MATHEMATICS F4
mozac / MODULE 1
PROGRAM BIMBINGAN
MATHEMATICS FORM 4
MODULE 1 TOPICS:
OBJECTIVE QUESTIONS LINEAR EQUATIONS I STANDARD FORM QUADRATIC EXPRESSIONS SUBJECTIVES QUESTIONS SOLID GEOMETRY QUADRATIC EQUATION
1
MATHEMATICS F4
mozac / MODULE 1
MODUL BIMBINGAN MATHEMATICS ( FORM 4) MODULE 1 PAPER 1 1 Round off 23 881 correct to three significant figures A
2 388
B
2 389
C
23 880
D
23 900
5
0.08
B
0.080
C
0.0803
D
0.08028
A B
1.73 103 1.73 101
C
1.73 10 1
D
1.73 103
6. State 3.07 × 10
2 Round off 0.080281 correct to three significant figures A
Express 0.00173 in standard form.
6
as a single number
A 307 000 B 3 070 000
3 Round off 0.0009055 correct to two significant figures
7
C
30 700 000
D
307 000 000
48000 8 10 7
A B
0.00091 0.000910
A
6 10 4
C
0.000906
B
6 10 10
D
0.00190
C
6 × 10 10
D
6 × 10 12
4 Express 2970000 in standard form. 8. The mass of an atom 6.02 × 10 29 kg. The mass in g, of 100 atoms are
A B
2.97 10 6 297 10
C
2.97 10 6
A
6.02 × 10
D 297 10 4
B
6.02 × 10
C
6.02 × 10
D
6.02 × 10
4
2
21 24 26 27
MATHEMATICS F4
9
14. Given that 2(p ─2) = 3(p +3), then p =
4.2 × 10 8 −6.3 × 10 7 A B
10
mozac / MODULE 1
2.1 × 10
7
2.1 × 10
8 7
C
3.57 × 10
D
3.57 × 108
4.2110 7 2.6 10 8 A
1.61 108
B
1.61 10
C
3.95 10 8
D
3.95 10 7
A
– 13
B
–6
C
–5
D
–1
15 Given that 12 = 2h – 3(2h – 2), then h =
A
7
2 B
−
C
−
D
−
11. 3k(2 – k) −5(2k – 1) = A
−5k −5
B
−5k + 5
C
−3k 2 −4k −5
D
−3k −4k + 5
9 2
7 2 5 2
16. x 2 −5x + 6 =
2
12. 3(h – 1 ) + 4(1 – 2h) = A
h+3
B
−5h + 3
C
−5h + 1
D
1 17.
13. Given that m – 3 = 2, then m = A
−3
– 5
B
–1
C
1
D
5
3
A
(x + 6)(x – 1)
B
(x + 1)(x+6)
C
(x – 3)(x – 2)
D
(x – 3)(x + 2)
x 2 −x −6 = A
(x + 6)(x – 1)
B
(x + 1)(x + 6)
C
(x – 3)(x – 2)
D
(x – 3)(x + 2)
MATHEMATICS F4
mozac / MODULE 1
18. x 2 + 7x + 6 =
20.
(4y – 1) 2 – 4y 2 =
A
(x + 6)(x – 1)
A
(3y – 1)(4y – 1)
B
(x + 1)(x+6)
B
(2y – 1)(6y – 1)
C
(x – 3)(x – 2)
C
(y – 1)(12y – 1)
D
(x – 3)(x + 2)
D
(2y + 1)(6y + 1)
. 19. x 2 −5x −6 = A
(x −6)(x + 1)
B
(x + 1)(x+6)
C
(x – 3)(x – 2)
D
(x – 3)(x + 2)
PAPER 2 2 1. Solve the quadratic equation x 4 = x 5
2. Solve the quadratic equation y 2 + 3 = 7(y – 1)
4
MATHEMATICS F4
mozac / MODULE 1
3. Solve the quadratic equation q = 12 4q q
4.
Solve the quadratic equation
2m 2 12 = −m 5
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 that the diameter of the cylinder and the cone base is 9 cm. Using = 3.142, calculate the volume of the remaining solid.
