This document contains a 14-question math exam covering topics like functions, graphs of quadratic functions, logarithms, vectors, and geometric progressions. The questions require students to find values, ranges, equations, expressions, and solutions. An answer key is provided with the numerical solutions or expressions for each problem.

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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

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3. Given the functions f(x) = 4x – m and
16
9
)(1
+=−
kxxf , 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
+=−
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

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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 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

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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

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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

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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

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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

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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 jyix
~~
+
PQ dalam bentuk jyix
~~
+
[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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17. Given ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
=
3
4
h , ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−
=
0
2
k and ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=+
m
kha
6
, find the values of a and m. [3 marks]
Diberi ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
=
3
4
h , ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−
=
0
2
k dan ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=+
m
kha
6
, 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

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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 42 <<− x
7 k = 44
8
2
1
=α ,
4
9
=p
9 x = 5
10 x = 3
11 x =
7
3
−
12
2
2 mn +
13 40
14 0.6
15
99
1
16
(a) ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−
5
2
(b)
~~
86 ji−
17 a = 2 , m = – 6
18
(a) k =
3
14
−
(b) AB : BC = 3 : 2