KSS 2023 Prelims 4NA AMaths P2-1

Candidate Name: __________________________ ( ) Class: _________ KRANJI SECONDARY SCHOOL Preliminary Examination Secondary 4 Normal (Academic) ADDITIONAL MATHEMATICS 4051/02 Paper 2 Wednesday 2 Aug 2023 1 hr 45 min KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY K RANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRAN JI SECONDARY KRANJI SECONDARY KRANJI KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY K RANJI SECONDARY KRANJI SECONDARY KRANJI KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI READ THESE INSTRUCTIONS FIRST: Do not open this question paper until you are told to do so. Write your name and register number in the spaces at the top of this page. Write in dark blue or black pen. You may use HB pencil for any diagrams or graphs. 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 70. ___________________________________________________________________________________ Setter: Mdm J Yap _________________________________________________________________ This question paper consists of 16 printed pages including the cover page [Turn over 4N(A) Session 2 Question Marks 1 2 3 4 5 6 7 8 Total

2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation ,02  cbxax a acbbx 2 42  2. TRIGONOMETRY Identities AA AA 22 22 tan1sec 1cossin   cosec2 A = 1 + cot2 A BA BABA BABABA BABABA tantan1 tantan)tan( sinsincoscos)cos( sincoscossin)sin(      A AA AAAAA AAA 2 2222 tan1 tan22tan sin211cos2sincos2cos cossin22sin    Formulae for ABC Cab Abccba C c B b A a sin2 1 cos2 sinsinsin 222   

3 1 (a) Solve the equation 2 3 32 24 8 x x x   . [5]

4 (b) The coordinates of the points P and Q are  6, 5 and 2, 10 . Find the equation of the perpendicular bisector of PQ. [4]

5 2 A rectangular block has a square base of side  10 2 cm and a height of h cm. The volume of the rectangular block is 52 28 5 cm3. Without using a calculator, find the height of the rectangular block, in cm. Give your answer in the form  5ab cm where a and b are integers. [5]

6 3 (a) Given that A is an acute angle and that 5sin , 7A find the exact value of sin 2 .A [3] (b) Solve the following equations (i) sec(2 15 ) 2x  for 0 180 ,x   [ 4 ]

7 (ii) 27sec 6 tan 23 0AA  for 0. A  [4]

8 4 (a) A biologist modelled the population, N, of bacteria in a sample by the equation 32 41 60 500,2Nt t t    for 52 5t , where t is the temperature of the sample in degree Celsius. (i) At what temperature does the number of bacteria reached the maximum? [3] (ii) Find the maximum bacteria population. [2]

9 (b) Given that 2 3 4y x  for 0x , find dy dx and explain why y is a decreasing function. [3]

10 5 (i) Differentiate 5 11 x  with respect to x. [2] (ii) Hence find the exact value of 2 64 1 (1 )x xd x  . [ 4 ]