Hougang 4E AM P2 MYE 2021

1 NAME: ( ) CLASS: SEC 4E ( ) 11 May 2021, Tuesday 2 hours 15 minutes MAKE THE DIFFERENCE RESPECT OURSELVES RESPECT OTHERS MAKE THE DIFFERENCE RESPECT OURSELVES RESPECT OTHERS MAKE THE DIFFERENCE MAKE THE DIFFERENCE RESPECT OURSELVES RESPECT OTHERS MAKE THE DIFFERENCE RESPECT OURSELVES RESPECT OTHERS MAKE THE DIFFERENCE MAKE THE DIFFERENCE RESPECT OURSELVES RESPECT OTHERS MAKE THE DIFFERENCE RESPECT OURSELVES RESPECT OTHERS MAKE THE DIFFERENCE MAKE THE DIFFERENCE RESPECT OURSELVES RESPECT OTHERS MAKE THE DIFFERENCE RESPECT OURSELVES RESPECT OTHERS MAKE THE DIFFERENCE MAKE THE DIFFERENCE RESPECT OURSELVES RESPECT OTHERS MAKE THE DIFFERENCE RESPECT OURSELVES RESPECT OTHERS MAKE THE DIFFERENCE Instructions to students:  Write your name, class and register number in the spaces at the top of this page.  Write in dark blue or black pen on spaces provided.  You may use a HB pencil for any diagrams or graphs.  Do not use staples, paper clips, glue or correction fluid.  Answer all the questions in this paper.  Give non-exact numerical answers correct to 3 significant figures, or one decimal place in case of angles in degrees, unless a different level of accuracy is specified in the question.  The use of an approved scientific calculator is expected, where appropriate.  You are reminded of the need for clear presentation in your answers. Information for pupils  The number of marks is given in brackets [ ] at the end of each question or part question.  The total mark for this paper is 90. Calculator Model: ______________________ This question paper consists of 19 printed pages (including this cover page). [Turn over HOUGANG SECONDARY SCHOOL MID-YEAR EXAMINATION 2021 ADDITIONAL MATHEMATICS 4049/02 SECONDARY FOUR EXPRESS 90

2 Mathematical Formulae 1. ALGEBRA 2For the equation 0, Quadratic Equation ax bx c   a acbbx 2 42  1 2 2( ) .... .... 12 n n n n n r r n Binomial Theorem n n na b a a b a b a b b r                          where n is appositive integer and !)!( ! rrn n r n       = ! )1.().........1( r rnnn  2. TRIGONOMETRY Identities AAec AA AA 22 22 22 cot1cos tan1sec 1cossin    sin ( ) sin cos cos sinA B A B A B   cos( ) cos cos sin sinA B A B A B BA BABA tantan1 tantan)tan(   AAA cossin22sin  AAAAA 2222 sin211cos2sincos2cos  A AA 2tan1 tan22tan  Formulae for ABC C c B b A a sinsinsin  Abccba cos2222  1 sin2 ab C

3 1 Express 3 3 3 4 2xx xx   in partial fractions. [6]

4 2(a) Solve the equation 3 4 2 0xx [4] 2(b) The lengths of the two shorter sides of a right-angled triangle are  35 cm and  48 20 cm respectively. Find the area of the triangle in the form  15ab cm2. [3]

5 3(a) Given that 2 22 d ax bxxdx x    , find the values of a and b. [4]

6 3(b) (i) The equation of a curve is 2 2 . 1 xy x   Find an expression for .dy dx [3] 3(b) (ii) Using the result in (i) above, explain, with working, why the curve 2 2 1 xy x   has no turning points. [2]

7 4(a) The diagram shows the straight line graph obtained by plotting xy against 1 x . The line passes through the points . Express y in terms of x. [4]    1,1 and 4,11 (1, 1) (4, 11)

8 4(b) An experiment on the discharge of an electrical circuit was conducted. It is known that V volts, the voltage of the electrical circuit and t seconds, the elapsed time since the removal of the power source, are related by the equation ktV Ae , where A and k are constants. The table below shows corresponding values of t and V. t 1.0 1.5 2.0 2.5 3.0 V 2.80 2.20 1.35 1.39 1.10 (i) On the grid given in page 9, plot a straight line to illustrate this data. Use the graph to estimate the values of A and k. (ii) Estimate the initial voltage of the electrical circuit [5] [1] (iii) It was subsequently discovered that one of the readings was wrongly recorded in the table. Using the graph, determine which value of V, in the table above, is the incorrect recording. Estimate a value of V to replace the incorrect recording of V. [2]

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10 5(a) (i) Find the range of values of p for which the equation 2 6 2 9x x p px    has real and distinct roots. [4] (ii) Using your answer in (i), deduce whether the curve   2 3yx will meet the line 18 9yx . [2]