Additional math paper

1. x
B
x
B
TEST CODE 01254010
FORM TP 2016036 MAY/JUNE 2OI6
CARIBBEAN EXAMINATIONS COUNCIL
CARIBBEAN SECONDARY EDUCATION CERTIFICATE@
EXAMINATION
ADDITIONAL MATHEMATICS
Paper 01 - General Proficiency
I hour 30 minates
READ THE FOLLOWING INSTRUCTIONS CAREFULLY.
This test consists of 45 items. You will have I hour and 30 minutes to answer them.
In addition to this test booklet, you should have an answer sheet.
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.
A list of formulae is provided on page 2 of this booklet.
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 ltem
I
2
3
4.
5.
2
(4-,),.[*)
(A)
(B)
(c)
(D)
4-2
4-l
40
42
SampleAnswer
o
6
7
The best answer to this item is cc40",
So (C) has been shaded.
If you want to change your answer, erase it completely before you fill in your new choice.
When you are told to begin, turn the page and work as quickly and as carefully as you can
If you cannot answer an item, go on to the next one. You can return to that item later.
You may use silent, non-programmable calculators to answer items.
DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO.
I
06 JUNE 2016 (p.m.)
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Copyright @ 2Ol4 Caribbean Examinations Council
All rights reserved.
n racrn tn/l] an lz
@

2. -2
LIST OF FORMULAE
Arithmetic Series Tn: d + (n - l)d t,: tlLa
+ (n - l)dl
Geometric Series T --af t sn
aQt'- l) s-7-'
a
-1 <rcl or lrl<ln r-
Vectors lvl
Trigonometry sin ('4 + B)= sin I cos B + cos A sin B
cos (l + B) =cos ,,{ cos,B Tsin A sin B
tanA + tan B
tan(A + B) = 1 + tan Atan B
d
Differentiation E (ax+b)':an(ax+S)n-r
d .inr:cos.x
dr
f,"otx:-sin.r
Circle
Statistics
Probability
Kinematics
f +f +2fx+2g+ c=O (x+fl' +(Y+ g)2=f
nv^a'bv:- cosu:' lvl lal x lbl
(f + f) where v : xi+ Yi
f,, f f,*, ttr-rl' i.f,r,'
i=A -i1-, ^s'='=' : =*--(7)'
" Lf, n Zf,
P(A w B) = P(A) + P(B) - P(A a B)
n11<rn I Ala'trllA
V=4+Ot tP=U2+2AS s:ut*!or
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3. -J-
I The function_f(x) :2x3
- f + hx -6 can be
expressed as /(x) : (2x + I ) (x + 2) (x - 3).
What is the value of /r?
Which of the following graphs BEST
representslf(x) : x (l - x)?
3
4.
(A)
2
(A)
(B)
(c)
(D)
rs
(B)
(D)
-13
-12
7
l3
l3
, * 3+ *, _n expressedasasinglefraction
x
(B)
(c)
x
(D)
x
Given tharf (x): af + bx * c, f (x) canbe
expressed in the form
(A)
x
x'-q
x'-6
(-r'? -9)(x + 3)
x+6
x'-9
4
x+3
(c)
(A)
( o'al x+- |
2a)
,(..*)'
'(..:)'
' 4ac -b'*-
4a'
ac-b2
+-
a
ac -b2+-----;-
a-
' 4ac-b'
4a
(B)
(D)
(c)
( tal x+- |
2a)
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4. 4
5.
6.
