Post on 07-Apr-2018
8/4/2019 Solaf 2011 Add Maths Set 1 Paper 1[Question Paper]
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NAMA .
TINGKATAN .
JABATAN PELAJARAN PERAK
JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU
Kertas soalan ini mengandungi 13 halaman bercetak.[Lihat halaman sebelah
3472/1 2011 JPN PERAK SOLAF1 SULIT
SOALAN LATIH TUBI BERFOKUS 1 3472 / 1ADDITIONAL MATHEMATICS
Kertas 1
April
2 jam Dua jam
Untuk Kegunaan Pemeriksa
Kod Pemeriksa :
SoalanMarkah
Penuh
Markah
Diperoleh
1 3
2 3
3 3
4 3
5 4
6 3
7 28 3
9 3
10 3
11 4
12 3
13 4
14 4
15 3
16 3
17 418 3
19 3
20 3
21 3
22 3
23 3
24 3
25 4
Jumlah 80
1. Kertas soalan ini mengandungi 25 soalan.
2. Answer all questions.
3. Write your answers in the spaces provided
in the question paper.
4. Show your working. It may help you to
get marks.
5. If you wish to change your answer, cross
out the answer that you have done. Then
write down the new answer.
6. The diagrams in the questions are not
drawn to scale unless stated.
7. The marks allocated for each question are
shown in brackets.
8. You may use a scientific calculator.
SULIT
8/4/2019 Solaf 2011 Add Maths Set 1 Paper 1[Question Paper]
2/13
For
Examiner,s
Use
SULIT 2 3472/1
Answer all questions
1 Diagram 1 shows an incomplete arrow diagram which represents the relationship
between setXand set Y.
State(a) the values ofp and q,
(b) the type of the relation.
[ 3 marks]
Answer :
(a)
(b)
2 Functionsfand g are such that f:x 2x5 and g :x 1hx.
Given that g1(1 ) = 4,
find
(a) the value of h,
(b) g(8).
[ 3 marks]
Answer :
(a)
(b)
3472/1 2011 JPN PERAK SOLAF1 SULIT
2
1
q
p
1
X square of Y
Diagram 1
3
1
3
2
8/4/2019 Solaf 2011 Add Maths Set 1 Paper 1[Question Paper]
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SULIT 3 3472/1
3 Functionsfand g are such that g :xx7 and gf:x 2x1.
Find
(a) gf(3),
(b) f(2).[3 marks]
Answer :
(a)
(b)
For
Examiner,s
Use
4 Diagram4 shows the graph of a quadratic functiony =f(x) with an axis of
symmetryx = 1.
(a) Find the value ofh.
(b) Solvef(x) 0.
[3 marks]
Answer :(a)
(b)
Lihat Halaman Sebelah
3472/1 2011 JPN PERAK SOLAF1 SULIT
3
3
x
y
O
y = f(x)
Diagram 4
2 h
3
4
8/4/2019 Solaf 2011 Add Maths Set 1 Paper 1[Question Paper]
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For
Examiner,s
Use
SULIT 4 3472/1
5 Both the quadratic equations,px28x + 6 = 0 and 3x
2+ 6xp + 1 = 0, wherep is a
constant, have two different roots.
Find the range of values ofp.
[4 marks]
Answer :
6 Diagram 6 shows some information about the graph of the quadratic function
y = ka(x + h )2, where a , h and kare constants.
(a) State the values ofh and k.
(b) Calculate the value ofa.
[3 marks]
Answer :
(a)
(b)
3472/1 2011 JPN PERAK SOLAF1 SULIT
4
5
y-intercept = 5
Coordinates of maximum point = ( 1 , 7 )
Diagram 6
3
6
8/4/2019 Solaf 2011 Add Maths Set 1 Paper 1[Question Paper]
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SULIT 5 3472/1
7 Given that 4x
= N, express 8x
in terms ofN.
[2 marks]
Answer :
For
Examiner,s
Use
8 Solve the equation:
3x( 12 x
) = 3
[3 marks]Answer :
9 Simplify logb 8 log4b2
log27 3.
[3 marks]
Answer :
Lihat Halaman Sebelah
3472/1 2011 JPN PERAK SOLAF1 SULIT
2
7
3
8
3
9
8/4/2019 Solaf 2011 Add Maths Set 1 Paper 1[Question Paper]
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For
Examiner,s
Use
SULIT 6 3472/1
10 Solve the equation:
log5 ( 4x1 ) = 1 + log5 ( 7x )
[3 marks]
Answer :
11 It is given that a, 4, 11, b, . 46 is an arithmetic progression.
Find
(a) the value ofa and ofb,
(b) the number of terms the progression has.
[4 marks]
Answer :
(a)
(b)
3472/1 2011 JPN PERAK SOLAF1 SULIT
3
10
4
11
8/4/2019 Solaf 2011 Add Maths Set 1 Paper 1[Question Paper]
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SULIT 7 3472/1
12 In a geometric progression, the ratio of the fifth term to the second term is27
1 .
