P2 AM QP (caifan exam)

Preliminary Examination Paper 2 The caifan Exam (final)Time: 2 hours 15 minutes Name: …………………………….(Paper 2 Question Paper)Marks: 90 Topics: everything other than trigonometry, differentiation, and integration(do paper 1 first!)Pages: 30 90 READ THE INSTRUCTIONS FIRST 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.

Formula List:………………………………..…………………………………………………………………………………………….O Level Additional Mathematics 4047/1 To all viewers (and holy grail moderators):setter of this paper is a sec 4 student who has taken a deep and fond interest in my beloved, amath1) thank you holy grail mods!2) this paper, if you are using it as practice, is much more difficult from the regular question types. in my opinion, amath questions has gotten more vanilla and less interesting once you start to try more papers, hence this paper showcases how some amath questions can truly be very difficultthis amath paper consists of a mishmash of small miscalleneous chapters, from quadratic functions to plane geometry (which is why it’s named the caifan paper)3) similarly, marks might not be given as fairly in this paper as in normal papers4) if you really want to do it timed, I suggest giving more time (about 15 minutes) to balance the fairness of this paperinspiration for some qns:nchs, tkss, gess, blss, nhhs, mgs

…………………………………………………………………………………………………………… O-Level Additional Mathematics 4049/2 Answer all questions. 1Solving the inequality kx > 2x + n, the solutions are x > 3 + 2√3 and x < 3 – √p , where k, n, and p are rational constants. – –2 Find the values of k and n. [2] (a) (b) [2] The diagonals of a rhombus are of length (1 + 2√3) cm and x cm respectively.The area of the rhombus is (8 + 5√3) cm . Find the perimeter of the rhombus, in the form a√b + c √3 cm, where a, b, and c are integers in simplest possible form. –2– ––––––––

…………………………………………………………………………………………………………… O-Level Additional Mathematics 4049/2 2 h / cm O d / cm Diagram 2.1 Look at Diagram 2 below closely. It shows a fish jumping out of its tank into another empty tank.After the fish jumps out of the tank, at a certain time in the air, the movement of the fish can be plotted as a parabolic curve below. The height h axis cuts the centre of the fish while the distance d axis lies on the openings of the fish tanks. The equation of the curve is h = ad + bd + c, where a, b and c are constants. (i) 2 im nothing like y’all The maximum value of h is 7.2 cm when the horizontal distance from the h axis was 2 cm.The fish travelled a horizontal distance of 12 cm from the initial opening of the fish tank to the other opening of the fish tank. Find the equation of the curve, in the form given above.[3] ⊥ #

…………………………………………………………………………………………………………… O-Level Additional Mathematics 4049/2 (ii) [1] The horizontal line where both of the water in the fish tanks lie on the line h = –4.2 .Find the horizontal distance travelled by the fish from the water in the left tank into the water in the other tank. x y O y = ax + bx + c2 (iii)Look at the diagram below. It shows a quadratic graph being drawn below. Its maximum point lies on the x axis. Diagram 2.2 [1]Determine the conditions of a, b, and c. #

…………………………………………………………………………………………………………… O-Level Additional Mathematics 4049/2 3A polynomial P(x) has a function where if P(x) is divided by x – 9, its remainder is –8x + 6.When P(x) is divided by x + 9, its remainder is 5x – 2.Find the remainder of P(x) when it is divided by x + 3x + 9x + 27. (i) 2 2 23 [3] (ii)When P(x) Q(x) is divided by (x – 3), where Q(x) is a polynomial, its remainder is k, where k > 0. Find the smallest value V added to Q(x) such that (x – 3) is a factor of (Q(x) + V), in terms of k if needed. [1]

…………………………………………………………………………………………………………… O-Level Additional Mathematics 4049/2 4(a)Express ––––––––––––––––––––––– in partial fractions.(x + 5) (x + 5)2 2 x + 8x + 12x + 20x + 85234 [4]

…………………………………………………………………………………………………………… O-Level Additional Mathematics 4049/2 (b) (i) The polynomial f(x) is such that the coefficient of x is 2. The roots of the equation f(x) = 0 are – and –1. f(x) has a remainder of –8 when divided by (x – 1) and a remainder of 28 when divided by (x + 2). 32 4 Find an expression for f(x), given its highest degree is 4. Hence determine the number and nature of the roots of e = 1. [3] (ii)Expand and simplify f(x) in descending powers of x. Hence solve 2 + y – 5y – 6y = 0.826 [2] f(x)

…………………………………………………………………………………………………………… O-Level Additional Mathematics 4049/2 5 (i) Solutions to this question by accurate drawing will not be accepted. [3] The diagram shows a kite ABCD in which A, B and C are points on a circle C . The coordinates of A and B are (–2, 7) and (5, 8) respectively.The lines AC and BD intersect at point E, the centre of the circle. BD makes an angle θ with the x axis such that cos θ = – . 1 D A (–2, 7) B (5, 8) C O x y E Find the coordinates of C. θ 35 Diagram 5 ·>

…………………………………………………………………………………………………………… O-Level Additional Mathematics 4049/2 (ii)It is further given that the ratio of BE : BD = 2 : 7.Find the coordinates of D. [1] (iii) [1] The centre of another circle lies on BD and touches D.It intersects the circle C at two distinct points.Find the range of possible values of the radius r units of the circle.1 (iv)Calculate the difference in the shaded area. [1]