[PDF] 09.CSEC Maths JUNE 2008 T_T.pdf

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(TRINIDAD AND TOBAGO PAPER ONLY)

1.÷a. Required To Calculate:

Calculation:

Numerator:

Hence,

b.÷Data: Table showing the tax allowances for Mr. Allen. (i) Required To Calculate: His annual salary.

Calculation:

For 2007 Mr. Allen's monthly salary is $7 500.

Hence, annual salary

851311512!

1513152033154511334

511

311512

form)exactin(158138

151381315138511513

8

51311512

125007$!=

00090$=Copyright © RSG)H Some Rights ReservedH wwwHfaspassmathsHcomPg G of LS

www.faspassmaths.com (ii) Required To Calculate: Total allowances for 2007.

Calculation:

Total tax allowances for Mr. Allen according to the given table:

For self $10 000

For wife $ 5 000

For 3 children $ 7 500

Total ERR OSS

8iiiC Required To Calculate: Mr. AllenÕs income tax for 2007.

Calculation:

Taxable income = Gross salary Ð Tax allowances

Mr. AllenÕs income tax

(iv) Required To Calculate: Percentage of Mr. AllenÕs annual salary paid in income tax.

Calculation:

Percentage of Mr. AllenÕs annual salary paid in income tax

2.!a. Required To Simplify:

Solution:

( )25003!

50067$50022$00090$

50067$10022!=

85014$=

%5.16100

0009085014100

SalaryGrossTaxIncome

2 13!a

1691339131313

222
aa aaaaaaCopyright © RSG)H Some Rights ReservedH wwwHfaspassmathsHcomPg R of LS www.faspassmaths.comb.!Data:

Required To Make: p the subject of the formula.

Solution:

c.!Required To Factorise (i)

Solution:

(i) (ii) (This is a difference of 2 squares) d.!Data: and

Required To Calculate: x and y

Calculation:

Let

É(1)

É(2)

From equation (1)

Substituting in equation (2)

pq+=35 8 C qqpqpqpqqpqpqpq 35

355315335

13 5 222

25)(,63qpiinmn!!

nnmnnmn!!!"="23363 2 ( )nmn23!= 2222

525qpqp!=!

( )( )qpqp+¢=55

1923=!yx432=+yx

1923=-yx

432=+yx

31921923

yxyx

12938443331922343

31922
yy yyy yCopyright © RSG)H Some Rights ReservedH wwwHfaspassmathsHcomPg L of LS www.faspassmaths.com When

Hence, and .

OR Let

É(1)

É(2)

Equation (1)

É(3)

Equation (2)

É(4)

Substitute in equation (1).

Hence, and .

OR

213262613381213

y yy

2!=y( )19223=!!x

51534193

x xx

5=x2!=y

1923=÷yx

432=+yx

3!

5769=!yx

2!

864=+yx

5136565138645769

x xyxyx 5=x

224421519219253

y yyy

5=x2!=yCopyright © RSG)H Some Rights ReservedH wwwHfaspassmathsHcomPg P of LS

www.faspassmaths.com

Finding the coordinates of 2 points on the line.

x y L T O Y G

Find the coordinates of R points on the lineH

x y TG R ( TP If we draw the two straight lines on the same axesA The point of intersection is 8OA TRC from which we deduce and H OR Let

É(1)

É(2)

Expressing in matrix form

Let

19321923

xyyx

423432

xyyx

5=x2!=y

1923=!yx

432=+yx

419
3223
yx '=3223ACopyright © RSG)H Some Rights ReservedH wwwHfaspassmathsHcomPg O of LS www.faspassmaths.comDet

Matrix equation

Equating corresponding entries.

and .

3.!a. Data: Venn diagram.

( ) ( )2233!""!=A

èae

èae

133

132132

1333233

13113
1 A 1! A

132613651312

1338138

13574

133191324

132191334

19 13 3

132132

133
1 yxy xIy xAA '=25

5=x2!=yCopyright © RSG)H Some Rights ReservedH wwwHfaspassmathsHcomPg F of LS

www.faspassmaths.com(i) (a) Required To List: Members of .

Solution:

as seen on the given diagram. (b)!Required To List: Members of .

Solution:

(ii) Required To Find: .

Solution:

(iii) (a) Required To Describe: U in words.

Solution:

U = {Even numbers from 2 to 30 inclusive}

(b)!Required To Describe: H in words.

Solution:

H = {multiples of 6}

(Since the universal set is from 2 to 30 we need not say Ômultiples of 6 from 2 to 30Õ). b. (i) Required To Construct: Quadrilateral PQRS, in which PQ = 8 cm,

QR = 4 cm, PS = 6.5 cm, and .

NOTE: The angles 125

0 and 70 0 cannot be constructed and are drawn using the protractor. HG! { }24,12=÷HG HG-" HG GH ( )HGn-

930,18,6,24,12,20,16,8,4

HGnHG

¡=125ˆRQP°=70ˆSPQCopyright © RSG)H Some Rights ReservedH wwwHfaspassmathsHcomPg Y of LS

www.faspassmaths.com

Solution:

(ii) Required To Find: Length of RS.

Solution:

RS = 8.6 cm (by measurement)

4.!Data: Given a triangular prism with right-angled isosceles triangles at both ends.

a. Required To Calculate: Area of

Calculation:

Area of

ABC!

244!="ABC

2 cm8=Copyright © RSG)H Some Rights ReservedH wwwHfaspassmathsHcomPg ( of LS www.faspassmaths.com b.!Required To Calculate: Length of edge CD.

Calculatio

n: Volume of prism = Cross-sectional area Length CD c. Required To Calculate: Length of edge AC.

Calculation:

d. Required To State: Number of faces, edges and vertices of the prism.

Solution:

No. of faces: 2 triangular

1 !rectangular side 1 !rectangular base 1 !rectangular sloping

Total O

NoH of edges: ABA BCA ACA EFA FDA EDA AEA BEA CF

Total = )

NoH of vertices: AA BA CA DA EA F

Total = F

OH!Data: drawn on labeled axes.

a. Required To Draw: Line on the diagram.

Solution:

Line is shown on the diagram.

cm9728 CDCD 2222
AC ACAC LMN! 4=x

4=xCopyright © RSG)H Some Rights ReservedH wwwHfaspassmathsHcomPg ) of LS

www.faspassmaths.com b. Required To Draw: , the image when is reflected in the line

Solution:

as shown on the diagram. c.!Data: (i) Required To Draw: .

Solution:

, and plotted and drawn, as shown on the diagram. (ii) Required To Describe: The transformation that maps onto

Solution:

and pass through O. by an enlargement, centre O and scale factor 2. d.!Required To Calculate:

Calculation:

Since,

Then,

NML!!!"LMN!

4=x ( ) ( ) ( )2,5and6,5,1,7

4xinReflection

NMLNMLLMN

( ) ( ) ( )4,6,12,6,2,2!!=""!!=""!!=""NML

NML!!!!!!"

L¢¢M!!N!!NML!!!!!!"

LMN!

NML!!!!!!"

MMLL¢¢¢¢,NN¢¢

MLLMNLLNMN

NM 2 48

NMLLMN!!!!!!"#"$

LMNofAreaNML!ofArea!!!!!!

1:2:=!!!!LMML

1412

LMNofAreaNML!ofArea

22
!!!!!!Copyright © RSG)H Some Rights ReservedH wwwHfaspassmathsHcomPg GS of LS www.faspassmaths.com

6.!Data: Table showing the population of country in five year periods from 1980 to 2005.

a. Required To Draw: Line graph to represent the information given.quotesdbs_dbs7.pdfusesText_13

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