# Add Maths (Q) 2011 by speedracerijok

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```									SULIT
NAMA           ……………………………………………………………………….

TINGKATAN ………………………………………….

JABATAN PELAJARAN PERAK

SOALAN LATIH TUBI BERFOKUS 1                                                        3472 / 1
Kertas 1
April
2 jam                                                                                 Dua jam

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU
Untuk Kegunaan Pemeriksa
1.      Kertas soalan ini mengandungi 25 soalan.           Kod Pemeriksa :
Markah   Markah
Penuh  Diperoleh
1           3
in the question paper.                                  3           3
4           3
5           4
get marks.
6           3
7           2
8           3
out the answer that you have done. Then
write down the new answer.                              9           3
10           3
6.      The diagrams in the questions are not                  11           4
drawn to scale unless stated.                          12           3
13           4
7.      The marks allocated for each question are              14           4
shown in brackets.                                     15           3
16           3
8.      You may use a scientific calculator.                   17           4
18           3
19           3
20           3
21           3
22           3
23           3
24           3
25           4
Jumlah        80
Kertas soalan ini mengandungi 13 halaman bercetak.
[Lihat halaman sebelah
3472/1 2011 JPN PERAK SOLAF 1                                                            SULIT
For       SULIT                                            2                           3472/1
Examiner,s
Use

1   Diagram 1 shows an incomplete arrow diagram which represents the relationship
between set X and set Y.

X        square of          Y

2●
●   p
1●
● 1
q●

Diagram 1
State
(a) the values of p and q,
(b) the type of the relation.
[ 3 marks]
(a)
1
(b)
3

2   Functions f and g are such that f : x → 2x – 5 and g : x → 1 – hx.
Given that g – 1(– 1 ) = 4, find
(a) the value of h,
(b) g (8).
[ 3 marks]
(a)

(b)

2

3

3472/1    2011 JPN PERAK SOLAF 1                                            SULIT
SULIT                                           3                                  3472/1       For
Examiner,s
Use
3   Functions f and g are such that g : x → x – 7 and gf : x → 2x – 1.
Find
(a) gf(3),
(b) f(– 2).
[3 marks]
(a)

(b)

3

3

4   Diagram 4 shows the graph of a quadratic function y = f(x) with an axis of
symmetry x = 1.
y

y = f(x)

x
–2 O        h

Diagram 4

(a)      Find the value of h.
(b)      Solve f(x) ≤ 0.
[3 marks]
(a)

(b)
4

3

Lihat Halaman Sebelah
3472/1    2011 JPN PERAK SOLAF 1                                                 SULIT
For       SULIT                                          4                                 3472/1
Examiner,s
Use
5   Both the quadratic equations, px2 – 8x + 6 = 0 and 3x2 + 6x – p + 1 = 0, where p is a
constant, have two different roots.
Find the range of values of p.
[4 marks]

5

4

6   Diagram 6 shows some information about the graph of the quadratic function
y = k – a( x + h ) 2, where a , h and k are constants.

y-intercept = 5
Coordinates of maximum point = ( 1 , 7 )

Diagram 6
(a)     State the values of h and k.
(b)     Calculate the value of a.
[3 marks]
(a)

(b)

6

3

3472/1    2011 JPN PERAK SOLAF 1                                                 SULIT
SULIT                                                 5                  3472/1      For
Examiner,s
Use
7   Given that 4x = N, express 8x in terms of N.
[2 marks]

7

2

8   Solve the equation:
3– x ( 12 x ) = 3
[3 marks]

8

3

9   Simplify logb 8 × log4 b 2 ÷ log27 3.
[3 marks]

9

3

Lihat Halaman Sebelah
3472/1   2011 JPN PERAK SOLAF 1                                         SULIT
For       SULIT                                               6                       3472/1
Examiner,s
Use
10    Solve the equation:
log5 ( 4x – 1 ) = 1 + log5 ( 7 – x )
[3 marks]

10

3

11 It is given that a, 4, 11, b, ……………………. 46 is an arithmetic progression.
Find
(a) the value of a and of b,
(b) the number of terms the progression has.
[4 marks]
(a)

(b)

11

4

3472/1     2011 JPN PERAK SOLAF 1                                           SULIT
SULIT                                            7                                     3472/1      For
Examiner,s
Use
1
12   In a geometric progression, the ratio of the fifth term to the second term is       .
27
Given that the first term is 12, find
(a) the common ratio,
(b) the sum to infinity.
[3 marks]

