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MATHEMATICS F4 EMaS 07 / MODULE 1
2007 Hak Cipta JPNT 2
MODUL BIMBINGAN EMAS
MATHEMATICS ( FORM 4)
MODULE 1PAPER 1
1 Round off 23 881 correct to three
significant figures
A 2 388
B 2 389
C 23 880
D 23 900
2 Round off 0.080281 correct to three
significant figures
A 0.08
B 0.080
C 0.0803
D 0.08028
3 Round off 0.0009055 correct to twosignificant figures
A 0.00091B 0.000910
C 0.000906
D 0.00190
4 Express 2970000 in standard form.
A 2.97 10 4
B 297 106
C 2.97 106
D 297 104
5 Express 0.00173 in standard form.
A 1.73 10
B 11.73 10
C 11.73 10
D 1.73 10
6. State 3.07 10 6 as a single number
A 307 000
B 3 070 000
C 30 700 000
D 307 000 000
77
48000
8 10
A 6 10
B 10
6 10
C 6 1010
D 6 1012
8. The mass of an atom 6.02 10 29 kg.
The mass in g, of 100 atoms are
A 6.02 10 21
B 6.02 10 24
C 6.02 10 26
D 6.02 10 27
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MATHEMATICS F4 EMaS 07 / MODULE 1
2007 Hak Cipta JPNT 3
9 4.2 1086.3 10
7
A 2.1 107
B 2.1 10 8
C 3.57 10 7
D 3.57 108
10 87 106.21021.4
A 81061.1
B 71061.1
C
8
1095.3
D 71095.3
11. 3k(2 k) 5(2k 1) =
A 5k 5
B 5k + 5
C 3k2 4k 5
D 3k2 4k + 5
12. 3(h 1 ) + 4(1 2h) =
A h + 3
B 5h + 3
C 5h + 1
D 1
13.Given that m 3 = 2, then m =
A 5
B 1
C 1
D 5
14.Given that 2(p2) = 3(p +3), then p =
A 13
B 6
C 5D 1
15 Given that 12 = 2h 3(2h 2), then h =
A 2
3
B
9
C 7
D 5
16. x 2 5x + 6 =
A (x + 6)(x 1)
B (x + 1)(x+6)
C (x 3)(x 2)
D (x 3)(x + 2)
17. x
2
x
6 =
A (x + 6)(x 1)
B (x + 1)(x + 6)
C (x 3)(x 2)
D (x 3)(x + 2)
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MATHEMATICS F4 EMaS 07 / MODULE 1
2007 Hak Cipta JPNT 4
18.x 2 + 7x + 6 =
A (x + 6)(x 1)
B (x + 1)(x+6)
C (x 3)(x 2)
D (x 3)(x + 2)
.
19.x2 5x 6 =
A (x 6)(x + 1)
B (x + 1)(x+6)
C (x 3)(x 2)
D (x 3)(x + 2)
20. (4y 1)2 4y 2 =
A (3y 1)(4y 1)
B (2y 1)(6y 1)
C (y 1)(12y 1)
D (2y + 1)(6y + 1)
PAPER 2
1. Solve the quadratic equation5
42 x= x
2.Solve the quadratic equation y 2 + 3 = 7(y 1)
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MATHEMATICS F4 EMaS 07 / MODULE 1
2007 Hak Cipta JPNT 5
3. Solve the quadratic equation q =q
q412
4. Solve the quadratic equation5
122 2 m= m
5.
The diagram shows a solid cylinder with
the height of 15 cm. Some parts of the
cylinder which is in the form of a cone has
been taken out.
The height of the cone is 7.5 cm. Given thatthe diameter of the cylinder and the cone
base is 9 cm.
Using = 3.142, calculate the volume of
the remaining solid.
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MATHEMATICS F4 EMaS 07 / MODULE 1
2007 Hak Cipta JPNT 6
6
7.
M L
KJ
In the diagram , a hemisphere is joint to the base ofa right cone
Given that , the radius of the hemisphere and the base ofthe cone is 3.5 cm , and the height of the cone is 14 cm.
