SA2 2011 ANS

7/28/2019 SA2 2011 ANS

1/15

REPRODUCTION OF ANY PART OF THIS QUESTION PAPER WITHOUT PERMISSION IS STRICTLY PROHIBITED.

Class Index Number Name

MARIS STELLA HIGH SCHOOL

SEMESTRAL EXAMINATION TWO

SECONDARY ONE

MATHEMATICS 11 October 2011

2 hoursAdditional Materials:

Graph paper

INSTRUCTIONS TO CANDIDATES

Write your class, index number and name on all the work you hand in.Write in dark blue or black pen.

You may use a pencil for any diagrams or graphs.

Do not use paper clips, highlighters, glue or correction fluid.

Answer all questions.

If working is needed for any question it must be shown with the answer.Omission of essential working will result in loss of marks.

You are expected to use a scientific calculator to evaluate explicit numerical expressions.If the degree of accuracy is not specified in the question, and if the answer is not exact, giveyour answer to three significant figures. Give answer in degrees to one decimal place.

For, use either your calculator value or 3.142, unless the question requires the answer in

terms of.

At the end of the examination, fasten all your work securely together.The number of marks is given in brackets [ ] at the end of each question or part question.

The total number of marks for this paper is 80.

For Examiners Use

This document consists of 16 printed pages.

80

7/28/2019 SA2 2011 ANS

2/15

2


1 Evaluate23

2.145

2.452.6

, giving your answers to 2 significant figures.

fig)sig2(020.0

01987.02.145

2.452.623

=

=

[A1]

Answer ................................................................. [1]

2 Express

(a)16

38as a percentage,

%5.23716

38= [A1]

Answer (a) ................................................... % [1]

(b) the ratio5

7:

10

1:01.0 in its simplest terms.

5

7:

10

1:01.0

100

140:

100

10:

100

1

140:10:1 [A1]

Answer (b)............... : ............... : ............... [1]

3 (a) Express 540 as the product of its prime factors.

53254032= [A2]

Answer (a) 540 = ............................................. [2]

(b) Hence, find the smallest possible positive value ofp such that p540 is a perfect cube.

252=p

50= [A1]

Answer (b) p = ................................................ [1]

7/28/2019 SA2 2011 ANS

3/15

3


4 Three different buses services arrive at a bus-stop every 6 min, 10 min and 15 min

respectively. All the three buses come together at 8.45 am.

At what time do they next arrive together at the bus-stop?

326 =

5210 = [M1]5315 =

LCM of 6, 10 and 15 = 532 [M1]

30=

Time arrived = 9.15 am. [A1]

Answer ....................................................... [2]

5 Farah counted the number of cars in a carpark based on its colour and presented the data in

the form of a bar chart and a pie chart.

The column for white cars is missing in the bar chart below.

Find the number of white cars if the angle which represents the white cars in his pie chart

is 60 .

No. of white cars =20+ 40+10

300

60 [M1]

14= [A1]

Answer ........................................................ [2]

No. of cars

red blackblue white

40

20

10

0

7/28/2019 SA2 2011 ANS

4/15

4


6 Expressx

3

2+ x

2+1 as a single fraction.

x

3

2+ x

2

+1

6

6

6

)2(3

6

2+

+

=

xx[M1]

6

6)2(32 ++=

xx

6

6362 +=

xx[M1]

6

x

= [A1]

Answer ........................................................ [3]

7 A formula is given as2

1

x

yz

= .

Given further that 3=y and 4=z , find the values ofx.

2

)3(14

x

= [M1]

2

3116

x

+

=

4

12=x

2

1=x [A1] or

2

1=x [A1]

Answer=x

................. or................. [3]

7/28/2019 SA2 2011 ANS

5/15

5


8 Solve5

7123 =

+

x

x.

5

7123 =

+

x

x

5

812=

+

x

x[M1]

xx 8)12(5 =+ [M1]

xx 8510 =+

52 =x

2

12=x [A1]

Answer ........................................................ [3]

9 (a) Solve the inequality 312

+

x

x.

Show your solution on the number line below.

312

+

x

x

xx 312 +

x1

1x [A1]

[A1]

Answer

[2]

(b) Hence, or otherwise, find the smallest possible prime number ofx for 312

+

x

x.

