ACSBR 2024 Sec Prelim Add Math P1

Full Name Class Index No Class Anglo-Chinese School (Barker Road) PRELIMINARY EXAMINATION 2024 SECONDARY FOUR EXPRESS / FIVE NORMAL (ACADEMIC) ADDITIONAL MATHEMATICS 4049 PAPER 1 2 HOURS 15 MINUTES Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your index number and name in the spaces at the top of this page. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. 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 23 printed pages and 1 blank page. For Examiner’s Use

Anglo-Chinese School (Barker Road) 2 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Additional Mathematics 4049 Paper 1 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 2 0ax bx c+ + = , 2 4 2 b b acx a −  −= Binomial expansion ( ) 1 2 2 12 n n n n n r r nn n na b a a b a b a b b r − − −     + = + + + + + +           , where n is a positive integer and ( ) ( ) ( )11! ! ! ! n n n n rn r r n r r − − + == − 2. TRIGONOMETRY Identities 22sin cos 1AA+= 22sec 1 tanAA=+ 22cosec 1 cotAA=+ ( )sin sin cos cos sinA B A B A B =  ( )cos cos cos sin sinA B A B A B= ( ) tan tantan 1 tan tan ABAB AB = sin 2 2sin cosA A A= 2 2 2 2cos 2 cos sin 2cos 1 1 2sinA A A A A= − = − = − 2 2 tantan 2 1 tan AA A= − Formulae for ABC sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + − 1 sin2 bc A=

Anglo-Chinese School (Barker Road) 3 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Additional Mathematics 4049 Paper 1 1 The line 3=− yx intersects the curve 0193 22 =++− yxyx at the points P and Q. Find the coordinates of P and of Q. [5]

Anglo-Chinese School (Barker Road) 4 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Additional Mathematics 4049 Paper 1 2 Solve the equation 12 3(2 ) 7xx+−+= . [5]

Anglo-Chinese School (Barker Road) 5 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Additional Mathematics 4049 Paper 1 3 Express the equation 24log log ( 1) 3xx+ − = as a cubic equation in x. [4]

Anglo-Chinese School (Barker Road) 6 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Additional Mathematics 4049 Paper 1 4 The diagonals of a cyclic quadrilateral PQRS intersect at U. The tangent to the circle at R meets PS produced at T. If QR = RS, prove that (a) QS is parallel to RT, [3] (b) triangles QUR and RST are similar. [3] P S T R Q U

Anglo-Chinese School (Barker Road) 7 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Additional Mathematics 4049 Paper 1 TURN OVER FOR QUESTION 5

Anglo-Chinese School (Barker Road) 8 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Additional Mathematics 4049 Paper 1 5 The diagram shows points A(5, 0), B(a, 3a) and C(−2, 6) such that the line AB is perpendicular to the line BC. (a) Show that a = 2.5. [3] B (a, 3a) C (−2, 6) A (5, 0) y x O

Anglo-Chinese School (Barker Road) 9 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Additional Mathematics 4049 Paper 1 5 (b) Find the coordinates of the midpoint of AC. Hence find the coordinates of D such that ABCD is a parallelogram. [3] (c) The area of triangle AEC is 5 units2. Find the value of x given that the point E is (x, 2x), where x > 1. [2]

Anglo-Chinese School (Barker Road) 10 Preliminary Examination 2024 Secondary 4 Express / 5 Normal (Academic) Additional Mathematics 4049 Paper 1 6 (a) Express 2 13 6 (2 3) x xx − − in partial fractions. [5]