CAPE Pure Mathematics (2016) U2 P1 Answers

-Lt

TEST CODE

FORM TP 2016281

O2234OIO

MAY/JUNE 20I6

CARIBBEAN EXAMINATIONS COUNCIL CARIBBEAN ADVANCED PROFICIENCY EXAMINATION@ PURE MATHEMATICS ANALYSIS, MATRICES AND COMPLEX NUMBERS

UNIT2-Paper0l

t

hour 30 minutes

0l JUNE 2016 (a.m.) READ THE FOLLOWING INSTRUCTIONS CAREF'ULLY. This test consists of 45 items. You will have t 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 items in this test.

4

Each item in this test has four suggested answers leftered (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 conesponds to your item and shade the space having the same letter as the answer you have chosen. Look at the sample item below.

are

Sample Itern

The expression ( I

(A) (B)

4

(c)

l+3"6 4+2Jl

(D)

6' ' 7

ffi

8. 9'

t

+.6 )' is equivalent

to

Sample Answer

@

l0

The best answer to this itenr is *4 +

2.6,,, ,o (D)

If you want to change your answer,

erase it conrpletely before you

has been shaded.

When you are told to begin, turn the page and work as quickly and as carefully as you can retul.t'l to that itenr Iater.

You nray do any rough work in this booklet. The use of silent, non-prograrrnrable scientific calculators is allowed. Exanr ination Materials:

E

A list of ,rather,atical fornrulae and tables. (Revised 2olz)

-

-t

in your new cSoice.

If you canllot answer an itern, go on to the next one. You ntay

E

E E E

fill

DO NOT TURN THIS PAGE UNTrL YOU ARE TOLD TO DO 02234010/CAPE 2016

Copyri glrt A 20 I 4 Caribbean Exanr inations Counci All rights reserved.

I

SO.

-2I

The complex number z

=r|

-i

can

represented on an Argand diagram as

(A)

be

2

Which of the following is a sketch of the locus of the point represented by the complex number z, given that lz + 5ii: 3?

tm (A)

-t I zt7, i)

I

i

I

3

.r

Re

z

-3

(B)

Im (B)

Re

-I (c)

z (1, -1)

-3

3

fm

(c) z

Gl' l) 3

Re

(D)

fm

-3

I , I

T

&

(D)

I

-1

7'7

Re -3

02234010/CAPE 2016

3

GO ON TO THE NEXT PACE

,|, i i I

.l

-J-

I

i I

-1

Theexpresssion to

3

I I

i[(l + i)r-(l - i),] isequal

7

.

The derivative of ln

xl

is

l

I

(A) (B)

i

(c)

I

il

I t I

4

I

(A)

-.3X

(B)

-3x

-2 2 4

(D)

I

(c)

l,l

3x

t

4.

!l

ir

lf

xzy

- xt' =

10, then

lZ

(D)

is equal to

3x

li :i

rt

l0 2x-2y

(A)

rl I

li tl

+

(B)

I li il

il Ji

li 1,

ii

i j

I

8.

ff

*:Zxy,thenthe

value

of

*

atthe

point (1, 2) is

(c) x'-Zry 'i^-"

(A) (B)

(D)

(D)

6 8

(c)

Y'.-zxY

t2 16

2xy

I t,

I J

i,

9

I 1

5.

The value

of

(A)

t

cos-+rslt'l-

22

Ifi*=

IS

(A)

"'" (;)-'

-l

(B)

Ztan-t (2x) + c

2

(c)

tan-t (2x) + c

(D)

-tan 2

)_

,

lfT

-2

(B)

(c)

I

(D) {

I I

1

t I ''4

i

:

6

I

sec'x Ztan x

_ 10

-611s (A)

I

1lnlr".'*l+"

i

i n

lnltan xf+c

(c)

2lnf sec .xf +c

(D)

2lnf tan.rf+c

+c

A curve is given parametrically by the x = t2 - 2t, y = 12 + Zt. The

expression 2

(,

equations

i

(B)

-l

(A)

f",

*

is given by

t-1 t+l

il

ii

(B)

t+l r

I

(c)

-l

2t-l 2t+l

I

t

I tl t.

i I

(D)

2t

+l

2t

-l

i

I,

ti

GO ON TO THE NEXT PAGE

-4-

il

(A)

(B)

J{cosAx

+ coslx)dx

J(cos8,

- cos2x)dx

1

(c)

2

2'J

(cos8x

(A) (B)

-

4i

f(x,

y) is such that

af -e'-,.sin (x+y), then which of the

b=

following is TRUE?

- cos2x)dx

One square root of 3

lf

*ox = ,'[-sin (r+y) + cos (x + y)] and

I (cos8x + cos2x)dx

1

(D)

t2

14.

J(cosSx cos3x)dx=

(A)

f(x,y) =e'sin (x+y)

(B)

f

(c)

f (x, y)

(D)

f

is

Ji

+zi

15.

e'sin (x + y) +cos (x +y)

y):

e" cos (x +

y)

* tan2x, L *rr,,

fi 4

|(x-l)(x+3),d*=

(D)

cos (x + y)

4

4

22 II x-l 3(x+3)

(D)

4

16.

rI 3(x-l) (x+3) -+_

l3 ( _+-2(x-t)

l-1t

dx

22

,+-) ( 2(x-t)

n

(c)

J

(c)

d

tr

(A)

2!

(B)

:

Given secr.r= I

(B)

(A)

(x,

y):

Ji -zi

(c) 2- i (D) 2+i l3

(x,

2(x+3)

2(x+3)

dx

If the ternts of the sequence ur, u2, j ..,, un... satisfy the recurrence u

relation u,n, = dx

dx

u

,*

3, n

Zl, then the r,l, term

may be expressed as

* $77 * 3tt

(A) (B)

tt, u,

(c)

ut+3(n-l) u,+6(n-l)

(D)

GO ON TO THE NEXT PAOE

I 1

J

l 1

i

lj

-5-

i I

i

4

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