NHHS 2022 Math PRELIMS P2 (Solution)

This paper consists of 28 printed pages and 3 blank pages. Page 1 of 28 Name ( ) Class PRELIMINARY EXAMINATION 2022 Subject : Mathematics Paper : 4048/02 Level : Secondary Four Express Date : 18 August 2022 Duration : 2 hours 30 minutes READ THESE INSTRUCTIONS FIRST Write your name, class and index number on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue, or correction fluid. Answer all questions. If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. The use of an approved scientific calculator is expected, where appropriate. 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  . The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100. For Examiner’s Use Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 TOTAL NAN HUA HIGH SCHOOL

Nan Hua High School Preliminary Examination 2022 Mathematics 4048/02 Page 2 of 28 Compound interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 r Area of triangle ABC = Cabsin2 1 Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sinsinsin == 2 2 2 2 cosa b c bc A= + − Statistics Mean = f fx   Standard deviation = 22        −  f fx f fx

Nan Hua High School Preliminary Examination 2022 Mathematics 4048/02 Page 3 of 28 Answer all questions. 1 (a) Simplify 22 3 3 12 .5 25 ac b ab  22 3 22 3 2 2 2 2 2 32 4 2 3 12 5 25 3 144 5 625 3 625 5 144 125 48 ac b ab ac b a b a a b bc a bc  = = = Answer …………………………... [3] (b) n is a positive integer. Show that, for all n , 22(3 2) (3 2)nn+ − − is a multiple of 3. Answer 22(3 2) (3 2) (3 2 3 2)[3 2 (3 2)] (6 )(4) 24 3(8 ) nn n n n n n n n + − − = + + − + − − = = = Since n is a positive integer, 3(8n) is a multiple of 3. [2]

Nan Hua High School Preliminary Examination 2022 Mathematics 4048/02 Page 4 of 28 (c) Solve the equation 27 1.4 3 2 x xx +=−− 2 2 27 14 3 2 2(3 2) 7 ( 4) 1( 4)(3 2) 2(3 2) 7 ( 4) ( 4)(3 2) 4 8 12 0 2 3 0 ( 3)( 1) 0 3 1 x xx x x x xx x x x x x xx xx xx x or x +=−− − + − =−− − + − = − − − − = − − = − + = = =− Answer x = …..………. or …………… [4] (d) Use the quadratic formula to solve the equation. 23 7 4 0xx− − =