2011 Secondary School

Examination Papers

Secondary Two Express Mathematics

Paper 1 & 2

1 Admiralty Secondary School SA2 2 Ang Mo Kio Secondary School SA2 3 Beatty Secondary School SA2 4 Bedok Town Secondary School SA2 5 Bowen Secondary School SA2 6 Bukit Batok Secondary School SA2 7 Bukit Merah Secondary School SA2 8 Chung Cheng High School SA2 9 Clementi Town Secondary School SA2 10 Geylang Methodist Secondary School SA2 11 Jurong West Secondary School SA2 12 Northland Secondary School SA2 13 Ping Yi Secondary School SA2 14 Shuqun Secondary School SA2 15 Tanjong Katong Secondary School SA2 16 Yishun Secondary School SA2 17 Yuhua Secondary School SA2

I NAME: NO: CLASS: ADMIRAL TY SECONDARY SCHOOL

4 " II

~.!'!..~ END OF YEAR EXAMINATION 2011 II

SUBJECT : Mathematics PAPER : 1

LEVEUSTREAM : Sec 2 Express DATE : 10 October 2011 (Monday) TIME : 1000 - 11 00 DURATION : 1 hour

Instructions lo candidates:

1. Write your name, class and index number.

2. Answer ALL questions.

3. Use an electronic calculator lo evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question. and if the answer is not exact, give the answer lo three significant figures.

Give answers in degrees to one decimal place. For rr. use either your calculator value or 3.142, unless the question requires the answer in terms of rr.

4. EssenLial workings must be shown. Loss of essential workings and illegible handwriting will lead to loss of marks.

DO NOT TURN OVER THIS PAGE UNTIL YOU ARE TOLD TO DO SO.

This question paper consists of 11 printed pages ineluding this cover page.

Mensuraiion

S1atistics

Mathematical Formulae

Curved Surface Area of a Cone = 7frl

Surface Arca of a Sphere = 4 7fr 1

. . I 2 Volume of a Cone = - Jff '1

3

4 l Volume of a Sphere = :;- Jrr

.>

"[, j-.; Mean= J

2

1. Express eacii map scale in the fomi I : r .

(a) 3 cm : 24 m (b) 7 cm : 42 km

Answer. (a)

(b) 2. A 1s inversely proportional to 8 . Given lhat A = 8 and 8 = 36, find an equation connecting A

and B.

12) [21

Answer: ...................... ... (3)

3

3. Polygon ABCDEFGH is similar to polygon PQRSTUVW. find PQ. The two polygons are not drawn to ~le.

Q,_-----.R A s ~m n 1.5 Clll

T ~--'s

- - - -F t;

u v

11 1 1 f ' w II II ' G II D 2 Clll (.

Answer:

4 If x .Y =.!., find the val1Je of~ . 2y+3x 4 y

6 Clll

(2)

Answer: .... ............... (2]

5. Simplify the following expression: (a) (2A ; Sy)-3(5., -2y)

5a +4h 2h-3o (b) 2 + 3

cd' c~ cdl! (c) - >< -+-' 4 2

s

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

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

(c) ........ .. ... ........... [2]

6. Expand (9a+4b)(1a-5b) .

Answer: .. ..... ................. [2)

7. Factorise 2x' 1 J.t - 27.

Answer: ........................ [1)

8. The diagonal of a square is 9 cm. Find lhe perimeter of the square.

Answer: .................. cm (4)

6

9. A pottion of a pyramid with a square base ls removed, resulting in the following sohd. 11J and SQ are the diagonals or the base or lho original pyramid and R w is the perpend1culnr height. Grvon that TS = 29 cm and RW = 57 cm. find

(a) lhe base area or the solid. (b) lho volume or the solid.

T Q

s

s

7

w

Answer: (a)

(b)

~._ ~7 cm

LI

... cm' (1]

.. cm3 (2)

10. A solid 1s made up ol a cylinder and a cone with dimensions as shown below. Taking If - l.142 . find (a) lhe slant height of the cone. (b) (I) the ouNed surface area of cone.

(II) the total surface areil or solid. (c) (t) the volume of cone,

(ii) the vofume of the solid. Give your answer in 3 significant figures

..

Answer:

L------.i. I Y cm --...l lllcm

8cm

(a) ............... ... cm

(b) (i) 2 .................. cm

(ii) cm2

(c) (i) ... .............. cml

(ii) ............ cm3

[3]

(1 I (3)

(1 J (2)

11. The following numbers are the number of words in each line from a page or a novel. (a) Fill in the given frequency table. (b) Calculate the

(i) mean, (ii) median. (iii) mode.

8 8 8 11 14 9 11 7 8 13 12 2 13 14 3 12 11 11 14 10 13 2 11 9 13 13 13 13 4 8 11 .13 10 11 13 12 13 10 3 13 9 14

Solution: (a) x f f.~ 2

-3 4

7 -8

g

10

11 - -12

13 14 Total [3]

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

(ii) Median .. .... .. ..... (1)

(iii) Mode .. ... ...... .. . [1]

9

12. It is given that & = (x: x is an integer. I < x < 50) and sets A, 8 and Care defined as follows: A - {x: x is divisible by 7) H = { . .: x is a multiple of 14) c ; {x: x is multiple or 3) (a) List the elements of A n C . (b) Find n(

13. A bag contained 6 blue balls and 7 red balls. If a ball is picked at random from tho bag, find the probability that a red ball is picked.

Answer:

End of Paper

11

[1)

1. Express each map scale in the rorm l : r . (a) 3 cm: 24 m (b) 7 cm: 42 km

Solulion:

(a) 3cm : 24 m 1 cm:8m ....... .. . Ml 1 : 800 .... .. ......... A1

(b) 7 cm : 42 km 1 cm:6 km ..... .. .. M1 1 : 600000 .......... A1

Answer: (a)

(b) 2. A is inversely proportional to B. Given that A; 8 and B; 36, find an equation connecting A

and B.

Solution k A --JJ

8-~ K M l 16

k =8x36 -288 K Ml

288 II :-K Ill R

(21

[2)

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

3

3. Polygon ABCDEFGH is similar LO polygon PQRSTUVW. find PO. The two polygons are not drawn to scale. Q R A 8cm

1.5 cm T s

p ,...---------.

u v

, .. w G Solution: Sine polygon PQRS"J"UVWis similar to polygon ABCDEFCH.

l'Q RS -,=-

AB CD PQ = l.S K K Ml 8 2

f'Q =~x8 2

= 6cm K K Al

D 2cm c

6 (an

Answer: .................. cm

x - y I r 4 If - - =-, find the value of:.. . 2y+3.r 4 y

Solution: x-y

~

2y +3x 4 4(x y) = 2y+3xKKMI 4x-4y=2y+3x

x=6y

~=6KKAI y

(2]

Answer: ... . . . .. ... ... .. ..... [2)

4

5. Simplify the following expression. (a) (h+Sy)-3(5r-2y)

5,,. 411 2b - lo (b) + 2 3

cd' Ct' cdt' (c) x +-.1 4 2

$olut10n (a) (2n 5y) - 3(Sr - 2y)

2~ Sy- ISx+6yKKMI -13.\ 11.vKKK Al

'\11 I 4/1 2b )(I (b) t 2 3

(c)

1(S" I 4b) 1 2(2/i 3n2 K K Ml 6 6

1511 I 12h I 4/, (111 6

9u I l(Jb 6

K K K K Al

cdJ C(' e1.lc: ~ T

1 4 2

.. ,/ "'

2 KKMI x x

' -I ,.,,~

..,, K K Al

" 6

Answer: (a) ....................... (2) (b) ........................ l:?J (c)

[2]

6. Expand (9C1 ~ 4b}(7C1 - 5b}.

Solution: (9CI I 4b)(7a - 5b) = 9a(?a-5b) +4h(?a -Sb) - 6JC1' - 45ab+ 28a/1- 20b' K K Ml =63a' - 17ab-20b 2 KK KKAI

7. Factorise 2x2 +3x-27.

Solution:

2x1 +3x - 21 = (2x+9)(x -3) KAI

Answer:

2x .., +9 +9x ,' ,,

.< / ' -3 -6x

-27 +)x

Answer:

8. The diagonal of a square is 9 cm. Find the perimeter of the square.

Solution: Let the breadth of the square = b cm By Pythagoras' Theorem,

b 1 +b1 - 92 K K M l

2b' = 31 h ' - 40.5

h .J40.5 K Ml = 6.36396103067

Perimeter of the Square

= 4 x J40.5 OR = 4 >< 6.364 (at least 4 s.j .) K Ml = 25.5 (3 s.J.) = 25.456 K K Al

Answer:

6

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

........ . ..... .. .. ...... (1 ]

.............. . ... cm [4)

9. A portion ol a pyramid with a square base is removed. resulting on the follOWJng solid. ru and SQ are the diagonals or tho base or the O

10. A solid is made up or a cylinder and a cone with dimensions as shown below. Taking n 9 3.142, find (a) the slant height of the cone, (b) (i) the curved surface area of cone.

(II) !he total surface area of solid, (c) (i) the volume of cone,

(ii) the volume or the solid. Give your answer in 3 significant figures. Solution:

,_____, 19 cm ____ ,Ill cm

Scm

(a) Let the slant height or the cone be I cm. } Ml Sy Pythagoras' Theorem.

I= J97 : 9.849957802

11 :91 +41 - 81+16 = 97KK Ml

(b) (i) Curved surface area or cone - 3.1 42 'I( 4 )( ~) .84? - 123 . 782232 = IZlcm' (3 s.f.)K Al

(Ii) Curved surroce area of cylinder "'3. 142 xSx I I

~ 276 .496 cm' K MI Base area of cylinder

~3. t42 x4x4

= 50 .272 cm' K M I Total surface area of solid

= 123.78+276.496 +50.272 = 150.548 - 451 cm' (Js.f.)K 81

8

"9.85 cm (3 s.f.) K Al

(c) (i) Volume of cone I ~-xl. 1 42 x 4 x4x9 3 ~ 150.816 CIU l = 151

11. The following numbers are the number of words in each line from a page of a novel. (a) Fill in the given frequency table. (b) Calculate the

(i) 1nean, (ii) median. (iii) mode.

8 8 8 11 14 9 11 7 8 3 12 11 11 14 10 13 2 11 4 8 11 13 10 11 13 12 13

(a) Solution:

I .< I f< 2 2 4

-3 2 6 4 1 4

- 7- 1 7 ----8 5 40

-

9 3 27 10 3 30 11 7 77

12 3 36 13 11 143 14 4 56

-

~

Total 42 430 I

- -l"requency Table - A3, 1 mark per column+ 1 mark for totals

(b) (i) Mean= 430 + 42 =10.2 (3 s.I.) ....... ........ 81

(Ii) 42 +I = 2 1 .5 2

Middle Values are 21" value and 22"" value Median = 11 ......... 111

(iii) Mode = 13 ............ 111

9

Answer:

13 12 2 13 14 9 13 13 13 13 10 3 13 9 14

(3)

(b) (I) Mean= . ....... . . ... . . (1 )

(ii) Median = .. ........ ... (1)

(Iii) Mode= .............. [1)

12. ll is given that c = {x: x is an integer. I < x < 50) and sels A, Band Care defined as follows: A - {x: x is divisible by 7) 8 : {.

13. A bag contained 6 blue balls and 7 rod balls. If a ball is picked at random from the bag. find the probability that a red ball is picked.

Solution: /~Red ball is picked)

7 6 I 7 7

13 K K A I

Answer: ....... . 11r

End of Paper

11

I NAME: NO: CLASS: ADMIRAL TY SECONDARY SCHOOL

II END OF YEAR EXAMINATION 2011 II SUBJECT : Mathematics PAPER : 2 LEVEUSTREAM : Sec 2 Express DATE : 12 October 201 1 (Wednesday) TIME : 07 50 - 09 20 DURATION : 1hour 30 min

Instructions to candidates:

1. Write your name, class and index number.

2. Answer ALL questions.

3. Use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and ii the answer is not exact, give the answer to three significant figures.

Give answers in degrees to one decimal place. For;r , use either your calculator value or 3.142, unless the question requires the answer in terms Of IT ,

4. Essential workings must be shown. Loss of essential workings and illegible handwriting will lead to loss of marks.

DO NOT TURN OVER THIS PAGE UNTIL YOU ARE TOLD TO DO SO.

This question paper consists of!! printed pages including this cover page.