5
MATHEMATICS F4
mozac / MODULE 1
6
L
M
J
The diagram shows a right prism is combined with one half of a cylinder at a rectangular plane JKLM. Given that JK = 7 cm, KL = 10 cm and the height of the prism is 5 cm.
K
Using =
22 , calculate the volume 7
of the combined solid.
7. In the diagram , a hemisphere is joint to the base of a right cone Given that , the radius of the hemisphere and the base of the cone is 3.5 cm , and the height of the cone is 14 cm.
Using = solid.
6
22 , calculate the volume of the combined 7
MATHEMATICS F4
mozac / MODULE 1
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
8.
. ( Use =
9.
A
B
P Q D
C
24 cm
22 ). 7
In the diagram, a solid hemisphere with diameter PQ was taken out from the solid cuboid with a square base. P dan Q are the midpoints of sides AD and BC respectively.. Using =
22 , calculate the volume of the remaining 7
solid. . H
G
15 cm E
F
FORMULAE Volume of a cylinder = r 2 h 1 Volume of a cone = r 2 h 3 4 Volume of a sphere = r3 3 Volume of a right prism = cross sectional area × length
7
MATHEMATICS F4
mozac / MODULE 2
PROGRAM BIMBINGAN
MATHEMATICS FORM 4
MODULE 2 TOPICS:
OBJECTIVE QUESTIONS LINEAR EQUATIONS II REARRANGING FORMULAE I INDEX SETS SUBJECTIVES QUESTIONS SIMULTANEOUS EQUATIONS METHEMATICAL REASONING
1
MATHEMATICS F4
mozac / MODULE 2
MODUL BIMBINGAN MATHEMATICS FORM 4 MODULE 2 PAPER 1 1
2
8 p 2k pk k , express 3 p in terms of k.
A
k p 8 3 k
B
k p 3 k 8
C
5k p 3 k 8
D
5k p 8 3 k
4m 4 1 m
B
4m 4 1 m
C
m 1 1 m
D
3
4
4 n Given that m , then n = 4 n
A
A
5
b 3 b , then a
3 b 1 a
B
3a b 1 a
C
3 b 1 2a
s 3 Given that p , express s in terms 2s of p.
A
3 p
B
3 2 p 1
C
3 1 2 p
D
3 2 p 1
m 3
Given that pm 2 p , express m in terms of p.
m 1 1 k
Given that
a b 1 2 a
D
Given that
2
A
6p 3 p 1
B
6p 3 p 1
C
2p p 1
D
2p p 1
MATHEMATICS F4
6
mozac / MODULE 2
Given that P {2,3,5,6,7,9} , then
n (S ') n (S R ) , find the values of x.
one of the subsets of P is
A
{2,3,5,7}
B
{1, 2,3,5,7}
C
{2,3, 4,5,6}
D
{5,6,7,8,9}
9
A
7
B
8
C
9
D
10
The diagram below is a Venn diagram with the universal set X Y Z .
7
The following diagram shows the Z
sets M, N and P such that the univesal set M N P .
C D
X A
M
Y
B
P N
Which of the regions, A, B, C or D, represent the set X 'Y 'Z
10
The shaded region represents the set
8
It is given that the universal set {x : 11 x 25, x is an integer}. Set P ={x : x is multiple of 3} and set Q = {x : x is a prime number}. Find set ( P Q )’.
A
( M N ) P
B
( M N ) P
C
( M N ') P
A
{11, 13, 17, 19, 23 }
D
( M ' N ) P
B
{ 11, 14, 16, 20, 22, 25 }
C
{ 12, 15, 18, 21, 24 }
D
{ 12, 14, 16, 18, 20, 22, 24 }
The diagram below is a Venn diagram which shows the number of
11 Given that 2m – 7 = 4(2 – m), then m =
element in set R, set S and set T. T
A
2 5
B
5 2
C
2 5
D
5 2
4 6 5
7 x-1 x-2
3
R
S
Given that the universal set R S T and
3
MATHEMATICS F4
12
A
–6
B
–2
C
2
16
1 1 m2 p3 Simplify 3 m n 2 5 p
A
6n p2
B
9n p2
C
9mn p2
D
9m4 n p2
6
Given that 3k – (k – 1) = 9, then k = A
14
2
Given that 2 - 1 w = 4 , then w = 3
D
13
mozac / MODULE 2
1
B
2
C
4
D
5
17
Given that y +
y = 15, then y = 2
p
Simplify pk 3 A
p 5k 10
A
5
B
p 3k 14
B
10
C
p 3k 10
C
15
D
p 2k 5
D
20
4
1 6 3
15
Given that
r + 1 = r, then r = 2
18
Simplify
1 3
A
2 p
B
1 4
B
2m p
C
3 4 C
8 mp
D
8m p4
D
8m p mp 3
A
4 3
4
1 2
2
k
5
.
