1 霹雳怡保培南独立中学 SEKOLAH MENENGAH POI LAM (SUWA) SECOND MONTHLY TEST 2022 ADVANCED MATHEMATICS (I) ___________________________________________ DATE : 19.08.2022 (FRIDAY) TIME : 1325 – 1455 (1 ½ HOURS) ____________________________________________ NAME : _____________________ REGISTRATION NUMBER: _____________ CLASS : S3LI INSTRUCTIONS TO CANDIDATES 1. Begin each question on a fresh page. 2. Use only blue or black ink to write your answers and use pencil for drawing only. 3. Do not copy the questions, but the answer to each question should be clearly numbered. 4. Show all mathematical working clearly. Geometric figures should be drawn where necessary. 5. Unless otherwise specified, the prescribed electronic calculators may be used. 6. Arrange the answer scripts in numerical order and tie them together. 7. The total number of marks for this paper is 60. Do Not Turn Over This Page Until You Are Told To Do So ________________________________________________________________________________ This document consists of 3 printed pages (including this page) Prepared by : Ms Chai Siew Yin Checked by : Mr Yeow Ghee Ruey Signature : _________________ Signature : __________________
2 1. Simplify 2 2 − 4 3 − 2 2 + −2 . Hence, find 0 1 2 2 − 4 3 − 2 2 + −2 . [4] 2. (a) − 1 and − 2 are factors of = 3 + 2 − 7 + where p and q are constants. Find p , q and the remaining factor. [2] (b) If the roots of the equation 2 + + 1 + 2 − 5 = 0 are real, find the range of possible values of k. [2] 3. (a) Let log 12 = and log 36 = , express log 54 in terms of a and b. [5] (b) Solve the equation 2 + 8 − 6 + 1 = 1. [5] 4. In the figure, OPQ is a sector with centre O, PR OQ, PQ = 4 5 cm and PR = 8 cm. P O R Q Find (a) the radius of the sector, [2] (b) angle POR, in radians and correct to 2 decimal places, [2] (c) the perimeter of the shaded region, [2] (d) the area of the shaded region. [4] 5. (a) The sum of the squares of the distances from P(x, y) to the origin O and to A(– a , 0) is equal to 2 . Prove that the locus of P is a circle and find its centre and radius. [4] (b) A straight line passes through the origin and forms a triangle of area 2 with the lines + = and = 0. Find the equation of the straight line. [6]
3 6. (a) Find the coefficients of the first three terms in the expansion of 3 + 1 2 4 . [2] (b) (i) If the three coefficients in part (a) are in an arithmetic progression, find n. [3] (ii) Hence determine whether the binomial expansion in part (a) has any constant term. [5] 7. A function is defined by : → + 1. Another function g is such that ∘ : → 3 2 + 6. Find the function g. [3] 8. (a) Given that = 4 3 − 6 2 + 1 and when = 2, = 9. Express y in terms of x. [2] (b) If = 2 2 3 , Find . [4] Hence, find the value of 0 1 3 + 2 3 dx. [3] END OF PAPER