Mensuraiion

S1atistics

Mathematical Formulae

Curved Surface Area of a Cone = 7frl

Surface Arca of a Sphere = 4 7fr 1

. . I 2 Volume of a Cone = - Jff '1

3

4 l Volume of a Sphere = :;- Jrr

.>

"[, j-.; Mean= J

2

1. A map is drawn to a scale of 1 200 000 (a) The MRT station and the s~ 1s O. 7 cm apart. Find the actual distance, 1n km (b) The school field has an area of 2.6 km2 Find its area on the map.

Answer: {a) (b) ___ _ km cm'

2. Two pipes, A and B, take 7 hours and 11 hours respectively to fill up a swimming pool. After two pipes are turned 011 for an hour. Pipo A is turned off. How long does ii take for Pipe B to fill the remainder'?

Answer: hrs r~

.1

3. Answer this whole question on a piece of graph paper. The following table gives corresponding values of x and y which are connected by the equation

y ~ l 9 -4x -3x1 .

~j~;=: ~,_,__~-3~'-,--~-3 ...,--._,_~~~:~....,..-~_1 ~'~_:_9~~-:_2~~-~~~~:~1 -~ (a) Calculate the value of p and the value of q. (b) Using a scale of 2 cm lo represenl 1 unit on the x-axis and 2 cm for 1 O uni ls on lhe y-axis.

draw the graph of y = 19 - 4x - Jx2 for- 4 5. x 5. 4.

(c) Draw and label the line of symmetry for the curve. (d) Draw y ~ 15- 2x on the same graph. (e) Solv'ey = 19 - 4x - 3x2 and y = 15- 2x graphically.

4. There are" benches and y students in an auditorium. When a bench is seated with 3 students. 18 are left standing. If a bench is sealed wilh 4 students. 3 benches would be empty. (a) Write 2 equations showing the relationship between x benches and y studenls. (b) Find the number or benches and students.

Answer: (a)

(b) benches students (;

5. The heights of 20 students are shown on a stem and lear diagram below. Steam

12 13 14

1

3 1

3 4 2

3 4 ,,

Key: 12 11 means 1?1 cm

3 4

5

Leaf 4

x

6

5

5 6 8 9

(a) 1r the modal height is 13~ cm and the mean height or the students is 133.65 cm, !ind the values or x and y.

(b) Betty is the shortest in the group of studonts. How tall is she? (c) tr a student is pieked at random What Is the probability of choosing a student with hoi9ht

123 cm?

Answer: (a) ' = )' =

(b) (c)

cm

I

6 The diameters of 50 ball .bearings produced by a factory measured in mm (correct to 2 significant figures) are given in the table below.

Diameter (mm) 5.0 - 5.2 Frequency 6

(a) State the median class. (b) State the modal class.

5.3 -5.5 8

(c) Fill in the frequency table below. (d) Calculate the mean.

(c) Solution:

Diameter f Mid-Value (x) 5.0- 5.2 5.3 - 5.5

.

5.6 -5.8 5.9-6.1 6.2 - 6.4 6 .5 - 6.7

Total

5.6 -5.8 5.9 - 6.1 6.2-6.4 6.5- 6.7 12 11 7 6

J<

Answer: (a) ~~~~~~~~

(b) ~~~~~~~~

(d)

6

[

r [' 1

7 A hollow hemispheric container has an external radius of 15 cm and an internal radius 12 cm. Given that ,,. = 3.142,

(a) find the total surface area of the container. {b) find the volume of the container. (c) If the hemispheric container is melted and recast into small cubes of length 2 cm on each

side. Find the maximum number of cubes which can be made. t5 cm - --- -- --- ~

< 12cm

Answer: (a) cm2 (b) cml (c)

7

[: [: 1:

8 A square pyramid has a base renglh of 10 cm The height of one of its triangular f

(a) The MRT station and the school is 0.7 cm apart. Find the actual distance, in km. (b) The school field has an area or 2.6 km'. Find its area on the map.

Solution: (a) 1 : 200 000

0.7: 0.7 x 200000 ...... M1 0.7 : 140 000 Actual distance = 140 000 + 100 000 .. M 1

= 1.4 km .. ................ A1

(b) 1 cm : 200 000 cm 1cm:2km 1 cm2 : 4 km2 . : . . ....... . M1 Area on the map= 2.6 + 4 ... ... M1

= 0.65 cm2 ... . A1

2. Two pipes, A and B, lake 7 hours and 11 hours respectively to fill up a swimming pool. After two pipes are turned on ror an hour, Pipe A is turned ofl. How long does it take for Pipe B lo fill the remainder?

Solution:

In 1 hour,

Pipe A can fill 1 or the swimming pool. 7

Pipe B can fill ~or lhe swimming pool. 11

Arter 1 hour, Pipe A and Pipe B filled ( J + ~) : !.! of the swimming pool. . ..... M 1 7 11 77

18 (1 --) 77

59 r . . . 11 ct - o the swimming is not 1 le ....... M1 77

59 : I - 59 x II K K K K Ml

77 I I 77 59 7 3

- l) - OR ""8.43(3s. j.) K K Al 7

3

3. Answer this whole question on a piece of graph paper. The following table gives corresponding values of x and y which are connected by the equation

y=l9 - 4x - 3x' .

0 1 2 3 4 19 12 -1 q -45

(a) Calculate the value of p and the value of 'I (b) Using a scale of 2 cm to represent 1 unit on the x-axis and 2 cm for 10 units on the y-axis,

draw lhe graph of y = 19- 4x - 3x2 for - 4 :S x :S 4 .

(c) Draw and label the line of symmetry for the curve. ( d) Draw y = I 5 - 2x on lhe same graph. (e) Solvey = 19 - 4x- 3x2 andy = 15-2x graphically.

Solution:

(a) p = l9 - 4(- 1) 3(- 1) ' = 20 KKK Al

q = l 9 - 4(3) - 3(3)' = -20 K K K ; fl

(b) Scale [.41] Plot points for y = 19 - 4x - 3x ' [M1J

Draw and label curve y = 19 - 4x- 3x' (A1]

(c) From lhe graph, line of symmetry: .r " - 0.65 (,t1]

(d) Plot points for y = 15 - 2,, [M1J x -3 0 3 y 21 1 15 9

Draw and label line y ~ 15 - 2x (111 )

(e) From lhe graph, x = - 1.5 0. 1 y = l8 1 KK Al x = 0.85 1: 0. 1 y = 13.5 I KK Al

4. There are benches and y students 1n an auditorium. When a bench 1s seated with 3 students,

18 are left standing. If a bench is seated with 4 students. 3 benches would be empty. (a) Write 2 equations showing the relationship berween x benches and y students. (b) Find the number or benches and students

Solution

(a) 3.r+ 18 }'/\ /\ /\ Al 4x - 12 - y/\/\/\ Al

(b) 3x t 18 y /I /I (I) 4A 12 )' /I /I (2) Substituting ( 1) 1rito (2).

4x t2=3x+l8 .> 30 KKBI

Subs111u11ng this into (1 ), 3(30) t t 8 )'

y 108 K K Bl There arc 30 benches and 108 students .. .A I

5. The heights of 20 students are shown in o stem and leaf diagram below. Steam Leaf

12 1 3 3 3 4 5 13 3 4 4 4 x 5 G 14 1 2 y 5 G

Key 121 1 means 121 cm

8 9

(a) If the modal height 1s 134 cm and the mean height of the students is 133.65 cm, find the values of 1 and y.

(b) Betty 1s the shortest in the group or students How tall is she? (c) If a student is picked et random Whal is the probability of choosing a student with height

123 cm?

Solution:

(a) x - 4 /\ /\ Al Total height - 20 >< 133.65

2673 A/\ Ml Remaining l teight -2673 - 121 1(123) - 124 - 125 IJJ 4(134) - IJS - 136 - IJS - 119 141 142 l4S 116 - 14}

y = 3 A A II (b) Betty's height 1s 121 cm. ..... A1

(c) ?{choosing a student .with height 123 cm) = 2. K Al 20

6 The diameters or 50 ball bearings produced by a factory measured in mm (correct lo 2 significant figures) are given in the table below.

Diameter (mm) 5.0 - 5.2 5.3 - 5.5 5.6 -5.8 5.9 - 6.1 6.2 - 6.4 6.5 - 6.7 Frequency 6

(a) State the median class. (b) State the modal class.

8

(c) Fill in !he frequency fable below. {d) Calculate the mean.

Solution:

12 11

(a) 50 + 1 = 25.5 Middle values are 25' value and 26"' value 2

Median Class = 5.6 - 5.8 K Al

(b) ModalClass =S.6 -5.8 K A l (c)

Diameter I Mid-Value (x) />: 5.0-5.2 6 5.1 30.6 5.3 - 5.5 8 5.4 43.2 5.6 -5.8 12 5.7 68.4 5.9-6.1 11 6 66 6.2-6.4 7 6.3 44.1 6.5 - 6.7 6 6.6 39.6

-Total 50 291.9

7

1 mark per column A3, I mark 2 lol3ls 1/ I

(d) Mean = 291.9 50 = 5.838 ... .. A1

6

6

7 A hollow hemispheric container has an external radius of 15 cm and an internal radius of 12 cm. Given that ;r = 3.1 42,

(a) find the total surface area of the container. (b) find the volume or the container. (c) If the hemispheric container is melted and recast into small cubes of length 2 cm on each

side. Find lhe maximum number of cubes which can be made.

Solution:

(a) Surface Area of brim or hemisphere= 3.142(15)' - 3.142(12)' = 254.502K M l

Total Surface Area or the hemisphere

= lx4x3.142x(15}' +lx 4 x3. t42x(12)' ~254.502K Ml 2 2 1413.9 ~904.896+254.502

-2573.298 cm ' K Al

(b) Volume of lhe outer hemisphere = lx~x3.142x(l 5)' 2 .l

=7069.Scm ' K Ml

Volume or the inner hemisphere = .!..x ~ x 3.142 x (12)' 2 .)

= 36 I 9.584 cm' K MI

Volume of the hemisphere = 7069.5-3619.584

-3449.916 cm' K Al

(c) Volume of each cube= 2x 2x 2 -8cm' K Ml

Number of cubes= 3449 .9 16 + 8 K M I

= 43 1.2395 .:431 K Al

1

t 5 cm ----------

c 12 cm

6 A sQuare pyramid has a 'base length of 10 cm. The height of one of its triangular faces is h cm. Given that h is 8.5, (a) find the area of one triangular lace. (b) find the total surface area.

Solution:

(a) Area of one triangular face=~ x I 0 x 8.5 2

= 42.5 cm' K Al

(b) Base area = IOx l O - IOOcm' K Ml

To1al surface area = 42.5 x

..

Class Index Number rmc

ANG MO KIO SECONDARY SCHOOL FINAL EXAMINATION 2011

SECONDARY TWO EXPRESS

Mathematics Part One

Seiter: Mr Tan Wee Hong

M onday 10 OCTOBER 2011

candidates answer on !he OUeshon Paper

READ THESE INSTRUCTIONS FIRST

Write your name, index number and class on all lhe work you hand in. Write in dark blue or black pen on both sides of lhe paper. You may use a pencil for any diagrams or graphs. Do not use highlighters. glue or correclion Ould.

/\nswor alt questions. If working is needed for any queslion it must be shown with lhe answo1. Omission of essential working will reStJlt in loss of marks. Calculators should be used where appropriflte.

1 hour

If the degree of accuracy is not spcohocf in tho queslion. and if the answer is not exact, give lhe

Part I (50 Marks) Answer ALL the quest ions.

In the figure bcl(>W, A8CD is a trnpezium s~ich that LDAB = LADC .._90 and CD - 21 cm. E is a point on AC such 1ha1 A = 24cm, EB ~ 18 cm and .t.AEB = 90.

D 21 cm

24cm 18 cm

A 8 (i) F'ind the leng1h of A8.

(ii) Given rhat !he area of rrapeziurn ABCD is 510 cm2, !ind !be length of AD. (iii) Hence, calculate the lenglh of EC.

Ans: (i) _________ c;::.m"- [I]

(ii) cm [2] ---------"""--

(iii) ----------C"-11"-1 f2)

2 (.1) 1 he distance be1ween Ang Mo Kio Secondary School and Tan Tock Seng llospital on a map ts .17 cm.

( i) Given that lhe actual distance bc1ween the two locations is 6.8 km. find the scale of the map rn 1hc fonn I n .

(i i) Calculate the actual area of Oishan Park, in km2, if its area on 1hc map is 3.25 cm2

(b) h takes 5 air pumps working 1ogcthcr at the same ra1c to inflate a bouncy castle completely in 36 minutes. If one of the nir pumps is out of o rder, how much longer do the remaining air pumps take to inflate the bouncy c:~~t lc?