Given that the first term is 12, find
(a) the common ratio,
(b) the sum to infinity.[3 marks]
Answer :
For
Examiner,s
Use
13 An arithmetic progression has 11 terms. The first term is7 and the sum of the
last 7 terms is 441.
Find
(a) the common difference,
(b) the middle term.
[4 marks]Answer :
(a)
(b)
Lihat Halaman Sebelah
3472/1 2011 JPN PERAK SOLAF1 SULIT
3
12
4
13
8/4/2019 Solaf 2011 Add Maths Set 1 Paper 1[Question Paper]
8/13
For
Examiner,s
Use
SULIT 8 3472/1
14 The variablesx andy are related by the equationm
y= nx
2+ m, where m and n
are constants and m < 0. A straight line graph is obtained by plottingy againstx2
as shown in Diagram 14.
Find the value ofm and ofn.
[4 marks]
Answer :
15 The variablesx andy are related by the equationy = 10x3. When log10y is plotted
against log10x, a straight line graph passing through the point ( 2 , k) is obtained.
Find the value of k.
[3 marks]
Answer :
3472/1 2011 JPN PERAK SOLAF1 SULIT
4
14
3
15
9
y
x2
O 6
Diagram 14
8/4/2019 Solaf 2011 Add Maths Set 1 Paper 1[Question Paper]
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SULIT 9 3472/1
16 Point P moves such that it is equidistant fromR(1 , 3 ) and S( 2 , q ).
It is given that the equation of the locus ofP is 6x + 4y = 19.
(a) Express the coordinates of the midpoint ofRS in terms ofq.
(b) Hence, find the value ofq.
[3 marks]Answer :
(a)
(b)
For
Examiner,s
Use
17 Diagram 17 shows a straight line PQR with equationy = 2x + 3. Point P lies on the
y-axis.
Given that PQ : QR = 1 : 2, find
(a) the value ofh,
(b) the coordinates ofQ.
[4 marks]Answer :
(a)
(b)
Lihat Halaman Sebelah
3472/1 2011 JPN PERAK SOLAF1 SULIT
3
16
4
17
x
y
O
R( h , 15)
P Q
Diagram 17
8/4/2019 Solaf 2011 Add Maths Set 1 Paper 1[Question Paper]
10/13
For
Examiner,s
Use
SULIT 10 3472/1
18 In Diagram 18,ABCis a sector of a circle with centreB andADB is a semicircle
with diameterAB.
Given that ABC
= 2.5 radians, calculate the perimeter, in cm, of the shaded
region. [3 marks]
Answer :
19 Diagram 19 shows a quadrant PQR with centreR and a sector QXYof a circlewith centre Q.
Given that XQY
=3
radians, calculate the area, in cm2, of the shaded region.
[3 marks]
Answer :
3472/1 2011 JPN PERAK SOLAF1 SULIT
3
18
3
19
Diagram 18
DC
BA
10 cm
Q
X
RP
Y
Diagram 19
6 cm
2 cm
8/4/2019 Solaf 2011 Add Maths Set 1 Paper 1[Question Paper]
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SULIT 11 3472/1
20 Diagram 20 shows part of the graph ofy =f(x).
[3 marks]
Given that 2
0123 dxxf )( , calculate the area of the shaded region PQR.
Answer :
For
Examiner,s
Use
21 Given that 2
12
523 dxxfx )( , find the value
2
1dxxf )( .
[3 marks]
Answer :
Lihat Halaman Sebelah
3472/1 2011 JPN PERAK SOLAF1 SULIT
3
20
3
21
x
y
O
R( 2 , 7 )P
Q
Diagram 20
y =f(x)
8/4/2019 Solaf 2011 Add Maths Set 1 Paper 1[Question Paper]
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For
Examiner,s
Use
SULIT 12 3472/1
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]
Answer :
23 Diagram 23 shows a graph with equationy =x312x + 8.
Given that point P is the maximum point of the graph, find the coordinates ofP.
[3 marks]
Answer :
3472/1 2011 JPN PERAK SOLAF1 SULIT
3
22
3
23
x
y
O
Diagram 23
P
8/4/2019 Solaf 2011 Add Maths Set 1 Paper 1[Question Paper]
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SULIT 13 3472/1
24 The set of numbers 2, 7, 4, 11, 5, n has a mean of 6.
Find
(a) the value ofn,
(b) the median.
[3 marks]Answer :
(a)
(b)
For
Examiner,s
Use
25 Diagram 25 shows some information about a set of numbers.
Given thatx2 = 8 and it is taken out from the set.
Calculate the standard deviation of the remaining numbers in the set.
[4 marks]
Answer :
END OF QUESTION PAPER3472/1 2011 JPN PERAK SOLAF1 SULIT
3
24
4
25
Numbers : x1 ,x2 ,x3 ,x4 ,x5
x= 28 , x2
= 170
Diagram 25