1 霹雳怡保培南独立中学 SM POI LAM (SUWA) IPOH FINAL EXAMINATION 2022 Mathematics Paper 2 DATE: TIME : 17th Nov 2022 (Thursday) 1310-1540 (2 hour 30 minutes) NAME：______________________ REG NO: ________________ CLASS：S2HE/QI/AI/ZI/YI/PI READ THESE INSTRUCTIONS FIRST 1 This question paper consists of three sections: Section A, Section B, Section C. 2 Answer all questions in Section A and Section B, and only one question from Section C. 3 Write your answers in the provided examination scripts. 4 Show your working. It may help you to get marks. 5 You may use a non-programmable scientific calculator. 6 The number of marks for each part of the question are shown in the brackets []. 7 The total mark for this paper is 100. DO NOT TURN OVER THIS PAGE UNTIL YOU ARE TOLD TO DO SO! This paper consists of 12 printed pages. Prepared by ： ………………… (Mr. Soo Jian Yuan) Checked by： ………………… (Mr. Ong Eik Hooi) Section Question Marks Allocated Marks Obtained A 1 4 2 4 3 3 4 4 5 5 6 4 7 4 8 4 9 5 10 3 B 11 9 12 9 13 9 14 9 15 9 C 16 15 17 15 Total 100
2 MATHEMATICAL FORMULAE NUMBERS & OPERATIONS 1 × = + 2 ÷ = − 3 ( ) = 4 = √ 5 Simple interest, = 6 Compound interest, = (1 + ) 7 Total repayment, = + ALGEBRA 1 Distance, = √(2 − 1 ) 2 + (2 − 1 ) 2 2 Midpoint, (, ) = ( 1+2 2 , 1+2 2 ) 3 Average speed = 4 Gradient, = 2−1 2−1 5 Gradient, = − − − 6 −1 = 1 − ( − − ) MENSURATIONS & GEOMETRY 1 Pythagoras’ Theorem, 2 = 2 + 2 2 Sum of interior angles in an n-sided polygon = 180°( − 2) 3 Circumference of a circle = = 2 4 Area of a circle = 2 5 Length or arc = 360 × 2 6 Area of sector = 360 × 2 7 Area of kite = 1 2 × 8 Area of trapezium = 1 2 × × ℎ 9 Surface area of a cylinder = 2 2 + 2ℎ 10 Surface area of a cone = 2 +
3 11 Surface area of a sphere = 4 2 12 Volume of a prism = − × ℎ 13 Volume of a cylinder = 2ℎ 14 Volume of a cone = 1 3 2ℎ 15 Volume of a sphere = 4 3 3 16 Volume of a pyramid = 1 3 × × ℎ 17 Scale factor, = ℎ ℎ 18 2 = PROBABILITY & STATISTICS 1 Mean, ̅= ∑ 2 Mean, ̅= ∑ ∑ 3 Variance, 2 = ∑(−̅) 2 = ∑ 2 − (̅) 2 4 Variance, 2 = ∑ (−̅) 2 ∑ = ∑ 2 ∑ − (̅) 2 5 Standard deviation, = √ ∑(−̅)2 = √ ∑ 2 − (̅) 2 6 Standard deviation, = √ ∑(−̅)2 ∑ = √ ∑ 2 ∑ − (̅) 2 7 () = () () 8 ( ′) = 1 − ()
4 Section A [40 marks] Answer all the questions in this section. 1 Diagram 1 shows a right prism. The base and are rectangles which are horizontal planes. Diagram 1 Calculate the volume of the right prism, in 3 . [4 marks] 2 Diagram 2 shows two parallel lines, and drawn on a Cartesian plane. Diagram 2 It is given that the equation of the straight line is = −2 − 3. (a) Find the equation of the straight line . [2 marks] (b) State the -intercept of the straight line . [2 marks]
5 3 (a) State the inverse for the following implication. Hence, state the truth value of the inverse. [2 marks] (b) Premise 1: If = 0, then 2 + + is not a quadratic expression. Premise 2: ___________________________________________________________ Conclusion: ≠ 0 [1 mark] 4 Diagram 3 shows the motion of Suhaila’s car for a period of 18 seconds. Diagram 3 (a) Calculate the acceleration, in / 2 , for the last 6 seconds. [2 marks] (b) Calculate the total distance travelled, in , for the first 14 seconds. [2 marks] 5 Mr. David buys a car worth . He pays 10% down payment and the balance are financed with a loan from bank for a period of 6 years with a simple interest rate of 3% per annum. Given the monthly instalment of Mr. David is 1194.05, calculate the value of to the nearest . [5 marks] 6 A café sells two types of drinks, drink and drink . Jane paid 17.00 for 2 cans of drink and 3 cans of drink . Molly paid 27.00 for 3 cans of drink and 5 cans of drink . Using the matrix method, calculate the price, in , of a can of drink and a can of drink . [4 marks] If ( + )( − ) > 0, then 2 − 2 > 0.
