CXC CSEC Mathematics 2017 January P1

FORM

TP 2017016

CARIBBEAN

EXAMINATIONS

COUNCIL

CARIBBEAN SECONDARY EDUCATION

CERTIFICATE@

EXAMINATION

MATHEMATICS

'

_.

_{Paper 01}

-

General

ProficiencY

I

hour 30 minutes

READ THE

FOLLOWING

INSTRUCTIONS CAREF'ULLY.

This test cons'ists of 60 items. You

will

have

I

hour and 30 minutes to answer them. In addition to this test booklet, you should have an answer sheet.

A list of formulae is provided on page 2 of this booklet.

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.

bn yotr

answgr sheet, find the number which corresponds to your item and shade the space

having the same lettet as the answer you have chosen. Look at the sample item below. Sample Item

2a

* 6a:

Sample Answer

I 2 3 4 5

(Af

(B)

(c)"'

(D)

'84

8a2

l2a

l2a2

o@o@

6 7

Th*e best answer to this item is "84", so (A) has been shaded.

lf

you want to clfange y@rr answder, 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.

lf

you cannot aryswer

anitem,

go on to the next one. You may return to that item later.

t

You may do any rough work in this booklbt.

Figures are not ngcessarily drawn to

scale.

f?':r

Calculators and mathematical tables are NOT allowed for this paper.

DO NOT

TURN

THIS

PAGE

UNTIL

YOU ARE

TOLD TO DO

SO.

8

9

04 JANUARY2017 (p.mJ

i.w

10.

COpyright O 20 \ 6 Cmibbenn F'ratnirrttiorrs C <rrrtrci\

LIST

OF'FORMULAE

Volume of a prism

Volume of cylinder

Volume of a right pyramid Circumference

Trigonometric ratios

Area of triangle

Sine rule

Cosine rule

sin0:

opposite side -nypoffiuse-adjacent side where

r:

a*b*c

2

abc

sin

.4

lln

E

_{ain C}

ci

:

bz

r

c1

_-

2bccosA

v:

Ah where

I

is the area

of

a cross-section and

ft

is the perpendicurar length.

v:

nf

h where

r

is the radius of the base and ft is the perpendicular height.

I

v

:

_,

Ah

wherel

is the area ofthe base and ft is the perpendicular height. C

:

2xr

where

r

is the radius of the circle.

Arc

length

": l:o

x

2nr

where

0

is the angle subtended by the arc, measured in

degrees.

Area of a

circle

A:

xf

_where

_r

_{is the radius of the circle.}

Area of a

sector

n: #x

_zrl

_{where 0 is the angle of the sector, measured in degrees.} Area of

trapezium

A: +

_{@ + b) ft where}

_a

_{and b are the lengths of the parallel}

sides and 7,

is _{the perpendicular distance between the parallel sides.} Roots of quadratic

equations lf

ax2 + bx

*

c

:

0,

then

x

: -utEW

cosO:

hypotenuse opposite side

tanO:

Adjacent adjacent Skle

Area of

A:

_|-

on

*n"r"D

is the length of the base and & is the perpendicular height.

Area of A

ABC

: !

_ab

sin C

2

Area of A

ABC

:

s(s-a)(s-D)(s-c)

B

Opposite b ,\la.'l4a\ln/t A \!r I A D\//t' a^I -e C a _c A

ait.) ( _{).\ l1 )} 1 ill: _)-.i:)r. i l'r.iii

1 is equalto (A) (B)

(c)

(D)

2.

If 4.3 x 0.37

:

I .591, then 0.43 x 370 is

There are 40 students in a class. Cirls

make up 60%o

of

the class and 25%o

of

them wear glasses. How many girls in the class wear glasses?

(A)

6

(B)

8

(c)

r0

(D)

rs

If

3n is an even number, which

of

the

following

is an odd number?

(;)

6. 7 10

(A)

(B)

(c)

(D)

(A)

(B)

(c)

(D) 4 6 4

;

_J 2 9 4 9

In

standard notation, 208.06 is written

as

3n-l

3n

-2

3n+2

3n+2n

(99x100)+l

(99

x 100)-(99 x

_l)

(99x100)+(99x1)

(99

x

100) (99

x

l)

(A)

(B)

(c)

(D)

(A)

(B)

(c)

(D)

(A)

(B)

(c)

(D) 1.59t 15.91 159.r 1591.0 2.0806

x

10'? 20.806

x l0l

21806

x l0-l

0.20806

x

103

8.

