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8/11/2019 Pure Maths Unit 1 Paper 1 2013
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l:EST CODE 2134 1
ORM TP
2 1323
MAY/JUNE 2013
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CARIBBEAN
EXAMINATIONS
COUNC IL
CARIBBEAN ADVANCED
PROFICIENCY
EXAMINATION
PURE MATHEMATICS
ALGEBRA,
GEOMETRY
AND CALCULUS
Unit 1
Paper
01
hour
3 minutes
12 JUNE 2013 (p.m.))
READ
THE FOLLOWING
INSTRUCTIONS CAREFULLY.
1. This test consists
of
45 items. You will have 1 hour and 30 minutes to
answer
them.
2. In addition to this test booklet, you should have an answer sheet.
3. Do not be concerned that the answer sheet provides spaces for more answers than there are
items in this test.
4. Each item in this test has four suggested answers lettered A), B), C), D). Read each item
you are about to answer and decide which choice is best.
5. On your answer sheet, find the number which corresponds to your item and shade the space
having the same letter as the answer you have chosen. Look at the sample item below.
Sample Item
The expression 1 J3 )
2
is equivalent to
A)
B)
C)
D)
4
10
1+3.J3
4 +
2.J3
Sample
Answer
The
best answer to this item is
4
2 J3 ,so
answer
space D) has been shaded.
6. If you want to change your answer, be sure to erase it completely before you fill in your new
choice.
7. When you are told to begin, turn the page and work as quickly and as carefully as you can .
8.
9.
If
you cannot answer an item,
omit
it and go on to the next one. You can return later to the
item omitted. Your score will be the total number of correct answers.
You may do any rough
work
in this booklet.
The use of silent, non-programmable scientific calculators is allowed.
Examination Materials:
A list of mathematical formulae and tables. Revised 2012)
DO NOT TURN
THIS
PAGE UNTIL YOU ARE TOLD
TO
DO SO.
Copyright 2010 Caribbean Examinations Council
All rights reserved.
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8/11/2019 Pure Maths Unit 1 Paper 1 2013
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1.
2.
3.
-2 -
J8
+
J32 .Jl62 can be simplified as
A)
-2J2
B)
C)
D)
If p
and
q are positive integers
such
that
p < q then which of he following statements
is/are correct?
I.
- p> - q
II.
pz
> pq
III. p -
I
I
x
I a> 0, are
A)
B)
C)
D)
a
x
< o r
x
>a
3
a
x
a
3
a
x > a
andx
< -
3
a
x
-
3
The statement p
v -
p is a
A) converse
B) tautology
C)
contradiction
D) contra positive
The statement - p v - p 1\ q)) is logically
equivalent to
A)
B)
C)
D)
p A q
p :::::> - q
p A q
-p:: : : :>-q
GO ON TO THE NEXT PAGE
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- 5 -
16
A vector equat ion ts
gtven
as
s[ tG
[ he values of
sand
tare,
respectively
A) -2 and -1
B) -2 and 1
C)
2 and 1
D) 2 and -1
17. sin
30-
A) is equal to
A)
1
J
.
- cosA - sm
2 2
B)
1 J
. A
- cosA + sm
2 2
C)
J
1 .
- cosA
+ - sm
2 2
D)
J 1 .
- cosA sm
2 2
18
2 sin e cos is equivalent to
A) sin 8
+
+ sin 8 -
B)
s i n 8 + ~ ) - s i n 8 - ~ )
C) c o s 8 + ~ ) + c o s 8 - ~ )
D)
c o s 8 + ~ ) - c o s 8 - ~ )
19
The
equation of
the
circle
whose
centre
has coordinates 4, I) and whose radius is
7 units is
A) x +
y
+
8x
+ y 49 = 0
B)
x
2
+y 8x y 32
=
0
C)
x
2
+y - 8x y + 49
= 0
D) x
2
+
y
+
8x
+
2y
+ 66 = 0
0213401
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2013
20
21.
22.
is an
acute angle and cos
=
2 _
, then
13
s e c ~ =
A)
5
13
B)
12
13
C)
13
-
12
D)
13
5 ,
The
point 2, 3) is at
one end
of a diameter
of the circle whose equation is
x
2
+
y 1 x
+
2y
+
1 = 0.
The
coordinates of the other end of the
diameter are
A) -12,
-5)
B) -12,
-1 )
C) 8, -5)
D)
8,
-1)
The value of s i n [ ;+ p is
A) - sinp
B) -
cosp
C) sinp
D) cosp
GO ON TO THE NEXT PAGE
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- 6 -
23.
What
value
of e
0 :S
e
S n, satisfies the
27. If p =
2i+
j andq = /.. i+6j are perpendicular
equation 2 cos
2
e
+ 3 cos
e-
2 =
0?
vectors, then the value of/.. is
7
(A)
-3
(A)
6
B)
-1
7
(C) 0
B)
4
D)
2
c)
7
3
28.
The general solution for sin
29
=
JC.
sm-ts
6
D)
7
2
{
2nJC
+ -
. 6
(A)
B=
JC
2n+1) -
24 With
respect
to
an ongm 0, A has
16
coordinates (3,
-2 .
The position vector
of3
O
is
{ M ~
B)
B= 12
(A)
3 , -6
JC
nJC -
12
B)
(9, - 2
{
(
nJC
(C)
(C)
B= 12
JC
2n7r) -
_:)
12
D)
{
nJC -
D)
B=
6
JC
25.
The expression sin
6A
+ sin 4A may be
n+1)
written as
29.
The cosine
of
he angle between the vectors
(A) sin lOA
-6 j and i + j is
B)
-2 cos 2A
(C)
2 cos
SA
sin A
-1
D)
2 sin 5AcosA
(A)
J2
26.
1 +
cos
4
A -
sin
4
A =
B)
1
J2
(A)
1
+cos 4A
B)
2cos
2
A
(C)
cos2A
(C)
- 5
J2
D)
2 cos
2
A sin
2
A
D)
6
J2
GO ON TO
THE
NEXT PAGE
0213401
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: r ; ~
30.
31.
32.
- 7 -
Item 30 refers to the diagram below.
y
l=x
In the diagram above showing
y
=
x,
y
is
NOT
defined for
A) X = 0
B) X ~ 0
C) x> 0
D) X