MATHEMATICS F4
19
Simplify
mozac / MODULE 2
m6 16n 2 1 4 8 4
m n
1 2
3
..
20
r 5 can be written as A
3
r5
5
r
A
4m5 n
B
B
4m 2 n
C
r
D
5r
C
8m5 n
D
16m5 n
3
5
3
3
PAPER 2 1
Calculate the value of m and of n that satisfy the following simultaneous linear equations:
1 m 2 n 11 2 3m 4 n 14
5
MATHEMATICS F4
2
mozac / MODULE 2
Calculate the value of x and of y that satisfy the following simultaneous linear equations:
x 2 y 9 3x y 13
3
Calculate the value of p and of q that satisfy the following simultaneous linear equations:
1 2 p q 5 2 3 p q 18
6
MATHEMATICS F4
4
mozac / MODULE 2
Calculate the value of d and of q that satisfy the following simultaneous linear equations:
3d 2 q 9 6d q 2
5
Calculate the value of d and of e that satisfy the following simultaneous linear equations:
3d e 12 d 2e 10
7
MATHEMATICS F4
6
(a)
mozac / MODULE 2
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
(b)
-4
Combine the following pair of statements to form a true statement : Statements 1: 6 ÷ ( -2) = 3 Statements 2: 36 is a perfect square ……………………………………..……………………………………….............
(c)
Write down Premise 2 to complete the following arguments: Premise 1 : If ABCD is a rectangle, then ABCD has two axes of symmetry. Premise 2 : ............................................................................................................. Conclusion : ABCD is 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. '5m 10 if and only if m 2'
Implication 1 :....................................................................................................... Implication 2 :…………………………………………………………………..
8
MATHEMATICS F4
(c)
mozac / MODULE 2
Complete the following arguments:
Premise 1 : ............................................................................................................. Premise 2 : PQRS is a quadrilateral. Conclusion : PQRS has a sum of interior angles equal to 360 o.
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: 10 32 1 28 33 1 82 34 1 244 35 1
… = ……
9
(a)
(b)
………………………………………………
State whether each of the following statements is true or false: 64 4
(i)
3
(ii)
5 8 and 0.03 3 10 1 …………………………………………......
…………………………………………….
Write down two implications based on the following sentence. ABC is an equilateral triangle if and only if each of the interior angle of ABC is
60o .
9
MATHEMATICS F4
mozac / MODULE 2
...……………………………………………………………………………… ……..................................................................................................................
(c)
Complete the premise in the following argument: Premise 1
: ……………………………………………………………………
Premise 2
: 90o x 180o
Conclusion : sin xo 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 x 5 , then x 3 . ……………………………………………………………………………….
(ii)
If y = 7, then y + 2 = 9 ……………………………………………………………………………….
(d)
Make a conclusion using inductive reasoning for the number sequence -2, 0, 4, 12, ……… which can be written as follow 2 (4 21 ) 0 (4 2 2 ) 4 (4 2 3 ) 12 (4 24 )
… = ……
..………………………………………………
10
PROGRAM BIMBINGAN
MATHEMATICS FORM 4
MODULE 3 TOPICS:
OBJECTIVE QUESTIONS ALGEBRAIC FRACTIONS POLYGONS THE STRAIGHT LINE SUBJECTIVES QUESTIONS SETS THE STRAIGHT LINE
1
MODUL BIMBINGAN MATHEMATICS ( FORM 4) MODULE 3 PAPER 1 1
Express
3 p 2 as a single 4p p
3
2
3 m m 6 as a single m 2m
fraction in its simplest form.
fraction in its simplest form. A
Express
11 4 p 4p
A
3 2
B
5 4 p 4p
B
12 3m 2m
C
11 4 p 4p
C
12 3m 2m
D
5 4 p 4p
D
6 3m m
p 1 2 p Express as a single 5p p
4
A
B
6 p 9 5p
3 p 5 p 2 2 as a single 4 12 p
fraction in its simplest form.
fraction in its simplest form.
