Answer Marking Scheme F4 Add Math (1)

7/29/2019 Answer Marking Scheme F4 Add Math (1)

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SULIT 3472/1/2

SEKOLAH MENENGAHKEBANGSAAN TINGGI

KAJANGJALAN SEMENYIH, 43000 KAJANG, SELANGOR

PEPERIKSAAN PERTENGAHAN TAHUN 2012

ADDITIONAL MATHEMATICS

Answer and Marking Scheme

Prepared by : Checked by: Verified by:

........................................ ........................................... ..( NG KOK LYE ) (NOORAIDA MOHD ZIN) ( SOH BOON CHUAN )

This question paper consists of7printed pages and 1 blank page

3472/1/2 SULIT

FORM IV 2012


2/8

SULIT 3472/1/2SECTION 1

BAHAGIAN 1

[ 44 marks/markah ]Answerall questions /Jawab semua soalan.

1. Diagram 1 shows the relation between setA and setB.Rajah 1 menunjukkan hubungan antara set A dan setB.

Set A Set B

(a) Express the relation in the form of ordered pairs.Ungkapkan hubungan itu dalam bentuk pasangan tertib.

(b) State the type of the relation. Nyatakan jenis hubungan itu [ 3 marks/markah ]

Answer/Jawapan:

(a) {(1,p), (2,r), (3,s), (4,p)} 2Any one pair correct B1 DIAGRAM 1

Rajah 1

(b) many to one 1

2. Diagram 2 shows the linear functionf. Rajah 2 menunjukkan fungsi linear f.

(a) State the value ofw. Nyatakan nilai bagi w.

(b) Using the function notation,

express f in terms ofx.

Dengan menggunakan tatatanda

fungsi, ungkapkan f dalam sebutan x.

[ 2 marks/markah ]

Answer / Jawapan: DIAGRAM 2

Rajah 2

(a) 7 1

(b) f(x) = x + 2 or f : x x + 2 1

3472/1/2 SULIT2

2

2

2

r examiners

use only

x f(x)f

2

3

w

10

0

1

5

8

33

1

1

2

3

4

p

q

r

s

5


3/8

mx,x23

5x

+

3

2

2

3

2

1x,

12x

3x5

2y3

5yx

+

=

SULIT 3472/1/2

3. Diagram 3 shows the graph of the functionf(x) = |3x 2|, for the domain 0 x 5.Rajah 3 menunjukkan graf bagi fungsi f(x) = |3x 2| untuk domain 0 x 5. [ 3 marks/markah ]

State /Nyatakan

(a) the value ofm. ynilai m.

(b) the range off(x) corresponding to the given domain. f(x) = |3x 2|

julat bagi f(x) sepadan dengan domain yang diberikan.

Answer /Jawapan:2

(a) 1

0 m 5

(b) 0 f(x) 13 2 DIAGRAM 3Rajah 3

13 B1

4. Two functions are defined by f : x 2x + 1 and g :x x2 + 2x 6.Given that gf : x 4x2 + px + q, find the value ofp andof q.

Dua fungsi ditakrifkan sebagai f : x 2x + 1 dan g : x x2 + 2x 6.Diberi gf : x 4x2 + px + q, cari nilai p dan nilai q. [ 3 marks/markah]

Answer /Jawapan:

p = 8, q = 3 3 (both correct)

4x2 + 8x 3 B2

(2x + 1)2 + 2(2x + 1) 6 B1

5. The function off is defined as f(x) = mx,x23

5x

+. Find,

Fungsi f ditakrifkan sebagai f(x)= . Cari [ 3 marks/markah]

(a) the value of m,

nilai m,

(b) )x(1f .

Answer / Jawapan:

(a) 1

(b) f -1(x) = 2 B1

3472/1/2 SULIT3

For examiners

use only

33

4

3

3

3

33

5

9


4/8

5

2

2(5)

2)4(5)(3)(3)(x

2

=

2

5

SULIT 3472/1/26. Determine the roots of the quadratic equation 5x 2 = 3x + 2.