(ii) (b) _ _____ _

[I I km1 [2)

minut~ [2)

(Tum ovct

3 Given that f) and q are integers such that - 2 5 p 5 5 and - I 5 q 5 6, fi nd (a) the least possible value of pq, (b) the greatest possible value of p-3q ,

(c) the least possible value of q; . p

Ans: (a) ( I ] ---------~

. x+ I I I Solve the equation --+ = -4

.

5x - 1 2(1 - 5x)

(b) -----------(c) ----------

[I J ( I I

Ans: _::x_= _ ___________ 13]

5 l11s given that 2p = Jq' -3p . {i) Express q in terms cif p,

(ii) Hence, or olherwise, find lhe value of q when p = -3 .

Ans:

6 Factorise 1he following expressions complclcly.

(a) 36x' y-49y',

{b) 4a' + 2ab-10a -5b .

(ii) q =

(b) ___ _

.

l 2J [ I J

[2J [2)

[Turn over

7 Simpli fy the following expressions.

(a) 7a(a+5)-(a-2)(a+l),

(b) 2 ' x-y . x -y 2a -3b y 4a -Gl>

Ans: (a) --------- 131

(b) ------- - [2]

8 (ii) The following shows 1hc number of books read by a group of chi ldren dunns 1hcir December hohday:;.

s, 7, 5, 3, 4, 7, 2, 6, x, 5.

( i) Jf tl1ere are 2 values for mode, wrilc down 1he v;ilue of x. (i i) Hence. calculate the mean.

(b) During a health check-up, lhc weights uf20 Secondary One s11Jde111s of1hc same hcighl were recorded . The s1crn-und-leafdingram below illustrate:> their results.

3

4

5

6

5 0

0 1 4

8 0

6

3 4

0

7

4

...

2

6 7

3

8

9

8

(i) If the median weight of the s1111fo111s 1s 56 kg. writ

9 (a) Given c = {all the households in a HOB block}, A ~ {households who subscribe to broadband intcmet} and fl - {households who subscribe to cable TV}.

(i) Express An B 'f. in words. (ii) F.xpress, in set notation, the statement that all households who subscribe to

c.able TV r1lso subscribe 10 broadband internet.

{b) Shade the region r~-presenting the sci (CvD)'v(C n D) in the Venn diagram below.

c c D

[, ,

---------------- --- [I] (ii) ---------- Ill

-.

10 The diagram below

11 The diagram below shows a sequence of figures made up of sin~ll s haded ;ind unshaded triangles.

h. A Fig. I Fig. 2 Fig.3 Fig. 4

The !able below shows the number of each type of small triangles in each figure.

Figure I 2 3 4 5 ... n Total number of triangles ~-

4 9 16 25 p ... Number of shaded triangles 3 6 9 12 q ... Number of unshaded triangles I 3 7 13 2 1 ... r

(a) Stale lhc values of p and '/

(b) (i) In figure 11, the number of unshaded triangles is r, express r in tem1s of11. ( ii) Figure k has 133 unshaded triangles, find the value of k .

Ans: (a) p = ( I J _.:_q _= _______ _ _ [I]

(b) (i) --------- [ q (ii) k = (I I

12 11ic dingram below shows a mclallic cube. A pyramid WXYZ is cur our from 1he cube

such 1ha1 XY = rz = WY - 6 cm.

,

,

,

:w r . F

(a) Calculate 1he volume oft he pyramid ll'Xl'Z. (h) 111c pyramid WXYZ is mcllcd and used 10 make spherical mcrallic bc.1ds of

radius 0.3 cm. Find the number ofbc.1ds 1ha1 can be made from 1he pynunid

WXYZ. (Take tr - 3.142)

Ans: (a) _____ _

(b)

cml (2)

beads (2)

(Turn over

1 l The diagram below shows 1hc graph of x - >

,.

3

7

:r: J 3 "

:r: -y ~ I

.7

(a) The 1ablc

Qn

l(i)

l(ii)

-I (iii)

2(:t)( i)

!(aXnl

!(b)

l(a)

l(b) -

Secondary Two Express Fin:il Examination 2U 11 Parer One Marking Scheme

Ans,vcr M~rk.ing Scheme

AB =J24 1 + 181 =30cm. Bl

.!_ (21+30XAD)510 2

Ml

AD= 20cm. Al

AC = J20' ~2 1 1 w29cm. Ml EC = 29- 24 5 cm. Al

(Ambiguous case)

A1ter-na1ive :inS\\'Cr I : AreaofBEC

I - SJO - - x 21x20-

2 I 2

x24x l 8 = 84cm2.

Hence, EC 84 ~ 1 ~ 18 w ') 1 cm. 2 3

or

Allernative llOS\Yt r 2: BC' 202 +91 = 481 l!.'C' + 18' BC' EC' = 481 324 157 F.C = 12. 5 cm (3sf)

----

.

17 r,m : 6.8 km 17; 680000 I : 40000. 01

~

lcm 0 4km I cm2 : 0. 16 knl Actual Area

- 3.25x 0. 16 Ml 0.52 km'. Al ~--

-5 pump~ 4 36 nun l pump -+ 180 min 4 pumps-+ 45 min Ml Additional tim~ laken - 45 - 36 = 9 min . Al

(- 2X6)=-12. Bl

(5) - 3(-1)=8 -Bl

l(c}

4

6 ( I)' 6.

.\+ I + =-5, I 2(1- 5x) 4

2(x I 1) I I 2(5x- 1)- 2{5x I) 4 21 ~2 - 1 I 2(5x 1) 4 2x t I I

2(5x -1)"4 4(2.i + 1) = 2(5x- 1) BA ~ 4 = 10x -2 2x 6 x 3

Altcmnhvely, 2(\ 1 1X1 - 5x)+(SA- 1) I

J(~ r- IX1 - s . ) "'4 !Ot' - 8x+2+Sx - 1 I 2( 2sl +10;-if - 4 10t'-3x+ I I

--=-~0.\ 1 ~ 20x-2 11 10t 1 - 12.-+4 SOr' +20.r 2

101 -32x+6=0 s.' 16xi3-0 5. 1Xx-3)=o

I s

or

rcJcctc

(,(hi 4a1 +2ab - 1011 5b .. 211(211 t b)-5(2a +I>)

(2a 1-bX2a -S}.

7(a) 1a(a t 5) -(o -2~a+I) -

1a' 1-350 - (11' - a-2) "

7a2 +35a-a' H1+2

-6a' t36a+2.

7(b) ~y . ..,1 -y' 2a - 3b 4a-6b

l - y 2(2"-3b) - )(

2o - 3h (x I yXx - y) 2

- A+y

8(a)(i) x 7

8()(ii) Menn - 5.1.

8(b)(i)_ w 5.

S(b)(ii) 6 - xl00=30%. 20

9(n){i) Some household~ subscnbe to both broadband 1111cmc1 and cable TV.

\l(a)(1i) II~ A.

9(b)

IO(b) 2x' +4x 60 (2x-t 6Xx- 1)=0 k - ), /r s l

t

Ml Al

Ml Ml Al

Ml

Al

Bl

Bl

Bl

01

131

Bl

Bl

Bl. 131

IC 0 f Symmetry IO(c) I or

ll(a)

ll(b)(i}

x

p

"

Alt r

r

.l+I 2

- I

(5 I I)' =36 . 3(5)- 15.

(11 I t)' - 311 cn1ntivc anS\YCrs:

(11 - 1)1 +11 11 1 - 11 .. 1

II (bXii} Jr ' i+l=l33 k' k - 132 =0 (k 12Xk+11)~ 0 k s 12ork=-ll.

(rejected)

All ow tnal-and-error. -lume of ryrarn1d 12(a) Vo

1 xGx6x6)x6 3 3 6 cm1

12(h) Nu mhcr of beads

13(a)(i) q

3

3 3

" : ~ (3 .1 42Xo. J') 18.268 187 18

--

3.

---

Bl

Bl B l

81-

HI

.

-

Ml

Al

--

Ml

Al

111

I 3(a)(1i) Graph of 2x+3y = 7

. '

I 3(b)

ANG MO KJO SECONDARY SCHOOL FINAL EXAMINATION 2011

SECONDARY TWO EXPRESS

MATHEMATICS PART TWO

Setter: Mdm Leong Cbuin Sia

Fridy

AddutoN1 matC"fl.als. Ans'Cf Paper flectron1c Caleula1ur

7 October 20 II I llOUR IS M INUTES

Gl'\l hPa r I ;,.hc...-ct) ----~---------------

R EAD T HESF. INSTIUJCT IO NS fl!RST

Write your na1nc, clnss and index 11u1n1Jcr in lhc spaces provided on the answer ptlpcr Write your answers and working on 1hu separate answer paper provided. Write in dark blue or black pen on holh side~ of the paper. You may use a pencil for any diagram~ or graphs. Do not use staph~. paper clips. highlighters. glue or correction fluid.

Answer all questions.

Show all your working on the same page ns the rest of the an.-.vcr. Orrnss1on of essential working wrll result rn loss of marks. Cnlculnt

2

3

4

2

Scclion A (22 ma.-ks) Answer ALL the qucsrions

Make m the subject of the following fonnula 2 - m

()

(b)

( a)

(b)

n=-- . 2111 13

Solve rhc inequal ity 3.(-5 < x+ I S 2(x+.!..). 2

Hence, state the small cs1 value of x'.

x y Y c I Expr~s --+ --- - - a .. "i ;1 1rtt\;t1on "'1th

3

5 (a) Given that x = - I is a solution of the equation mx' + (m2 + l)x + 3 = O, tind the possible values of m.

(b) II is given lhal A is directly proportional to r' . When r = 5, A= 500.

(i) (ii)

fonn an equation connercscntcd in the table below.

Nunberof chi ldren I 2 3 4

Number of fa mil ics x 23 y 5

(a) Show thal x -i y ~ 22.

(b) If the mean number of children per family is 1.88, show that x+ 3y = 28 .

(c) Solve lhc s imultaneous equat ions from (a) and (b) 10 find the values of. ::incl ,v.

(d} Find the percentage offomilies with J or more children. (e) Using your answer from (c), state the median.

[31

[2) [I ]

(I l (21

f21 [I) (I]

AMK~S _201 l rv 2E MATHS P2 (Tum Over

,

4

7 Jn lhe figure, WXYZ is a rectangle in which XY = (3.

s

8 Figur" l shows an invened right circular cone with IOp radius 6 cm and height 14.4 cm.

Figure I

(>i) Calculate

14.4 cm

(i) lhe slant height of the cone,

Figure II

(ii) the curved surface area of the cone, leaving your answer in 1erms of Jr.

(b) Water is poured into tltc cone to till up -~of its capacity. Find the volume of water in the cone::, le.aviug your ans,vcr in terms of ff.

(c) Figure II shows a container formed by atlaching a hollow cylinder IQ a11 open hcn1isphcrc. A ll the water in the cone is 00\V p0urcd intv the container

10 figure II. 111c container is tille

6

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

A ball is thrown upwards from the edge of the top of a ven ical building. Its [Tum Over

JlOsition during its flight is represented by the equation h; -x' +9,r ~ 12, wnere It metres is the height of the ball above the ground and x metres is its horizontal distance from the foot o f the building.

(a) Some corresponding values of .r and h arc given in the following table.

x 0 I 2 3 4 5 6 7 8 9

h 1'2 20 26 30 32 32 30 26 20 12

Using a scale of2 cm to I unit, draw a horizontal x-ax is for 0 :S x :S 9.

Using a scale of 4 cm to 5 units, draw a venical h-axis for I 0 5 It 5 35. On your axes, plot the points given in the table and join them w ith a ~111ooth curve.

(h) Use your graph to find

(i) the greatest height reached by the ball,

(ii) how far the ball has travelled horizontally when it first reaches the height of 25 metres.

(c) A tree of height k metres is located 8.4 metres from the foot of the building. Given that the ball pt!S$CS 3 metres above the top of the tree, use yot1r graph to estimate the value of k.

l".nd of Part 2

AM KSS_201 I FY_2E_MA111S_P2

131

f I ]

(I]

r IJ

_Qn I

--

- -

2 a

-

,_

I ,.

