Geylang Methodist 2024 AM P1 PRELIM Student

[Turn Over Candidate Name Class Index Number ADDITIONAL MATHEMATICS Paper 1 4049 / 01 4 Express/5 Normal(A) Candidates answer on the Question Paper. No Additional Materials are required. 2 hours 15 minutes Setter: Mr Johney Joseph 12 August 2024 READ THESE INSTRUCTIONS FIRST Write your name, class and index number in the spaces at the top of this page. Write in dark blue or black pen. You may use a soft pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, 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 score for this paper is 90. For Examiner’s Use This document consists of 19 printed pages and 1 blank page. Geylang Methodist School (Secondary) Preliminary Examination 2024

GMS(S)/AMath/P1/Prelim2024/4E/5N(A) 2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 02 =++ cbxax , a acbbx 2 42 −−= Binomial expansion ( ) nrrnnnnn bbar nbanbanaba ++     ++     +     +=+ −−− 221 21 , where n is a positive integer and ( ) ( ) ( ) ! 11 !! ! r rnnn rnr n r n +−−=−=       2. TRIGONOMETRY Identities 1cossin 22 =+ AA AA 22 tan1sec += AA 22 cot1cosec += ( ) BABABA sincoscossinsin = ( ) BABABA sinsincoscoscos = ( ) BA BABA tantan1 tantantan  = AAA cossin22sin = AAAAA 2222 sin211cos2sincos2cos −=−=−= A AA 2tan1 tan22tan −= Formulae for ABC C c B b A a sinsinsin == Abccba cos2222 −+= Cabsin2 1=

GMS(S)/AMath/P1/Prelim2024/4E/5N(A) [Turn Over 3 1 Find the range of values of p for which the curve ( ) 2 2 2 7y px p x p= + + + + has no x-intercepts. [4]

GMS(S)/AMath/P1/Prelim2024/4E/5N(A) 4 2 Given that 232 xxy e e −=+ , and that 2 2 2 dd dd xxyy y Ae Bexx −+ + = + , find the values of each of the constants A and B. [5]

GMS(S)/AMath/P1/Prelim2024/4E/5N(A) [Turn Over 5 3 The equation of a curve is 4 3cos 2yx=− . (a) State the period and amplitude of y. [2] (b) Sketch the graph of 4 3cos 2yx=− for 02 x  . [3]

GMS(S)/AMath/P1/Prelim2024/4E/5N(A) 6 4 For a particular curve 2 2 d 32d y xx =− . The tangent to the curve at the point ( )4, 40A − is parallel to the line 3x – y = 2. Find the equation of the curve. [6]

GMS(S)/AMath/P1/Prelim2024/4E/5N(A) [Turn Over 7 5 The triangle ABC is such that its area is 216 7 10 cm2 + , the length of AB is ( )3 2 5+ cm, and AB is perpendicular to BC. (a) Find the length, in cm, of BC in the form ( )25ab + , where a and b are integers. [3] (b) Find an expression, in 2cm , for 2AC in the form 10cd+ , where c and d are integers. [3]

GMS(S)/AMath/P1/Prelim2024/4E/5N(A) 8 6 The function f is defined by f(x) = 3sin 4cos 2 , 0 2x x x −   . (a) Explain with working, whether f is an increasing or a decreasing function. [4] A point P moves along the curve y = f(x) in such a way that the x-coordinate of P is increasing at the rate of 2 units per second. (b) Show that the y-coordinate of P increases at the rate of 11 3 units per second when 6x = . [3]

GMS(S)/AMath/P1/Prelim2024/4E/5N(A) [Turn Over 9 7 (a) By considering the general term in the expansion of 10 2 3 2 xx  − , explain why there is no term in 6x . [3] (b) Find the coefficient of 6x in the expansion of 10 6 2 3 2 3 8 xxx  −−   . [4]

GMS(S)/AMath/P1/Prelim2024/4E/5N(A) 10 8 The diagram shows the junction of two corridors of width 9 m and 4 m which are at right angles. P and Q are variable points and PBQ is a straight line. (a) Given that the length of CP is x m and the length of AQ is y m, show that 364y x=+ . [3] A Q C P B 9 m x m y m 4 m