6 7 It is given that the probability that it will rain on Monday, Tuesday and Wednesday are 2 3 , 3 7 and 5 9 respectively. Determine the probability that (a) it will rain on one day only, [2 marks] (b) it will rain at on least one day. [2 marks] 8 Given a sequence of numbers with common difference as follows: 136, 428, 5, 9, 4, … Find (a) the value of , and , [3 marks] (b) the 8 th term in base 7. [1 mark] 9 Mr. Mustafa has total annual income 58200 for the year 2021. He donated to the welfare fund which is approved by the government. Diagram 4 shows the information for the tax reliefs claimed by Mr. Mustafa. Diagram 4 Given that the chargeable income is 32300, calculate (a) the value of , [2 marks] (b) the income tax payable by Mr. Mustafa. [3 marks]
7 10 (a) It is given that set = { } and set = { 4}. Complete the Venn diagram below to show the relationship between set and set . [1 mark] (b) The Venn diagram in Diagram 5 shows the sets , and . Diagram 5 State the relationship represented by the shaded region. [2 marks]
8 Section B [45 marks] Answer all the questions in this section. 11 Based on Diagram 6, answer the following questions: Diagram 6 (a) Write down three linear inequalities that define the shaded region. [3 marks] (b) If the shaded region is reflected on the -axis, draw and shade the position of the region. [1 mark] (c) Write down three linear inequalities that satisfy the image of the shaded region after the reflection. [2 marks] (d) If the original shaded region is reflected on the -axis, draw and shade the position of the region. [1 mark] (e) Write down three linear inequalities that satisfy the image of the shaded region after the reflection. [2 marks]
9 12 Diagram 7 shows a network. The weightages given are the distances between the villages , , , , , , and , in kilometers. Diagram 7 (a) Find the shortest distance between the villages below: (i) and , [1 mark] (ii) and , [1 mark] (iii) and , [1 mark] (iv) and . [1 mark] (b) Determine the vertex/vertices with (i) the largest degree, [1 mark] (ii) the smallest degree, [1 mark] (iii) an even degree, [1 mark] (iv) an odd degree. [1 mark] (c) Determine the sum of degrees for all vertices. [1 mark] 13 Given a data set of 12 numbers such that ∑ = 192 and ∑ 2 = 4320. (a) Calculate the mean and variance for the data set. [3 marks] (b) If a number 13 is added to the set of data, calculate values the new mean and the new variance. [2 marks] (c) If a number equal to the mean is removed from the original set of data, how would the mean and the variance differ? [2 marks] (d) State how a number is added to the original data set to increase the value of the standard deviation. [1 mark] (e) State how a number is removed from the original data set to increase the value of the standard deviation. [1 mark]
10 14 Diagram 8 shows the annual premium rate schedule per 1000 face value of a yearly renewable term insurance offered by an insurance company. Diagram 8 Based on Diagram 8, (a) State four factors that will affect the value of the premium payable. [3 marks] (b) Johan is 32 years old and he is a smoker. He wants to buy an insurance policy with an insured sum of 120000. Calculate the annual premium payable by Johan. [2 marks] (c) Ms. Cheng is 34 years old and she is a non-smoker. She wants to buy an insurance policy with an insured sum of 180000. Calculate the annual premium payable by Ms. Cheng. [1 mark] (d) Mdm. Kamisah is 31 years old and she is a smoker. If her annual premium payable is 240. What is the sum insured of her insurance policy? [2 marks] (e) What advice will you give to insurance buyers so that the premium charged is reasonable. [1 mark] 15 Given that a quadratic function () = 2 + + 3 has an -intercepts of 1 2 and 3. Find (a) the value of and , [2 marks] (b) the equation of the axis of symmetry, [1 mark] (c) the maximum or minimum point of the function, [2 marks] (d) the quadratic function in the form () = 2 + + when it is reflected on the -axis, [2 marks] (e) the quadratic function in the form ℎ() = 2 + + when it is reflected on the -axis. [2 marks]
11 Section C [15 marks] Answer one questions from this section. 16 Diagram 9 shows an observer with his eye level, ℎ viewing a lamp pole from a place which is from the base of the lamp pole. Diagram 9 (a) Given that ℎ = 1.6, = 30 and the angle of depression of from is 18°, find the value of and the height of the lamp pole. [4 marks] (b) What conclusion can be made about Δ and Δ? [1 mark] (c) Show a method to determine the relationship between Δ and Δ. [2 marks] (d) Given that = 4.874 and Δ is the image of Δ under the combined transformation . Describe in full the transformations and . [5 marks] (e) Describe a single transformation that is equivalent to . [2 marks] (f) Express the area of Δ in terms of the area of Δ. [1 mark]
12 17 Diagram 10 shows the IQ of 40 students in schools and . Diagram 10 (a) Based on the table given, complete the table below in the answer space provided. [3 marks] (b) By using the scale of 2 to 5 on the horizontal axis and 2 to 5 on the vertical axis, draw both ogives on the same axes for the data given. [3 marks] (c) Using the ogives drawn, find (i) the first quartile, (ii) the median, (iii) the third quartile, for both schools. [6 marks] (d) Using the values obtained, compare the IQ level of students from both schools. Justify your answer. [3 marks] ---------------------------------------------------END OF PAPER--------------------------------------------------