I " 3 I

--

....__

1-

'"" 3 b ,_

--

--

7

Secondary Two Express Final Examination 2011 P1>cr Two Marking Scheme

Solutions Marks 2- m

11 ---2m +3

n(2m + 3) = 2 - m -21nn+Jn-... 2-m Ml

2m11+m=2-311 m(2n +1)=2 - 311 Ml

2 - 311 Al 111=--

2n+I

.Or 311 - 2 Ill= -2n-I

I 3x-5

8 ~

4 u P/"\R1or(P1 V R) 1 or (P/"\R)'riP B I

b A = 6, 9, '~- 15. 18, 2 1. 24. 27. 30} B; 41 Ca 1.2.3.4.51

bi BriC =l4l B l bii A r'I B = por{J BI bii i nlAuB) ' ~ 20 B I

5 a When x = - 1,

I m(-1)2 +(m2 +1)(-1) +3= 0 m - 1111 - I ~ 3 = 0

1112 - 111-2 ;;Q MI (m + l)(m - 2) = 0 Ml

1n e- l or 1n e 2 Al

bi A = kr'

- - --

When r = 5 , 11 = 500 -

500 = k(S)' '---

k = 4 Ml A = 4r1 Al

hii -

When A = 180, I 08 = 4r' r =3 fl I

-

6 a x + y + 23 + .s = 50 Bl x + y = 22 (shown)

I b x + 2(23) + 3y + '1(5) = 1.88(50) Ml x+ 46+3y+ 20=94

-

x+3y=28 (shown) Al

c ..:+ y= 22 --------{I) x+3y = 28 -------- (2)

f- Eon 12\ I I ). M l 2y = 6 .v=3 Subs1itutc y ~ 3 into ( l ), x+3 = 22 x= 19 TI1crcforc, x = 19 and y = 3. /\ l

d 16% Bl

AMKSS_201 I J Y _2E_MATllS_112

9

e 2 Bl

7 a I 2 I Arca of /\A/JC --(- X W)( X l')

2 3 J I 2 I Ml

= {(-(3.r)](-(3r+9)J 2 3 3 I 2

(2x)(x+3)

= (x)(x-+ J) or x1 +3x Al

b Arcn ofrcc1ongle = (3x + 9)(3.r) Shud~d region = (3.r + 9)(3x) - (x1 1 3x) M l 80 9x1 +27x-x' - Jx

-I l!O Sx' 1 24.r -o-sx' +24x 80 -~

- I -1''"'"'' " (ShO\\n) Al ..=_j..: o - ~'3x 10 0 ( ' - 2)(x + 5) Ml

\' .. 2 or x=-5 (NA) A l ~ t ti When '=2. -1

l'cnmc1cr = 2{J(2) + 9 + J(2)j - f, - . ~i . ,, - 6' + 14.4:2 Bl -

- -I 15.6cm 81

=--~ "" Curvctl surface area 1rrl I IT X 6 x 15.6 M l ~ 9J.6JT Al

b Volume of\\alcr 5 (I nr' lz) 6 1

-~ 5 I

x n x62 x14.4 Ml

= )(

6 1 -~ 144JT c1n" A l

>----c Lei lhc radius of1he hemisehere be r cm.

Radius ofcvlindcr- rem Hcioh1 of cvlonder = r cm 0=-j Volume of waler in conl.Uner = 144.T ems -

AMKSS_ZUl l FY _2r MAlHS ~2

10

Vol of hcmisnhcrc +Vol of cvlinder = 14411' 2 . Ml m' + m' (1') = I 44tr 3

- 2 r 1 ~r'= \ 44

3 2 ' l- r= l44 3

r' =86.4 Ml r = 4.42 cm 13sl) Al ~ 9 Please refer-to l!raoh in a seoarate file.

a -- correct scale and labellino of axis Bl -- corrects JOints Bl -- smooth cu1ve Bl

bi Max h = 32.25in Bl lacccntable ran"C J2

)v

- ...

.

- ... ; - _]b.1)

Jo

- . )5-

(P\)_._ (.)!iYtcl f (A,ll. . - ~/}j15 1 llAhtll1j1-~ I ~ ~ttt ,m.m - W1 I

' ~ . -. ....... !- ... t ....

.. . -

-

'

- -- -.

_.....B I (,]11) !VI AX n_"' 3.J.. JS '(YI _,f' ( :!:. C 5)

lb11) 'f./-0 lN-(11\.~ (t.01)- BL .. (.1.,) ~ 'b"/,\r ~; J.:' K-4-J I,;:. ! i-"/-

t-J:r ~ \vtt ~ Ii - 3 \l ~ /lt M~-- .Bl

h = --~;1-ih. t I). \ \

'\ \

\ \

\

BEATIY SECONDA RY SCHOOL END-OF-YEAR EXAMINATION 2011

SUBJECT : Mathematics LEVEL : Sec 2 Express

PAPER : 1 DURATION : 1 hour 15 minutes

SETTER : MdmToh. PL DATE : 7 October 2011

I CLASS: ! NAME : I REG NO ;' ~ .................. ........ . .. . ........ .. ... ...............................

READ THESE INSTRUCTIONS FIRST

\\' rite yur name, closs and index numher 1n the sprtces on 1bc cop oflhis page. \\'rite in dark blue or h1ack r>c'" You n1ay use a pencil for any d1ag.ru1ns 01 graphs. Oo 001 u~ ~1aplc~. p.ipcf c liJ)S. highlighters. gh1e or corT~tivn OuiJ.

Ans"'cr all qucstio11s.

(f \VOrking is needed fOr any question, ii n1usc be ~ho\vn \Vi1h the l'.lnswcr. On1ission of essential \vorking 'viii result in loss: of n1arks. You are expected to use a scientific calculator to evaluate cx1>ficiL riuo1cnc.:al cxpr~s.~1011!'.i. If chc degree of accorncy is nol specified in the question. and if the ails,vcr is 001 exact. give the ans\''er IQ three significant figures. d ive an.s,vers in degrees 10 one dccinH1l place. F

3

Answer aU the questions.

I (n) Solve the inequ~1li1y 2(1 - x) < - 6.

(h) Hence write down 1hc smallcsr square number which satisfies 2( I - x) < - 6.

A 11.ttver: (a)

(b) ______ _

l x1 - a Givenlha1 P;--, a

(a) find, in tenns of" the v~luc of P when x- 5a, (b} expressx in tcnns of Panda.

Answer: (a) P *

(b) --------

121

Ill

121

(21

F"r Eram111~

Use

4

(n) Express 540 as a product of its prime factors, giving your answer in index no1ation.

(b) Hence, find the least integer value of q given that 540q is a pe1fcct square.

A11s11rer: (ll) 540 = 121

(b) q ~ ______ _ Ill

4 A bag contains>' red sweets, 3 yellow sweets and I green sweet.

() (b)

Find the value of y given that tbe probability of drawing a red sweet is 3 . 5

Two red sweets arc drawn out of the bag and are not replaced. Find the probability

that the nexi weet clr.1wn will be yellow.

(") y = _______ 121

(h) --------- (21

for i!xomfnt:t

u,,.

5 (n) (b)

Factorise Sxy- I Ox - y + 2.

. x 2 25 S11npl1fy 1 _ .r -2.r-l)

5

121

(b) ____ _ 131

6 A wall has an area of 40 m2. Eight tms of paint :ire needed to coat the wall S lime

7 6

The diagram shows an cquil>1cral triangle f'QR wnh PQ ~ (2x- I) em, QR~ (2y + 3) em and PR = (r + y + 2) cm.

p

x+y+2

Q'---l---l R x + 2y - I

Usmg sm1ultancou.< equation,, find the value of x und of y.

A11swer: \' ---- (41

8

7

Lei c {I, 2, 3, 4, 5, 6, 7, 8, 9 }, A= (x: x is n prime number) and R /> : ' is an odd number} (a) lllu~lralc lhc infonnation in the Venn diagram below.

(b) L1s11hc clcmcnt(s) of ser (A v B)' (c) Find 11(111'\B)

A 11swcr : (b)

(c) ---

121

III

Ill

, .. (},. tu1nl11t

'''"

9

8

In the diagram. MBC is similar 10 AEBD. AD-7 cm,/)/)' 2 cm, BE ~ t:C 3 cm and AC~ 12 cm. /.BDE - 47 and L.BAC = 29".

B

(a) Find /A/IC. (b) Calcululc 1he length of /)Ji.

7cm

3cm

Answer:

A

12cm

c

(11)

(b) /)~;-

111

------ ,.,,, 121

10 Consider two numbers 24 24 - and-- ,

x x+ I . I bcrwccn the numbers is 3,

() show that x' + x - 72 = 0 .

9

where x is a positive integer. If the difference

121 (b) Hence, find the value of x, where x 0 and xis a positive integer.

(b) X G --------- 121

FOr E'

10

11 (a) Expand and simplify (a+ 3)' +(a+ 7)(a - 4). (b) Express os u single fraction

I-~.

12

11

The graph below shows a line/, which crosses the y-axis and x-axis at A and B(- 5, 0) respectively. y

I

B (-5, 0) 0

(a) Given the gradient of line I is 1.5, write down the coordinates of A. (b) Find the cquution of the line I.

Ansver: (a) - --------

(b) ---------

[21

[ l J

For lixo111i11c.

Utt

13

12

Tho diagram shows lhe unifom1 cross-seclion ABCD or a tank. ABCD is a trapezium such that AL) = 35m. BC - I Sm and CD - 29m.111e iank is completely filled with water.

A B

lS "' lllili1llii11f jir,, ~"' iii!!i!/~:;::=::: 29 Ill

D (a) Find the area A/JCD. (b) Water is discharged through an outlet at D al a constant rate. It takes 7 hours to

empty the tank. By letting the length o r the tank be Im or otherwise. !ind lhe time

taken for the water level to fa ll 5 m below AB. Oiv,, your answer in hours and

n1inutes

(a) 121

(b) hours ---

1nint1tes [31

End of Paper J)o nt>t fin-get 10 clu~ck ; 1011r H1ork! :)

Far

13 Answer Key

(a) x < 2 (b) Smallest square number = O

2 (n) 25n-I (b) x =JPa+a

3 (a) 540 = 21 )( 3} x 5 (h) q = 15

4 (n) y 6 (b) 3 P(yellow) = -

8

5 (a) (y - 2)(5x- 1) (h) (x1 5)

(x+J)

6 12 tins

7 .r -5,y=3 8 (a) c

4 2

9 6

8

(b) (AuB)' = {4, 6j (c) 11(A l'"\ 8) 3

14

9 (a} LABC= 104 (b) D=4cm

JO (b) .r-8 or x=-9 (NA)

11 (a) 2a' +9u- 19 (b) 5

x+3

J2 () p=7.5 (b) y = l.5x+1.5

13 (a} AB = 21 (b} I hour 24 minutes

..

BEATTY SECONDARY SCHOOL END-OF-YEAR EXAMINATION 2011

SUBJECT : Mathematics LEVEL : Sec 2 Express

PAPER : 2 DURATION : 1 hour 30 minutes

SEITER : Mr Bernard Lee DATE : 13 Oct 2011

l CLASS : l NAME: I REG NO: ........ ..................................... ....................... . ... ..

READ THESE INSTRUCTIONS FIRST

\\'rite:. your n(lmc;, class and index nun1bcr in Lhc spaces 011 the top of thii:: pttge. \Vrite in dal'k blue or blru;k pen, You Jnay use a pencil for anydiagnuns or gr(lf>hs. Do not use staples, paper clips. higl11igl11cr.;, gluo or COITCCtion Ouid.

Answer nll questions.

rf \\'Ofk.iug is needed for any qucs11011, ii n1ust he shown \vilh !he 30S\VC( Omission of cssc-ntial worki1lg v.ill rcsuh in loss or n1ttrks. Calculnh)rs: should be used uhcrc apprQpria1c. If ihc degree of accuracy is not specified in 1he question, .a11ct if die aus,vcr is not c.'act. give th(! an~v.icr 10 thri'..e significant figures. Give a1'1S\vers 111 degfecs 10 one decnnal ploce For tr, use either your ca1culator valut' or 3.142> unit!SS lh~ qtrcstion requires 1he ans,i,.er in tern1s of

'"

Af the c11d of lhe examination, fasten all your \11ork securely to~cthcr. The 11u1nbcr of m3rks is given in bracke1s [ 1 at the end of eaeh question or 1xu1 question. 111e 101(11 number of n1arks for this p3per is SO.

This paper consists of 2.. printed pages (including this cover page) !'furn over

2

A road of20 km is represented by a 10 cm line on Map A. (n) Express the scale of Map A in the form I : 11. The scale of Map B is I : 50 000.

(2]

(h) What is the length, in cm, of the same road in Map B? 121 (c) A lield is represented by an area or 3 cm' on Map A. What is the area of the

same lield on Map B'?

