HCI Practice Paper A Sec 1 Math

1 Name: __________________________________ ( ) Class: _____ HWA CHONG INSTITUTION Practice Paper A INTEGRATED MATHEMATICS Level : Secondary One Duration : 2 hours Do not open this booklet until you are told to do so. INSTRUCTIONS TO CANDIDATES Write your name, class and index number on all the work you hand in. Answer all questions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in d egrees to one decimal place. For , use either your calculator value or 3.142, unless the questio n requires the answer in terms of . INFORMATION FOR CANDIDATES The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 80. You are expected to use an electronic calculator to evaluate ex plicit numerical expressions. The use of a graphing calculator is not permitted. You are reminded of the need for clear presentation in your ans wers. Omission of essential working will result in loss of marks. This question paper consists 5 printed pages, including this page.

2 1 (a) Express 9261 as its prime factors. Hence, find 3 9261 without the use of a calculator. [3] (b) Given that 9261 and a number N has an LCM of 37044 and a HCF of 9, Find the smallest N. [3] 2 (a) Without the use of the calculator, estimate 9.03 7.99 3.998 2.02   correct to 1 significant f i g u r e . [2] (b) Show how you would arrange the following in descending order: 10.17, 0.17, 0.18, , 0.17877     [3] 3 (a) Given that 11 835x , find the greatest possible value of x if x is a rational number. [2] (b) If m and n are positive integers less than or equal to 22 such that 13 14 16 17 m n , find the possible values of m and n where m n is recurring. [2] 4 Given that 37 QRP Q  , (a) calculate the value of P when R = 20 and Q = 11, [2] (b) express Q in terms of P and R. [3] 5 Evaluate without the use of a calculator, 3 284 4 5 π 3.102.52 5    [3] 6 Solve the equation 31 2 (2 ) ( 34 )46 3xx x   . [3] 7 To earn extra money, Fanny works temporarily at Burger Queen’s Fast Food Restaurant. In a particular week during the school holidays, she worked twice as many hours on Tuesday as she did on Monday but 7 8 of the hours on Wednesday compared to Monday. (a) If Fanny worked x hours on Monday, write down an expression each for the number of hours she worked on Tuesday and on Wednesday. [2] (b) For these three days she received $139.50. If she is paid $4.50 per hour, how many hours did Fanny work on Monday? [3]

3 8 (a) A n-sided polygon has 4 interior angles measuring 120 each. The remaining interior angles all measure p each. Find an expression for p, in terms of n . [3] (b) In the figure below, AB is parallel to DE and BD = CD. Given that 71ABD  and 35CDE  , find the reflex angle BCD denoted by y . [3] 9 The solid triangular prism, shown in the diagram, stands on a h orizontal rectangular base BCZY. The triangles ABC and XYZ a r e v e r t i c a l p l a n e s a n d t h e f a c e s ABYX and ACZX are rectangular. (a) (i) Given that AB = AC = 17 cm and BC = 16 cm, show using Pythagoras’ Theorem that the height of A above the base is 15 cm. [3] (ii) If CZ is 28 cm, calculate the volume of the prism. [2] (b) If the prism with dimensions in (a) is to be sent as a gift and posted overseas, find the total surface area of the prism required to be wrapped and calcualte its mass if the density is 0.97g/cm3. [4] 35 y 71 A E C B D Z A B C X Y

4 10 (Not examinable in 2020) Answer the whole of this question on a sheet of graph paper. Two mobile companies in Mexico, S1 and S2, offer plans with talk time rates as shown in the following tables. S1: Charges ($) 0 1 2 3 4 Time (min) 10 22 35 47 60 S2: Charges ($) 0 1 2 3 4 5 Time (min) 20 28 36 44 52 60 (a) Using a scale of 2 cm to represent 10 units on the horizontal a xis and 4 cm to represent 1 unit on the vertical a xis, plot the graphs of Charg es ($ ) aga inst Tim e ( m i n ) f o r t h e t w o c o m p a n i e s . [4] (b) If Porky wants to pay only $7 for a talk time plan per month, w hich company should he choose? Explain your answer. [2] 11 Answer the whole of this question on a sheet of plain paper. Construct a quadrilateral ABCD such that AB = 6 cm, BC = 4.5 cm, CD = 13 cm, ABC = 112˚ and BCD = 95˚. Construct a perpendicular bisector of AB and name the intersection point with AB, M and the intersection point with CD, N. Measure and write down the size of MNC. [4] 12 Xiao Ming borrowed $50 000 from O CBD bank at a simple interest rate of 14% per annum. He also borrowed $50 000 from UOC bank at 10% compounded half-yearly. He will return $73 205 to OCBD bank and UOC bank after p years and q years respectively. (a) Find the value of q. [3] (b) Are the values of p and q the same? If not, explain why there is a difference. [2] [Given that 1 100 n rAP   ] 13 (Not examinable in 2020) Find the equation of the line parallel to 7 x + 5y = 49 and passing through the point (10, 2). [3]

5 14 (Not examinable in 2020) (a) Copy the Venn diagram below and shade () 'PP Q  . [2] (b) Express in set notation (as simply as possible), the shaded region in the Venn d i a g r a m b e l o w . [2] (c) Given A  B and B  C = . (i) Illustrate the above information with a Venn Diagram. [1] (ii) I f n ( ) = 42, n(A) = 15 and n(C) = 23, what are the possible values of n(B)? [2] 15 (Not examinable in 2020) (a) The prices, in Pounds, of Logo sets in a shop are given in the table below: Price (£) 6 7 8 9 10 11 12 Frequency 11 14 x 28 12 13 18 (i) State the greatest possible value of x if the mode is 9. [1] (ii) Given that x = 18, construct a bar graph for the distribution. [2] (b) If the total number of Logo sets in the shop is 142, find (i) the value of x, [2] (ii) t h e m e d i a n p r i c e , [2] (iii) t h e m e a n p r i c e . [2] End of Paper P  Q R P

6 Paper A Sec 1 Mainstream Answer Key 1 (a) 3337 ; 37 2 1 (b) 36N  2 (a) 3 (b) 10.18, 0.1787, 0.17, 0.17, 7     3 (a) x = 123 5 or 324 5 (b) 9m , 11n or 18m , 22n 4 (a) 11 2P or 15 2 (b) 7 3 PQ PR  5 1.4 6 36 2 or 217 17 7 (a) 2x and 7 8 x (b) 8x 8 (a) 180 840 4 np n   (b) 288 9 (a) (i) 15 cm (ii) 3360 cm3 (b) 3259.2 g or 3.2592 kg 11 12 (a) 2 or 4q (b) 3.315p . Thus and are not the same.pq Because compound interest usually takes a shorter time to accumulate more amount than simple interest or Because both r and T are different.