SMK GAJAH BERANG MELAKA
MATHEMATICS–T STPM 2014 TRIAL EXAM (Paper 954/1)
SECTION A (45 Marks) : Answer all questions in this section. 1. (a) Solve the equations ─ 2 = 3 (4)
(b) The function f and g are defined by
,x > −1
(i) Give a reason why the f -1 exists. Hence find the f -1 . (4) (ii) Find gοf-1 and its range. (3)
2. (a) If z = 2 + 3i, show the complex number can be express as – i.
Hence, determine the modulus and argument in radians for .
(b) Find all the cube roots of 8.
3. (a) Given that Matrix is singular. Find
the possible values of k.
(3) (b) Solve the following system of linear equations using Gaussian elimination.
-x + 3y + 2z = 1
x – 2y + z = 2
2x – 3y + 4z = 5
The equation of a hyperbola is 4x2 − 9y2 −24x − 18y − 9 = 0
(i) Obtain the standard form for the equation of the hyperbola
(2) (ii) Find the vertices and equations of the asymptotes of the hyperbola. Hence, sketch the graph. (4)
5. If f(r) = , simplify f(r) − f(r + 1), (3) Hence find (4)
Please join StudyMode to read the full document