2 A cone has a volume o1'2592n cm' and a radius of 18 cm. (:i) Calculate the vertical height of the cone. (b) Show that the slam height of the cone is 30 c m.

+ 0

-

-

Cylinder D

' .

' 0 .

: '

Rocket Toy

The cone is cur horiwntally to form Cone /J and f'rustrum C. Cyli nder D of radius 9 cm 1s then placed between Cone /J and Frustrum C to produce a rocket toy. as shO\vn 1n the diagran1.

(3]

121

111

(c) The rocket toy has twice the volume of the original cone. Calculate the height 121 of Cylinder D.

(d) C"lculate the total surface area of the rocket toy.

l Volume of cone = ~ nr' h, Curved surf.lee area of cone = rrrl 1 '

Ill

3

3 A photo fr.une consists of a centre measuring I 0 cm by 15 cm, and a wooden hordcr of thickness .r cm surrounding H. as shown in the figure.

i xcm

)( c '. 15cm

fu JO cm

() Show that the area of the border 1s 4.r' + 50x. 121 (b) Given that the area of the honlcrcquals to the area of the centre, find the 141

valueofA.

4 2 laddc'fs. PQ and A 8 are resting ugnins1 opr>Osllc walls of an al Icy. PQ and A fl are 8 metres and 4 metres above lhc ground rcspcctivdy. Tis 1hc point where the 2 luddc-n; mccl. The diagram b

4

5 The do1 diagram below shows the number of people living in each house on a street.

-1-f- I 1-J-J I 0 1 2 3 4 5 6

No. of people living in each house {a) Sl;ile

(i) the median. (ii) the mode.

(b) Calculate lhc rncM 1lUmbcrofpcoplc living in each house {c) Calculn1e Ute percentage of houses that are not occupied.

6 (a) Show lhal (2x 1 3)2 - {2x + y)(2x-y)- y(y + 3) can be reduced LO 3(4.1 - y + J).

(h) Hence. solve 1hc following sinu~taneous equations. (2.i +3)' - (2x+ y)(2> - y) - y(y+ 3) : 0

4y- 3x=l2

111 111 121 121

141

5

7 The figure below shows o circle of centre 0, with mdius r metres. A and B an: points on the circle such that AH 16 m. M 1s the midpoint of All and Mis on ON such that MN= x meircs.

o, ' ' ' '

' r

' ' ' ' '

A M, x 8 ~ N

-16m ~

(a) B)onsidcriug 60MH. show that " ' - 2r.

6

Answer the whole of this question on the graph paper provided. 8 Mr Ong stood on the roof of a building ond threw a ball upwards. Al time 1 se

Name:

Class: Sec --- --- Expected Grade:

Value-Added Grade:

Review:

Bedok Town Secondary School Challenged to Excel

5 October 2011 Wednesday

Success Through Perseverance

2nd Semester Examination 2011 Mathematics [4016/1]

Paper1 Secondary 2 Express

READ THESE INSTRUCTIONS FIRST Write your name, class and register number 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 staples, paper clips, highlighters, glue or correction fluid.

Answer aU questions.

If working is needed for any question it rnust be shown with the answer.

Omission of essential working will result in loss of marks.

1040 -- 1155hrs 1 hr 15 min

You a.-e expected to use a scientific calculator to evaluate explicit numerical expressions.

If the degree ofaeeuracy is not specified in the question, and it: the answer is not c;xact, give the answer

three significant figures. Give answers in degrees to one decimal place.

'for n, use either your calculator value or 3.142, unless the question requires the answer in tcnns of n.

At the end of the examination, fasten all work securely together.

'Ilic number of marks is given in brackets [] at the end of each question or part question. The total of the marks for this paper is 50.

This question paper consists of t) printed pages.

Setter's Name: Mdm Yeo Liew ctieng

Compound interesr

/1tfens11ra1ion

Trigo110111et1J'

Sratistics

2

il1athematical Formulae

Curved surface area of a cone ; wl

Surface area of a sphere = 4m 2

1 Volume ofa cone ~ - nr2h 3

. I 1 h 4 I Voumeo asp ere = 1rr 3

Arca ofa triangle ABC - .!.ahsin C 2

Arc length = rB , whereO is Ill radians

Sector area ~ .!.,.29, whereB is in radians 2

a b c - - = - = --sin A sin R sin C

a' - b1 +c' - 2hccos A

~'i Mean = _,_,,_ .. '.f

Standard deviation = / 'f.Jx - "i,fx r-; -( . )2 ~ 4( 4!

I.

2.

3

Answer all the questions.

0.325 Evaluate ~ ,

-.V20.5 - 2.74

(a) showing all the figures on your calculator display, (b) giving your answer correct to 2 significant figures .

. .

Answer: (a) ______ _

(b) - --------(a) Write lhe following numbers in descending order

2.35, 2.335 '2.:l5' 2.J.5' 2;')

(b) State the largest integer which satisfy 2 x 5 3_. 47 3

Answer:

(a) _ _ ,_, __ , __ , _ _ (2] (b) _________ _ (2)

20l l -SA2-2E F.M-l'I .doc

Fur xcuni

(h;

5

5. (a) Sublracl lhe sum of 3x3 t- 7 x - 8 and 9.r2 - 6x + 12 from 8x3 - 5x2 + 17 x - 21 . (b) Factorise completely

(i) 8a3 - 72ab2, (ii) ;~.x - 12 .

Answer: (a) _ _ _____ _

(bi) __

(bii) _ _ _

201 1-S/\2-2E-EM-1'1.doc

(3) (2)

(I)

Fo Exa11

6

6. In the diagram, find angles x and y. State your reasons clearly for your working.

Answer:

(a) x ~ ------ - 0 (2]

(b)y - 0(2]

7. (a) London time is 7 hours behind Singapore time. A non-stop flight from London to Singapore is scheduled to take 13 hours and 29 minutes. If the flight is to arrive in

Singapore on Saturday at 17 18 Singapore time, find the departure day and time

of the flight in London time.

(b) Given y is inversely proportional to (x+ I). lfy ~ 7 when x = 4, find (i) the equation relating x and y, (ii) the value ofy when x = 2.5.

Answer:

(a) ________ _ (2}

(bi) - - - ----- ---- l2]

(bii) ---------- (1}

?.O I l -SA2-2E-J::M-Pl.do

7

8_ Solve the following pair of simultaneous equations.

5x - Gy " 27

2y = 3x- IJ

Answer:

x - - --------

y= _ (3)

9. A right circular cone has a curved surface area of 136 cm2. Given the radius

of cone is 5 cm, find

(a) the slant length, /,and (b) the height of the cone, h.

201 l-SA2-2-LM-Pl.doc

Q _____ ___ _ 5

Answer: (a} ________ cm (2)

(b) ________ cm [2)

Fo.

8

I 0. ln the year 2009, Sandra earned 20% more than what she earned in 2008. In 20 I 0, she earned 15% more than what she earned in 2009.

(a) By letting $x to he the amount Sandra earned in 2008, express in terms of x, the amount Sandra earned in 2010.

(h) Calculate the total percentage increase in her earnings from 2008 to 2010.

Answer: (a)$ ____ _

--- [2) (b) _________ % [2]

11. In the diagrams shown below PQRS = J"UVS. L.STU = 113, RS = l 8 cm, QR= 12 cm, PS - 9 cm, / PSN= 62 and L.QRS= 74. Find (a) (b) (c) (d)

the length of SV,

the length of l'V, L.PQR, L.QP/I.

20 I 1-SA2-2E-EM-P I.doc

R

12cm

Q

Ans,ver:

(a)

(b)

(c)

( d)

T

cm [ 1 J

cm [ I ]

o [I ]

___

0 11 1

FfJr E\"Ullll

Us

12.

9

The following data shows the number of hours 24 students of a class spent studying per day.

4 3 4 6 I 4 0 5 ~ .> 4 4 4 5 6

0 3 4 0 4 0 3 3

(a) Using the grid below, draw a dot diagram to represent the above data. {2]

I-

(b) What is the modal number of hours the students spent srudying" (c) Calculate the mean number of hours the students spent studying. (d) If the above data was presented on a pie chart, what is the size of the angle that

represents the number of students who study at least 3 hours a day.

(c) What is the probability of a student studying 4 hours a day')

Answer:

(b), __ _:_ ___ _ hours [l J

(c) hours (I)

([I} (c), _ _ _ _____ _

ENO OF PAPER

20 t J-SA2-2E-EM-P I.doc

Fo1 E.ta111.

U:

Class: Sec ___ __ _ Expecled Grade:

- ----

Value-Added Grade:

Re1tlew:

Bedok Town Secondary School Challenged to Excel

7 October 2011 Frida y

Success Through Perseverance

2nd Semester Examination 2011 Mathematics [4016/2]

Paper2 Secondary 2 Express

Ri,;A 0 THESE INSTRUCTIONS Fl RST

Write your name, class and register number 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 1101 use staples, paper dips, highlighters. glue or correction fluid .

Answer all questions.

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

Ca cul a tor.. should be used where appropriate.

0930 - 1045 hrs 1hr15 mins

If the degree of accuracy is not specified in the question, and if the answer 1s nol exact, give the answer

three significant figures. (jive an~wcrs in degrees to one decimal place. For n, use either your calculutor va lue or 3. 142, unless the question requires the answer in tenns of n.

At the end of the examination, fasten ull work securely together.

The number of marks is given in brackets r J al the end of each question or part question. The total of the marks for this paper is 50.

This queslion paper consists of 6 printed pages.

Setter's Name: Mdm Yeo Liew Cheng

Compound interesr

/1tfens11ra1ion

Trigo110111et1J'

Sratistics

2

il1athematical Formulae

Curved surface area of a cone ; wl

Surface area of a sphere = 4m 2

1 Volume ofa cone ~ - nr2h 3

. I 1 h 4 I Voumeo asp ere = 1rr 3

Arca ofa triangle ABC - .!.ahsin C 2

Arc length = rB , whereO is Ill radians

Sector area ~ .!.,.29, whereB is in radians 2

a b c - - = - = --sin A sin R sin C

a' - b1 +c' - 2hccos A

~'i Mean = _,_,,_ .. '.f

Standard deviation = / 'f.Jx - "i,fx r-; -( . )2 ~ 4( 4!

l. (a) Factorise completely

(i) 2x2 + 6x,

(b)

(ii) 2x 2 -18.

s rf 2x2 +6x imp i Y 2x2 -18 .

J

Answer all the questions.

(c) (i) 2x2

.l.6x Make x the subject of y = 2

2x - 18 (ii) Hence, find the value of x when y = 5.

(d) The masses of 12 bags of potatoes arc shown in the stem-and-leaf diagram below.

(i) (ii)

Stem Leaf

0 7

3

9

5 6

2 0 5 3 4 7

6

Key: 0 17 means 0.7 kg.

Calculate the mean mass of the bags or apples. Find the median mass of the bags of apples.

8

[I J (2)

( l J

[3]

[l]

(2) [l]

2. It is given that. f>- { lettrs in the word 'examinations' }, A= {letters in the word 'taxation' } and B - {letters in the word 'extension'}. (a) List the elt::ments of F:, A and B. (b) List the clements of AuB and Ar>B. (e) Represent the given set using a Vem1 diagram. (d) lf a letter is picked at random, what is the probability that the letter

(i) is found in both set A and B, (ii) is found in A hut not in B?

201 I SA2-2E-EM-l'2.doc

(3] f2] [21

[I] [I]

3. The diagram below shows a trapezoidal plot of land such that AB = (x + 4) m, !JC ~ ( 11 - 2x) m, CD = (3x + l) m and AD = (3x - 5) m.

(x+4) m

{3x- 5) m

D (3x +I) m c

(a) Write, without expanding, an expression, in tenns ofx, for the area ofirapezimn ABCD.

(b) Given that the area of the trapezium is 34 m2, fonn an equation and show that it [I]

reduces to 12x1 - 5x - 93 = 0. 121

(c) Solve 12x2 - 5x - 93 = 0, and hence state the leni,>th of BC. (3] ( d) The owner of the land wants to fence up the area. The fencing costs$ 89.00 perm

run. Calculate the total cost the owner has to pay for the installation. [2] ( e) This area of land is plotted onto a map with a scale of l: 200. What would be the

area of this land on the map in crn2? [2]

2011 -SA2-2E-EM-P2.doc

5

4. (a) The diagram below shows the base of a righl regular hexagonal pyramid such CD = 6 cm and GJ-1 = 5.2 cm.

A B

' ' ' '\G.'