Smallest prime = 2

Answer (b) =x ............................................ [1]

5 0 5

7/28/2019 SA2 2011 ANS

6/15

6


10 Factorise the expression xyxyx 22 2 + completely.

xyxyx 222

+ yxyxx += 222

)1()1(2 = xyxx [M1]

)1)(2(

= xyx [A1]

Answer ........................................................ [2]

11 The first three figures of series of figures of squares are shown below.

Figure 1 Figure 2 Figure 3

(a) Find the total number of squares in figure 4 and figure 5.

Figure 4 : 13 [B1]

Figure 5: 17 [B1]

Answer (a) Figure 4 : ...................................

Figure 5: ................................... [2]

(b) Write, in terms ofn, the total number of squares for figure n.

Total number of squares = 34 n [B1]

Answer (b) ......................................................... [1]

7/28/2019 SA2 2011 ANS

7/15

7


12 In the diagram,

ARB, QGPand CEFGD are straight lines.

AB is parallel to CD and AEis parallel to QG.

= 60FGP , = 50EAF and

= 95RQG .

Stating clearly the reasons, find

(a) QGD ,

QGD = 60 ( vert opp s) [A1]

Answer (a) QGD = ................................. [1]

(b) AEF ,

AEF = 60 ( corrs s,EA // PQ ) [A1]

Answer (b) AEF = ................................. [1]

(c) AFG ,

AFG += 6050 (ext= sumof int opp)

=110 [A1]

Answer (c) AFG = ................................. [1]

(d) QRB .

QGD = 6095 ( alt s,AB // CD)

= 35 [A1]

Answer (d) QRB = ................................. [1]

A B

C D

P

FE G

Q

R

60

95 50

7/28/2019 SA2 2011 ANS

8/15

8


13 A,B and Care the points (4, 2), (1, 4) and (4, 1).

(a) Mark and label on the grid below the pointD with the coordinates (2, 0).

Answer

[1]

(b) Find the gradient ofAC.

Gradient of AC44

)1(2

= [M1]

8

3= [A1]

Answer (b) ...................................................... [2]

(c) ABCEis a parallelogram. Find the coordinates of the pointE.

)3,1( E [B1]

Answer (c) ( .............. , .............. ) [1]

(d) Fis the point (k, 4) and the area of triangleABFis 3 units2.

Find the two possible values ofk.

=k 2 [B1] or 4 [B1]

Answer (d) =k ................. or................. [2]

2 4 60246

2

4

2

4

x

y

A

B

C

D

7/28/2019 SA2 2011 ANS

9/15

9


15 A van leaves Town P and travels on a straight road at a constant speed ofx km/h to Town Q.

A car leaves Town P 45 minutes later and travels at a constant speed 15 km/h faster than the

van. Eventually, the car catches up with the van after travelling for 2 hours on the same road.

(a) Write down an expression, in terms ofx, for the distance travelled

(i) by the car when the two vehicles meet,

Distance travelled = )15(2 x+

)302( += x km [A1]

Answer (ai) ................................................ km [1]

(ii) by the van when the two vehicles meet.

Distance travelled =

+

60

452x

x

4

11= km [A1]

Answer (aii) ............................................... km [1]

(b) Form an equation in terms ofx and hence, find the speed of the car.

3024

11+= xx

304

3=x

40=x [A1]

Speed of the car 1540 +=

55= km/h [A1]

Answer (b) .............................................. km/h [2]

7/28/2019 SA2 2011 ANS

10/15

10


16 A cylinderial vase is made up of two cylinders with diameters 14 cm and 21 cm and heights6 cm and 12 cm respectively as shown in the diagram below.

(Take7

22= )

(a) Find the total surface area of the cylinderial vase.

Let the smaller cylinder be A and the larger cylinder be B.

Curved surface area of A for the vase 5)14( =

5147

22=

220= cm2 [M1]

Total surface area of B for the vase

22

2142

22110)21(

+=

22

2

14

7

222

2

21

7

221021

7

22

+=

1199= cm2

[M1]

Total surface area 1199220+=

=1419 cm2

[A1]

Answer (a) ............................................... cm2 [3]

5 cm

10 cm

14 cm

21 cm

A

B

7/28/2019 SA2 2011 ANS

11/15

11


(b) Find the total volume of the cylinderial vase.

