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Section A (40 Marks)

Answerall questions in the spaces provided on this question paper.

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You are advised not to spend more than one hour for this section.

1 The diameter of a spherical particle is 3 nanometres. Calculate thevolume, in m3 , of the particle, giving your answer in standard form.

[Volume of a Sphere =3

3

4r ]

Answer m3 [2]

2 (a) Factorise 254 2 x completely.

Hence

(b) solve the equation 0254 2 =x .

Answer (a) [1]

(b) =x [1]

Tanjong Katong Girls School Sec 3 Mid-Year Exam 2010 4016 Mathematics

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3 Alice wants to save $ x a month in the next six months. She plans tosave at least $ 150 a month but not more than $ 400 a month.

(i) Using suitable mathematical symbols, write down twoinequalities for the above information.

Hence, state the

(ii) maximum amount of saving

(iii) minimum amount of saving

Answer (i)

[1]

(ii) $ [1]

(iii$ [1]

Tanjong Katong Girls School Sec 3 Mid-Year Exam 2010 4016

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For Examiners

Use4 (a) Simplify 3 12343y

For Examiners

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(b) Show that )4(84 20)25(20 = mm . [2]

Answer(a

[1]

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5 The equation of a curve is ( ) ( )xxy 2123 += .

(a) Write down the x intercepts of the curve.

(b) Sketch, on the answer space below, the graph of ( ) ( )xxy 2123 +=.

Answer : [2]

Answer (a) [1]

Tanjong Katong Girls School Sec 3 Mid-Year Exam 2010 4016 Mathematics

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6 A line intersects the y axis at 3=y and the x axis at 5=x . It passes

through the point ( )pP ,5 . Find

(i) the distance between the two points where the line intersects theaxes.

(ii) the value of p .

(iii) the equation of the line.

Answer (i) units [2]

(ii) [2]

(iii

[1]

Tanjong Katong Girls School Sec 3 Mid-Year Exam 2010 4016 Mathematics

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7 The deposit required by a club to reserve a ballroom for a party onweekends is $ 600. In addition, the club charges $ 40 for every guestinvited. Let $y be the total amount charged forx invited guests.

(i) Complete the following table and draw the graph in the grid provided.[2]

Number of guestsinvited,x

20 40 60 80

Total amount charged, $y

(ii) Write down a linear equation connecting x and y .

(iii) What does the gradient represent ?

(iv) What does they intercept represent ?

Answer (ii) [1]

(iii[1]

(iv) [1]

Tanjong Katong Girls School Sec 3 Mid-Year Exam 2010 4016 Mathematics

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200 40 60 80 100

2000

3000

4000

1000

Number of guests invited,x

Total amount charged, $y

7/27/2019 TKGS 2010 Sec 3 MYE MA

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8 Joyce walked from her home to a bookshop and stopped to buy somestationery. She then walked to a supermarket and stopped to buy hergrocery. Finally, she walked back home.

The diagram below shows her distance-time graph.

(a) She took 20 minutes to walk to the bookshop. Find her speed.

(b) Write down the time she spent in the supermarket.

(c) Find the distance between the bookshop and the supermarket.

(d) Find the total distance she walked in the 80 minutes.

(e) Find her average speed for the entire journey.

Answer (a) m / min [1]

(b) minutes [1]

(c) meters [1]

(d) meters [1]

(e) m / min [1]

Tanjong Katong Girls School Sec 3 Mid-Year Exam 2010 4016 Mathematics

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80

200

150

100

50

Distancefromhome(metres)

O 604020

time (t minutes)

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9 (a) The estimated population of China as of April 2010 was1,337,030,000 which was approximately 19.6% of the world

population. Giving your answer correct to 6 significant figures,

(i) write down the population in billion,

hence,

(ii) estimate the worlds population.

(b) Given that 1851

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1

0

The diagram above shows a straight line, l, and a triangleABC.

(a) Write down the equation of(i) the lineAB.(ii) the y axis .