F --------:t:--- .. ---- c: '. ,

' . '

:' :s:2 c , . '

, '

11

(i) Cal~ulatc the base area of the. pyrnmid. f I J (ii) Given that the height of the pyramid is 7 cm, find the volume oflhe PJ~amid. f2] (iii) This solid pyramid is melted down and moulded into small spherical halls of

diameter 4 cm. Show that the maximum number of whole balls that can be made is6. (3]

(b) /\.sheet of coloured paper has length 47 cm and width 35 cm. What is the maximum number of 3 cm hy 3 cm whole squares that can be cut from this sheet of paper? [2)

-~--------------

201 l -SA2 -2F.- F.M-P2.doc

6

5. Answer the whole of this question on a piece of graph paper.

The variables x and y are connected by the equation y "' -x1 - x + 6.

Some corresponding values ofx andy arc shown in the table below:

I : I ~ I ~ I ~ 1 -~~- 1 : 1->I :] ~. I (a) Calculate the value of a and of b. 121 (h) Using a scale ot2 cm to I unit on the x-axis and I cm to I unit on they-axis,

draw the graph of y = ~x2 - x -1 6 for values of x in the range - 4 $ x ~ 3 . (31 (c) On your graph, draw and state the equation of the line of symmetry for this

curve. [2] (d) Use your graph to find the values ofx wheny = -2. (2) (c) On the same graph, draw the line y = I - 2x . (2) (I) Using your graph drawn in pa1t (e), state the solutions of - x 2 - x + 6 = I - 2x. (11

End of Paper

20 I l -SA2-2F.-F.M-P2.doc

Answers

lai . 2x(x + 3) 2(x+3Xx - 3) b. x II. x - 3

3y ii. 3 .75 di. I. 925 kg x= -- 11. y-l

ci.

2a. b.

b. = {e,x,a,111,i,n,t,o,s} , .11 = {r,a,x,i,0,11} , B = {e,.x,t,n,s, i,o} Au 8 = {t,a,x,i,o,n,e,s}, AnB = {t,x,i,o,n}

di. 5 l II.

3a. 9 I (3x - 5X4x+5) 2

d. $2314 4ai. 93.6 cm2

11. 11.

9

c.

8.5 cm2 218.4 cm3

31 3 x= - - ~cm 12 ' . ' .

b. 165

l.7kg

c:a_s_s __ ~l_F_u_n_N_a_m_e ________ ~-----~' -ln_d_e_x_N_u_m_b_e_r _ __ _

>- ,

-, "" l:>o\,ven I l>elieve, therefore I arn

END OF YEAR EXAMINATION 2011 0

MATHEMATICS PAPER 1 Secondary 2 Express

11 October 2011

4016~01 j. 1 hour 15 min

-----

INSTRUCTIONS TO CANDIDATES

Write your name, class and index number on all the work you hand in. Write in dark blue or black pen on the question paper. Answer all the questions. Write your answers and working on the space provided.

l

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. f At the end of the test, fasten all your work securely together.

INFORMATION FOR CANDIDATES

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 50. The use of electronic calculators is allowed in this paper. You are reminded of the need for clear presentation in your answers.

DO NOT OPEN THIS PAPER UNTIL YOU ARE TOLD TO DO $0

For Examiner's Use

This document consists of.!!. printed pages, including this cover page. Setter: Miss Melissa Chong

l

I .

ELECTRONIC CALCU LATORS ARE ALLOWED TO BE USED IN THIS PAPRR.

In the figure, if All is para! lei to CD, ~11_ = ~ and AE = 9 cm, calculate CE. CD 3 (The diagram is not drawn to scale.)

Ans: CE -= _ _ _ ___ cm f2)

Solve the simultaneous equation using the elimination method only.

5y - 7.\=-38 5x + 2 ~-Sy

2

Ans: x = .Y " -- [3 J

Nothing i~ to be wrillcn oil tlus margin.

3 p

x-2

R~---------__LJ Q x+ S

The diagram shows t\J>QR in which L.PQR = 90, PQ - (x 2,) cm,

QR = (x + 5) cm and PR-= (2x - I) cm. (a) Using Pythagoras' Theorem, fonn an equation in x and show Lhat it

reduces to x 2 - Sx - 14=0. (h) I Jenee, ealculnte the perimeter and Area of t!J'QR .

f2]

Ans: (b) Perimeter = _____ cm Arca = ___ _ cm' (41

3

Notl!iff8 is to Ix. written Ol'l ll1 tJ margin,

4 (a) Ex.press in set notation, the set represented by the shaded area in terms of A and B.

Ans: (a) I I]

(b) On the Venn diagram shown below, shade the set {Au B)'v(A !l B). [I j f;

5 Al a strawberry farm, the number of strawberries Sus ie gathered over the past I 0 days are as follows 39, 37, 35, 48, 47, 44, 39, 44, 35, 44. (a) Construct a stem and leaf diagram to represent the above data. f2] (h) Fincl the median of this distribution

Ans: (b) Median ~ _ _ ___ _ _ t21 I

4

Norki.rig u to IN '-'t'iuen C)n rlru marg1'n.

6.

/

/ /

- .. ,. .

\' .....

\ , '

. '\ '

.-

The diagram shows a solid made up of a hemisphere, a cone and a right cylinder. The radii or the hemisphere and the cone are 12 cm each and the cylimler has a radius of 4 cm. The heights of both the cylinder and the cone are 16 cm.

(a) Find the volume of the solid. (b) Find the total surface area of the solid.

Round both your ans wers off to 2 decimal places.

Ans: (a) _ _______ cm3 [4)

(b) _ _ ~ _ __ cm2 LSJ

5

N

7. It is given thaty is inversely proportional toV~. When x = 27,y - 12. (a) Find the equation eonnectingx and y. (b) Find the value of x when y ~ 7.2.

(a) _ _ _ _ _ ___ _

(b) ___ _

8. 6 cards numbered 1, 3, 4, 5. 7 and 9 are placed into a bag. A card is then drawn at random from the bag. Find the probability that the number on the card dt :iwn is (a) a 4, (b) an even number, ( e) a prime number, (d) greater than 9.

[2)

L2J

Ans: (a) _ ____ _ -_. - (1]

(b) _ ___ _

(c)

(d) _ _ _ _ _

6

llJ (1]

II J

1Wwhing i> tu bt l'.d11e" ou rl1tJ margm.

9. The graph of y = (x + h)(2- x), where Ir is a constant, cuts the x-axis at B and C. Tt cuts the y-axis at A(O, l 0).

(a) Show that the value of Ji is S. [ l] (b) Write down the CoQrdinal~ of 8. (c) J\ line parallel to AB passes through C. Find the equation of this line.

(b) '-- --' ___ __, (c) _ _____ _

7

(2]

131

Nothing H. to b. wnl/~u on tl1l'S mU~ffl

10.

11.

l 3x - 2 3 . gl fi . Express -- + 1 - --1 as a sm e ract1on. xd 3x 47x - 6 9-x

2 (a) Solve--x + 2

x_ = I. x 13

Ans:-- ---- -----

(b)(i) Factorise 2x1 + 13x + 15.

(ii) Hence, write down two factors of21 315.

Ans: (a) __

(b)(i), ___ _ _ _

(b)(ii) END OF PAPER

8

[41

[J I [ 1]

12]

NtJllr"'X 11 to bt KTIU('ff OfJ t#iiS

'""'~"'

._j c_i_a_ss _ _ _.I Full Name

_> - '-..

--., ~ ' .I" b(. \). ! ( '" ') ) /V - JI.

I bcltcv

RLECTRONIC CALCULATORS ARE ALLOWED TO 8 USED IN THIS PAPER.

In the figure, if AB is parallel to CD, AB = ~ and AE = 9 cm, calculate CE. CD 3

(The diagram is not drawn to scale.)

Triangle ABE is similar to Triangle CDE. AB 4 . - = -

CD 3

3 p

.x - 2

R ..::;__~~~~~~~~~-LIQ i\' + 5

The diagram shows t;.PQR in which L PQR = 90, PQ = (x - 2) cm,

QR = (x t 5)cmandPR= (2x - l)cm. (a) Using Pythagoras' Theorem. fonn an equation in x and show lhat it [2]

reduce..~ to x 2 - 5x - 14 = 0 . (b) 1 lcnce, calculate lhc perimeter nnd area ofM'QN .

(t+S)'+(x - 2)2 - (2x-l)2 IMiJ x ' + I Ox 1 25 1 x 2 4x 1- 4 = 4x1 4x 1 I

(a) 2x 2 l l0x +28 '-' 0 2x 2 -lOx - 28-0

' ' - 5x-14 = O(show11)EJ

(2.\ - 14)(x I 2)= 0 2x - 14 =0

(b) 2 .. - 14 x = 7

OR .\.11 x~ 2 0 x - 2(rejected) ~ Perimeter - 2(7)-1 1(715) 1 (7-2) =30cmLJ

Arca Y, x (7+5) x (7-2) = Yi x 12 x 5 - 30cm2 ~-]

Ans: (h) Perimeter _ ___ _ cm Area = ___ _ cm' [41 l

3

,\'olhmx is to f wrifu:n.on thi,f lttOl"gi ll

4

5

(a) Express in set notation, the set represented by the shaded area in terms of A and B.

/\ns: (a) _ _ _ AnB' _ _ _ _ _ _ [ I )

(b) 011 the Venn diagram shown below, shade the set (A v B)V(/I n 8). [ I) t;' __ -----::: ______

A

Al a strawberry fann , the number of strawberries Susie gathered over the past JO days arc as follows 39, 37. 35, 48, 47, 44, 39, 44. 35, 44. (a) Construct a stem and leaf diagram to represent the above data. (b) Find the median or this distribution

(a} Stern Leaf

3 4

5 5 7 9 9 4 4 4 7 8

Key: 3j5 represents 35 ~ )~

(b) Median = (39+44) / 2 - 83 I { MI l - 41.5 I I Al

4

[2]

Nothmg is tu Ix wnlftn on ll1b' rnarxin.

6. Ans: (b) Median ~ ------ (2J

,; .....

/ ' ' \

/// \,\. ( ) l ~ ... .. /

'----... --r--!

The diagram shows a solid made up of a hemisphere, a cone and a right cylinder. The radii of the hemisphere and the cone are 12 cm ench and the cylinder has a radius of 4 cm. The heights of both the cylinder and the cone arc 16 cm.

(a) Find the volume of the solid. (b) Find the total surface area of the solid.

Round both your answers off to 2 decimal places.

I 2 I 4 J R (a) Volume= - tr{l2)1 (16)+tr(4) {16)+ - x - tr(l2) =6836. 1 Jcm' (2dp) Al ~ '-;==-, .J ~ -

~ ~ ~J lb) Let the s lanted height of the cone be I cm. f 127 + 162 ,,, .. 400

I 20 G ~'Ar- ~ ' tr(12)(20)+2n(4){16)+ 1 x4tr( l2) 7 +2;r(12 1 - 42)

Total surface area = 2 ~ = 2865. 13cm'(2dp) ~

Ans: (a) - ----- cm3 (4)

(b) _ ______ cm2 l5J

5

No11tmx if rob. nll~lt Oil lhis """R'"

II is given thal y is inversely proportional to !J x. When x = 27, y - I 2. (a) Find the equation conncctingx andy. (b) Find the value ofx wheny = 7.2.

(a)y(Vx) - k G 12(V27>= k Therefore k - 12 x 3 = 36 v('Jx )- 360 (b) 7.2(Vx )= 36 v;_5G x -1250

(a)

(b) __ _

8. (l cards numbered I, 3, 4, 5, 7 and 9 are placed into a bag. A car

9. The graph of y = (~ h )(2 - x) , where h is a constant, cuts the x-axis at B and C. It cuts the y-axis at A(O, I 0).

y

(a) Show that the value of h is s: [ 1 I (b) Write down the coordinates of B. (c) A line parallel to AR passes through C. Find the equation of this line.

(a) Subst. (0, I 0) into the equation.

1 o -co + h)(2 - oG l0 - 2h h = 5 (shown)

(b) y = (x ~ 5)(2 - x) Subst. y - 0 into the equation. G O =

10.

11.

I 3x - 2 3 . I r Express ---1 1 - --1 as a sing c iracllon. x+3 3x +1x - 6 9 x I 3x - 2 3

--+ - -x+3 3x2 ~7x - 6 9 - x 2

I 3x - 2 3 - --+

x+J Q,-l)JJJ}, GI I I 3

= + x+3 x+3 (3+x)(3-x)

_ (3-x)+(3 - x) - 3 [ I - Ml (3 + x)(3 - x).

