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SMJK SAM TET IPOHPEPERIKSAAN PERCUBAANPENGGAL 1 STPM 2015MATHEMATICS (T) 954/1Paper 1(1 hours)

Disediakan oleh : En Wang Yaw Weng Cik Ong Siew Eng

Disahkan oleh : . Pn Ng Sook Chin (PK Tingkatan 6)

Disemak oleh : En Wang Yaw Weng (Ketua Panitia Matematik)

A list of mathematical formulae is provided on page 4 of this question paper.

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This question paper consists of 4 printed pages.

SMJK SAM TET 2013

Section A [45 marks]Answer all questions in this section.1The functions f and g are defined as f : x 3x 5, x and g : x e2x, x (i) State the range of g. [1](ii) Sketch, on the same axes, the graphs of the inverse functions of f 1 and g1.[3] (iii) State, giving a reason, the number of roots of the equation f1(x) = g1(x). [1](iv) Evaluate fg( ), giving your answer to 3 decimal places. [2]

2Express the complex number in polar form. [3]Hence, (a) find z4, [2](b) solve the equation z3 = [3]

3The matrices A and C are given by A = , C = (i) Using elementary row operations, obtain the inverse of A. [5](ii) Find the matrix B satisfying BA = C. [2]

4A geometric progression has positive terms. The sum of the first six terms is nine times the sum of the first three terms. The seventh term is 320. Find the common ratio and the first term. [4]Find the smallest value of n such that the sum to n terms of the progression exceeds 106.[3]

5Show that the point P(2sec + 2, tan 3) lies on the curve x2 4y2 4x 24y 36 = 0. [2]Expressing the equation of the curve in standard form, determine whether it is a parabola, an ellipse or a hyperbola. [2]Sketch the curve. [2]Find the centre, the vertices, the foci and the equations of asymptotes (if any). [4]

6Two lines have equationsr = ( i + 5j + 2k ) + s ( i 2j + 3k) and r = (i j + 10k ) + t (3i + 4j 5k)(i) Show that the lines meet, and find the point of intersection. [4](ii) Calculate the acute angle between the lines. [2]

Section B [15 marks]Answer any one question in this section.7 (a) Find the value of a for which (x 2) is a factor of 3x3 + ax2 + x 2.Show that, for this value of a, the cubic equation 3x3 + ax2 + x 2 = 0 has only one real root. [5](b) Determine the solution set of the inequality > 2. [4] (c) Obtain the first three terms in the expansion, in ascending powers of x, of

, stating the set of values of x for which the expansion is valid.

Hence, find , correct your answer to four decimal places. [6] 8The plane passes through the points A(-2, 3, 5), B(1, -3, 1) and C(4, -6, -7).(i) Find AC x BC. [3]Hence, find(ii) the area of the triangle ABC. [2](iii) the equation of the plane in the form r . n = p. [2]The perpendicular from the point D(14, 1, 0) to meets the plane at the point E.Find(iv) the equation of DE. [2](iv) the coordinates of E. [3](vi) the angle between the line AD and the plane . [3]

MARKING SCHEMETRIAL PENGGAL 1STPM 2015

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