1.0 modul super score kertas 1 set 1 (1)

MODUL SUPER SCORE SBP 2014

©Panel Perunding Mata Pelajaran Matematik Tambahan,

KERTAS 1 SET 1

NAMA : MARKAH TARIKH :

Answer all questions. Jawab semua soalan.

1. The diagram shows the relation between set X and set Y.

Rajah menunjukkan hubungan di antara set X dan set Y. State /Nyatakan (a) The range of the relation

Julat hubungan itu (b) The value of x

Nilai x [2 marks]

[2 markah] Answer / Jawapan :

2. Given the function g : x → 5−x . Find the values of x if g(x) = 4. [2 marks]

Diberi fungsi g : x → 5−x . Cari nilai-nilai x jika g(x) = 4. [2 markah] Answer / Jawapan :

For examiner’s

use only

2

2

2

1

x g(x)

– 4

x

1

4 6

3

2

– 2

x

Set X Set Y



3. Given the functions f(x) = 4x – m and 169)(1 +=− kxxf , where k and m are constants. Find the

values of k and m. [3 marks]

Diberi fungsi f(x) = 4x – m dan 169)(1 +=− kxxf , dimana k dan m adalah pemalar. Cari nilai-

nilai bagi k dan m. [3 markah]

Answer / Jawapan : 4. Diagram shows a graph of a quadratic function f(x) = ‒2(x + h)2 ‒ 2 where k is a constant.

Rajah menunjukkan graf fungsi kuadratik f(x) = ‒2(x + h)2 ‒ 2 dimana k ialah pemalar.

Find Cari (a) the value of k

nilai k

(b) the value of h nilai h

(c) the equation of axis of symmetry. persamaan bagi paksi simetri.

[3 marks] [3 markah]

Answer / Jawapan :

For examiner’s

use only

3

3

3

4

x 0 (-3, k) •

f(x) = −2(x + h)2 − 2

y



5. Find the values of p if the quadratic function f(x) = 2x2 + 2px – (p + 1) has a minimum value of – 5 [3 marks] Cari nilai-nilai bagi p jika fungsi kuadratik f(x) = 2x2 + 2px – (p + 1) mempunyai nilai minimum – 5


6. Find the range of values of x for xx 624)4( 2 −<− [2 marks]

Cari julat nilai x bagi xx 624)4( 2 −<− [2 markah]

Answer / Jawapan :

For examiner’s

use only

2

6

3

5



7. One of the roots of the quadratic equation 032 2 =−− kxx is – 4. Find the value of k.

[2 marks] Satu dari punca persamaan kuadratik 032 2 =−− kxx ialah – 4. Cari nilai k. [2 markah]

Answer / Jawapan :

8. One of the roots of the equation 3x2 – 6x + p = 0 is three times the other root , find the possible

values of p. [3 marks] Salah satu punca bagi persamaan 3x2 – 6x + p = 0 adalah tiga kali punca yang satu lagi, cari nilai yang mungkin bagi p. [3 markah] Answer / Jawapan :

3

8

2

7

For examiner’s

use only



9. Solve the equation 06216 42 =− +− xx . [3 marks] Selesaikan persamaan 06216 42 =− +− xx [3 markah]

Answer / Jawapan :

10. Solve the equation 2x • 5x +2 = 25000. [3 marks] Selesaikan persamaan 2x • 5x +2 = 25000. [3 markah]

Answer / Jawapan :

3

9

3

10

For examiner’s

use only



11. Solve the equation log2 (x – 3) = log2 4x + 1 [3 marks]

Selesaikan persamaan log2 (x – 3) = log2 4x + 1 [3 markah]

Answer / Jawapan : 12. Given that log2 x = m and log2 y = n. Express log4 (xy2) in terms of m and n. [3 marks]

Diberi log2 x = m dan log2 y = n. Nyatakan log4 (xy2) dalam sebutan m dan n. [3 markah]

Answer / Jawapan : lum

3

11

4

12

For examiner’s

use only



13. Find the sum to infinity of the geometric progression 20, 10, 5, ... [2 marks] Cari hasil tambah ketakterhinggaan janjang geometri 20, 10, 5, ... [2 markah]

Answer / Jawapan :

14. Given a geometric progression has the first term and the sum to infinity are 25 and 62.5

respectively. Find the common ratio of the progression. [2 marks] Diberi satu janjang geometri mempunyai sebutan pertama dan hasil tambah hingga ketakterhinggaan adalah 25 dan 62.5 masing-masing. Cari nisbah sepunya bagi janjang tersebut. [2 markah]

Answer / Jawapan :

2

14

2

13

For examiner’s

use only



15. Write 0.01010101... as a single fraction in the lowest terms. [3 marks]

Tulis 0.0101010... sebagai satu pecahan tunggal dalam sebutan terendah. [3 markah]

Answer / Jawapan :

16. The diagram below shows two vectors OP and OQ .

Rajah di bawah menunjukkan dua buah vektor OP dan OQ .

Express Ungkapkan

(a) OP in the form ⎟⎟⎠

⎞⎜⎜⎝

⎛

yx

.

OP dalam bentuk ⎟⎟⎠

⎞⎜⎜⎝

⎛

yx

.

(b) PQ in the form jyix ~~ +

PQ dalam bentuk jyix ~~ + [4 marks]


3

15

4

16

For examiner’s

use only

P(– 2 , 5)

Q(4 , – 3 )

x

y



17. Given ⎟⎟⎠

⎞⎜⎜⎝

⎛

−=

34

h , ⎟⎟⎠

⎞⎜⎜⎝

⎛−=

02

k and ⎟⎟⎠

⎞⎜⎜⎝

⎛=+m

kha6

, find the values of a and m. [3 marks]

Diberi ⎟⎟⎠

⎞⎜⎜⎝

⎛

−=

34

h , ⎟⎟⎠

⎞⎜⎜⎝

⎛−=

02

k dan ⎟⎟⎠

⎞⎜⎜⎝

⎛=+m

kha6

, cari nilai bagi a dan m. [3 markah]

Answer / Jawapan :

18. Points A, B and C are collinear. It is given that 6 4AB a b= −

uuur

% % and 4 (2 )BC a k b= + +

uuur

% %, where k is

a constant. Find Titik A, B dan C adalah segaris. Diberi bahawa 6 4AB a b= −

uuur

% %dan 4 (2 )BC a k b= + +

uuur

% %, dengan

keadaan k adalah pemalar. Cari (a) the value of k

nilai k

(b) the ratio AB : BC nisbah AB : BC

[4 marks] [4 markah]

Answer / Jawapan :

3

17

4

18

For examiner’s

use only



Jawapan/Answer : No Answer

1 (a) {– 2, 2, 3, 6} (b) x = 0

2 x = 1, x = 9

3 k = 41

, m = 49

4 (a) k = – 2 (b) h = 3 (c) x = – 3

5 – 4, 2 6 42 <<− x 7 k = 44

8 21

=α , 49

=p

9 x = 5 10 x = 3

11 x = 73

−

12 2

2 mn +

13 40 14 0.6

15 991

16 (a) ⎟⎟

⎠

⎞⎜⎜⎝

⎛−

52

(b) ~~86 ji−

17 a = 2 , m = – 6

18 (a) k = 3

14−

(b) AB : BC = 3 : 2

1.0 modul super score kertas 1 set 1 (1)

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