4 p 9 5p
Express
A
p 1 6p
B
4 p 2 2 6p
C
2 p 9 5p
C
2 p 2 1 6p
D
6 p 9 5p
D
2 p 2 1 6p
2
MATHEMATICS F4
5
mozac / MODULE 3
Express 3 2 m as a single 2
2m
7
3m
In the diagram below, PQRSTU is a regular hexagon.
fraction in its simplest form.
7m 4 6m 2
A B
11m 4 6m 2
C
2m 5 2 6m
6
R
U
x
S
11m 4 6m 2
D
P
Q
o
T
The value of x is
In the diagram below, PQRST is a regular pentagon and SUVWXY is a regular hexagon.
A
30o
B
40o
C
50o
D
60o
P U
Q
8
V
In the diagram below, ABCDE is a regular pentagon.
T R
xo
D
SS C
xo
W
E
yo C
o
15
Y
X
A
B
The value of x + y is
The value of x is A
18
A
134
B
33
B
144
C
48
C
154
D
60
D
180
3
MATHEMATICS F4
9
mozac / MODULE 3
In the diagram below , PQRSTU is a regular hexagon. LTS is a straight line. P x
11
O
R
350
12
Find the value of x.
10
15
B
25
C
35
D
60
1 2
B
1 2
C
2
D
2
S
T
A
A
Q
U
L
Find the x-intercept of the straight line 3y = 4x + 8
The Following Diagram, MN is a straight line. y
9
(- 4,1)
In the diagram below, ABCDEF is a regular hexagon. GAB and GFD is a straight lines.
E
0 M
D yo
What is the gradient of MN ?
F
C
xo G
A
B
B
90o
C
120o
D
150o
2
B
1 2
D
o
60
A
C
The value of x + y is A
N
4
1 2
2
x
MATHEMATICS F4
13
mozac / MODULE 3
In the Diagram bellow, LM is parallel to RS.
15
The following diagram shows a straight line PQ on the Cartesain plane
y R
L y = –2x+3
x 2y = px – 5
14
The gradient of straight line PQ is
S A
2
M
B
1 2
Find the value of p.
C
D
2
A
–1
B
–2
C
–3
D
–4
16
1 2
The following diagram shows a straight line PQ.
The straight line VW has a gradient of 4 and y-intercept
3
= 12. Find its x-intercept. A
16
B
9
C
9
The equation of the straight line PQ is
D
16
A
4x + 3y = 24
B
4x 3y = 24
C
4x 3y = 24
D
4x + 3y = 24
5
MATHEMATICS F4
17
18
mozac / MODULE 3
The gradient of the straight line 4x + 2y = 7 is A
4
B
2
C
2
D
4
19
B(10, -2) A(m, 6) If the gradient of AB is
Given that 2x + 3y = 6 is parallel to mx + 2y = 6, m = A
4 3
B
3 4
C
3 4
D
4 3
The following diagram shows a straight lines AB.
1 , find the 2
value of m.
20
A
10
B
6
C
20
D
26
Which of the following points lies on
1 2
the straight lines y x 9 ?
6
A
(4, 11)
B
(2, 8)
C
(2, 8)
D
(4, 11)
MATHEMATICS F4
mozac / MODULE 3
PAPER 2 1
Venn Diagram in answer space shows the sets P, 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. [ 3 marks ]
Answer :
Q
(a)
P
2
Q
(b)
P
R
R
The Venn diagram in the answer space shows sets A, B and C. Given that the universal set A B C . On the diagram provided in the answer spaces, shade (a)
the set ( A B ) ' ,
(b)
the set ( A B ) ( B C ). [ 3 marks ]
Answer :
A
B
(a)
(b)
C
7
A
B
C
MATHEMATICS F4
3
mozac / MODULE 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) (b)
P
.1 .3
P Q R P Q R'
Q
.5 .2
.6
.7
Answer :
.4
.8 R
(a)
[ 3 marks ]
(b)
4
The Venn diagram in the answer space shows set P, Q dan R.. On the diagram provided in the answer spaces, shade (a) P Q (b) (Q R P) Q
[ 3 marks ] Answer : (a)
P
R
P
Q
(b)
R
8
MATHEMATICS F4
5
mozac / MODULE 3
In the following diagram, O is the origin, point K and point P lies on the x-axis and point N lies on the y-axis. Straight line KL is parallel to straight line NP and straight line MN is parallel to the x-axis. The equation of straight line NP is x 2 y 18 0
y
L(4,7)
K
P x
O
M
N
(a)
State the equation of the straight line MN.