Tentukan punca-punca bagi persamaan kuadratik 5x2 = 3x + 2. [ 3 marks/markah]

Answer / Jawapan:

x = or 0.4 , x = 1 3 (both correct)

(5x + 2) (x 1) = 0 B2 or B2

5x2 3x 2 = 0 B1

7. Find the range of values ofkif the following quadratic equation (k + 1)x2 + 6x + 3 = 0 which

has two different roots. Cari julat bagi nilai k jika persamaan kuadratik berikut (k + 1)x2 + 6x + 3 = 0 mempunyai dua

punca

yang berbeza.[ 3 marks/markah]

Answer / Jawapan:

k < 2 3

62 4(k + 1)(3) > 0 B2

62 4(k + 1)(3) or b2 4ac > 0 or a = (k+1), b = 6, c = 3 B1

8. Given that and are the roots of the quadratic equation 2x2 5x + 3 = 0. Form thequadratic

equation whose roots are 2 and 2 . Diberi dan adalah punca-punca bagi persamaan kuadratik 2x2 5x + 3 = 0. Bentuk satu

persamaan kuadratik yang mempunyai punca-punca 2dan

2

. [ 3 marks/markah ]

Answer /Jawapan:

x2 5x + 12 = 0 3

4 = 122( + ) = 5 B2 (both)

+ = B1 (both correct)

= 3

3472/1/2 SULIT4

33

7

r examiners

use only

33

6

3

3

8

9


5/8

SULIT 3472/1/2

9. Diagram 3 shows the graph of a curve y = a(x +p) + q that passes through the point (0, 3)and has the minimum point (2, 1). Find the values of a,p and q.

Rajah 3 menunjukkan geraf bagi satu lengkung y = a(x + p) 2 + q yang melalui satu titik (0.3) danmempunyai titik minima (2 , 1). Cari nilai-nilai a, p dan q.

[ 3 marks/markah ]

Answer /Jawapan:

p = 2 1

q = 1 1

a = 1 1

10. Find the range of values ofx for which x(x 3) 4. Cari julat bagi nilai x yang mana x(x 3) 4. [ 3 marks/markah]

Answer /Jawapan:

1 x 4 or x 1 , x 4 3

(x + 1)(x 4) 0 B2 or or B2 B2

x x

x2 3x 4 0 B1

11. Solve 243x3

1x81

=

[ 4 marks markah]

Answer /Jawapan:

x = 3 4

4x 4 = 5 + x or 3x 4 = 5 B3

3 4 x 4 = 3 5 + x or 33 x 4 = 35 B2

34 or 35 B1

3472/1/2 SULIT5

33

9

43

11

DIAGRAM 3

Rajah 3

For examiners

use only

(2, 1)

(0, 3)x

y

0

33

10-1 4

+

+ +

++-1 4

10


6/8

3

13

0.3

0.72(0.3)+

lg2

lg52lg2 +

lg2

lg20

k

2k3 +

xlog

x2log53log

5

55 +

xlog

xlog125log

5

255 +

xlog

125xlog

5

25

2

2n

2

5

SULIT 3472/1/2

12. Given that lg 2 0 3= and lg 5 = 0.7. Find, without using scientific calculator or mathematicaltables, the value of log 2 20.

Diberi lg 2 = 0.3 dan lg 5 = 0.7. Cari, tanpa menggunakan kalkulator saintifik atau jadual sifir

matematk, nilai bagi log2 20.

[ 4 marks/markah]

Answer /Jawapan:

or 4.333 4

B3

B2

B1

13. Given that log5x = k, find logx 125x2

in terms of k.Diberi log5x = k, find logx 125x

2 dalam sebutan k.

[4 marks/markah ] Answer/Jawapan:

4

B3

B2

B1

14. Express 3 12 2 5(2 )n n n+ + in the simplest form. [ 3 marks/markah ] Ungakapkan 2n + 3 2n + 5(2n 1) dalam sebutan paling ringkas.

