HCI Paper E Sec 1 IP

1 Name: _____________________________ ( ) Cl ass: ________ HWA CHONG INSTITUTION PAPER E 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 degrees to one decimal place. For  , use either your calculator value or 3.142, unless the question 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 explicit numerical expressions. The use of a graphing calculator is not permitted. You are reminded of the need for clear presentation in your answers. Omission of essential working will result in loss of marks. This question paper consists 7 printed pages, including this page.

2 1 (i) Express the numbers as a pr oduct of its prime factors. (a) 28 (b) 63 [2] (ii) Using the results from (i), explain why 28 63 is a perfect square. [1] (iii) T h e n u m b e r 28k is a perfect cube. Find the smallest positive integer value o f k. [ 1 ] 2 (a) 1 , π , 4 , 3 64 , 5.2  , 1 2 , 10 2 , 13 From the given numbers above, state (i) t h e p r i m e n u m b e r s , [ 1 ] (ii) t h e i r r a t i o n a l n u m b e r s . [ 1 ] (b) While climbing a mountain, Joel discovers that the temperature decreases by 2 C for every 300 m that he climbs upwards. The temperature at the foot of t h e m o u n t a i n i s 18 C . (i) Find the temperature after Joel has climbed a height of 3.75 k m from the foot of the mountain. [2] (ii) Find the height, in km, that Joel has climbed from the foot of t h e mountain if the temperature is 13 C  . [2] 3 (i) Estimate the value of 35.71 14.63 24.49  , giving your answer correct to 1 significant figure. [2] (ii) Using the result from (i), estimate the value of 3571 14.63 0.2449  . [2] 4 The area of a reservoir is 180 000 m 2. It is represented on a map by an area of 2 cm2. (i) Find the scale of the map in the form 1 : n. [ 2 ] (ii) The shoreline of the reservoir is 5.4 km long. Find, in cm, th e length of the s h o r e l i n e o n t h e m a p . [ 2 ]

3 5 S i m p l i f y (a) 74 3 5 2x xx , [ 2 ] (b) 51 27 43 yy . [ 3 ] 6 Factorise completely (a) 218 24ab a , [ 1 ] (b) 242pqq r p r  . [2] 7 Solve the equation (a)  329 2 5xx x   , [ 2 ] (b) 42 5173 zz  . [ 3 ] 8 (a) Solve the inequalities 1 12 5 23 x xx  . Hence illustrate your solution o n a n u m b e r l i n e . [ 4 ] (b) G i v e n t h a t 21 3 ba b   , express b in terms of a. [ 2 ] 9 A motorist took 1 hour and 45 minutes to travel from Town P t o T o w n Q w i t h a n average speed of x km/h. On his return journey, he travelled faster by 15 km/h an d his travelling time was shortened by 20%. (i) Find the time taken, in hours, for his return journey. [1] (ii) Form an equation in x and solve for x. Hence find the average speed for the r e t u r n j o u r n e y . [ 3 ] [Turn Over

4 10 The first four terms of a sequence are given by 16, 25, 36, 49 , ….. (i) Write down the value of T5. [ 1 ] (ii) Find an expression for Tn, the nth term of the sequence. [1] (iii) In a second sequence, the first four terms are 19, 28, 39, 52, ….. By comparing this sequence with the first, and using your answer in (ii), write down an expression, in terms of n, for the nth term of this sequence. [1] (iv) Explain why 125 is not a term of the sequence in (iii). [1] 11 Three petrol stations, Vibe, Enoc, Topz, were having a price war. (a) Andrew pumped petrol at Vibe which offered a 15% discount. The price of the petrol was $2.28 per litre before discount. He paid $75.52 for his petrol. How many litres of petrol did he pump? [2] To reward loyal customers, Enoc and Topz introduced privilege cards which comes with the following benefits: Enoc 12% off all petrol plus $1 off for every $20 on final bill Topz 10% off all petrol plus 3% off the final bill ( b ) Bryan holds privilege cards from these two stations. He was de ciding which petrol station to go, in order to save more money. He needed to pump 44.5 litres of petrol. Given that the price before discount is $2.24 per litre, which petrol station should he go to? [3] 12 In the diagram, trapezium ADEC is inscribed inside a semicircle OABC, centre O. Find the area of the shaded region. [3]

5 13 (a) In the diagram, ABCD is a parallelogram and CEFG is a rhombus. 98BAG  , 25ABG  , 51CDH  and 80CEF  . Find, giving reasons for each answer, (i) GBC , [ 1 ] (ii) BGC , [ 2 ] (iii) GCD , [ 1 ] ( i v ) DFC . [ 2 ] (b) I n t h e d i a g r a m , ABCDEF is a regular hexagon. (i) ABPQ is part of another regular polygon where its interior angle is 165 . How many sides does this polygon have? [2] (ii) Calculate PBC . [ 2 ] [Turn Over 25°

6 14 (Not examinable in 2020) A class of 30 students was randomly divided into two equal groups, A and B. Their marks in a common test are shown in the stem-and-leaf d iagram below. (i) Find the modal mark of Group A. [ 1 ] (ii) Find the median mark of Group B. [ 1 ] (iii) John said that ‘Group A performed better in the common test’. Do you agree? Justify your answer. [2] Leaves for Group A Stem Leaves for Group B 8 2 7 6 0 0 3 2 8 2 4 5 6 5 1 5 5 9 9 9 9 3 6 0 1 6 0 7 2 7 8 9 8 0 1 9 6 9 Key: 2 | 7 means 27 marks

7 15 Diagram I Diagram II Shampoo Herbal comes in two types of bottles. Diagram I shows the first type of shampoo bottle in the shape of a cone. The diameter of the bas e of the cone is 12 cm and the height of the cone is 10 cm. (a) Calculate the volume of the cone. [2] Diagram II shows the second type of shampoo bottle which is ma de up of a cylindrical neck and a hemispherical base. The height of the c ylindrical part is 4 cm and the radius of the hemispherical part is 6 cm. (b) Calculate (i) the volume of the hemispherical base, [2] (ii) the curved surface area of the hemispherical base. [2] (c) Find the radius of the cylindrical part, given that the volum e of the cylindrical part is 150 cm 3. [ 2 ] 16 Answer the whole of this question on a sheet of plain paper. On a scale drawing, a park is in the form of a quadrilateral ABCD with AB  9 cm, 70ABC  , BC  3.3 cm, AD  7 cm and diagonal BD  8.5 cm. (i) Construct the quadrilateral ABCD. [ 2 ] (ii) Construct the perpendicular bisector of AD. [ 1 ] (iii) Construct the bisector of BAD . [ 1 ] (iv) A café is to be built in the park, nearer to A than to D and nearer to AD than t o AB. Shade the region where the café is to be built. [1] End of Paper

8 Short