(b)
Find the equation of the straight KL and hence, state the coordinate of the point K. [5 marks]
9
MATHEMATICS F4
6
mozac / MODULE 3
The following diagram shows, O is the origin. Point D lies on the x-axis and point B lies on the y-axis. Point B is the midpoint of AC and the gradient of BD is 4 .
5
y A(−3, k)
4
B
C (3 , 2)
D
O
x
(a) Calculate the value of k. (b) Find the equation of the straight BD. (c) Find the x-intercept of the straight line BD. [5 marks]
10
MATHEMATICS F4
7
mozac / MODULE 3
The following diagram shows, O is the origin. Point B and C lies on the x-axis and point A and D lies on the y-axis. AB is parallel to CE. The equation of the straight line BE is y + 2x + 12 = 0 y 4 A
0
B
C
x
y + 2x + 12 = 0 D
E (−3, −6)
(a)
Find the x-intercept of the straight line AB.
(b)
Find the equation of straight line CE and hence, state the coordinates of the point D. [5 marks]
11
MATHEMATICS F4
8
mozac / MODULE 3
The following diagram shows, O is the origin. The straight line RT is parallel to the y-axis and OQ = OS.
y
R
Q
P
O
T
x
S
Given the straight line ST is 2x – y – 4 = 0. Find (a)
the equation of the straight line PR
(b)
the coordinates of R. [5 marks]
12
MATHEMATICS F4
9
mozac / MODULE 3
The following graph shows, PQ, QT and RS is a straight lines. PQ and RS is parallel. Point R lies on the QT and O is the origin.
y S
Q
R (5, 6)
x
O P
T (12, -1)
Given the straight line ST is y = 3x + 12. Find (a)
the equation of the straight line RS,
(b)
the y-intercept of the straight line QRT. [5 marks]
13
PROGRAM BIMBINGAN
MATHEMATICS FORM 4
MODULE 4 TOPICS:
OBJECTIVE QUESTIONS LINEAR INEQUALITIES PROBABILITY CIRCLES GRAPHS OF FUNCTIONS I SUBJECTIVES QUESTIONS STATISTICS
1
MODUL BIMBINGAN MATHEMATICS FORM 4 MODULE 4 PAPER 1
1
2
The solution for 6 x 3x 18 is
A
x 6
B
x 3
C
x 3
D
x 6
5
List all integers x that satisfy the 1 inequalities x 4 and 1 5 x 9 . 2
C
5, 6
D
4, 5, 6
List all the integer values of q which satisfy both the inequalities 3q 2q 1 17 and 18. 2 A
9, 10, 11
B
9, 10, 11, 12
A
x 2
C
8, 9, 10, 11
B
x 6
D
8, 9, 10, 11, 12
C
2 x 8
D
2 x 8 6
It is given that set K is {0, 1, 2, 4, 5, 7, 11, 15, 19, 21, 27}. A number is
3
4
The solution for A
n 4
B
n 4
C
n 4
D
n 4
n 1 2n 7 is 2
choosen at random from the elements of set K. Find the probability that the number chosen is a prime number.
List all the integer values of m which satisfy both the inequalities m 6 and 15 2m 7.
A
5
B
4, 5
2
A
4 11
B
5 11
C
6 11
D
7 11
MATHEMATICS F4
7
mozac / MODULE 4
A beg contains 4 red pens, 2 black
probability that the student knows
pens and a number of blue pens. A
how to swim is
pen is chosen at random from the
1 . Six students who 3
beg.
do not know how to swim then join
The probability of choosing a black
the class. If a student is now chosen at random, calculate the probability
1 . 8
pen is
that the student does not know how
Find the probability of choosing a
to swim.
blue pen.