Using =7
22 , calculate the volume of the combined
solid.
The diagram shows a right prism is
combined with one half of a cylinderat a rectangular plane JKLM.
Given that JK = 7 cm, KL = 10 cm
and the height of the prism is 5 cm.
Using =7
22, calculate the volume
of the combined solid.
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MATHEMATICS F4 EMaS 07 / MODULE 1
2007 Hak Cipta JPNT 7
8.
9.
In the diagram, a solid cone is taken out from a solid
hemisphere.Given that, the diameter of the hemisphere is 8 cm, and
the diameter of the cone is 4 cm. The height of the cone
is 6 cm.Calculate the volume of the remaining solid
. ( Use =7
22).
In the diagram, a solid hemisphere with diameter PQ wastaken out from the solid cuboid with a square base. Pdan
Q are the midpoints of sides AD and BC respectively..
Using =7
22, calculate the volume of the remaining
solid.
.
FORMULAE
Volume of a cylinder = r2 h
Volume of a cone =3
1r
2h
Volume of a sphere = 4
r3
Volume of a right prism = cross sectional area length
F
GH
E
AB
CD
Q
P
15 cm
24 cm
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MATHEMATICS F4
MODUL BIMBINGAN EMaS
MATHEMATICS FORM 4
MODULE 2
PAPER 1
1 Given that 8 2
3
p kpk k, express
pin terms ofk.
A8 3
kp
k
B3 8
kp
k
C 5
3 8
kp
k
D 5
8 3
kp
k
2 Given that 4
4
nm
n, thenn=
A 4 4
1
m
m
B 4 4
1
m
m
C 1
1
m
m
D 1
1
m
k
3 Given that 3 b
ba
, then
A 3
1
b
a
B 3
1
ab
a
C 3
1 2 b a
D1 2
ab
a
4 Given that 3
2
sp
s
, expresssin terms
ofp .
A 3
p
B 3
2 1p
C 3
1 2p
D
3
2 1p
5 Given that3
2 m
ppm , expressm in
terms of p.
A13
6
p
p
B13
6p
p
C1
2
p
p
D
1
2
p
p
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MATHEMATICS F4 EMaS 07 / MODULE 2
6 Given that {2,3,5,6,7,9}P , then
one of the subsets ofPis
A {2,3,5,7}
B {1,2,3,5,7}
C {2,3,4,5,6}
D {5,6,7,8,9}
7 The following diagram shows the
setsM, NandPsuch that the
univesal set N P.
The shaded region represents the set
A ( ) N P
B ( ) N P
C ( ') N P
D ( ' ) N P
8 The diagram below is a Venn
diagram which shows the number of
element in set R, set S and set T.
Given that the universal set
S T and
( ') ( )S n S R , find the values ofx.
A 7
B 8
C 9
D 10
9 The diagram below is a Venn diagram
with the universal set X Y Z.
Which of the regions, A, B, C orD,
represent the set ' 'Y Z
10 It is given that the universal set
xxx ,2511:{ is an integer}.
SetP={x: x is multiple of 3} and setQ= {x: x is a prime number}.
Find set ( P Q).
A {11, 13, 17, 19, 23 }
B { 11, 14, 16, 20, 22, 25 }
C { 12, 15, 18, 21, 24 }
D { 12, 14, 16, 18, 20, 22, 24 }
11 Given that 2m 7 = 4(2 m), thenm =
A5
B5
C
5
D5
MP
N
T
RS
5 3x-2
x-17
4
6
X
Y
Z
A B
C
D
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MATHEMATICS F4 EMaS 07 / MODULE 2
12 Given that 1
2 - w = 43
, then w =
A 6
B 2
C 2
D 6
13 Given that 3k (k 1) = 9, then k=
A 1
B 2
C 4
D 5
14 Given that y + y
2= 15, theny =
A 5
B 10
C 15
D 20
15 Given that2
r+ 1 = r, thenr=
A 1
3
B1
C
D
16 Simplify
21 3
1 25
3m n
A2
B2
C2
9mn
D2
9m n
17 Simplify 4
3 1 2pk p k
A 10k
B 14
k
C 10k
D 5k
18 Simplify
153
23
8 p
mp
.
