Springfield Mathmatics 4Exp Amaths Paper 2 Prelim 2021

[Turn Over SPRINGFIELD SECONDARY SCHOOL Preliminary Examination 2021 STUDENT NAME CLASS S - INDEX NUMBER ADDITIONAL MATHEMATICS 4049/02 Secondary 4 Express 30 Aug 2021 2 hours 15 minutes Candidates answer on the question paper Additional Materials: Graph paper READ THESE INSTRUCTIONS FIRST Write your class, index number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the 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. 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 90. For Examiner’s Use Total /90 Do not turn over this question paper until you are told to do so. ____________________________________________________________________________ This question paper consists of 13 printed pages.

2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 02  cbxax , a acbbx 2 42 Binomial Expansion  nrrnnnnn b...bar n...banbanaba         221 21 where nis a positive integer and   ! 11 !! ! r rn...nn rnr n r n    2. TRIGONOMETRY Identities 1cossin 22  AA AA 22 tan1sec  2 2cos 1 cotec A A  BABABA sincoscossin)sin(  BABABA sinsincoscos)cos(  BA BABA tantan1 tantan)tan(   AAA cossin22sin  AAAAA 2222 sin211cos2sincos2cos  A AA 2tan1 tan22tan  Formulae forABC Abc Abccba C c B b A a sin2 1 triangleof Area cos2 sinsinsin 222   

3 [Turn Over 1 Express 3 3 2 2 1x x x   in partial fractions. [6]

4 2 The table shows experimental values of two variables x and y. x 0 1 2 3 4 5 y 10 25 50 280 260 480 (a) Variables x and y are related by the equation xy ma , where m and a are constants. Explain how m and a can be calculated when a graph of lgyagainst x is drawn. [3] (b) On the graph paper, draw a straight line graph to illustrate the experimental values. [3] (c) Hence, determine the values of a and m. [2] (d) One of the pairs of values is wrong. What should be the correct x value or y value? [2]

5 [Turn Over 3 The diagram above shows a straight line 34y nx  , where n is a constant, intersecting the curve 2 6 16y x x   at two points A and B respectively. Point A is the highest point of the curve 2 6 16y x x   . (a) Find the value of n. [4] (b) Show that the coordinates of B is (6 , 16). [3] (c) Find the area of the shaded region. [3] A B 34y nx  2 6 16y x x  

6 4 (a) Determine the range of m if 2 2 1 1 x x mx x     has no real roots. [4] (b) Find the range of values of x for which 2 2 51 3 x xx    . [3] (c) It is given { : 2 or 5}x x x  is the solution set of the quadratic inequality 21 02x px q   . Find the values of p and q. [3]

7 [Turn Over 5 (a) Given that 3 4 0 3f ( ) f ( ) 5x dx x dx   . Find (i) 4 3 0 42f ( ) f ( ) x dx x dx  , [2] (ii) the value of k for which   3 0 f ( ) 8x kx dx  [3] (b) Find  sind x xdx . Hence evaluate 2 0 cos x x dx   . [5]

8 6 (a) Use the substitution 2xu to solve the equation 22 7 2 12 0x x   . [4] (b) Solve the equation 4 1log log 8 2xx  . [8]

9 [Turn Over 7 The equation of the curve is 4 1 xy x  . (a) Find an expressions for 2 2 and dy d y dx dx . [6] (b) Find the coordinates of the stationary point. [3] (c) Find the nature of the stationary point [2]

10 8 (a) A line M passes through P(-3 , -1) intersects at right angle with another line L, whose equation is 4y x  at point C. Find the equation of the line M. [3] (b) A circle C1 has P as its centre and PC as its radius. Find the equation of the circle. [5]