(b) Find the area of the triangleABC.Hence,(c) find, d, the perpendicular distance fromB to the lineAC.

Answer (a)(i) [1]

(ii) [1]

(b) units 2 [2]

(c) =d units [2]

Tanjong Katong Girls School Sec 3 Mid-Year Exam 2010 4016 Mathematics

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l

B (4,3)

0

(0, 3)

C(1, 1)

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Section B (50 Marks)

Answerall questions on the writing paper provided.

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Begin each question ona fresh page and arrange your answers innumerical order before handing in.

1

1 (a) Express 432 += xxy in the form of ( ) baxy += 2 . [2]

Hence,(b) find the coordinates of the turning point. [1]

(c) sketch the graph of 432 += xxy . [2]

(d) state the equation of the line of symmetry. [1]

1

2(a) Solve 0

5

2

2510

12

=

+ xxx .

[4]

(b) If the solutions of the equation 02 =++ cbxax are

2

1 and 3,

find the values ofa, b and c. [3]

1

3 (a) Simplify( ) 03

1

5

3 5

3

2

1

3

)2(24

2qp

p

p

p

p

[3]

(b) Solve 625)5125( 3 = x [3]

(c) Given that 52 =x , find the value of ( )x

x

+ 8

12

2 . [3]

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The diagram shows a rectangular thin sheet ABCD . The length,AB , isx cm which is 10 cm longer than its width BC. A square of length 35 cmshorter than AB, is removed from each corner of the thin sheet ABCD .The remaining sheet is then folded to form an open box.

(a) Write down an expression, in terms ofx , for the width of the thinsheet ABCD . [1]

(b) Write down an expression, in terms ofx , for the length of thesquare.

[1](c) The area of the base, MNPQ , of the open box is 600 cm2 .

Write down an equation , in terms ofx , to represent thisinformation. Show that the equation simplifies to

036001302

=+ xx . [3]

(d) Solve the equation 036001302 =+ xx . [2]

(e) Find the total surface area of the vertical faces. [2]

1

5 (a) Solve

(i) 19223 3 = x [2]

(ii) 31

2

1

1=

+

xx[4]

(b) Solve 205123

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1

6

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

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

wherex

y 2= .

x -1.25 -1 -0.75 -0.5

-0.25 0 0.25

0.5 0.75

1 1.25

y 0.420

0.5

0.595

p 0.841

1 1.19

1.41

1.68

2 2.38

(a) Find the value ofp . [1]

(b) Using a scale of 4 cm to 1 unit, draw a horizontal x-axis for5.15.1 x .

Using a scale of 4 cm to 1 unit, draw a verticaly-axis for30 y .

On your axes, plot all the points in the table and join them witha clear and smooth curve. [3]

(c) Use your graph, to solve the equation xx

22 = . [2]

(d) By drawing a tangent, find the gradient of the curve at 5.0=x .[2]

(e) Use your graph, to solve the inequality 5.02 p

(b) (b)(ii) -3

6(i) 83.5 units 10(a)(i) 3=y

(ii) 6=p (a)(ii)0=x

(iii)3

5

3+= xy (b)(i) 4 units

2

7(i)

Numberof guestsinvited,x

20 40 60 80

Totalamount

1400

2200

3000

3800

(b)(ii) 58.3 units

15

X

(1

2, 4)

O

x

3

-

1

21

1

2

-3

l

- 32

5

0

0

ll

200 40 60 80 100

2000

3000

4000

1000

Number of guests invited, x

Total amount charge, $y

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No. Answer Keys (Section A) No. Answer Keys (Section A)

(ii) xy 40600+=

(iii) Amount charged by the hotel for everyguest invited

(iv) The deposit

No. Answer Keys (Section B No. Answer Keys (Section B)11 (b)

4

31,

2

11

15(a)(i)

4=x

(c) (a)(ii) 26.1=x or 59.1=x

(d) The equation of the line of symmetry is

2

3=x .

(b)(i)3

5

31