A2
B m
Cp
D4
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MATHEMATICS F4 EMaS 07 / MODULE 2
19 Simplify
16 2 2
14 8 4
16.
m n
m n
.
A
B
2
C
58m
D16m
20
3
5r can be written as
A 3 5r
B 5 3
r
C 5r
D 35r
PAPER 2
1 Calculate the value of m and of n that satisfy the following simultaneous linear
equations:
1
2 11m n
3 4 14m n
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MATHEMATICS F4 EMaS 07 / MODULE 2
2 Calculate the value of x and of y that satisfy the following simultaneous linear
equations:
2 9x y
3 13x y
3 Calculate the value of p and of q that satisfy the following simultaneous linear
equations:
15p q
3 18p q
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MATHEMATICS F4 EMaS 07 / MODULE 2
4 Calculate the value of d and of q that satisfy the following simultaneous linear
equations:
3 2 9d q
2d q
5 Calculate the value of d and of e that satisfy the following simultaneous linear
equations:
3 12d e
10d e
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MATHEMATICS F4 EMaS 07 / MODULE 2
6 (a) Complete the following mathematical sentences using the symbol > or < in
the empty box to form
(i) a true statement
-4 4
(ii) a false statement
(-2)3 -4
(b) Combine the following pair of statements to form a true statement :
Statements1: 6 ( -2) = 3
Statements2: 36 is a perfect square
...............
(c) Write downPremise2 to complete the following arguments:
Premise1 : If ABCDis a rectangle, then ABCDhas two axes of symmetry.
Premise2 : .............................................................................................................
Conclusion: ABCDis not a rectangle.
7 (a) State whether the following statement is true or false.
' 3 ( 5) 15 and 8 6 '
.
(b) Write down two implications based on the following sentence.
'5 10m if and only if 'm
Implication1 :.......................................................................................................
Implication2 :..
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MATHEMATICS F4 EMaS 07 / MODULE 2
(c) Complete the following arguments:
Premise1 : .............................................................................................................
Premise2 :PQRSis a quadrilateral.
Conclusion: PQRShas a sum of interior angles equal to 360o.
8 (a) Explain why '3 ( 5) 8' is a statement.
..
(b) Complete the following statement using a quantifier to make the statement true.
. odd numbers are multiples of 7 `.
(c) Make a conclusion using inductive reasoning for the number sequence 10, 28, 82,
244, which can be written as follows:
210 3 1
328 3 1
482 3 1
5244 3 1
=
9 (a) State whether each of the following statements is true or false:
(i) 3 64 4 .
(ii) 8 and 10.03 3 10 ......
(b) Write down two implications based on the following sentence.
BCis an equilateral triangle if and only if each of the interior angle of BCis
60o.
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MATHEMATICS F4 EMaS 07 / MODULE 2
...
..................................................................................................................
(c) Complete the premise in the following argument:
Premise1 :
Premise2 : 90 180 ox
Conclusion : sinxo is positive.
10 (a) Determine whether the following is a statement and give a reason for your answer.
' 2 3 5 1 '
(b) Complete the following statement using and or or so that the statement is false.
60 is a multiple of 12 . 20 is a factor of 30.
(c) State the converse of each of the following implications and state its truth value
(i) If 5 x , then 3 x .
.
(ii) If y= 7, theny + 2 = 9
.
(d) Make a conclusion using inductive reasoning for the number sequence -2, 0, 4, 12,
which can be written as follow
1(4 2 )
0 (4 2 )
(4 2 )
12 (4 2 )
= ..
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2007 Hak Cipta JPNT 2
MODUL BIMBINGAN EMAS
MATHEMATICS ( FORM 4)
MODULE 3PAPER 1
1 Express2
4
p
p as a single
fraction in its simplest form.
A 11 4
4
B5 4
4
p
C11 4
4
D 5 4
4
p
p
2 Express1 2
5
p p
p p
as a single
fraction in its simplest form.
