SPM 2014 Add Math Modul SBP Super Score [Lemah] K1 Set 1 Dan Skema

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MODUL SUPER SCORE SBP

2014

©Panel Perunding Mata Pelajaran Matematik Tambahan, Page 1

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 →

x



5

. Find the values of x if g(x) = 4. [2 marks] Diberi fungsi g : x →

x



5

. 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

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MODUL SUPER SCORE SBP

2014

3. Given the functions f(x) = 4x – m and

16 9 ) ( 1 _ _  kx x

f , where k and m are constants. Find the values of k and m. [3 marks] Diberi fungsi f(x) = 4x – m dan

16 9 ) ( 1 _ _  kx x

f , 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

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MODUL SUPER SCORE SBP

2014

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

[3 markah] Answer / Jawapan :

6. Find the range of values of x for (x4)2 246x [2 marks] Cari julat nilai x bagi (x4)2 246x [2 markah] Answer / Jawapan : For examiner’s use only 2 6 3 5

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MODUL SUPER SCORE SBP

2014

7. One of the roots of the quadratic equation

2 x

2



3 x



k



0

is – 4. Find the value of k.

[2 marks] Satu dari punca persamaan kuadratik

2 x

2



3 x



k



0

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

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MODUL SUPER SCORE SBP

2014

9. Solve the equation

216

x2



6

x4



0

. [3 marks] Selesaikan persamaan

216

x2



6

x4



0

[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

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MODUL SUPER SCORE SBP

2014

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

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

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MODUL SUPER SCORE SBP

2014

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]

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

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MODUL SUPER SCORE SBP

2014

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

_











y

x

. OP dalam bentuk

_











y

x

. (b)

PQ

in the form x~i y~j

PQ

dalam bentuk x~i y~j [4 marks] [4 markah] Answer / Jawapan : 3 15 4 16 For examiner’s use only

P(– 2 , 5)

Q(4 , – 3 )

x

y

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MODUL SUPER SCORE SBP

2014

17. Given

_















3

4 h

,

_













0

2 k

and

_















m

k

h

a

6

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

Diberi

_















3

4 h

,

_













0

2 k

dan

_















m

k

h

a

6

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

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

uuur

% % and BC4a(2k b) uuur

% %, where k is

a constant. Find

Titik A, B dan C adalah segaris. Diberi bahawa AB6a4b

uuur

% %dan BC4a(2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

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MODUL SUPER SCORE SBP

2014

Jawapan/Answer : No Answer 1 (a) {– 2, 2, 3, 6} (b) x = 0 2 x = 1, x = 9 3 k = 4 1 , m = 4 9 4 (a) k = – 2 (b) h = 3 (c) x = – 3 5 – 4, 2 6



2 

x



4

7 k = 44 8 2 1   , 4 9  p 9 x = 5 10 x = 3 11 x = 7 3  12 2 2nm 13 40 14 0.6 15 99 1 16 (a)

_











5

2

(b) ~ ~ 8 6i j 17 a = 2 , m = – 6 18 (a) k = 3 14  (b) AB : BC = 3 : 2