7
Aquadratic equation is such thatthe sum of
its roots i, -3 and the product of its roots
3
i, 1. Tn" quadratic equation is
4
(A) l2x2+8x+9:0
(B) lz:c-8x-9=0
(C) l2i - 8x + 9:0
(D) l2x2+8x-9=0
The range of values for which
f-7x+10<0is
9. The functions / and g are defined by
.fl x --+ 2x- sand g : x --+ 4*1,, * 0 . The
x
composite function gfis defined bY
(A)
(B)
gf:x-+9-5,r*o
x
gf:x--+3+9,x*O
x
8x -17 5.r-+-. x t-
2x-5' 2
- 8x-20 5
gl :x_+
Z;:1,
x*,
(c) d
8. tff (x): x', x € R and --2 <x < 4, then
(D)
10. Which ofthe following graphs is a function?
v
(A)
(B)
(c)
(A)
(B)
(c)
(D)
-5<x<2
2<x <5
x<2andx> 5
x<-5 andx>-Z
I
The setofvalues ofxforwhich
T,
o
ts
Y
(A) x2l
I
v
(B)
(c)
(D)
I
16) --
2
,>-1 andx)l
2
,< -1 orx>l
2
x
1
8
(A)
(B)
(c)
(D)
-8 <f (x) < 6a
8 <f (x) 564
-l s/G) s I
v
I
asf@)sa
0125401olF 2016
(D)
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5. -5-
11
t2
14.
Afunction isdefined byf:x--+fi, , * -,
The value of /-r (l) is
(A)
(B)
(c)
(D)
15
16.
t7
.6-r
t+J5
The expression
equal to
when simplified is
0
1
2
I
2
(B)
(A) 3
(c)
(D)
(
(
I
J
I
)
I
3
I
2
.6
(.6
(:
,.6)
-3)
-3)
..6)
<li-27; is equal to
(A) 3n
(B) 3n+3nr
(c) tfl3,"
3n+l
(D) 3n
(A)
(B)
(c)
(D)
4nt
l0
log 2
log,,6
log,,4
2
(A)
(B)
(c)
(D)
60
600
630
I 960
The value ofx for which
logr(2x + l):2 + log, (3x-l l) is
(A) s
(B)
(c)
(D)
(c)
(D)
What isthe sum oftheODD integers between
I 0 and 50?
The series -z*!-!
rimit 3 g* "' converges to the
(A) -6
(B) 6
23
4
4
67
r6
13. The value ofx for which 9.*r= 3 is
(A)
(B)
(c)
(D)
3
2
I
2
3
2
5
2
Given that log,X:6 and log, )z:4, the value
ofrog, (f,) ''
6
'=
5
I5
01254010/F 2016
r8.
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6. -6-
19
20.
2l
22.
(A)
(B)
(c)
(D)
The sum of the first n terms of a geometric
series is S. : 4' - l. For this series
I. the common ratio is 4
Il. the first 3 terms are 3, 15 and 63
III. Sr:20'- |
Which of the statements above are correct?
The points of intersection of the line with
equation y - x - 2 : 0 andthe circle with
equation f +f :10are
(A) (3, l) and (-1, -3)
(B) (3, -l ) and (1, -3)
(C) (-3, -l) and (-1, -3)
(D) (-3, -l) and (1, 3)
24. Two vectors are equal if they
23
25
(A)
(B)
(c)
(D)
I and II only
I and III only
II and III only
l, II and Ill
gl
The sum of ). . is
7ak
I
(A) 1
I
(B)
,
(c) 1
5
(D) +6
have the same magnitude and
different directions
have the same magnitude and same
direction
are parallel and in different
directions
have different magnitudes and are
in the same direction
The vector a is given as 5i + 127. A unit
vector parallel to a is
The coordinates of the centre of a circle with
equation (x - 1)' + (y + 3)' : 36 is
(A) (r, -3)
(B) (-1,3)
(c) (3, -r)
(D) (-3, l)
The line through the points Q(ft, 2) and
R(4, 8) is parallel to the line with equation
2x + y - l0:0. The value of ft is
(A)
(B)
(c)
(D)
26. The position vectors of A and B relative to
an origin o a.e (3) una (-i) ."rp"ctirely
The acute angle AOB is given by
I
2
-7
7
(A) tli +36 j
(B) l95i+4687
(c) f,O,
*tri>
(D) f,o,
*tzil
(A) *.[#)
(B) ."'[#)
(c) -'[#)
(D) *'(#)
01254010/F 2016
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7. -7 -
27 Given that x is acute and cos r : 1 , then the 29. The graph of y= sin 2r is
value of sin 2x is 5
Item 28 refers to the following protractor
which represents half of a circle. The
protractor has a radius of 1.5 metres and the
angleAOB measures 45o.
o
1.5 m
What is the arc length, x, in metres, along the
outer edge ofthe protractor?