3 -2x = (3 -tx)(3 - x) 0

2 x (a) Solve - = 1 . X+2 A+)

(b)(i) Factorise 2x2 -1 I 3x -t 15.

An~: ___ __ ---- - --

(ii) Hence, write down two factors of 21 3 15. 2 x -- - - - = I x+2 x +J 2(x 1 3) - x(x-t 2) = 1 (x+2)(x+3) l?iJ

- x2 + 6 = I

x +5x+6 (a) x 2 ~6 = A 2 +5x+6

-2x 2 -5x O G x(- 2x - 5) - 0 x =O

OR -2x- 5 = 0 -2x = 5 x: -2.5 (bXi) 2x7 + 13x + 15 = (2x+ 3)(x + 5) 0 (ii) Let x be 100.

2(100)2 + 13(100) + 15 = 21 315 = (200 ;- 3)(100 + 5) 0 The two factors are 203 and l 05. 0

ENO OF PAPER

8

[4}

No11J1111,t11ol "'-l'fllen Oft Jlus

mcl~'"

Paper 2

fo F..xand,,er's 3. ""

.

for The number of hours per week spent in doing Mathematics homework by some pupils is shown in the table below

No of hours per week 5 6

Frequency 6 10

(a) Write down the largest possible value of x if the mode is 7. ( b) Write down the value ofx if the median is 6.5. ( c) Calculate the value ofx if the mean is 7.

7 8 II x

Answer ( a) _ _I I I (b) ___ [ I) (c) ___ [2)

4. (a) Factori7.e completely 471rl/r + 2m2 ,

I 'l

( b) Solve the simultaneous equations 5x - 6 y = 27 and 4x - 2y = 16 by substitution method.

Answer (a) _ ________ _ [11 (b)x - ___ ,y-__ _ [3]

3

, 6.

I I ! i

Given that a= J, (a) find the value of a 2 if b =I , c = ! and d = 5,

4 ( b ) express b in terms of a, c and d.

Answer (a)--- - -- - [I J (b) _ ____ [3J

/\ 13 m wire connects two poles of different heights. The height of the taller pole is equal to the perpendicular distance between the two poles: If the height of the shorter pole is 7 m, find the height of the taller pole.

?m

Answer ____ m [ 4]

4

7. Diagram I shows a pencil. It is made up of a cylinder and a cone. The cylinder has a diameterof0.7 cm and height of 15 cm. The cone has a diameter of.0.7 cm and height of2 cm. Take tr = 3.142. ( a } Calculate the volume of the penci l.

Diagram I

Answer ( a ) -- __ cm.Ir 3 J

Diagram II ~hows twelve of these pencils, which just fit into a box.

Diagram n

( b) Show that the volumeofthc box is 99.96 cm3

( c ) Calculate the percentage of the volume of the box that is not occupied by the pencils.

(2]

Answer ( c) _ ___ % ( 2 ]

5

F F:,om1r..er"s 8. Express 2 3x as a single fraction in its simplest form. "" x 3

9. Solve the followir1g by factorization. (a) x' 2x

Answer __ f31

Answer (a) x = _ ___ _ [ 2)

( b) a(2a - 7)= 30

An.\wer ( b) a - --- --- - [ 4 l

10. Answer the whole of this question on a sheet of g.r>lph paper.

( a) Given that y " 4 - 3x - 2x2 , copy and complete the following table. [ 2 )

B I : ~ j1--2=.2---1-- .:..l---1_..:~'--+--_.:..1=====~2=~ ( b) Using a scale of2 cm t-0 l unit on the x-axis and l cm to l unit on they-axis, draw

the graph of y = 4 - 3x - 2x' for - 3 !> x :> 2. [ 3 ) ( c ) Write down the value(s) of x when

( i) y = 0 and (ii) y = 4 respectively.

( d) Find the equation of the line of symmetry of the curve. ( c) On the same axes, draw the graph of y = x ~ I . ( f) Hence, tin

Fw F.xaminer ':; I. A container has 80 markers, some of which are pink, some are yellow and the rest are

blue. A marker is drawn at random from the container. "Jbe probability of drawing a 1 I

pink marker is JO and the probability of drawing a blue marker is 8. Find the (a) number of yellow markers intbe.container, ( b) the munbcr of yellow markers that needs to be removed from the container so that

the probability of drawing a yellow marker from the remaining markers will be 0.75.

(a) No. of yellow markers= 80x 1---- ) ( I I'

. 10 8, 3

= 80x -4

= 62 [ A 1 ) ( b ) Let x be the no. of yellow markers being removed.

62 - x 3 80 - x 4

240 - 3x = 248 - 4x x=S [Al]

Answer (a ) _ 6_2 __ ( I l (b)~ [ I J

2. (a) In the space provided, draw the Venn diagram to represent two sets A and B such that An B = A . [ I J ((--)-A~

( b ) i; = { x : x is an integer , 4 $ x $ 14 } T = ( x : xis divisible by 2} F = { x: xis divisible by 5}

~~-- / -~--~-

( i) Draw a Venn diagram to illustrate this information. t

1 mark if one of the sets contain the correct elements

El y~-----46~ I t 5 10 s 12 ) I \____ t4 / l - . --79'"11 13.

( ii ) List the clements of the set (F v T)' . (iii) Write down n(T n F'):

Answer ( b ) ( ii ) (Fu Tf = { _2, ~-'-"-'11=-=-1-=-3 ___ _ (iii) _5 __

2

[ 2 J

) [ I J

[ I J

f.:Sautiner 115('

For l'w:1i1:er '.f 3. /ll('

The number of hours per week spent in doing Mathematics homework by some pupils is shown in the table below.

No of hours per week 5 6 7 8 Frequency 6 10 II x

(a) Write dovn1 the largest possible value ofx if the mode is 7. ( b) Write down the value of x if the median is 6.5. ( c) Calculate the value of x if the mean is 7.

( b ) 10 + x = 16 - 1

( c )

= 15 x = 5 (Al ]

5x6+6x l0+7"xll+8x = 7 [Ml] 6 + JO+ll+x

30 + 60 + 77 + 8x = 7 27+ x

167 ~~x= 7 27+ x

167 +Bx= 189 + 7x x = 22 [Al )

Answer ( a) _1_0 __ [ I J (b) _ 5 _ _ [ I)

(c) 22 [2)

4. (a) Factorize completely 4m'h + 2m2 , ( b) Solve the simultaneot1s equations 5x - 6y = 27 and 4x - 2y = 16 by substitution

method. ( b ) 5x - 6y = 27 . . . (!)

4x - 2y = 16 . . . @ fr. : 2x - y = 8

2 8 17'> y ~ x - "-"?/ subst.@ into (!) : 5x - 6 (2x - 8) = 27

5x - 12x + 48 = 27 - 7x = - 21

[Ml ]

x=3 ... (4) [Al) subst.@ into @ : y = 2 x 3 - 8

= 6 - 8 = - 2 [Al]

Answer (a) ~nr2(_~h + !) (b)x = _ 3 ___ ,y ~ - 2

3

[ I ]

[ 3]

For E:wmincr's

Fo, I F..'ff'"'"U'I'',( t 5. 11;.lf

I (a ) find the value of a2 if b = I , c = - and d = 5, 4

( b ) express b in tenns of a. c and d. (a) 02 =b-c

( b)

b+d 1- 1

= 4

1+5 3 =~

6

= ~ [Al] 2 b-c

a =--b+d

a2b + a2d = b - c a2b - b = - a2 d - c

b ( a2 - 1 } = - a2d - c -a2d-c b=---

a' - I

[Ml] [Ml]

(Al]

I Answer (a) _::,.8 _~--- [ 1 J

- a d- c b=---(b) __ __..a~2~-~1 __ [3}

6. A 13 m w;re connects two poles of different heights. The height of the taller pole is cyual to the perpendicular dis tance between the two poles. If the height of the shorter role is 7 m, find the height o f the taller pole.

Let the ht. of the taller pole be x metres.

( x - 7 )2 + x z = 137 ( Pythagoras' thm ) x2 - 14x + 49 + x2 : 169

2x2 - 14x - 120 = 0 x2 - 7x- 60 = 0

( x + 5 ) ( x - 12 ) = 0 x = - 5 ( rejected ) or 12

4

[ Ml]

[Ml ]

[Ml] [Al) An~wer 12

7m

__ m [ 4]

E.1.urmner~

Fr~ '"''''"'"''/''j 7. U,\('

l>iagram I shows a pencil. It is made up of a cylinder and a cone. The cylinder has a diameter of0.7 cm and height of 15 cm. The cone has a diameter of.0.7 cm and height of2 cm. Take tr= 3.142. (a) Calculate lhe volume of the pencil.

(0 7)' I (0 7)1 Volume = tr~ xl5+ J ;rrx ~ x2 = l.8375tr + 0.081611"

= 1.9t9t6tr

= 6.0300216 "' 6.03 cm3 ( 3 s. f.)

Diagram I

Answer(a) 6.03

Diagram II shows twelve of these pencils, which just lit into a box.

( h) Show that the Vlllume of the box is 99.96 cm3 .

Volume= ( 6 x 0 .7) x ( 2 x 0.7) x ( 15 + 2) = 4.2 x 1.4 x 17 = 99.96 cm1 (Shown)

Diagram II

( c ) Calculate the percentage of the volume of the box that is not occupied by the pencils.

'Yo required= 99.96 - 12x6.03 x!OO"/o 99.96

: 99.96 72.36 x I OO% 99.96

= 27

6 x 100%

99.96 = 27.611%

r 21

:.: 27.6 'Yo ( 3 S. f. ) Answer ( c) 27.6 % [2]

5

For fuomincr '. ''"

I or 1:~cm1 'll"' 'r 8. ,,,,,. Express 2 - 3x as a single fraction in its simplest fonn.

x 3

2(x - 3) - 3x = 2x - 6-3x [ M2 J x 3 x - 3

- x - 6 =--

x - 3

9. Solve the following by factorization. (a) x1 = 2x

(a ) x2 - 2x = 0 ( Ml ] x(x-2) =0 x = 0 or 2 (Al ]

(Al ] -x-6

A11swer x - 3 { 3 J

Answer (a) x _ 0 o_: 2 __ [ 2 )

(b) a{2a -7) = 30 ( b) 2oz - 7a = 30

2a7 - 7a - 30 = 0 ( a - 6 )( 2o + 5 ) = 0

o = 6 or - 2.5

[Ml ) [Ml] (Ml] (Al]

Amwer ( b) a - 6 or - 2.5 [ 4 l

I 0. Answer the whole of this question 011 a sheet of graph paper.

(a) Given that y = 4 - 3x - 2x1 , copy and complete the followi ng table. [ 2 J

I - I

2

( b) Using a scale of2 cm lo I unit on thcx-axis and I cm to I unit on they-axis, draw the graph of y = 4 - 3x - 2x1 for - 3 ::; x :>: 2. [ 3 ]

( c) W1ite down the value(s) of x when ( i) y - O and ( ii ) y = 4 respectively.

( d ) Find the equation of the line of symmetry of the curve. ( c) On the same axes, draw the graph of y = x ~ l . ( f) Hence, find the solution of 4 - 3x- 2x2 = x +I.

6

{ I J ( J J [ I l ( I J [ 2 J

F.XOJtl(ltf'T '.

!- - ..---, -r---r ' ' 'I .';> 1~ -r. 1-3 I - 1 j -/ i () i t' ; L ' ! ...!

b: ____ IRogNo -1 Clm 2E_ ~fl ..... ~~

BUKIT BA TOK SECONDARY SCHOOL

SECOND SEMESTRAl EXAMINATION 2011 - 11111 IAIK

UtUt llllll Seoondary Two Express

MATHEMATICS Part I 11 Oct 2011

1015-11 15

Candidates answer on the Question Paper

1 hour

READ THESE INSTRUCTIONS FIRST

Write your name, register number and class on this cover page. Write in dark blue or black pen in the spaces provided on the Question Paper. You may use a pencil for any diagrams or graphs. Do not use staples, paper cJips, highlighters, glue or correction fluid.

Answer all questions. The number of marks is given in brackets f ) at the end of each question or p.art question. The total number of marks for this paper is 40.

If working is needed for any question, 1t must be shown in the space" hclow ll1

S.i Z ZUIJ 11 t:xpress :lla1lislf'or; J

ANSWER Al .L TllE QUESTIONS ( 40 marks )

I. Oiven thatx2 + y 2 = 25 andxy = 12, lind the v:tlueof(x+ y)z.

Ans: _________ [2]

2. Factorise completely x3 - 2x2 + 2x - 4.

Ans: _________ (2]

3. If y is directly proportional to .JX and if y = 6 wh

4. Simplify 3b1ac' 18 a2b

(a) _ 2_c_ + c2 X b4 a3' y z _ ,,

(b) y2+1y l 3

5. If p = J s , y-2S

(a) cxprC$S sin tem1s of p a nd y ,

,~A .l 11111 t l brt3l /./~JJlt5 /Part I

A ns: (a)

(b) _ -

_ [2]

- [2]

(h) find the value of s when p = J3 and y = -1 .

