MathematicsT STPM Baharu TGANU 2012
Short Description
Mathematics STPM Baharu Trial 2012...
Description
2012 TRIAL STPM BAHARU
MATHEMATICS T
JPS TERENGGANU
Section A [45 marks] Answer all questions in this section. 1.
The function of f and g are define by , a) Find f and state the domain b) Find the inverse of g , and sketch its graph. Hence state the range.
2.
Express
[3m] [5m]
in ascending order powers of x up to and including the term in
By using the substitution x = , find an approximate value of
in the form ,
where p and q are positive integers. 3.
[6m]
The matrix
Given that
.
is a symmetry matrix.
.
Find a, b and c, hence solve the system of equations for
[8m] 4.
If + 2 i and = -3 -3 i, find the modulus and argument of and . Hence, find the modulus and argument of and ,and express and , in polar form. [7m]
5.
6.
The line and intersect the curve respectively where the x coordinates are positive. Find the coordinates of Calculate the perpendicular distance of to
Two line
have vector equation respectively. Find The position vector of their common point The angle between the lines.
at point
, where
[4m] [4m]
is origin
and [4m] [4m]
Page 1
© Jabatan Pelajaran Negeri Terengganu STPM 954/1
2012 TRIAL STPM BAHARU
MATHEMATICS T
JPS TERENGGANU
Section B [15 marks] Answer any one question in this section. 7.
The expression cos x - sin x may be written in the form r cos ( x + ) for all values of x, where r is positive and is acute. a) Determine the values of r and [3m] b) State the minimum and maximum values of cos x - sin x, and determine the corresponding values of x in the interval [3m] c) Sketch the curve y = cos x - sin x for [3m] By drawing an appropriate line on the graph, determine the number of roots of the equation cos x - sin x = in the interval [3m] d). Solve the equation cos x - sin x = 1 [3m]
8.
a)
b)
Given that , = and = . i) find the unit vector that is perpendicular to both vectors and ii) if is a triangle, show that for the smallest angle,
[4m]
. Hence calculate the area of triangle to the 3 significant figures
[6m]
Determine the coordinates where the line the plane
[5m]
intersect
Page 2
© Jabatan Pelajaran Negeri Terengganu STPM 954/1
2012 TRIAL STPM BAHARU 1.
a)
MATHEMATICS T
f
JPS TERENGGANU M1 A1 A1
b)
M1
= ,
A1
y 𝑔−1
D1 for D1 ( all correct)
0
x A1
2. = = ( 1 + 6x +
M1
= ( 1 + 6x + = = 1 + 7x + Substituting x = ,
Page 3
© Jabatan Pelajaran Negeri Terengganu STPM 954/1
2012 TRIAL STPM BAHARU
MATHEMATICS T
JPS TERENGGANU
3.
M1 either one M1 solving A1 all correct A1
From
B1
M1
M1 A1 (all correct)
4.
+2 -3
B1 ( both correct )
arg = =
B1
arg = =
B1 B1
arg
arg =
=0
B1
Page 4
© Jabatan Pelajaran Negeri Terengganu STPM 954/1
2012 TRIAL STPM BAHARU
MATHEMATICS T
JPS TERENGGANU
and
B1
arg
=
B1
Hence, 5
i)
and For
B1
coordinates P
For coordinates Q M1
M1
A1 ) ii)
A1
The straight line OQ B1 The perpendicular distance
M1
A1
,
6.
At the common to m and n
and
M1 A1 M1
The position vector is
ii)
From
A1
……………..
(i)
……………..(ii) The direction vector of
M1 either one
………………..(i)
The direction vector of
………………………..(ii)
M1 either one
Page 5
© Jabatan Pelajaran Negeri Terengganu STPM 954/1
2012 TRIAL STPM BAHARU
MATHEMATICS T
JPS TERENGGANU M1
The angle between line m and n is
7.
(a).
Let
cos x-sin x
= r cos ( x +
/
A1
,r>0
= r cos r sin
--------B1 either one
tan (b).
and r =
Minimum value is -
--------M1,A1(boths are correct )
when
----------B1
x= Maximum value is
when
-----------B1
x=
------------A1 [ boths are correct ]
(c). 1.5 2
1 𝜋 4
3 𝜋 4
7 D1-shape, D1𝜋 4 ), values (max-min
2𝜋
D1 All corrects-
− 2 0
Page 6
© Jabatan Pelajaran Negeri Terengganu STPM 954/1
2012 TRIAL STPM BAHARU
MATHEMATICS T
JPS TERENGGANU
x y
0
0.75
1.5
Number of roots = 3 (d). cos x - sin x = 1,
------- Line-B1,B1,A1
---------B1 ---------B1 x = 0,
8.
a)
-----------A1 (boths)
i.
M1
=2i – 2j –2k
A1 =
A1 A1 M1 either one M1 M1 A1
Area of the triangle
or equivalent .
b)
from
A1
and
…………………(*) sub to eqn
M1(all correct) M1 A1
M1 The coordinate is
A1 Page 7
© Jabatan Pelajaran Negeri Terengganu STPM 954/1
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