1 4
A
3 8
B
5 8
C
A
2 3
B
5 8
C
3 11
D
8 11
3 4
D
10
The table below shows the number of different coins in a handbag. The
8
Kartini buys three boxes of diskette.
frequency column is incomplete.
Each box has 180 diskette in it. All
Coin
Frequency
of the diskettes are put inside a
5 sen
3
container. The probability of
10 sen
choosing a spoilt diskette is
1 . 90
20 sen
5
50 sen
4
How many of the diskette are not spoilt?
If a coin is drawn at random from the handbag, the probability that it is a
9
A
531
B
534
C
537
D
538
coin with a value of less than 20 sen is
1 . Find the total number of coins 2
in the handbag.
A
6
In a class, nine students know how to
B
12
swim. If a student is chosen at
C
15
random from the class, the
D
18
3
MATHEMATICS F4
11
mozac / MODULE 4
Which of the following graphs
13
1 represents y ? x
y
A
y
A
Which of the following graphs represents y = 2 – x3 ?
x
0 O
x −2
B
y
y
B O
x 2
x
0
y
C
O
y
C
x
x
0 y
D
−2
O
x
y D
y
12
2
9
-3
0
O
14
x
The equation of the graph shown in
A
y x 2 9
B
y x 2 9
C
y x2 9
D
y x2 9
y
O
the above diagram is
x
x
─2
The equation of the graph shown in the above diagram is
4
MATHEMATICS F4
mozac / MODULE 4
16 3
A
y = x +2
B
y = x 3 ─2
C
y = ─x 3 + 2
D
y = ─x 3 ─2
In the diagram below, PST is a tangent to the circle centre O, at point S. Q
O
15
Which of the following graphs
54o
P
2 x
represents y ?
S T Find QOS
y
A
2
O
−2
x
y
A
36
B
72
C
108
D
126
B 17 O
x
In the diagram below, DE is a tangent to the circle ABCD at D. ACE is a straight line. B 800
y
C
C
2 A O
D
200 D
x
y The value of x is
2 O
x
5
A
30
B
40
C
70
D
110
E o
x
MATHEMATICS F4
18
mozac / MODULE 4
In the diagram below, RS is a tangent to the circle at S and PQR is a straight line.
20
In the diagram below, PQR is a tangent to the circle QSTW at Q.
T Q
P
R W
xº 40º
S
118º
S
x º 60 º Q
P The value of x is
19
The value of x is A
68
25
B
62
C
30
C
60
D
40
D
58
A
20
B
In the diagram below, PQR is a tangent to the circle with centre O at Q. S P
65º
100º O xº
R
Q
P
The value of x is A
40
B
50
C
65
D
115
6
R
MATHEMATICS F4
mozac / MODULE 4
PAPER 2 1
Data in table below shows the ages, in years, of 30 participants in a game on a Family Day.
(a) (b)
(c)
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
Based on the data in the table and by using a class interval of 5, complete the table 1 in the answer space. [4 marks ] 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. [4 marks ]
For this part of the question, use the graph paper provided on page 7 By using a scale of 2 cm to 5 years on x-axis and 2 cm to 1 participant on the yaxis, draw the histogram for the data. [4 marks ]
Answer: (a) Class Interval
Frequency
1-5 6 - 10
(b)
(i)
(ii)
7
Midpoint
MATHEMATICS F4
(c)
mozac / MODULE 4
Refer graph on page 27.
Graph for Question 1
©2007 Hak Cipta JPNT
8
MATHEMATICS F4
2
mozac / MODULE 4
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. [1 marks ]
(b)
(i)
Complete the table on the answer space.
