LVSS 2021 4E Prelims AMath P2

LOYANG VIEW SECONDARY SCHOOL Preliminary Examination 2021 Secondary Four Express CANDIDATE NAME MARKING SCHEME CLASS INDEX NUMBER CLASS CLASS INDEX NUMBER 0 0 ADDITIONAL MATHEMATICS 4049/02 Paper 2 1 SEP 2021 2 hours 15 minutes Candidates answer on the Question Paper. No Additional Materials are required. For examiner’s use only Question number Mark 1 2 3 4 5 6 7 8 9 10 11 Total READ THESE INSTRUCTIONS FIRST Write your Class, 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. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES.

Answer all the questions. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angle 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. Setter: Mr Sim LE This document consists of 22 printed pages. Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation

3 [Turn Over Binomial expansion where n is a positive integer and 2. TRIGONOMETRY Identities Formulae for 1 (i) Show that the line does not meet the curve for all real values of x. [4] (ii) If the roots of the equation are real, show that k cannot lie between 2 and 3. [4]

Q Solutions Mark s Remarks 1 (i) Hence, the line does not meet the curve. M1 M1 M1 A1 √M1 incorrect (ii) Hence, k cannot lie between 2 and 3. M1 M1 M1 A1 √M1 incorrect 3 2

5 Loyang View Secondary School Sec 4E Preliminary Examination Additional Mathematics 4049 /2 [Turn Over 2 (a) Solve the equation . [3] (b) Solve the equation log3 x – log3 = log9 (5x – 1) [5] Q Solutions Mark s Remarks 2 (i) M1 M1 A1 √M1 incorrect (ii) log3 x – log3 = log9 (5x – 1) log3 = log3 2x = log3 2x = log3 2x = log3 (5x – 1) log3 2x = 2x = (2x)2 = 5x – 1 4x2 – 5x + 1 = 0 M1 M1 M1 M1 √M1 incorrect quotient law change of base law power law

6 Loyang View Secondary School Sec 4E Preliminary Examination Additional Mathematics 404 9/2 (4x – 1)(x – 1) = 0 x = or x = 1 A1 3 The first four terms, in ascending powers of x, of is . (i) Find the value of p, of n and of q. [5] (ii) Using your answer in (i), estimate, to 5 decimal places, the value of . [3] Q Solutions Mark s Remarks 3 (i) Equating terms, B1 M1 A1 M1 A1 √M1 incorrect (ii) +… Substitute x = 0.01 into the expansion, M1 M1 A1 √M1 incorrect

7 Loyang View Secondary School Sec 4E Preliminary Examination Additional Mathematics 4049 /2 [Turn Over 4 It is given that . Given that , show that . [6] Q Solutions Mark s Remarks 4 (shown) ✓M1 ✓M1 ✓A1 ✓M1 ✓M1 ✓AG 1 √M1 without “C” √M1 due to imperfect answers from above Commented [1]:

8 Loyang View Secondary School Sec 4E Preliminary Examination Additional Mathematics 404 9/2 5 In the diagram, O is the centre of the circle ABDE with diameters AD and BE. CD is a tangent to the circle at D. (i) Show that . [2] (ii) It can be proven that . Given that , show that CD = AD. [4] Q Solutions Mark s Remarks 5 (i) Hence (AAA similarity) Hence, (ASA) M1 A1 √M1 incorrect for practice after exam given in question

9 Loyang View Secondary School Sec 4E Preliminary Examination Additional Mathematics 4049 /2 [Turn Over (ii) M1 M1 M1 A1 √M1 incorrect

10 Loyang View Secondary School Sec 4E Preliminary Examination Additional Mathematics 404 9/2 6 The diagram shows a container in the shape of an inverted pyramid. The top of the pyramid is a square base with an area of 64 cm2. The height of the container is 6 cm. (i) The container is filled with oil to depth of h cm. Show that the volume, V cm3, of the empty space in the container is given by . [3] (ii) Oil is poured into the container and the depth of the oil increases at a constant rate of 0.4 cm/s. Find the rate of decrease of the volume of the empty space in the container when the depth of the oil is 3 cm. [4] Q Solutions Mark s Remarks 6(i) Side of square top = 8 cm Volume of Pyramid By similar triangles, M1 √M1 incorrect h cm 6 cm Alternative: Similar figures; area and volume 4 h 6