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F.4 Summer Holiday Assignment – Multiple Choice
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F.4 Summer Holiday Assignment
Multiple Choice
Name : ____________________ Class :_________ (
) Mark :__________/100
Instruction:
1. Circle the correct answer.
2. (Rough) working step SHOULD BE MARKED on EACH QUESTION in this set of papers.
The work will NOT be counted if NO working step is shown in EACH QUESTION.
Factorization + Miscellaneous
1.
1
1


n 3 3n
A.
6
.
9  n2
B.
6
.
n 9
C.
2n
.
9  n2
D.
2n
.
n 9
2. If a > 0, then
C.
4.
5.
2
2
3 a
a


2
4a
A. 1.
3.
(CE 07)
B.
a.
D.
(CE07)
a
.
2
2 a.
1
1


x 1 x 1
(CE06)
A.
2
.
1 x2
B.
2
.
x 1
C.
2x
.
1 x2
D.
2x
.
x 1
pr  qr  ps  qs 
A. ( p  q)( r  s) .
C. ( p  q)( r  s) .
2
2
(CE06)
B.
D.
( p  q)( s  r ) .
( p  q)( s  r ) .
In the figure, the 1st pattern consists of 3 dots. For any positive integer n, the (n+1)th pattern is
formed by adding (2n + 3) dots to the nth pattern. Find the number of dots in the 6th pattern.
(CE06)
F.4 Summer Holiday Assignment – Multiple Choice
A.
C.
6.
7.
8.
9.
35
48
B.
D.
Page
37
50
If a  1 2b , then b =
(CE 05)
A.
a 1
.
2
B.
a 1
.
2
C.
1 a
.
2
D.
1 a
.
2
If n is a positive integer, then
1
1


1 2 n 1 2 n
A.
4 n
.
1  4n
B.
4 n
.
1  4n
C.
4 n
.
4n  1
D.
4 n
.
4n  1
If x 
y  2x
, then y =
2y
(CE 04)
A.
2x
.
1  2x
B.
2x
.
2x 1
C.
1 2 x
.
2x
D.
2x 1
.
2x
25a  4a 
A.
C.
(CE 04)
3 a.
21 a .
B.
D.
7 a.
21a .
10. Solve the equation (2x – 3)2 = 4.
5
2
A.
x=
C.
x =
B.
1
2
or
x=
x =
5
1
D. x =
2
2
2
3
or
or
x = –2
x=
5
2
10
3
11. Solve the equation 4( x  2) 2  ( x  2) 2 .
2
3
A.
x=
C.
x=6
(CE 05)
or
x = 6 B.
x=
6
5
or
x=
D.
x=
2
3
or
x =
2
3
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F.4 Summer Holiday Assignment – Multiple Choice
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12. If  and  are the two roots of x  px + q = 0, express ( + 2)( + 2) in terms of p and q.
A. p2 + q
B. 2p2 + q
2
C.
p2 + 2q
D.
p + q2
13. Find the length of the shortest side of a right-angled triangle, where the lengths of the three
sides are consecutive numbers.
A. 6 cm
B. 5 cm
C. 4 cm
D. 3 cm
14.
Matthew is 2 years younger than his brother, and 32 years younger than his father. Three years
ago, the product of the ages of Matthew and his brother was exactly 2 times the age of their
father. How old is his brother now?
A. 11
B. 12
C. 13
D. 14
15. If the solution of the quadratic equation (ax  b) 2  0 is
A.
2
3
C.

2
3
B.
3
2
D.