Total volume of A for the vase 5

2

142

=

52

14

7

222

=

770= cm3

[M1]

Total volume of B for the vase 102

212

=

102

21

7

222

=

3465= cm3 [M1]

Total volume 3465770 +=

4235= cm3 [A1]

Answer: (b) ............................................... cm [3]

(c) Water is poured at a constant rate of 385 cm3/ min into the cylinderial flask and filled

to the brim. Show the change in the water level of the container in the graph below.

Time taken for water level to reach 10 cm385

3465=

9= min

Time taken for water level to reach 15 cm from 10 cm 385

770=

2= min

Answer

[2]

Water level (cm)

Time (min)

5

15

10

0 2 4 6 8 10 12

[B1]

[B1]

7/28/2019 SA2 2011 ANS

12/15

12


17 In the diagram,AEYand YDXB are straight lines.

ABCEis a rectangle andACinterceptsBD atX.

It is given thatAB = 12 cm,DC= 8 cm and

DX= 6 cm.

Find

(a) the length ofXB,

DC

AB

XD

XB=

8

12

6=

XB[M1]

68

12=XB

9= cm [A1]

Answer (a) .................................................. cm [2]

(b) the ratio of the XDCofarea : the BXCofarea ,

XDCofarea : the BXCofarea = 6 : 9= 2 : 3 [A1]

Answer (b) ......................... : .......................... [1]

(c) the ratio of the XDCofarea : the XBAofarea .

XDCofarea : the XBAofarea = 82 : 122

= 64 : 144

= 4 : 9 [A1]

Answer (c) ......................... : .......................... [1]

(d) State the triangle which is similar to triangleEYD.

EYD is similar to AYB [B1]

Answer (d) EYD is similar to ................................................... [1]

A B

CDE

X

12 cm

8 cm

6 cm

Y

7/28/2019 SA2 2011 ANS

13/15

13


18 A trapezium-shaped figureABCD has a width of 4 cm,AB = 15 cm,BC=AD = 5 cm,

CD = 9 cm and == 126BCDADC .

(a) Find the area of one trapezium building blockABCD in cm2.

Area of ABCD 42

915

+

= [M1]

248 cm= [A1]

Answer: (a) ................................................. cm [2]

(b) A regular polygon structure is formed by placing identical trapezium figures like

ABCD side by side. Find the number of trapezium figures needed to form the regular

polygon.

Interior angle 2126360 =

(Adj. s at a pt.)

=108 [M1]

Exterior angle = 108180 (adj. s on a st. line)

= 72 [M1]

No of trapezium

=

72

360

5= [A1]

Answer: (b) ............................................................ [3]

A B

CD

5 cm 5 cm4 cm

15 cm

9 cm

126

A B

CD

7/28/2019 SA2 2011 ANS

14/15

14


19 Three pointsA,B and Care shown below.

Answer (b) and (c)

(a) Measure the reflex angleABC.

Answer (a) reflex angleABC =................................................. [1]

(b) Construct

(i) the perpendicular bisector ofAB, [2]

(ii) a line where any points on the line is equidistant toB and C. [2]

(c) Hence, draw a circle which passes through all the three points A, B and C. [1]

AB

C

7/28/2019 SA2 2011 ANS

15/15

15


20 Answer the whole of this question on a sheet of graph paper.

The table below gives some values ofx and the corresponding values ofy, where

22 +=x

y .

x 2 0 2 4

y a 2 1 0

(a) Find the value ofa. [1]

(b) Using a scale 2 cm to 1 unit for thex-axis and 4 cm to 1 unit for they-axis, draw the

line 22 +=x

y for .42 x [3]

(c) State the coordinates of thex-intercept of the line 22 +=x

y . [1]

(d) From the graph, find the value of x when 8.0=y . [1]

(e) On the same graph, draw

(i) 4.2=y , [1]

(ii) 5.1=x , [1]

(f) Hence, find the area of triangle bounded by the three lines 22 +=x

y , 4.2=y

and 5.1=x . [2]

End of Paper

Documents

SA2 2011 ANS