99

x

l0l

has the same value as

3

If

$560 is shared in the ratio 2:3:9, the difference between the largest and the smallest shares is

What is the LEAST number

of

apples that can be shared equally amqng either

6,Sor9children?

(A)

(B)

(c)

(D)

What is the value

of the

digit

2

in the number 48.621? 2 100 2 (B)

(c)

(D) 9 4

(A)

$

80

(B)

$240

(c)

$280

(D)

$360 36 48 54 72

5.

lf

6}Yoof a number is 90, what

is

J

of

the number?

_(A)

54 72 120 r50

l0

i1+' lr.e

Eit

2 200

1l

t2

13.

(A)

(B)

(c)

(D)

lf X

and

I

are

two finite

sets such

that

n(X)

:

9,

n(X

n

I')

:

4

and

n(Xu

I0:

15, then n(I/) is

(A)

s

(B)

6

(c)

r0

(D)

t2

Item 12

refers

to

the following

Venn diagram.

U

In

the Venn diagram, the shaded area

represents

Item 14

refers

to

the following

Venn diagram.

14.

In the Venn diagram

U:

{students who play games}

H:

{students who play hockey}

V:

{students who play volleyball}

The number

of

students

in

each set is indicated. How many students do NOT

play volleyball?

(A)

(B)

(c)

(D)

15.

The cost

of a

calculator exclusive

'

of

sales

tax is

$120.

Susan bought a calculator and paid sales

tax

of

l\Yo.

How

much change would she receive

from $ 140?

(A)

(B)

(c)

(D)

l6

At

the end

of

any year a car is wofth 5oZ less than what

it

was worth at the beginning ofthe year. If a car was worth 59500 in December20l6,then its value in January 20l61has P' (P

U

_Q)'

QUP'

Q

NP'

2 3 5 8

Of a class of 32 students,

l7

study Music and 20 study

Art.

What is the LEAST possible number

of

students who study BOTH Music and Art?

(A)

(B)

(c)

(D) 3 5

t2

l5

$8

$12 $28 $32

(A)

(B)

(c)

(D)

$

999s

sr0

000

$r0025

$r2000

ai(i ON l'O t'tl[:

NF:.](-

i'I',\Cl'.

v

3

t7

18. 19

(A)

(B)

(c)

(D)

(A)

(B)

(c)

(D) $20.00 $21.s0 $22.40 $31.s0 $ 175 $22s $4s0 $s00

An article bought for $125 was sold

for

$175. The profit as a percentage

ofthe

cost price was

(A)

28.6

(B)

40

(c)

s0

(D)

71.4

A television set costs $350 cash. When bought

on

hire purchase,

a

deposit

of

$35 is required, followed by

l2

monthly payments

of

$30.

How much is saved by paying cash?

(A)

(B)

(c)

(D)

A

company employs 12 gardeners at $26 per day, and 8 clerks at $l 7 per day. What is the mean daily wage, in dollars,

of the 20 employees?

If the simple interest on $800 for 3 years

is $54, what is the rate

of

interest per annum?

2t

22

(A)

(B)

(c)

(D) (B)

(c)

4 440 6 25x 8 25x 6

l0x

% 4 9% 2 sYo $10 $2s $40 $4s

Tom bought a pen for $60 and sold it to gain2l%o on the cost

price.

How much money did he gain?

(A)

(B)

(c)

(D)

42

$12 $40 $72 $80 23

5x

5x

(A)

Item 20

refers

to

the

following

table

which

shows the rates charged

by

an

insurance company.

House Insurance 251 per $100 50p per $100 Contents Insurance

How

much

will

a

person

pay for

insurance,

if

his

house

is

valued

at $50 000, and the contents at $10 000 ?

(D)

If

x

is

an

integer

that

satisfies

the inequality 6

<2x

< 8, then

(A)

3<x<4

(B)

3<x<4

(C)

_-3

<x<4

(D)

_-3<x<4

F's, 6

--5-x 24.

r :i,,

i)\

ii

)

_f

it5

_{NE;{T Pi\cE}

ffi

20.