(ii)
Calculate the estimated mean of speed. [6 marks ]
(c)
For this part of the question, use the graph paper provided on page 10 You may use a flexible curve rule. By using a scale of 2 cm to 5 kmj -1 on the x-axis and 2 cm to 5 cars on the y-axis, draw an ogive for the data. From the ogive, find the median. [5 marks]
9
MATHEMATICS F4
mozac / MODULE 4
Answer: (a)
(b)
(i)
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
(ii)
Upper Boundary
Mean speed =
(c) Refer graph on page 10 Median =
10
Midpoint
Cumulative Frequency
MATHEMATICS F4
mozac / MODULE 4
Graph for Question 2
©2007 Hak Cipta JPNT
11
MATHEMATICS F4
3
mozac / MODULE 4
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
35
34
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. [3 marks ]
(b)
Based on the table in (a), calculate the estimated mean of the donation collected by a pupil. [3 marks ]
(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 on x-axis and 2 cm to 1 pupil on the y-axis, draw fequency polygon for the data. [5 marks ]
(d)
Based on the fequency polygon in (c), state one piece of information about the donations. [1 marks ]
Answer: (a) Class Interval
Midpoint
Frequency
21 – 25
23
5
26 – 30
(b)
(c)
Refer graph on page 12
(d)
12
MATHEMATICS F4
mozac / MODULE 4
Graph for Question 3
13
MATHEMATICS F4
mozac / MODULE 5
PROGRAM BIMBINGAN
MATHEMATICS FORM 4
MODULE 5 TOPICS:
OBJECTIVE QUESTIONS REARRANGING FORMULAE II TRIGONOMETRY ANGLES OF ELEVATION AND DEPRESSIONS SUBJECTIVES QUESTIONS PERIMETERS AND AREAS OF CIRCLES LINES AND PLANES IN 3-DEMENSIONS
1
MATHEMATICS F4
mozac / MODULE 5
MODUL BIMBINGAN MATHEMATICS ( FORM 4) MODULE 5 PAPER 1
n 5 , then n 3n
1. Given that m
5 2m
A
5 3m 1
B
4
C
2 5
D
5 2
5 1 3m
C
5 3m 1
D
2 Given that
10 n 1 , then t = nt t
A
10 n 2 1
B
n 2 1 10
C
n 1 10
3 Given that
A
b=
3 1 a
B
b=
3a 1 a
C
b=
3 1 2a
D
b=
a 12 a
d 5. Diberi m d , maka e 3e
A
n 1 10
D
B
1 2 p 1 , then p = 4 2
C D
A
2 3
B
3 2
b 3 = b, then b = a
Given that
2
m 3d m 3d 2 m2 3d m 2d 3
MATHEMATICS F4
6
mozac / MODULE 5
In the diagram, P is a point on the arc of sector of a unit circle and with the origin O as the centre.
8.
In the diagram, ABC is a straight line and cos x 0 =
5
.
A
13
y B yº
P(−0.7.0.7)
x
O
D Find the value of cos y 0 .
Calculate the value of .
7
A
100 0
B
110 0
C
135
0
D
155
0
xº
C
In the diagram, QRS is a straight line and PQ = PR . 9
R
A
24 13
B
12 13
C
10 13
D
5 13
In the diagram, PSR is a straight line, and PS = 10 cm.
R
63º mº Q
R
S S
Q
10 cm
Find the value of cos m 0 . A
- 0.3313
B
- 0.5216
C
- 0.5225
D
- 0.8526
P 5 . 13
Given that cos PQR
Calculate the value of tan QSP.
3
MATHEMATICS F4
A
mozac / MODULE 5
5 3
B
5 2
C
5 3
D
5 2
12 In the diagram, the flag pole is vertical. Given that the angle of elevation of the flag A from P is 35 0 . A
P 5.42 m
10
The diagram shows graph of y = cos x y
Find, in m, the height of the pole. A
0.13
B
3.79
C
3.80
D
7.74
1
p
0o
x
-1
13
The value of p is A
90o
B
180o
C
o
270
D
360o
R
Q
11 Given that cos y 0 = 0. 1805 and 00
y 0 360 0
In the diagram, QR is a vertical pole with the height of 16 m. Points P and Q are on the horizontal line, 20 m apart.
P
Calculate the angle of elevation of R from P.
The
possible values of y are :
A
79.6 , 259.6
B
100.4 , 190.4
C
190.4 , 259.6
D
100.4 , 259. 6
4
A
38° 40´
B
41° 59´
C
48° 1´
D
51° 20´
MATHEMATICS F4
14
mozac / MODULE 5
In the diagram, P and Q are two pints on a horizontal plane, and PT is a vertical pole. 16
T
C
31.34
D
54.44
In the diagram, PR and QS represent two towers on the horizontal ground. Given that the angle of depression of R 0 from S is 18 .
