CHIJ KC 5NA AM Prelims 2021 P2 QP

Name: __________________________ ( ) Class: ______ This question paper consists of 21 printed pages. [Turn over CHIJ KATONG CONVENT PRELIMINARY EXAMINATION 2021 SECONDARY 5 NORMAL ACADEMIC ADDITIONAL MATHEMATICS 4047/02 PAPER 2 Duration: 2 hours 30 mins ____________________________________________________________________ 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/tape. 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. Omission of essential working will result in loss of marks. 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 100.

2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation ax2 + bx + c = 0, x = Binomial expansion , where n is a positive integer and 2. TRIGONOMETRY Identities sin2 A + cos2 A = 1 sec2 A = 1 + tan2 A cosec2 A = 1 + cot2 A sin 2A = 2 sin A cos A cos 2A = cos2 A – sin2 A = 2 cos2 A – 1 = 1 – 2 sin2 A Formulae for ΔABC

CHIJ Katong Convent Prelim Exam 20214047/02 Sec 5NA Name: _________________________ ( ) Class: ________ ___________________________________________________________________________ 3 [Turn over Δ = 1 The polynomial has roots of equations Given that the coefficient of is and that has a remainder of 20 when divided by , find the value of k. Hence, find the remainder when is divided by x – 10. [6]

CHIJ Katong Convent Prelim Exam 20214047/02 Sec 5NA ____________________________________________________________________________ 4 2 (i) Find the coordinates of the two points A and B on the curve whose

CHIJ Katong Convent Prelim Exam 20214047/02 Sec 5NA Name: _________________________ ( ) Class: ________ ___________________________________________________________________________ 5 [Turn over tangents pass through the point P (2, 6). [6] (ii) If the normals at A and B meet at the point Q, find the coordinates of Q. [4]

CHIJ Katong Convent Prelim Exam 20214047/02 Sec 5NA ____________________________________________________________________________ 6 3 Prove that . Hence, solve the equation , giving all solutions between 0 and [8]

CHIJ Katong Convent Prelim Exam 20214047/02 Sec 5NA Name: _________________________ ( ) Class: ________ ___________________________________________________________________________ 7 [Turn over 4 (i) A cylinder has a diameter of and a volume of cm3. Find the height of the cylinder in the form of cm. [4]

CHIJ Katong Convent Prelim Exam 20214047/02 Sec 5NA ____________________________________________________________________________ 8 (ii ) Given that , find the value of [3]

CHIJ Katong Convent Prelim Exam 20214047/02 Sec 5NA Name: _________________________ ( ) Class: ________ ___________________________________________________________________________ 9 [Turn over 5 Solutions to this question by accurate drawing will not be accepted. The diagram, which is not drawn to scale, shows a trapezium PQRS in which PQ is parallel to SR. The point P lies on the y-axis and the point Q is (7, 9). The point T(6, 7), lies on PR such that QT is perpendicular to PR. QT produced meets SR at U and QU = 3QT. Find (i) the equation of PR, [3]

CHIJ Katong Convent Prelim Exam 20214047/02 Sec 5NA ____________________________________________________________________________ 10 (ii) the coordinates of P, [2] (iii) the coordinates of V if PQRV is a kite, [2] (iv) the coordinates of U, [2]