7/31/2019 test form 4

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SEKOLAH TUN FATIMAH JOHOR BAHRU

UJIAN KEDUA TAHUN 2011

ADDITIONAL MATHEMATICS

TINGKATAN 4

7.309.30 (2 JAM)

NAMA :______________________________________ FORM : 4 S / T / F / J / B

___________________________________________________________________________

The following formulae may be helpful in answering the questions. The symbols given are theones commonly used.

ALGEBRA

1. x =a

acbb

2

42

STATISTICS /STATISTIK

1. x =N

x

2. x =

f

f x

3. =N

xx2)(

=2

2

xN

x

4. =

f

xxf 2)(=

22

xf

fx

5. Cf

FN

Lmm

2

1

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GEOMETRY

1. Distance =2

12

2

12 )()( yyxx

2. Midpoint , yx, =

2,22121

yyxx

3. A point dividing a segment of a line ,

nm

myny

nm

mxnxyx 2121 ,,

4. Area of a triangle = 3123121332212

1yxyxyxyxyxyx

TRIGONOMETRY

1. Arc length, rs

2. Area of sector, 2

2

1rL

3.C

c

B

b

A

a

sinsinsin

4. bccba 2222 cosA

5. Area of a triangle = ab2

1sin C

Answer ALL questions.

1 Solve the simultaneous equations : 2x y and 311

yx

.

Give you answer correct to three decimal places..[ 5 marks ]

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2. Diagram 2 shows a straight lineAC. The pointB lies onACsuch that 3:1: BCAB .

y

C(8,3)

O x

)9,4( A

Diagram 2

Find

(a) the coordinates ofB,(b) the equation of the perpendicular bisector of straightAC.

[5 marks]

3 In Diagram 3, point A ( -2, 4), C(6,2) and pointD are vertices of a triangle..

Diagram 2

It is given that a straight lineAD is parallel to the straight lineBC, point B (1,-1) andoACD 90 .

Find

(a) the equation of the straight lineAD and the straight line CD ,

(b) the coordinate of D,

x

A(-2,4)

B (1,-1)

C(6,2 )

Dy

B

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(c) the area of the triangle ACD,

(d) A point ),( yxP moves such that PBPA 2 , find the equation of the locus P.[10 marks]

4. A set of 16 numbers 1621 ........,,, xxx , has a variance of 56 and it is given that

92012 x . Find

(a) the mean , _x ,(b) the value of x .(c) the mean and the variance for the set of numbers 52........,,52,52 1621 xxx .

[5 marks]

5. Table 5 shows the marks obtained by a group of students in a test.

Marks Number of students

1019 5

2029 8

3039 x4049 11

5059 4

Table 5

(a) Given that the median mark is3

135 , find the value ofx.

(b) Hence , find the mean mark..

(b) Using a scale of 2 cm to 10 marks on horizontal axis and 2 cm to 2 students on thevertical axis, draw a histogram to represent the frequency distribution of the marks in

Table 4.

[10 marks]

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6. Diagram 5 shows sectors OPQ and ORS with centre O.

Diagram 5

Given that PR is 2 cm, the length of radius OR is 8 cm and the length of arc PQ is

twice the length of radius OP, find the perimeter of the shaded region.[5 marks]

7. Diagram 7 shows a right-angled triangle POQ and PQR is a sector with center Q.

P Q

P

R O

S

Q

Given that TOUSP is a semicircle and OP = PS = 8 cm.

Find

(a) the perimeter, in cm, of the shaded region.(b) the area , in cm2 , the region PRT.

[10 marks]

END OF UESTION PAPER

Diagram 7

T U

O

S

R