Ncse 2010 Mathematics P2 3i5i68

THEGOVERNMENToFTHEREPUBLICOFTRINIDADANDToBAGo IMINISTRY OF EDLTCATION

NATIONAL CERTIFICATE OF SECONDARY EDUCATIOI{ 20L0 (Level 1)

MATI{EMATICS PAPER 2

TIME: 90 MTNUTES

Student's Name School's Name

School's ID

Student's I\umber

F'OR EXAMINERS U$E ONLY

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II

2

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Section

II

7

8

9

INSTRT]CTIONS

Read the follor.ving insfiuctions carefully:

1.

This paper consists of trvo (2) sections - Sections I arrd II.

2.

There are six (6) questions in Section I and three (3) cluestions in Section II.

3.

Attempt

4.

Answer ANY T1VO (2) questions in Section II'

5.

Write your answers in the spaces provided in this test booklet.

6.

Write proper statements and show all working'

7

.

ALL six (6) questions in Section I.

If you have finished before time is called, go back

8.

g.

and check your rvork'

booklet: to complete the following on the cover of your allswer

-

Student's Name

-

School's Name

-

School's ID

-

Studerrt's Number

candidates are penrritted to use the following materials:

-

Calculators (Non-Programmable)

-

Geometry Set

-

GraPh PaPer (Provided)

NoPROGRANIN,IABLECALCULATORSMUSTBEUSED. NO CELLPHONE CALCI-ILATORS ARE ALLOWED.

SECTION I ANSWER ALL QUESTIONS IN THIS SECTION

\Yrite your ansrvers in the spaces provided and show ALL n,orkiug.

I (a) Calculate the extrct value of

1!2 *ll'il s 1rl l1 L)

[3 marlts]

-sl

(b) (i) Calculate the exrrct value of (0

-l)' s

3.7

(ii) \Vritc 0.167 in standard fbnn

[2 rnarlis]

[2 marks]

2. (a) The heiglrts of tu'o toddlers are in the ratio

7:9.If the heiglrt of the shoftertoddler is 63

centimetres, what is the height. in centimetres, of the taller one?

[3 marks]

fbr a plastic bag mauufactttliug cotllpally. He eams of $600.00 per rveek plus 5% commission on all sales over s1000.00.

(b) Ben q,orks

as a salesman

If in one week, Ben sold $3160.00 worth of plastic bags, what that'rl'eek?

a basic u'age

wats Ben's total earnings

for

[3 marks]

3.

'I.he students in aclass own cats and dogs as pets. The number

of students orvningthese dift'erent pets is showu in the Venn diagram below vi'here U is the universal set.

C:

{ students orvning cats }

D:

{ students ou'ning dogs }

U

(a) (i) How many students own both cats and dogs?

[1 mark]

(ii) Describe, in words, the pets owned by students belonging to the set C'n D? [1 mark]

4

(b) ABC.D is a parallelogram rryith DC:6 cm and BC : 5 ctn. The point E is located such that BCDE is a trapezium with DC parallel to BE and EB : 9 cm, as shown in the diagram below.

A

(i)

(ii)

9cm +

Find the length in cm, of DE.

Calculate the area in cm'. of the trapeziutn BCDE'

[2 marks]

[2 marks]

a. (a) Mr. Singh is havellingto ameeting that is scheduled to take place at a venue His average speed is 80 km per hour for the entire joumey.

(i) Write an expression, in d,for the time taken for

the

journey.

d

km away.

[l

mark]

(ii) If the time taken for the joumey was 30 minutes, find the value of d, the distance travelled to the meeting

(b)

venue.

[2 marks]

To convert degree Fahrenheit to deglee Celsius, the formula

C

= * C - 32) can be 9'

used, where C represents the measure of temperature in degrees Celsius and F represents

the measure of temperature in degree Fahrenheit. The weatherman reported that the temperature on Monday was 95 degrees Fahrenheit

fp). pinO the temperature in degrees Celsius (oC) on Monday. [3 marks]

6

5. (a)

A relation maPs elements of the input to elements of the oulput Set as shown in the table below.

INPUT

OUIPUT

x

(i)

1

2

2

5

4

T

5

26

Complete the table by filling in the missing output element in the box, in the table above.