A4 9
5
p
B 9
5
p
p
C9
5
p
p
D 95p
p
3 Express6m m
m
as a single
fraction in its simplest form.
A 3
2
B12 3
C12 3
D 3
4 Express
25 2
4 12
p p as a single
fraction in its simplest form.
A 1
6p
B
24 2
6
p
C
22 1
6
p
p
D
2
2 16
pp
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MATHEMATICS F4 EMaS 07 / MODULE 3
2007 Hak Cipta JPNT 3
5 Express2
3 2
3m as a single
fraction in its simplest form.
A7 4m
B2
11 4
6
m
m
C 5
6
m
m
D2
11 4
6
m
6 In the diagram below,PQRSTis a
regular pentagon and SUVWXY is a
regular hexagon.
The value of x is
A 18
B 33
C 48
D 60
7 In the diagram below,PQRSTU is a
regular hexagon.
The value ofx is
A 30o
B 40o
C 50o
D 60o
8 In the diagram below,ABCDE is a
regular pentagon.
The value of x+ y is
A 134
B 144
C 154
D 180
15
Q
P
C
Y
R S
T
U V
Wxo
X
x
PQ
S T
U
x
yE
D
C
BA
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MATHEMATICS F4 EMaS 07 / MODULE 3
2007 Hak Cipta JPNT 4
9 In the diagram below ,PQRSTU is a
regular hexagon.LTS is a straight
line.
Find the value of x.
A 15B 25
C 35
D 60
10 In the diagram below, ABCDEF is aregular hexagon.GABand GFD is a
straight lines.
The value of x +y is
A 60o
B 90o
C 120o
D 150o
11 Find thex-intercept of the straight line
3y = 4x + 8
A 1
2
B 1
2
C 2
D 2
12 The Following Diagram, MNis a
straight line.
What is the gradient ofMN?
A 2
B 1
2
C2
1
D 2
Ny
M
0 x
9
(- 4,1)
U
QP
S
xO
T
35
L
BA
F
E
D
C
y
Gx
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MATHEMATICS F4 EMaS 07 / MODULE 3
2007 Hak Cipta JPNT 5
13 In the Diagram bellow,LM is parallel
toRS.
Find the value of p.
A 1
B 2
C 3
D 4
14 The straight line VW has a
gradient of3
4 and y-intercept
= 12. Find itsx-intercept.
A 16
B 9
C 9
D 16
15 The following diagram shows a
straight line PQ on the Cartesain plane
The gradient of straight line PQ is
A 2
B1
C 1
D 2
16 The following diagram shows a
straight line PQ.
The equation of the straight line PQ is
A 4x+ 3y= 24
B 4x 3y= 24
C 4x 3y= 24
D 4x+ 3y= 24
y
x
y = 2x+3
2y = px 5
L
R
S
M
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MATHEMATICS F4 EMaS 07 / MODULE 3
2007 Hak Cipta JPNT 6
17 The gradient of the straight line
4x+ 2y = 7 is
A 4
B 2
C 2
D 4
18 Given that 2x+ 3y= 6 is parallel to
mx + 2y= 6,m =
A 4
B3
C3
D 4
19 The following diagram shows astraight lines AB.
If the gradient of AB is 1
, find the
value ofm.
A 10
B 6
C 20
D 26
20 Which of the following points lies on
the straight lines 91
xy ?
A (4, 11)
B (2, 8)
C (2, 8)
D (4, 11)
A(m, 6)
B(10, -2)
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MATHEMATICS F4 EMaS 07 / MODULE 3
2007 Hak Cipta JPNT 7
PAPER 2
1 Venn Diagram in answer space shows the setsP,Q and R. Given that the universal set,
=P Q R . On the diagram in the answer space, shade the region that represents:
(a) (P R)
(b) (P Q ) R.
[ 3marks ]
Answer:
(a) (b)
2 The Venn diagram in the answer space shows sets A, B and C. Given that the universal set
B C .
On the diagram provided in the answer spaces, shade
(a) the set ( ) 'B ,
(b) the set ( B ) ( B C ).