12

3

13    An arithmetic progression has 11 terms. The first term is – 7 and the sum of the
last 7 terms is 441.
Find
(a) the common difference,
(b) the middle term.
[4 marks]
(a)

(b)                                                                                           13

4

Lihat Halaman Sebelah
3472/1     2011 JPN PERAK SOLAF 1                                              SULIT
For       SULIT                                       8                                       3472/1
Examiner,s
Use
y
14    The variables x and y are related by the equation    = nx2 + m, where m and n
m
are constants and m < 0. A straight line graph is obtained by plotting y against x 2
as shown in Diagram 14.
y
9

x2
O           6
Diagram 14
Find the value of m and of n.
[4 marks]

14

4

15 The variables x and y are related by the equation y = 10x3. When log10 y is plotted
against log10 x, a straight line graph passing through the point ( 2 , k ) is obtained.
Find the value of k.
[3 marks]

15

3

3472/1   2011 JPN PERAK SOLAF 1                                                     SULIT
SULIT                                            9                                   3472/1       For
Examiner,s
Use
16   Point P moves such that it is equidistant from R( – 1 , 3 ) and S( 2 , q ).
It is given that the equation of the locus of P is 6x + 4y = 19.
(a) Express the coordinates of the midpoint of RS in terms of q.
(b) Hence, find the value of q.
[3 marks]
(a)

(b)

16

3

17   Diagram 17 shows a straight line PQR with equation y = 2x + 3. Point P lies on the
y-axis.
y
● R( h , 15)
●

P●       Q

x
O
Diagram 17
Given that PQ : QR = 1 : 2, find
(a) the value of h,
(b) the coordinates of Q.
[4 marks]
(a)

17

(b)                                                                                                4

Lihat Halaman Sebelah
3472/1   2011 JPN PERAK SOLAF 1                                                  SULIT
For       SULIT                                           10                                      3472/1
Examiner,s
Use
18   In Diagram 18, ABC is a sector of a circle with centre B and ADB is a semicircle
with diameter AB.

D                  C

10 cm
A       B
Diagram 18
Given that  ABC = 2.5 radians, calculate the perimeter, in cm, of the shaded
region.
[3 marks]

18

3

19   Diagram 19 shows a quadrant PQR with centre R and a sector QXY of a circle
with centre Q.                       Q

6 cm
X
Y
2 cm
P                  R
Diagram 19

Given that  XQY =             radians, calculate the area, in cm 2, of the shaded region.
3
[3 marks]

19

3

3472/1   2011 JPN PERAK SOLAF 1                                                         SULIT
SULIT                                             11                                   3472/1       For
Examiner,s
Use
20 Diagram 20 shows part of the graph of y = f(x).
y
P               ●   R( 2 , 7 )

y = f(x)
Q

O                            x
Diagram 20                               [3 marks]
Given that    2
0   3 f ( x) dx  12 , calculate the area of the shaded region PQR.

20

3

5
21   Given that  1 3x  2  f ( x) dx 
2
, find the value  21 f ( x) dx .

2
[3 marks]

21

3

Lihat Halaman Sebelah
3472/1   2011 JPN PERAK SOLAF 1                                                     SULIT
For       SULIT                                       12                                       3472/1
Examiner,s
Use
22   The area of a circle is increasing at a rate of 3 cm2 s – 1.
Calculate the rate at which the radius of the circle is increasing at the instant its
perimeter is 9 cm.
[3 marks]

22

3

23   Diagram 23 shows a graph with equation y = x 3 – 12 x + 8.
y
P
●

x
O

Diagram 23
Given that point P is the maximum point of the graph, find the coordinates of P.
[3 marks]

23

3

3472/1   2011 JPN PERAK SOLAF 1                                                      SULIT
SULIT                                                  13                      3472/1       For
Examiner,s
Use
24 The set of numbers 2, 7, 4, 11, 5, n has a mean of 6.
Find
(a)   the value of n,
(b)   the median.
[3 marks]
(a)

(b)                                                                                    24

3

25   Diagram 25 shows some information about a set of numbers.

Numbers : x1 , x2 , x3 , x4 , x5

∑ x = 28 , ∑x 2 = 170

Diagram 25
Given that x2 = 8 and it is taken out from the set.
Calculate the standard deviation of the remaining numbers in the set.
[4 marks]

25

4

END OF QUESTION PAPER
3472/1     2011 JPN PERAK SOLAF 1                                             SULIT

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