2015 H2 Mathematics Prelim Paper 2 Solutions
Qn
1.
(a)
Solutions
Locus of R is a straight line passing through the origin and parallel to AB .
1.
(b)
a and b are parallel
a = ( 2aib ) b
2
a = 2 a b co
FS
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PR
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PA
G
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3
U
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C
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EC
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Composite
functions,
transformations
and inverses
3.1 Kick off with CAS
3.2 Composite functions and functional equations
3.3 Transformations
3.4 Transformations
Skill Sets
Chapter 5 Functions
No.
1.
Skills
Sketch the graph of the
function according to the
domain.
Examples of questions involving the skills
(Lecture Notes Example 2 (b)
g : x x2 2 x 1, x , x 2

Functions Summary
1. Definitions
Domain ( D f ) : set of x values for which the function f (x) is defined.
Range ( R f ) : set of y values for which the function f ( x) is defined.
For completeness of
A Level Mathematics Tuition
1 to 1 or small group
http:/alevelmathtuition.sg
94385929 / 81502027
H2 Mathematics 2016 Paper 2 Revision
1
The curve C has equation
f(x)
ax 2 bx 1
, where a, b and c are
Figuring out asymptotes in "exp" and "ln" functions
Objective: To find the horizontal asymptotes of functions such as f(x) = x2 ex
or g(x) = (ln x) / x. Recall, this involves taking limits as x
.
*
VECTORS
UNIT VECTOR
1 What is a unit vector?
3
2 Avectora=3ij+4k =[_1)
4
What is the unit vector 21 ?
1
3 What is the unit vector in the direction of [ 2 j ?
1
4 What is the formula for a vector?
1
5
VECTORS
ANGLE BETWEEN TWO VECTORS
1 What is the formula for the angle between two vectors?
2 From analysis of the forces in a new bridge it is calculated that the following forces are
imposed at one o
VECTORS
RELATIVE VELOCITY
1 A bus B is travelling past a tree at 45 km/h. To a passenger on bus B,
tree T appears to be moving at 45km/h backwards, i.e. in the opposite direction
of the motion of the
VECTORS
VECTOR EQUATION OF A STRAIGHT LINE
(VECTOR FORM)
1 at is the position vector of a fixed pointA on the line I . The line is parallel to AB
Find a vector equation of line I.
2 Let r be a variabl
VECTORS
LENGTH OF PROJECTION (i.e. ADJACENT)
1 What is the length of ON?
2 What is the length of ON in terms of vectors only?
3 Leta=() andb:(_;,).
Find the length of the projection of vector b onto
VECTORS
CROSS PRODUCT (VECTOR PRODUCT)
5 What are the laws for cross product?
6 How do we evaluate a><b ?
7 Given the three vectors a = ( i) , b = (
Find axb VECTORS
CROSS PRODUCT (VECTOR PRODUCT)
8 W
VECTORS
EQUATION OF A STRAIGHT LINE
(CARTESIAN FORM)
4
1 A straight line 1 passes through the point Q(2, 1, 2) and is parallel to AB> = 7 ]
Find a equation of line I in cartesian form.
2 The equation
VECTORS
FOOT (POSITION VECTOR OR LENGTH)
finding the foot of the perpendicular and distance
from a point to a line '
Referred to the origin 0, the position vectors of points A and B are
4i11j+4k and 7
VECTORS
FOOT PLANE
finding the foot of the perpendicular from a point to a plane
The line 1 passes through the points A and B with coordinates (1, 2, 4) and (2, 3, 1) respectively.
The plane p has equ
H2 Mathematics 2016 Paper 2 Revision Solutions
f(x)
ax 2 bx 1
1 bc ac 2
(ax b ac)
xc
xc
1
ax b ac 2 x 1
a 2 (ans) and b ac 1 b 2c 1 (shown)
Given c 1, f(x) 2 x 1
(i)
2
x 1
2
x 1
( x 1) y (2 x 1)(
Summary: FUNCTIONS
INVERSE functions
Key Concepts:
1)
For inverse function to exist, the function f(x) must be onetoone for the given
domain. When asked to determine if a function is onetoone, stu
Victoria Junior College
Preliminary Examinations 2014
H2 Mathematics H2 (9740) Paper 1
Solutions
1
Common Mistakes
3
dy
=m
m
dx
dy
dy
k
y 2 = kx 2 y
=k
=
dx
dx 2 y
Since the line is a tangent to the
H2 MATHS (9740) JC2 PRELIMINARY EXAM 2010
PAPER 1 SUGGESTED SOLUTIONS
Qn
1
Solution
Method of Differences
N
N
r 1
r
2
f (r )
r 1 ! r 2 !
r 2
r 2 r !
1 2 2
2! 1! 0!
2 3 2
3! 2! 1!
3 4 2
4!
TPJC 2014 JC2 Preliminary Examination
H2 Mathematics Paper 2 Solutions
Section A: Pure Mathematics
1 (i)
(8m)
Im (z)
z (9 4i) = 5
1
14
4
0
P
Re(z)
(9,4)
5
9
(ii)(a)
The smallest value of z is the leng
2010 TPJC H2 Mathematics (9740) Prelim Exam paper 1 Mark Scheme
1
Let x be the cost of each ride for the timid.
Let y be the cost of each ride for the adventurous.
Let z be the cost of each ride for t
2009 GCE A Level Solution Paper 1 (Contributed by Hwa Chong Institution)
1i)
Let un = an2 + bn + c.
u1 = a + b + c = 10
u2 = 4a + 2b + c = 6
u3 = 9a + 3b + c = 5
Using GC, a = 1.5, b = 8.5, c = 17.
u
TEMASEK JUNIOR COLLEGE, SINGAPORE
Preliminary Examination
Higher 2
MATHEMATICS
9740/01
Paper 1
15 September 2010
Additional Materials:
Answer paper
List of Formula (MF15)
3 hours
Solutions
This docume
HCI 2008 Prelim Paper 1 Solution
Qn
Solution
Let
x,
y
and
z
be
the
no
of
10
cent,
20
cents
and
50
cents coins respectively.
1
The 3 equations are 10 x 20 y 50 z 1500 , x y z
x yz
50 1500
2
10 20 50
2010 OTHER SCHOOLS PRELIM UESTIONS ANSWERS
1 4
(i)
From the graph of y : f (x) ,
f(a:)f(,6) ifSa<g%.
Infact, 1gf(a)<f(,8)1.
From the graph of y : g(x),
gf(05) < gb)
0r gfmg) Function f is a one