[ 3marks ]
Answer:
(a) (b)
C
A B
CBA
Q
P R
Q
P R
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MATHEMATICS F4 EMaS 07 / MODULE 3
2007 Hak Cipta JPNT 8
3 The Venn diagram shows the elements of set P, Q and R. Given that the universal
set= P Q R .
List the elements of set : -
(a) P Q R
(b) P Q R '
Answer :
(a)
[ 3marks ]
(b)
4 The Venn diagram in the answer space shows setP, QdanR..
On the diagram provided in the answer spaces, shade
(a) P Q
(b) ( )Q R P
[ 3marks ]
Answer:
(a)
(b)
P
Q
R
QP
.6
.2
QP
.3
.7
.5
.8.4
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MATHEMATICS F4 EMaS 07 / MODULE 3
2007 Hak Cipta JPNT 9
5 In the following diagram,O is the origin, point Kand pointPlies on the x-axis and pointNlies on the y-axis. Straight lineKL is parallel to straight line NPand straight lineMNis
parallel to the x-axis. The equation of straight lineNPis 2 18 0x y
(a) State the equation of the straight lineMN.
(b) Find the equation of the straightKL and hence, state the coordinate of the point K.
[5marks]
M
K
L(4,7)
O
y
xP
N
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MATHEMATICS F4 EMaS 07 / MODULE 3
2007 Hak Cipta JPNT 10
6 The following diagram shows,O is the origin. Point D lies on thex-axis and pointBlies
on they-axis. PointB is the midpoint ofACand the gradient ofBD is 4
5.
(a) Calculate the value ofk.
(b) Find the equation of the straightBD.
(c) Find thex-intercept of the straight line BD.
[5marks]
A(3,k)
xO
B
C(3 , 2)
4
D
y
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MATHEMATICS F4 EMaS 07 / MODULE 3
2007 Hak Cipta JPNT 11
7 The following diagram shows,O is the origin. Point B andClies on the x-axis andpointA andD lies on they-axis. ABis parallel to CE. The equation of the straight
lineBEisy + 2x + 12 = 0
(a) Find the x-intercept of the straight lineAB.
(b) Find the equation of straight lineCEand hence, state the coordinates of thepointD.
[5marks]
y
x0
A4
CB
D
E(3,6)
y+ 2x + 12 = 0
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MATHEMATICS F4 EMaS 07 / MODULE 3
2007 Hak Cipta JPNT 12
8 The following diagram shows, Ois the origin. The straight line RTis parallel to they-axis and OQ =OS.
Given the straight lineSTis 2xy 4 = 0.
Find
(a) the equation of the straight linePR
(b) the coordinates ofR.
[5marks]
O
S
Tx
R
Q
P
y
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MATHEMATICS F4 EMaS 07 / MODULE 3
2007 Hak Cipta JPNT 13
9 The following graph shows,PQ,QTand RSis a straight lines. PQand RSis parallel.PointR lies on theQTand O is the origin.
Given the straight lineSTisy = 3x+ 12.
Find
(a) the equation of the straight lineRS,
(b) the y-intercept of the straight lineQRT.[5marks]
T(12, -1)
S
R(5, 6)
Q
P
O x
y
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MATHEMATICS F4 EMaS 07 / MODULE 4
7 A beg contains 4 red pens, 2 black
pens and a number of blue pens. A
pen is chosen at random from the
beg.
The probability of choosing a black
pen is 1
8.
Find the probability of choosing a
blue pen.
A 1
B 3
8
C 5
8
D 3
8 Kartini buys three boxes of diskette.
Each box has 180 diskette in it. All
of the diskettes are put inside a
container. The probability of
choosing a spoilt diskette is 1
0.
How many of the diskette are not
spoilt?
A 531
B 534
C 537
D 538
9 In a class, nine students know how to
swim. If a student is chosen at
random from the class, the
probability that the student knows
how to swim is 1
3. Six students who
do not know how to swim then join
the class. If a student is now chosen
at random, calculate the probability
that the student does not know how
to swim.
A 2
3
B
C11
D11
10 The table below shows the number
of different coins in a handbag. The
frequency column is incomplete.
