Bendemeer 2021 Prelim Exam 4E Amaths P1 QP

Register No. Class Name : DATE : 25 August 2021 DURATION TOTAL : : 2 hours 15 minutes 90 Marks READ THESE INSTRUCTIONS FIRST Write your name, class and register number on the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a 2B pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid/tape. Answer all questions. Write your answers in the spaces provided on the question paper. All the diagrams in this paper are not drawn to scale. If working is needed for any question, it must be shown with the answer. Omission of essential working will result in loss of marks. The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For  , use either your calculator value or 3.142, unless the question requires the answer in terms of  . At the end of the examination, fasten all your work securely together. The number of marks is given in b rackets [ ] at the end of each question or part question. This question paper consists of 18 printed pages including this cover page. [Turn over Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School Bendemeer Secondary School BENDEMEER SECONDARY SCHOOL 2021 Preliminary Examination Secondary Four Express Additional Mathematics Paper 1 4049/ 01 90 FOR EXAMINER’S USE

Bendemeer Secondary School Page 2021 Preliminary Examination / Sec 4E / Additional Mathematics Paper 1 2 MATHEMATICAL FORMULAE 1. ALGEBRA Quadratic Equation For the equation 02  cbxax , .2 42 a acbbx  Binomial Theorem   nrrnnnnn bbar nbanbanaba                  ......21 221 , where n is a positive integer and   ! )1)...(1( !! ! r rnnn rrn n r n       2. TRIGONOMETRY Identities Formulae for  ABC .sin2 1 .cos2 .sinsinsin 222 Abc Abccba C c B b A a   

Bendemeer Secondary School Page 2021 Preliminary Examination / Sec 4E / Additional Mathematics Paper 1 3 1 (i) Find the value of 10 ,x given that 4x+1× 52x-3 = 103x. [3] (ii) Hence, solve 4x+1× 52x-3 = 103x . [1]

Bendemeer Secondary School Page 2021 Preliminary Examination / Sec 4E / Additional Mathematics Paper 1 4 2 (a) The equation of a curve is y = 3x2 + 5x + 1 . Find the set of values of x for which the curve lies completely above the line y - 3x = 2 . [3] (b) Find the range of values of m for which the equation mx2 + 2m = 3x(4 – x) has real roots. [3]

Bendemeer Secondary School Page 2021 Preliminary Examination / Sec 4E / Additional Mathematics Paper 1 5 3 (i) Express 14 8 2 2   x xx in partial fractions. [4] (ii) Use your results in part (i) to find    dxx xx 14 8 2 2 . [2]

Bendemeer Secondary School Page 2021 Preliminary Examination / Sec 4E / Additional Mathematics Paper 1 6 4 (i) Express 30+18√3 2+√3 in the form r + s 3 , where r and s are integers. [3] (ii) The diagram shows a triangle XYZ. XY is  324 cm and YZ is  3ba cm, where a and b are integers. The included angle XYZ is 150. Given that the area of the triangle is  3915 cm2, find the value of a and of b. [5] X Y Z  324 cm  3ba cm

Bendemeer Secondary School Page 2021 Preliminary Examination / Sec 4E / Additional Mathematics Paper 1 7 5 (a) The equation log2 𝑥 + log8 𝑥 = log7 49 has the solution 𝑥 = 2𝑎. Find the value of a. [4] (b) Show that the equation log3(4𝑥 − 11) − log3(𝑥 − 3) = 1 has no solution. [4]

Bendemeer Secondary School Page 2021 Preliminary Examination / Sec 4E / Additional Mathematics Paper 1 8 6 The equation of a curve is 𝑦 = 3 − 4𝑠𝑖𝑛2𝑥. (i) State the minimum and maximum value of y. [2] (ii) Sketch the curve 𝑦 = 3 − 4𝑠𝑖𝑛2𝑥 for 0 ≤ 𝑥 ≤ 2𝜋 [3]

Bendemeer Secondary School Page 2021 Preliminary Examination / Sec 4E / Additional Mathematics Paper 1 9 7 The function is defined by (𝑥) = 𝑥2−4 𝑥2+6 , x > 0. (i) Explain, with working, whether g(x) is an increasing or decreasing function. [4] (ii) A point P moves along the curve g(x), such that the y – coordinate of P is increasing at a rate of 0.04 unit per second. Find the rate of increase of the x – coordinate of P when x = 2. [2]

Bendemeer Secondary School Page 2021 Preliminary Examination / Sec 4E / Addit