CHIJ STC 2023 Prelim 4E5N A Math P1 mark scheme

CHIJ ST. THERESA’S CONVENT PRELIMINARY EXAMINATION 2023 SECONDARY 4 EXPRESS / 5 NORMAL (ACADEMIC) CANDIDATE NAME CLASS INDEX NUMBER ADDITIONAL MATHEMATICS 4049/1 Paper 1 29 August 2023 2 hours 15 minutes Candidates answer on the Question Paper. 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 pencil for any diagrams or graphs. Do not use paper clips, highlighters, glue or correction fluid. Answer all 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. This document consists of 17 printed pages.

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2023 PRELIMINARY EXAMINATION ADDITIONAL MATHEMATICS PAPER 1 2 1. ALGEBRA Quadratic Equation For the equation ax2 + bx + c = 0, x = a acbb 2 42 −− Binomial expansion (a + b)n = an + ban n 1 1 −       + 22 2 ban n−       + …+ rrn bar n −       + … + bn, where n is a positive integer and !)!( ! rrn n r n −=      ( 1)...( 1) ! n n n r r − − += . 2. TRIGONOMETRY Identities sin2A + cos2A = 1 sec2A = 1 + tan2A cosec2A = 1 + cot2A sin(A ± B) = sinAcosB ± cosAsinB cos(A ± B) = cosAcosB sinAsinB tan(A ± B) = tan tan 1 tan tan AB AB  sin2A = 2sinAcosA cos2A = cos2A − sin2A = 2cos2A − 1 = 1 − 2sin2A tan2A = 2 2 tan 1 tan A A− Formulae for ABC C c B b A a sinsinsin == a2 = b2 + c2 − 2bc cos A  = 1 sin2 ab C

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2023 PRELIMINARY EXAMINATION ADDITIONAL MATHEMATICS PAPER 1 3 1 Find the gradient of the normal to the curve 3 2 4y x x=+ at 5x= , leaving your answers in the form ( )5ab + , where a and b are constants. [4] 2 Integrate ( ) 2 54 31 1x x −+ − with respect to x. [4] At x = 5, Gradient of tangent = Hence, Gradient of normal B1 – Correct Gradient Function M1 – Using Gradient Function to find gradient of normal M1 – Rationalising denominator by multiplying correct conjugate surds A1 B1 – B1 – correct coefficient for ln function B1 – B1 – correct coefficient for power function and arbitrary constant

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2023 PRELIMINARY EXAMINATION ADDITIONAL MATHEMATICS PAPER 1 4 3 (a) Express 21 16 16xx−− in the