Coin Frequency
5 sen 3
10 sen
20 sen 5
50 sen 4
If a coin is drawn at random from the
handbag, the probability that it is a
coin with a value of less than 20 sen
is 1
2. Find the total number of coins
in the handbag.
A 6
B 12
C 15
D 18
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MATHEMATICS F4 EMaS 07 / MODULE 4
11 Which of the following graphs
represents 1
y ?
A
B
C
D
12
The equation of the graph shown in
the above diagram is
A 2
9y x
B 2 9y x
C 2 9y x
D 2
9y x
13 Which of the following graphs
represents y= 2 x3 ?
14
The equation of the graph shown
in the above diagram is
x
y
O
x
y
O
x
y
O
x
y
O
x
y
O
x
y
O
9
-3
0
2
B
0
2
0
2
D
x
y
0
2
y
x
2
O
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MATHEMATICS F4 EMaS 07 / MODULE 4
A y = x3
+ 2
B y = x 3 2
C y = x 3 + 2
D y =x32
15 Which of the following graphs
represents 2
y ?
A
B
C
D
16 In the diagram below,PST is a
tangent to the circle centreO, at
point S.
Find QOS
A 36
B 72
C 108
D 126
17 In the diagram below,DEis a
tangent to the circle ABCD atD.ACEis a straight line.
The value ofx is
A 30
B 40
C 70
D 110
x
y
O2
2
y
xO
2
x
y
O
2
x
y
O
T
P
Q
S
O
54o
80
xC
200
B
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MATHEMATICS F4 EMaS 07 / MODULE 4
18 In the diagram below,RSis a tangent
to the circle atS and PQRis a
straight line.
The value ofx is
A 20
B 25
C 30
D 40
19 In the diagram below,PQRis a
tangent to the circle with centreO atQ.
The value of x is
A 40
B 50
C 65
D 115
20 In the diagram below,PQRis atangent to the circle QSTW atQ.
The value of x is
A 68
B 62
C 60
D 58
x
0
P
65
Q
R
100P
P
x
O
118
x
S
T
W
60
P Q R
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MATHEMATICS F4 EMaS 07 / MODULE 4
PAPER 2
1 Data in table below shows the ages, in years, of 30 participants in a game on a FamilyDay.
3 14 18 12 18 23
12 24 7 13 22 13
16 13 19 27 6 16
24 29 9 13 25 8
11 20 17 15 14 17
(a) Based on the data in the table and by using a class interval of 5, complete thetable 1 in the answer space.
[4marks ](b) Based on your table in (a)
(i) State the modal class,
(ii) Calculate the estimated mean age of the data and give your answer correct
to 2 decimal places.[4marks ]
(c) For this part of the question, use the graph paper provided on page 7
By using a scale of 2 cm to 5 years onx-axis and 2 cm to 1 participant on the y-
axis, draw the histogram for the data.[4marks ]
Answer:(a)
Class Interval Frequency Midpoint
1 - 5
6 - 10
(b) (i)
(ii)
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(c) Refer graph on page27.
Graph for Question 1
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MATHEMATICS F4 EMaS 07 / MODULE 4
2 Table below shows the speed, in kmj-1
, of 40 cars which moving on a road .
Speed (kmj-1
) Frequency
35-39 0
40-44 4
45-49 5
50-54 7
55-59 9
60-64 6
65-69 5
70-74 4
Based on the table,
(a) state the modal class.[1marks ]
(b) (i) Complete the table on the answer space.
(ii) Calculate the estimated mean of speed.[6marks ]
(c) For this part of the question, use the graph paper provided on page 10You may use a flexible curve rule .
By using a scale of 2 cm to 5 kmj-1
on thex-axis and 2 cm to 5 cars on the y-axis,draw an ogive for the data.