(A)
(B)
(c)
(D)
(A) v
1
7E
(B)
lt 2n
x
(c)
x
(D)
T2
-1
30. If sin (.r + 20") = cos.tr, then the value of x is
(A) 35"
(B) 45"
(c) 55'
(D) 70"
1
5
T
5
t2
25
24
25
(A)
(B)
(c)
(D)
0
-1
x
2n
v
2
0
-7B
v
I
v
I
0
-1
%
28
0
7f
4
3tt
8
3r
4
1T
6
xlE
01254010/F 2016
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8. -E-
31. sin (o + 45') is equal to Given that y-lG, then !dx
I
Js-x
1
Js -,
I
ZJs-x
-l
ZJs-x
35.
The gradient at
y=cosxis
IS
on the curve
(A)
(B)
(c)
(D)
(A)
(B)
(c)
(D)
fr<ti"a+cosa)
lf t"oro -sina)
)orro+cosa)
){"oro-sina)
36
E
632. $ .adians converted to degrees is
5
(A) 287
(B) 288
(c) 28e
(D) s76
(A)
.,6
(c)
(D)
The curve C is given by the equation
y : 2x3 - 3f - lb + 6. The values ofx at
which stationary points occur are
(A) I and -2
(B) -l and?
(C) -t and--Z
(D) I and2
(B)
)
_1
2
I
2
',6
2
33 If sin 0 = 1 und 0 is obtuse, then tan 0 :
l3
(A) -12
l3
-5(B)
; 37
5
(c)
t2
l2
(D)
34.
l3
The trigonometrical expression
sin x sin -x
I -cos.x I +cosx
(A) 2 sin.x
(B) Ztan x
(c)
(D)
stn x
tan2 x
2
nrr</nln/tr ?nl6
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9. 38.
39
4t
-9
Giveny =b2 +3 cosx, then
d! : 42. If X:
dx
(A)
(B)
(c)
(D)
The curve C with equation y : ,f (x)
has a stationary point at (-2, 5). If
J" @) - t' - 15, then (-2, 5) is
43
[]X-la. anda<c<Dthen
x =['f@)a*+lo f{ia,
x = !" f t*) ax+[i f @) dx
x = !" f{*)a** lo f {i a,
x = li t<*> ax +
l',f (x) a, - ff ljtr> a*
J(cosx - Zs in x)dx =
x*sinx
.r - sln .x
4x-3sinx
4x + I5ipy
an intercept
a vertex
a minimum turning point
a maximum turning point
The region R is enclosed by the x-axis, the
curveJ,,=i+2x-1, the lines x:2and
x = 3. The area of R in unitsz is
(A) ls
(A)
(B)
(c)
(D)
(A)
(B)
(c)
(D)
40. If J"{O*fr) dx=72, where a > 2, then
3r
3
t9
J
59
;J
(B)
(c)
(D)
a
(A)
(B)
(c)
(D)
6
l0
36
72
,tl'*'d,
!i,'*
[,.'*
The region bounded by the curve y : x2,
thex-axis and the linesx : 0 and x : I is
rotated 360" about the x-axis. The volume
of the solid generated can be found from
44.
45.
(A)
(B)
(c)
(D)
(A)
(B)
(c)
(D)
rc l,' -f {Oa*= 6, then
l,o
+y1*1d* * s =
9
lt
29
44
(A)
(B)
(c)
(D) x
fl7' dx
-cos-r*sinx*c
cosx*2sinx1-c
cosr-sinx+c
2cosx*sinx*c
END OF TEST
IF YOU F'INISH BEF'ORE TIME IS CALLED, CHECK YOUR WORK ON THIS TEST.
01254010/F 2016