 1. A 2. D 3. B 4. C 5. C 6. B 7. C 8. B 9. C 10. D 11. A 12. C 13. A 14. D 15. B 16. B 17. C 18. C 19. A 20. D 21. C 22. A 23. D 24. B 25. B 26. C 27. D 28. B 29. C 30. A 31. C 32. D 33. B 34. B 35. C 36. D 37. B 38. A Paper 2 1. (a) q fi 1p3 q = kp3 4 = k13 k = 4 q = 4p3 (b) 108 = 4x3 x3 = 4 108 x3 = 1 27 x = 13 y = 500 2. (a) w fi x3 ! y w = kx3 ! y 27 = k33 ! 4 27 = k(27) 2 k = 2 w = 2x3 ! y (b) w = 2(4)3 ! 16 w = 2(64) 4 w = 32 3. (a) L = k!mn2 45 = k! 64 52 k = 25 × 4 8 × 5 k = 52 L = 5!m2n2 (b) L = 5! 81 2(32) L = 52 (c) 158 = 5!m 2(42) !m = 15 × 32 8 × 5 !m = 12 m = 144 4. (a) V = 13 πr2h h = 3Vπr2 h fi 1r2 (b) h = 5 when r = 4 h = kr2 5 = k42 h = 5 × 16 = 80 h = 8042 when r = 2 h = 8022 = 20 5. (a) k = pm2 n3 (b) k = 8(22) 43 k = 32 64 k = 12 (c) p = n3 2m2 12 = n3 2(32) 12 × 18 = n3 n = 3! 216 n = 6 6. (a) p = kq 2 = k(12) k = 16 p = 16 q (b) p = q6 x = 726 x = 12 3 = y6 y = 3 × 6 y = 18 7. (a) P fi !Q P = k!Q P = k! 6h + 4 P = k! (6 × 10) + 4 4 = k! 64 4 = 8k k = 48 k = 12 P = !Q2 (b) when P = 2 2 = !Q2 !Q = 2 × 2 !Q = 4 Q = 42 Q = 16 6h + 4 = 16 6h = 12 h = 2 (c) when h = 16 Q = 6h + 4 Q = 6(16) + 4 Q = 100 P = ! 100 2 P = 102 = 5 8. (a) q fi p! r q = kp! r 9 = k(3) ! 16 9 × 4 = 3k k = 363 k = 12 q = 12p ! r (b) 8 = 12(6) ! r 8! r = 72 ! r = 728 ! r = 9 r = 92 r = 81 9. (a) m fi 1y m = ky m = k 3x – 1 2 = k 3(5) – 1 2 = k 14 k = 28 hence, m = 28y (b) m = 28 3x – 1 (c) when m = 4 4 = 28y y = 284 y = 7 3x – 1 = 7 3x = 8 x = 83 x = 2 23 10. (a) p fi qr3 p = kqr3 108 = k(2)(3)3 108 = 54k k = 108 54 = 2 p = 2qr3 (b) p = 2qr3 p = 2( 34 )(43) = 96 CHAPTER 1 Answers Complete Answers (Paper 1) https://bit.ly/3JQiyOg Answers 1202BS Maths F5.indd 118 25/07/2022 5:24 PM