From the ogive, find the median.[5marks]
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MATHEMATICS F4 EMaS 07 / MODULE 4
Answer:
(a)
(b) (i)
Speed (kmj-1
) Frequency Upper
Boundary Midpoint
CumulativeFrequency
3539 0
4044 4
4549 5
50
54 7
5559 9
6064 6
6569 5
7074 4
(ii) Mean speed =
(c) Refer graph on page10
Median =
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Graph for Question 2
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MATHEMATICS F4 EMaS 07 / MODULE 4
3 Data in table below shows the donations, in RM, collected by 40 pupils.
49 26 38 39 41 45 45 43
22 30 33 39 45 43 39 31
27 24 32 40 43 40 38 3534 34 25 34 46 23 35 37
40 37 48 25 47 30 29 28
(a) Based on the data in the table and by using a class interval of 5, complete the
table in the answer space.
[3marks ]
(b) Based on the table in (a), calculate the estimated mean of the donation collectedby a pupil.
[3marks ]
(c) For this part of the question, use the graph paper provided on page 12
By using a scale of 2 cm to RM 5 onx-axis and 2 cm to 1 pupil on they-axis,draw fequency polygon for the data.
[5marks ]
(d) Based on the fequency polygon in ( c), stateone piece of information about the
donations.
[1marks ]
Answer:
(a)
Class Interval Midpoint Frequency
2125 23 5
2630
(b)
(c) Refer graph on page12
(d)
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Graph for Question 3
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MATHEMATICS F4 EMaS 07 / MODULE 5
2007 Hak Cipta JPNT 2
MODUL BIMBINGAN EMAS
MATHEMATICS ( FORM 4)
MODULE 5PAPER 1
1. Given that n
m3
5 , then n
A5
B3
5
C 31
5
D13
5
2 Given that 110
nnt
, then t=
A1
102
B10
12 n
C10
1n
D10
1n
3Given that
121
p, then p =
A3
2
B2
3
C5
2
D2
5
4 Given thata
b3 = b, then b =
A b =a1
3
B b =a
a
1
3
C b =a1
3
D b =a
a
1
5. Diberi de
dm
3, maka e
Ad
m
3
B23d
m
C
d
m
3
2
D
2dm
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2007 Hak Cipta JPNT 3
6 In the diagram,Pis a point on the arc of
sector of a unit circle and with the origin
O as the centre.
Calculate the value of.
A 100 0
B 110 0
C 135 0
D 1550
7 In the diagram, QRSis a straight lineandPQ = PR .
Find the value of cos m
0
.
A - 0.3313
B - 0.5216
C - 0.5225
D - 0.8526
8. In the diagram,ABCis a straight line
and cos x0
=13
5.
Find the value of cos y0
.
A13
24
B13
12
C13
10
D13
5
9 In the diagram,PSRis a straight line,and PS = 10 cm.
Given that cos13
5PQR .
Calculate the value of tan .QSP
y
xO
P(0.7.0.7)
Q R S
R
63
m
D
C
B
A
y
x
P
Q
R
10 cm
S
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2007 Hak Cipta JPNT 4
A 5
B5
C 5
D 5
10 The diagram shows graph ofy = cosx
The value of p is
A 90o
B 180o
C 270o
D 360o
11 Given that cosy 0 = 1805.0 and
0 0 y 0 360 0 Thepossible values of y are :
A 79.6 , 259.6
B 100.4 , 190.4
C 190.4 , 259.6
D 100.4 , 259. 6
12 In the diagram, the flag pole is vertical.
Given that the angle of elevation of the
flag A from P is 350 .
Find, in m, the height of the pole.
A 0.13
B 3.79
C 3.80
D 7.74
13 In the diagram, QR is a vertical pole
with the height of 16 m. Points P andQ are on the horizontal line, 20 m
apart.
Calculate the angle of elevation of R
from P.
A 38 40
B 41 59
C 48 1
D 51 20
P
5.42 m
A
0
1
-1
xp
PQ
R
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2007 Hak Cipta JPNT 5
14 In the diagram,Pand Q are two pints on
a horizontal plane, and PT is a vertical
pole.
Given thatPQ= 20 m and the angle ofelevation of T from Q is 32 . Theheight of the pole is
A 10.6 m
B 12.5 m
C 17 m
D 32 m
15 In the diagram, Mand Q are two points
on the horizontal field, while LKM is avertical pole
The angle of elevation of point L fromtitikQ is 65 and the angle of elevationof point K from Q is s 30.