2
a
, find the value of  .
3
b
3
2
16.
In the figure, the area of the smaller square (the shaded region) is 50.5 cm2, find the value of x.
A.
3.5
B.
4.5
C.
5.5
17. If 2 x(3x  1)  (2  3x)(3x  1) , then x =
A.
2
.
5
B.
1
.
3
C.
1
2
or
.
3
5
D.
2
1
or .
3
3
D.
6.5
F.4 Summer Holiday Assignment – Multiple Choice
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18. Solve b x  b(a  c) x  ac  0 .
2
A.
C.
a
b
a
x=
b
x=
2
c
b
or
x=
or
x =
B.
c
b
D.
a
b
a
x =
b
x =
c
b
or
x=
or
x =
c
b
19. Which of the following equations has/have two equal real roots?
I. (x + 2)2 + 4(x + 2) + 4 = 0
II. 16x2 = 1
III. x 
1
1
 2
x
2
A.
I only
B.
II only
C.
I and II only
D.
I and III only
20. Given that the length and the width of a rectangle are (x + 2) cm and x cm respectively. The
square of the half of its perimeter is equal to the sum of the squares of its length and width.
How many different rectangles can be formed according to the above conditions?
A. 0
B. 1
C. 2
D. 3
F.4 Summer Holiday Assignment – Multiple Choice
Function and Graph
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F.4 Summer Holiday Assignment – Multiple Choice
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F.4 Summer Holiday Assignment – Multiple Choice
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F.4 Summer Holiday Assignment – Multiple Choice
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15. Consider the graph of y  2 x 2  x  1 . Which of the following straight lines should be added in
order to solve the inequality 6 x 2  3 x  6  0 ?
A.
B. y  1
y  1
C.
D. y  5
y  5
y
16.
Solve y  x 3  2 x 2  x  2  0 graphically.
A.
B.
C.
D.
x =  1 , 1 or 2
x  1
 1  x  1 or x  2
x  1 or 1  x  2
4
y  x3  2x 2  x  2
2
-2
2
4
x
O
-2
-4
17.
In the graphs of the following quadratic functions, which one touches the x-axis?
A.
y = x2 – 6x – 9
B. y = –x2 + 6x + 9
C.
y = –x2 – 6x – 9
D. y = –x2 – 6x + 9
18. If f (x) = x  3 and g(x) = 2  x, then 3f (2)  g(3) =
A. 8.
B. 2.
C. 0.
D. 1.
19. If f (2x) = 16x2  8x + 4, then f (x) =
A. 8 x 2  4 x  4 .
C. 4 x 2  4 x  4 .
B.
D.
8x 2  4x  4 .
4x 2  4x  4 .
20. The figure shows the quadratic graph of y = f (x). Which of the following satisfies/satisfy
the inequality f (x) > 0?
I.
II.
III.
A.
B.
C.
D.
x = 6
x = 1
x=1
I only
I and II only
II and III only
I, II and III
F.4 Summer Holiday Assignment – Multiple Choice
1.
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Equation of Straight line
The following graph represents the line ax  by  c  0 . If a is a negative real number, which
of the following is true?
A.
C.
b  0 and c  0
b  0 and c  0
B.
D.
b  0 and c  0
b  0 and c  0
2.
Let A and B be the points (5, 5) and (–1, 3) respectively. The equation of the line, which passes
through the mid-point of AB and is perpendicular to AB, is
A. 3 x  y  10  0 .
B. 3 x  y  10  0 .
C. x  3 y  10  0 .
D. x  3 y  10  0 .
3.
Which of the following is not an equation of a straight line?
A. x  0
B. y  4
C.
4.
2x  3  y
D.
y  2x 2  3
In the figure, the equation of the straight line l is
0, 3 
A.
x  3y  3  0
B.
x  3y  3  0
C.
x  3y  3 3  0
D.
x  3y  3 3  0
F.4 Summer Holiday Assignment – Multiple Choice
5.
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In the figure, ABCD is a parallelogram. Find the slope of AC.
B(0, 3)
D(2, 0)
A.

C.
3
2
4
5
B.

D.
5
4
2
3
6.
Which pair of the straight line equations is not parallel?
2 y  4 x  2
2 x  4 y  4  0
A. 
B. 
 x  2 y  10  0
 y  2x  9
 y  5x  3
 y  7 x  10
C. 
D. 
2 y  10 x  12
2 y  14 x  0
7.
In the figure, PA and PB are parallel to the x-axis and y-axis respectively. Find the distance
between AB.
8x  7 y  13  0
P(6, –3)
A.
C.
8.
B.
10
103
D.
13
113
In the figure, two straight lines L1 and L2 are perpendicular to each other. If the equation of L2
x y
  1 , then the equation of L1 is
a bb
A. y  x  b
a
a
B. y   x  b
b
is
a
xb
b
C.
y
D.
b
y   xb
a
F.4 Summer Holiday Assignment – Multiple Choice
9.
Page
A(–2, 4) and B(–4, –3) are the end-points of a diameter of a circle. The coordinates of the
centre are
A.
1

  1, 
2

B.
1

  3, 
2

C.
7

 3, 
2

D.
 2,1
10. The slope of the line 6 x  3 y  7  0 is
A.
–2.
B.

1
.
2
C.
7
6
D.