Ans: (a) _ _ _ _ _ _ [3]

(b) _ _ _ _ _ _ [1)

Hab1Lt of Mind: Strivi11gfor accnrac,1 and pri'rision

I 6. In 1he figure below, liAFC is similar to liBDC. AC = 20 cm, BC = 8 3 cm mid FC = 3 cm. Find the length of AD.

Ans: _ _____ [1J

HahiL~ qrMlnd: StriiingfOr accurncy a1td pre

7. Solve 1hc following cqua1ions: a) 3x l - 14x = -8 b) 1 + _s_ = _ B_

X~ I zl-1

Hubits of Mimi. Sit fri11gfnr accuracy and precision

SAl 101112 F...xpre'O !tfotlt.s I Por1 I

Ans: a) _ _ _ _ _ _ _ [2)

b) _ _ ____ [3)

5

SAl 10! I ll E.r.pre . .._., .A1atliJ I l'nrr I

8. A stmight line l has a gradient of2 and passes through the point (3, 7). a) f ind the equation of line / ..

b) Complete the following table of values for line L.

F x - 1 0 2

y s

c) In the axes below, the line y = x + 2 is clrnwn. By drawing line l on the same axes, find the coordinates of the point of intersection of y = x + 2 and line/,.

ljl+r-~++ -r ;_ ~ : ; ~"" H-t- ._. j i ~-~ ! ' i I l - H !/; . I I I l ~ ~ ....-- -1-..l..J.'-.~ ...... _, .. :-.

. ~ tj-_ == .. _:_r_; ; ; -r -- ... r~ .. . , . -H11 ! - l ; : l - ~1- .;~; ~ ~ ~ : i I H-++H ! I ' 1

H+-+'+' i__j~~+ ...... ,_ +;-'-;'-t....,+H-t-'/~ i i i ;'-t' _,'-t'+ +H-t++'-:;: . ..;;...;~ .. ~-1-~'-:H--!1 .. ,.'-; -lJT-F i-+' -i1H1+ +H-+++;..,, .;,-"-,-I H-+-'-+-H_._ . .;,-++1-+, 1 1 ; : f H -+-t--!"'1H-H, 1-'-, -l ,_ I ! f

'I I;: H-r..--+-'-.;...;~+-': +~ ~ H,-+:~'1-+-1-~;...;:~_- "'"~''.'~'-t~-t+"-l~.+-1-'-1~~ ~ . l l

- 1+.-f-1-t++-H-+-+',-+,:-+-+-1 !-- I!;! I ! 1-t++~ t-f"J.' -f+H-H-W-t .. ! j ! :++-,H-++ +-1-+-+-+.1-; .;:...;. ... q

,_,_+-i ''>-+ '' -+--+r~if,. ... _'t-+' -+-'!'+; .:;.-:+-~H-'-l,-f.~ili r-H+ ,' -,,1-_.;J,--~.-:.:.+_:"'..,+~~1.:t-_.;.,.:;;.:: 1:~

S.tl JIJ/ f ll F.l:pn.nc/i/uths/Pan l

9. Given tha t = (x: x is an in teger, 1 $ x $ 10}. A = {x: xis a factor of 6}, B = {x: x is a prime number}.

a) List 1hc elemenls of 1hc set (A fl 8). h) Fiacl n(A V 8)'.

10. a) In the Venn Diagram helow, shade AV B' .

..--------~ E

Ans: a) _ __ _ _ _ _ [I]

b) ___ _ _ _ _ . 12J

[ I J

h) Express in set notalion, as s imply as possible, the scl shaded in the Venn Diagram.

-----~t:

Ans: b) - - -

_ _ _ [I]

7 Hnbit.f of Mmd: Stm'lngfor accurncy and precisf(ln

SAl 1011 /l t:xprtss .Hatlts /Pan I

11. The diagram shows the graph of a quadmtic equation. The curve cuts the x-axis al P( I, 0) and Q(?, 0).

y

a) Find the equation of the line of S)mmetry. b) Given that the equation of the curve is y = -x2 +ax - 7, find

(i) the value of a, (ii) the !,'featest vah1e ofy.

Ans: a) _ _ __ [I]

b) (i). ___ _ _ 12)

(ii) ___ _ [I)

8 Hubits ql:\1i11d: Striving.for C1cc,urac,:y and precision

S.411011 il /:Jpretr ,tfalhs i l'a11 l

12. John h,~s x rwo-dollar notes and y live-do llar notes. 'f he total va lue of the notes is S48. a) Form an equation connecting x :m

Mar king Scheme (Parl ll

I. (x+y)2 =x2 + 2xy+y2 Ml = 25 + 2(1 2) = 49 Al

2. x3 - 2x2 + 2x-4 = x2 (x-2) +2(x- 2) Ml = (x2 t- 2)(x - 2) Al

3. y = k./X, k is a constanl Substitute y = 6, x = 16, k = i M I :. y = ~./X Al

2

12

y 2-9 (y-3J(y+3) (b)-- = y'+4y+J (y.i)(y+J)

y-3 =-

y+J

5. (a) p = J s y-2< 2 s

p = 'Y-2s s = p1y- Zs112 s(l + lp2 ) = p2 y

~ ~ ,,2.v . l+lp2

M l

Ml

A l

(b) s (J3}2 (-t) l )

!+2(,/i)2 = -176 = - ,

6. .- t.AFC is similar i\IJDC. AC BC FC DC 20 8~ - = ...1. 3 DC DC = :'. cm

4

AO = AC - DC AO = L.0- ~= 18~cm

ll l

Ml

Al

Ml

Al

Ml

Ml

Al

7. (a) 3x2 - Hx = -8 3x2 - l4x + IJ = 0

Ox - Z)(x - 4) = 0 2

x= - orx=1 3

(b) 1 + -2._ = - 8-x+t xZ-1

x+6 8 - = x+1 (xH)(x- 1)

(x - l)(x + 6) = !J

x 2 + Sx -14 = 0

(x + 7)(x - 2) = O x = -7 orx = 2

8. (a) grndient = 2.

y = 2x + c

Ml 1\ I

Ml

Ml

Al

Since (3. 7) is a point on the line, 7 = 2(3) + c, c = l Ml

Equation of line : y = 2x + 1 A I

(c) Correctly drown line with label BI ft Point of intcrScction = ( 1. 3) BI

9. (a) A= {l,2,3,6} B = (2.3.5, 7}

A n B = (2.3} BI

(b) AU 8 = {l.2.3,5.6,7}

(AU B)' = (4.8,9,10) Ml

n(AU8)' = 4 Al

111 ft

10. n) In the Venn Diagram below, shade AU 8'.

E

'.

Bl

b)A n 8' Bl

Il.a)x = 4 Bl b)(i) y = - x 2 +ax - 7 and (1, O)is point on the curve,

0 =-l+a -7 Ml a = 8 Al

b)(ii)gre;itcsty-- 12 I 8(4) - 7 =9 BI

12.a)2x+Sy=48 Bl b) x+ 4 =y 131

2x ~ S(x + 4) = 18 MI x = 4 Al

I "'No -. I Cl"" 2E - . BUKIT BATOK SECONDARY SCHOOL

SECOND SEMESTRAL EXAMINATION 2011 lllrf .....

HCllHU ltlltl Secondary Two Express

MATHEMATICS Part II 11Oct2011

1125 - 1255

1 hour 30 minutes

Write all your answers on the writing papers provided.

READ THESE INSTRUCTIONS FIRST

Wlite your name. register numbc1 and class on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diag1ams or graphs.

i Do nl use staples, paper clips, highlighters. glue or correction fluid.

I Answer all the questions. If working is needed for any question it must oo shown with the answer. I Omission or essential working will result in loss ol marks.

Calculators should be used where appropriate. If the degree of accuracy is not specified in the Question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.

The number or marks is given in brackets [ ] at the end of each question or part question. The total number of marks ror this paper i s 60.

For Examiner's Use You should not spend too much time on any one question.

This paper consists ofS printed pages.

Answer all qu estions. 160 mar ksl

I. (a) Simplify n.2 - (11 + a.)(n - a) (b) Hente cv~luatc 3265418292 - 326541833 x 326541825. (c)

x+Z

5x - 1

The lengths of the three sides of a right-angled triangle are (x + 2) cm, (Sx - 1) cm and 5x cm respectively.

[I] 121

(i) Use Pythagoras' Theorem to form an equation in terms of x and show that \I reduces to x 2 - 6x + 5 = 0. i2]

(ii) Solve this equation to find the two possible values of x. 12]

2. In the diagram, AD and BC are horizontal and AC is vertical. CE is perpendicular to AB. It is given that AC = 4.2 m, CD = 5.6 m and LBAC = 55. Calculate (a) the length of AD, [2] (b) LACD, (2] (c) the length of CE, [2) (d) the length of AR. [2]

A D

Page 2 of S H'abits qf Mind: Stri11ing.for accuracy and pret:ision

SAJ 101 J J 2 .-/>' ~.u .~101h:-. / l'r111 II

3. The scale of map Xis 1 cm : 4 km. Suppose 1ha1 lhe actual area of a park is 64 kn1 2

4 .

(a) Find, in cm2, the area of lhe park on map X. [21

The ar~-a of 1he sam e park when drawn on map Y is 25 cm2 (h) Find the scale of map Yin lhc form 1 : 11. (c) A road is repn:scnled by a ll:ngth of 10 crn on map Y. Find its acrual length in

kilometres.

Rectangle A Rec1angle B

x

D x I 4 (21

I 1 l

Two rectangles, A and R, each have an ar~-a of 58 i cm2 The lenglh of rectangle A is x cm. The leoglh of rectangle Bis (x ~- 4) cm. (a) Find, in tem1s of x, an expression for !he wid1h of

(i) rectangl

S:':IZ 2011 I l :q>ress l1.f111hs,/ Pan JI

6. Crime has struck Gotham City again and Inspector Gorrlon is shining the Bar-signal into the clouds to inform Batman. The searchlight iir on the top of a building 400 rn high. It is given that the angle of elevation of the cloud from searchlight is 60, and the vertical distance of the clouds from the ground is 2000 m.

(a) Find the length of the. light beam. [2] (b) Batman is at point X as shown in the diagram when he saw the Bat-signal in the

clouds. Given that point Xis 3 km away from the building, find the angle of elevation of the Bat-signal from the point X. (4 J

Page 4 of S Habirs of Mind: Striving for accuracy and precision

SA}]()// I) xpr(.u ,\/a01s I Pm1 JI

7. A cylindrical so lid piece of wax (Figure I) is melted down to form the so hcl shown in Figure 2, which consists ofa hemisphere joined to acone. The radius of1he hemisphere is 22 cm and the height of the cone is 28 cm.

l 3r

! -~ . ---. -.. Figure l Figure 2

(a) Find the volume of the piece of wax in Figure 2. Leave your answer in tcnns of rr. [ 4)

(h) Given that the height of the cylinder i5 thrice it~ radius, find the radius or 01e cylinder. [ 4 J

(c) find the toll\ I surface area of 1hc cylrnder. PI

/J. Amwer the whofo of this q1111slion 011 u piect' 1if gra{lll paper.

The variables x and y are conncc1ed by the equation y == 30x - 5x2 . Some corresponding values of x and y arc given in !he table below:

F-=;--+1-~ (a) ('alculatc the values of a and b. [2) (b) Draw !lie graph ofy = 30x - Sx2 for 0 ~ x S 6, using a scale of 2 cm 10

represcn1 I unit on the x axis and 2 cm 10 represent 5 units on 1hc y-axis. [J] (C) Write down the equation of the line of S)'IDOletry of the graph. [ l) (d) Use your graph to find

(i) the value of y when x = 2.5. (I] (ii) the values of x when y = 20, [21 (iii) the maximum valucofy. [l)

(e) Ry adding a suitable line to the groph, solve the equation Sx 2 - 30x + 23 = 0. (2]

*"*End of Part II***

Pages of 5 ffubiis o/Mmd: Strfringfor accuracy and precl

Mad d ng Scheme (Part II) I. a) nZ - (n + a)(11 - a.) = 112 - (n2 - 11 2)

= a2