Calculate, in m , length of LK.
A 14.15
B 25.55
C 31.34
D 54.44
16 In the diagram, PR and QS represent
two towers on the horizontal ground.Given that the angle of depression of R
from S is .180
Calculate the distance between the two
towers.
A 76.94
B 80.90
C 26.29
D 25.00
17 The diagram shows a cuboid with
horizontal rectangle PQRS as the base.
R
V
W
T
P
QM
N
U
S
Q
T
20 m
Q
S
R
50 m
75 m
P
Q
L
K
M 20 m
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MATHEMATICS F4 EMaS 07 / MODULE 5
2007 Hak Cipta JPNT 6
MandNthe midpoints of PQand TU
respectively.Name the angle between the plane of
WPQ and plane ofPQUT
A WPT
B WMN
C WQS
D WQU
18 The diagram shows a right prism with a
horizontal rectangular base, EFGH.
Name the angle between the plane FHJ
and the plane GHJK.
A FJG
B FJK
C FHG
D FHK
19 The diagram shows a pyramid with ahorizontal rectangular base PQRS. M
andN are the midpoints ofQR andPS.
Vertex Vis right above of the point M.
Name the angle between the planePVS
and the planePQRS.
A VMN
B VNM
C VPQD VSQ
20 The diagram shows a pyramid with the
vertical rectangular base, ABCD. Theplane ABP is a horizontal plane.
Name the angle between line PC and
plane ABCD.
A
CPB
B
CPA
C PCD
D
PCA
F
K
J
H
G
E
Q
S
M
P
B
CD
A
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MATHEMATICS F4 EMaS 07 / MODULE 5
2007 Hak Cipta JPNT 7
PAPER 2
1 Diagram below shows a right prism. The base HJKL is a vertical rectangle. The rightangled triangle NHJ is the uniform cross section of the prism.
Identify and calculate the angle between the line KNand the plane HLMN.
[4marks]
M
N H
J
L
6 cm
12 cm
8 cm
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2007 Hak Cipta JPNT 8
2 Diagram below shows a cuboid with horizontal base TUVW.
Identify and calculate the angle between the plane PRVand the plane QRVU.
[4marks]
P Q
U
R
S
T
WV
5 cm
12 cm
4 cm
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MATHEMATICS F4 EMaS 07 / MODULE 5
2007 Hak Cipta JPNT 9
3 Diagram below shows a right prism with a horizontal square base ABCD. The rectangle
planeADPQis vertical and the rectangle plane PQRSis horizontal. TrapeziumABRQ is auniform cross-section of the prism with MandN are midpoints ofAB andDC respectively.
QR =PS= 8 cm and QA = PD= 10 cm.
Calculate the angle between the plane ABSand the plane ABCD.
[3marks]
M
A
B
CD
Q R
P
N
S
16 cm
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2007 Hak Cipta JPNT 10
4 Diagram below shows a sector OQRS with centre O. OQ and OS are diameters of two
semicircles.
Using =7
22, calculate
(a) the perimeter, in cm, of the whole diagram
(b) the area, in cm2 , of the shaded region
[6marks]
7 cm 120
O
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1
5 Diagram below shows a semicirclePQR with centre Oand sectorTRS with centreT. P is
the midpoint ofOR.
.
OP= 5 cm, QR= 6 cm and 60oRTS .
Using =7
22, calculate
(a) the perimeter, in cm, of the whole diagram
(b) the area, in cm2 , of the shaded region
[6marks]
P
Q
R
S
TO
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MATHEMATICS F4 EMaS 07 / MODULE 5
6 Diagram below shows a sectorOPQ with centreO. AOBRis semicircle withAOBas its
diameter andPO = 2 OA.
OB = 7 cm , POB = 45 dan AOR = 120.
Using =7
22, calculate
(a) the perimeter, in cm, of the whole diagram
(b) the area, in cm2 , of the shaded region
[6marks]
B
P
O A
R
Q
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