25.

lf

x:

4 and

y:2,

what is the value

of

x2

+3y,

xy

(A)

(B)

2!

2 a t

(c)

2;

(D)

₂₁

4

(A)

_-2x

_-

8

(B)

_-2x

+

I

(C)

-2x

-

4

(D)

_-2x

+ 4 (B)

James saves $x each month, but in March he saved

$5

less than

twice his

usual

amount. In March, James saved

If

3(x-l)

_-2(x-

l):7,

then the value

of

(x-

l)

is 29

(A)

(B)

(c)

(D)

30.

(8a)2:

(A)

(B)

(c)

(D)

(A)

(B)

(c)

(D)

1

4 6 7 8 9

26.

The expression

_-2(x

_-

4) is the same

as 31.

26 + 22

:

l6a

64a l6a2 64a2 23 24 2E 2t2

27. lfm*n:

_m

_-n2

then5*3:

32.

Two tonnes, 54 kilograms is the same as

(A)

(A)

56 kg

(B)

254 kg

(C)

2 054 ks

(D)

20

054kg

(D)

_$4

2 4

(c)

s

28.

(A)

(B)

(c)

(D) $5x $

l0x

$x-5

$2x-5

f?,r.

33

Item 33 refers

to

the

following

circle,

with centre O.

B

A

If

the circumference of the circle

is

l5

cm, then the length of the minor arc AB,

in centimetres, is

(A) 360

*

t5

120

(B) 120

x

15

360

Item 35 refers to the following diagram,

not

drawn to

scale,

which

shows the sector of a circle with centre O.

ln the diagram, the length ofthe minorarc, PQ, is 8

cm.

What is the circumference

of the circle, in cm?

(c)

(A)

(B)

(c)

(D) 360

-

x 15 360

_-

120 3s. 36. 37.

(A)

(B)

(c)

(D)

(A)

(B)

(c)

(D)

l6

24 48 64

Fifty

guests

each had

2

glasses

of

champagne.

Each

glass

held

150

millilitres.

How

many litres

of

champagne were used?

360

_-

120

-

x 15

360

Item 34 refers to the following diagram

which

shows a cylinder

with

diameter 6 cm and height 20 cm.

34.

The volume, in cm3, of the cylinder is

The area of a triangle is 60 cm2 and its

base is 12 cm. What is the perpendicular height, in cm, of the triangle?

(D) 0.1 5 1.5

l5

r50 cm

(A)

(B)

(c)

(D) 5

l0

13

t7

180 zr 240 n 360

x

720

x

The perimeterofa square is 52 cm. What is the area, in cm2?

(A)

(B)

(c)

(D) 'S+, 39 78 169

t96

(ii.)

(),\,

l'(

)

t'tlL. NL:)i

i't'A(it

120" 6cm rdiflt H'lrl{

H#

38

39

40.

How many students play cricket?

(A)

3s

(B)

120

(c)

2s2

(D)

300

4t

The median of the numbers

1,3, 4, 5,

5,9,9,

g, g,

_l0

_is

(A)

(B)

(c)

(D)

Item 40 refers to the following pie chart which shows the popular games played by 720 students.

If

the mean of the four numbers 4, 8, x

and 12

is

10, then

x

is

43. When three coins are tossed simultane-ously the possible outcomes are _{HHH,

HHT,

HTH,

HTT,

THH,

THT,

TTH,

TTT),

where H represents a head and T

represents a tail.

What

is

the probability

of

randomly obtaining at LEAST TWO heads when

the three coins aretossed simultaneously?

(B)

(D)

Item

44

refers

to

the

following

table

which

shows

the

frequency

of

scores obtained by students in a test.

Scores 2 aJ 5 6 8

lt

Students t2

ll

6 J 8 2

44.

The modal score is

(A)

2

(B)

8

(c)

il

(D)

t2

Each

of

the

letters

of

the

word

'CHANCE'

is

written on

a

slip of

paper

similar

in

size and shape. The slips

of

paper are then placed in a bag

and thoroughly

shaken.

What

is

the probability of randomly drawing a letter

.C'?