2 n -1(19) 3

2 n(8 1 + ) B2

2 n. 2 3 2 n + 5 B1

3472/1/2 SULIT6

44

13

r examiners

use only

44

12

3

3

14

11


7/8

2(3)

7)4(3)(33x

2

=

2

1y +

2

2

1y

+

+

2

1y

3(3)

19)4(3)(1212y

2

=

2x+

2x+

SULIT 3472/1/2SECTION 2

BAHAGIAN 2

[ 26 marks/markah ]

Answerall questions /Jawab semua soalan.

1. Solve the simultaneous equations. Give your answers correct to three decimal places.

Selesaikan persamaan serentak. Berikan jawapan anda betul kepada tiga angka perpuluhan.

1yx2 =

5xyy2x2

=++ . [ 5 marks/markah]

Answer /Jawapan:

y = 2x 1 P1 or x = P1

x2 + 2(2x 1) + x(2x 1) = 5 K1+ 2y + y = 5 K1

3x

2

+ 3x 7 = 0

3y2 + 12y 19 = 0 K1

K1 x = 1.107, - 2.107 N1

y = 1.214, - 5.214 N1 y = 1.214, - 5.214 N1

x = 1.107, - 2.107 N1

2. Given that f : x x2 2 and g : x 3x + 4. Diberi f : x x2 2 dang : x 3x + 4.

(a) (i) Determinef1(x). [ 2 marks/markah ]

Tentukan f1(x).

(ii) State whether thef1(x) exist. Give a reason to your answer by showing the evidence of

the reason given.

Nyatakan sama ada f1(x) itu wujud. Berikan sebab kepada jawapan anda dengan

menunjukkan bukti kepada sebab yang anda berikan. [ 3 marks/markah ]

(b) Given gh(x) = 6x + 7, determine h(x).Diberigh(x) = 6x + 7, tentukan h(x). [ 2 marks/markah ]

Answer /Jawapan:

(a) x = y2 - 2 K1

y2 = x + 2

f-1(x) = N1

Let x = any value,

f-1(x) = the value after substitution into , K1an object has two images or

its a one-to-many relation or the function undefined

Therefore the invest function does not exist. N1

3472/1/2 SULIT7

(b) Let h(x) = y

g(y) = 6x + 7

g(y) = 3y + 4

3y + 4 = 6x + 7 K1y = 2x + 1

h(x) = 2x + 1 N1

7

55


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SULIT 3472/1/2

3. (a) Simplify: Permudahkan:

4 x +2 2 2x + 3 [ 4 marks/markah ]

(b) Hence, solve the equation:Seterusnya, selesaikan persamaan;

4 x + 2 2 2x + 3 = 64 [ 2 marks/markah ]

Answer /Jawapan:

(a) 2 2(x + 2) 2 2x + 3 P1

2 2x . 2 4 2 2x . 2 3 K1

2 2x(2 4 2 3) K1

2 2x(8)

2 2x + 3 N1

4. The curve of a quadratic function f(x) = x2 + 2hx 5 has minimum point of (2, k).

Lengkung bagi satu fungsi kuadratik f(x) = x2 + 2hx 5 mempunyai titik minimum (2, k).

(a) State the equation of the axis of symmetry of the curve.

Nyatakan pesamaan paksi simmetri bagi lengkung itu. [ 1 mark/markah ]

(b) By using the method of completing the square, determine the value of h and of k. Dengan menggunakan kaedah penyempurnaan kuasadua, tentukan nilai bagi h dan bagi k.

[ 4 marks/markah ]

(c) Hence, sketch the graph of the curve.

Seterusnya, lakarkan graf bagi lengkung itu. [ 3 marks/markah ]

Answer /Jawapan:

(a) x = 2 N1

(b) f(x) = x2 + 2hx + h2 h2 5 K1= (x + h)2 h2 5 K1

h = 2 N1

k = h2 5

= 4 5

= 9 N1

(c) P1

P1 P1

END OF THE ANSWER & MARKING SCHMESKEMA PEMARAKAHAN DAN JAWAPAN TAMAT

3472/1/2 SULIT8

(b) 2 2x + 3 = 2 6 P1 2x + 3 = 6

x =2

3 N1

x

f(x)

20

-5

(2, 9)

1

4

3

8

64

2

Answer Marking Scheme F4 Add Math (1)

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