S
P
20 m
R
Q
50 m
Given that PQ = 20 m and the angle of elevation of T from Q is 32 . The height of the pole is
15
A
10.6 m
B
12.5 m
C
17 m
D
32 m
75 m
P
Q
Calculate the distance between the two towers.
In the diagram, M and Q are two points on the horizontal field, while LKM is a vertical pole
17
A
76.94
B
80.90
C
26.29
D
25.00
The diagram shows a cuboid with horizontal rectangle PQRS as the base.
L W T
K
V N
20 m
M
Q
U S
The angle of elevation of point L from titik Q is 65○ and the angle of elevation of point K from Q is s 30○.
R
P
Calculate, in m , length of LK.
M Q
A
14.15
B
25.55
5
MATHEMATICS F4
EMaS 07 / MODULE 5
M and N the midpoints of PQ and TU respectively. Name the angle between the plane of WPQ and plane of PQUT
18
A
WPT
B
WMN
C
WQS
D
WQU
Name the angle between the plane PVS and the plane PQRS. VMN VNM VPQ VSQ
A B C D
20
The diagram shows a pyramid with the vertical rectangular base, ABCD. The plane ABP is a horizontal plane.
D
The diagram shows a right prism with a
C
horizontal rectangular base, EFGH. K
A B F
G
J
P H
E
Name the angle between line PC and plane ABCD. A ∠ CPB B ∠ CPA C ∠ PCD D ∠ PCA
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 a horizontal rectangular base PQRS. M and N are the midpoints of QR and PS. Vertex V is right above of the point M.
V R
S N
P
© 2007 Hak Cipta JPNT
M
Q
6
MATHEMATICS F4
EMaS 07 / MODULE 5
PAPER 2 1
Diagram below shows a right prism. The base HJKL is a vertical rectangle. The right angled triangle NHJ is the uniform cross section of the prism.
K 6 cm J
12 cm
M L
N
H
8 cm
Identify and calculate the angle between the line KN and the plane HLMN. [4 marks]
© 2007 Hak Cipta JPNT
7
MATHEMATICS F4
2
mozac / MODULE 5
Diagram below shows a cuboid with horizontal base TUVW.
P
Q
5 cm
4 cm T
U R
S
W
V
12 cm
Identify and calculate the angle between the plane PRV and the plane QRVU. [4 marks]
8
MATHEMATICS F4
3
mozac / MODULE 5
Diagram below shows a right prism with a horizontal square base ABCD. The rectangle plane ADPQ is vertical and the rectangle plane PQRS is horizontal. Trapezium ABRQ is a uniform cross-section of the prism with M and N are midpoints of AB and DC respectively.
P
Q
D
R
S
N
C
16 cm A
M
B
QR = PS = 8 cm and QA = PD = 10 cm. Calculate the angle between the plane ABS and the plane ABCD. [3 marks]
9
MATHEMATICS F4
4
mozac / MODULE 5
Diagram below shows a sector OQRS with centre O. OQ and OS are diameters of two semicircles.
O
7 cm
o
120
Q
S
Using = 22 , calculate
7
(a)
the perimeter, in cm, of the whole diagram
(b)
the area, in cm2 , of the shaded region [6 marks]
10
MATHEMATICS F4
5
mozac / MODULE 5
Diagram below shows a semicircle PQR with centre O and sector TRS with centre T. P is the midpoint of OR.
.
Q
R
P
O
T
S OP = 5 cm, QR = 6 cm and RTS 60o . Using =
22 , calculate 7
(a)
the perimeter, in cm, of the whole diagram
(b)
the area, in cm2 , of the shaded region [6 marks]
11
MATHEMATICS F4
6
mozac / MODULE 5
Diagram below shows a sector OPQ with centre O. AOBR is semicircle with AOB as its diameter and PO = 2OA. P
O
B
A
R
Q OB = 7 cm , POB = 45° dan AOR = 120°. Using =
22 , calculate 7
(a)
the perimeter, in cm, of the whole diagram
(b)
the area, in cm2 , of the shaded region [6 marks]
12