(A)

(B)

iri+

(c)

The

circumference

of

a

circle

is

132

.2

cm. Given that

r

=

a

.theradius ofthe

7'

circle, in centimetres, is

(A)

42 2t J42

Jzt

(B)

(c)

(D) I 4 J 8 I 2

?

J

(A)

(c)

45 4 6. 7 8 9

(A)

(B)

(c)

(D) I 6

l

5

I

J 2

;

₎

(I()

_ON T'O

TIIE

NIJX

I

I'A(iF, Cricket Football 25Yo Basketball 30Vo l0yo 42 4 t0 t2 r6 (D)

46.

47

Which

of

the following line

graphs represents {

x

:

_-2

< x <

4

_}? (A)

_#

-3-2-t 0 I 2 3 4

5

( r o r rr

r I O r )

-3-2-t 0 I 2 3 4

5

(c)

_#

-3-2-r 0 I 2 3 4

5

(o)

_#

-3-2-1012345

Which of the following diagrams BEST illustrates a function?

(A)

The equation

of

the line which passes

through the point (0, 2) and has a gradient

^t

ot-rs

3

(A)

y:3x

(B)

y:3x+2

(D)

49.

lf

_/(*):2x2

_-

l, thenf-3)

:

(A)

_-32

(B)

_-l

e

(c)

t7

(D)

3s

50 Which

of

the

following

points lies on the line y

:2x -

3?

(A)

(2,3\

(B)

(4,

l)

(c)

(0,

_-3)

(D)

C2,

-t)

51 The range of

_f

:

x

--- _{-x2 for the domain}

{-2,-1,

0,

1,2}

is

(A)

_{1,4}

(B)

_{{-4, -1,}

0}

(c)

_{-4,

_-l

,

t,

4}

(D)

_{-4,

_{-t ,0,}

1,4\

Iir. 48 (B) I

y:

_

_x

J

v: !

x+z

J

(c)

(B)

(c)

(D) tsrH. ftd

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

( ir ) ; rr..

_ii)

_I

_iii.

..,i_

_{i i}

_l,\.i;l

Item 52 refers to the following diagram

of a circle.

52.

If

O is the centre of the circle,

theny'

is

(A)

25o

(B)

80o

(c)

90o

(D)

l00o

Which ofthe following angles are equal?

(A)

ZDBC

and ZCBE

(B)

ZCBE

and

tABE

(C)

ZABD

and

ZCBD

(D)

ZABD

and

ZCBE

Item 56 refers to the following diagram

of

an object and

its

image

after

a

translation.

v

B _B.

,t)

7) A A' (4,6) (2,5)

o

.r

In the diagram, the translation by which

l,B

is mapped onto

A'B'

is represented by 53 Underthe translation (3,

_-5)

is

[ ')

,n"imageof

\.-3l

55 56 57 (B) (D)

(A)

(B)

(c)

(A)

(1, --2)

(B)

(6,

l s)

(c)

(0,

_-3)

(D)

(s,

_-8)

Items

54-55 refer

to

the

following

diagram of a pair of intersecting lines.

AC and DE are straight lines intersecting at

B.

Angle

DBA:

58".

The measure of angle ABE is

(A)

58o

(B)

r22"

(c)

142"

(D)

302"

In triangle ABC, angle A

:

x" and angle B

:2xo.

What is the size of angle C?

(A)

(c)

(t)

(i)

(i)

(;)

(l

80

_-

3x)" F+, 600 30"

r

180\'

l_t

t^l

ii,r)

())\

l()

t'lltr

Ni:x

I

l'.\(it

54

o

Item 60 refers to the following diagram

which

shows

a

ladder

5

metres long leaning against a vertical

wall.

The foot of the ladder is 3 metres away from the

wall.

o

A _6cm

B M

3cm

N

58.

The length of MO, in centimetres, is

(A)

(B)

(c)

(D)

60

How

far

up the

wall

does

the

ladder reach?

Item 59 refers to the following diagram

of a right-angled triangle. A

(A)

(B)

(c)

(D)

4m

6m

8m

15m

c

59.

From the diagram above, sin C is

(A)

5

(B) 5

(c)

(D)

BND OF

TEST

Item 58 refers to the

following

pair

of

similar triangles. C .5

,

,

3 3 6 7

3m-*

5 B t2 l3 t2 t2 I3 l3 -5 l91*.

ffi