I I shown [1 mark]

(ii)

State, in

ofx, the relation which maps input elements to output elements' [2 marks]

(b)

ln the space below, draw and label an arrow diagram to represent the above relation. [3 marks]

6.

!:axis 6

:5 ,4 rg :

t2 I x-flxLS

-6-54-3-2-101234 -1

-2 -3

4 -5 -6

O(0,0), X(6,2)' Y(3'3) The diagram above shows the plane shape OXYZ with coordinates and

\3,6).

of the shape (a) Using the axes above, draw on the same graph sheet the irnage OtXtYtZ' [3 marks] OXI.Z after areflection in the y-axis' and (b) The point y undergoes a translation of 2 trnits parallel to the x-axis to the y-axis.

- 6 units parallel

under the (i) Locate and label on the same glaph sheet. the point Y" the image of Y

tl

translation (ii)

State the coordinates of the point

Y''

mark]

[2 marks]

SECTION

II

ANSWER ANY TWO (2) QUESTTONS

7, At a school cafeteria it costs $1.25 to produce

a)

one chicken pie

(i) How much will it cost the cafeteria to make twenty (20) similar chicken pies?

I

(ii) lf the chicken pies are sold at $3.00 each, calculate the total profit twenty (20) chicken pies

b)

mark]

made on selling all

[2 marks]

The same cafeteria makes fresh fruit punch at a cost of $2.50 per bottle and sells them at $4.00 each.

If the cafeteria

makes twenty (20) bottles of fresh

fruit punch but only

sells fourteen (14) bottles. Calculate the profit or loss made by the cafeteria if the remaining fruit punch were to be discarded.

[3 marks]

c)

'Ihirtr'(30) students in a Fomr 3 class uere given a spelling test r.r'hich cornprised 5 items and rvas marked out of a totarl of 5 mzults rvith 1 mark aw arded for each con ect item. ]he actrnl scores of the students in the spelling test are presented b),the data belorv.

101544315432213 5 -5 31313 3 3 0 23222 (i)

Cornplete the fi'equency table belou' to represent the data above.

Tnsr Sconp

[3 martrrs]

Fnnqtrexcv

(ii) Ilolv many students spelt exactly trvo (2) words correctly?

I

(iii) Holr, manv students spelt three (3) or Inore

t0

r'r'ords correctly?

ntark]

[2 rnarksl

8. The diagram below shows the graphs of two linear functions.

a)

State the coordinates of the point B, where

I

LineZ cuts they-axis

b) State the coordinates of the point of intersection

mark]

of the two linear graphs. [2 marks]

c) A student named Sham suggests that Line I represents the equationy : another student named Brian suggests that Line

I

2x

*

3,

may be represents the equation

y:-x+6' Using the information given in the diagram, determine by calculation whether Sham or Brian is correct. [3 marks]

ll

d) In

flre

diagram belorv, the line QR is parallel to the line ST and angle KLQ

:

55o and

N,{NO:70"

State the size of the

following angles giving reasons lbr each answer:

n

(i) IVILP

[2 marks]

n

(iii)

NN,IO

[2 marks]

(iii)

n oPR

[2 marks]

t2

'a

9.

ffi (o)

The cliagram shows a ladder of length 10 metres leaning on a r.vall rvith its foot on the horizontal grouncl at a clistance of 6 metres from the lrase of the wall' (i) Compute h, the height. in rnetres. above the g'ound where the ladder tottches the rvall. [2 marks] that the grouncl is horizontal and the wall is vertical] [A*ssume

(ii)

Calctrf,ate the size of the acute angle which the ladder makes

with the gtound

(i.e. RPQ ) [3 rnartrs]

13

r'

(b) (i)'I'he

c:uboid trc:lorv t'epresents a closed box r.i,ith the folloi.i,ing climelsions: le'gth:60 crn. ri'idth 30 crn- and height = 25 cm. i-ising this infbnnation. ct'arv a ner of the ctrboicl

:

cleiu-ly shorving the dinrensions of each lace.

f3 nrarksl

60 cm

J,,.'

(ii) I ising the rret that you have

drarlvn irr Part b

(i), calc,ulate the total surtbce area of the

cuboid.

[4 nrarks]

EI{D OF TEST L.t t+