7
6
.
.
11. If the line kx  6 y  7 passes through the point (k, –3), then k =
A.
7
3
.
B.
5.
C.
–5.
D.
–5 or 5.
12. Which of the following statements about the straight line 2 x  y  3 is true?
A.
The slope of the line is negative.
B.
C.
The x-intercept of the line is 3.
The line is parallel to the line 2 x  4 y  7 .
D.
The y-intercept of the line is –3.
13. If a  0 and b  0 , which of the following may represent the graph of y  ax  b ?
A.
B.
C.
D.
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F.4 Summer Holiday Assignment – Multiple Choice
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14. If the length of the line segment joining the points (3, 2) and (1–k, k) is 4, then k 
A. 2.
B. 4.
C.
D. –2 or 2.
0 or 4.
15. In the figure, the area of ABC is
A. 4.
B. 8.
C. 16.
D. 32.
x=6
16.
P10,8 and Q 4,6 are two points. If R is a point on the x-axis such that PR  RQ ,
then
the coordinates of R are
A.
4,0
B.
3,1
C.
3,0
D.
2,0
17. In the figure, the straight lines L1 and L2 intersect at 2,4 . Find the equation of L1 .
A.
x  2 y  10
B.
x  2 y  6
y
L1
L2
(2,4)
C.
2x  y  8
D.
2x  y  0
x
In the figure, OABC is a parallelogram. If the equation of OC is 2 x  y  0 and the length of
18.
CB is 4, find the equation of AB.
A.
B.
C.
D.
E.
x  2y  4  0
2x  y  4  0
2x  y  4  0
2x  y  8  0
2x  y  8  0
F.4 Summer Holiday Assignment – Multiple Choice
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19. If k >0, which of the following may represent the graph of the straight line x  y  k
A.
B.
O
O
C.
D.
O
O
20. If the straight line 7 x  3 y  42 cuts the x -axis and the y-axis at A and B respectively, then
the coordinates of the mid-point of AB are
A. (3, –7)
B. (–3, 7)
C. (7, –3)
D. (–7, 3)
Trigonometry
1.
2.
1
1
1
sin 
1
1
1
sin 
=
A.
2 tan .
B.
2 tan2 .
C.
2
.
tan 2 
D.
2 sin 
.
cos 2 
If cos  = x and 0o <  < 90o, then tan =
1
A.
B.
1  x2
2
1 x
C.
3.

1  x2
x
D.
x
1  x2
If 0o   < 360o, which of the following equations has exactly one root?
A.
sin  = 1
B.
sin  = 
C.
sin  = 0
D.
sin  = 2
1
2
F.4 Summer Holiday Assignment – Multiple Choice
4.
Page
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In the figure, a : b : c =
A.
3 : 2 :1.
B.
C.
2 : 3 : 1.
D.
9 : 4 : 1.
3 : 2 : 1.
30o
a
b
60o
c
5.
6.
7.
In the figure, B = C = 90 . If AB = p and BC = q, then CD =
o
p + q tan .
B.
p+
C.
p + q cos .
D.
p +
If tan x = 
3
4
sin x + cos x?
A.

C.
1
5
C
q
A

p
and x is an angle in the second quadrant, what is the value of
7
5
B.

D.
7
5
I only
III only
B.
D.
1
5
II only
I, II and III
sin   cos sin   cos


sin   cos sin   cos
A.
4 sin  cos .
B.
2 sin  cos
.
sin 2   cos 2 
C.
4 sin  cos
.
sin 2   cos 2 
D.
2
.
sin   cos 2 
2
D
q
.
tan 
If A + B = 180o, which of the following is/are true?
I. sin A = sin B
II. cos A = cos B
III. tan A = tan B
A.
C.
8.
q
.
tan 
A.
B
F.4 Summer Holiday Assignment – Multiple Choice
9.
Page
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AB and CD are two buildings of heights h and d respectively. The angles of elevation of C
from A and B are respectively  and 45o. d =
A.
h(1 + tan ).
B.
h(1  tan ).
C.
h
.
1  tan 
D.
h
.
1  tan 
C
A

d
90o
45o
B
10. In the figure, ABCD is a square of side 2a. M and N are the mid-points of AB and CD
respectively. h is the height of the parallelogram MBND. h =
1
2
A
A.
a
B.
a
2
5
C.
5
a
2
D.
D
2
a
3
M
11.
D
N
h
tan 2 
+ cos2 =
2
1  tan 
A.
1.
B.
1
+ cos2.
2
C.
cos2.
D.
1+ tan2.
B
C
12. In the figure, BCD is a straight line. ADC = 90o and BC = 10. AD =
A. 10 cos70o.
B. 10 sin70o.
o
C.
10 sin 20
.
sin 55o
D.
10 tan 20
.
sin 55o
13. In the figure, cos  =
1
.
4
A.

C.
1
.
4
A
o
B

D.
1
.
2
D
C
1
.
2
B.
70o
35o
2

3
4
F.4 Summer Holiday Assignment – Multiple Choice
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14. In the figure, AB = x and AC = 2x. The area of ABC is 16. x (correct to 2 decimal places) is
A. 2.83.
B. 4.00.
A
C. 4.30.
D. 5.66.
o
x 30
2x
15. The greatest value of
B
3
is
4  2 cos
A.
3.
B.
3
.
2
C.
3
.
4
D.
3
.
5
C
16. In the figure, B = 90o and BCD is a straight line. If AB = p and BC = q, then cos  =
A.
p
p2  q2
.
B.
q
p2  q2
.
A
C.
p
p q
2
2
.
D.
q
p2  q2
.
p

B
17. In the figure, PQRS is a square inscribed in ABC. AB = AC and PQ = a.q AB =
A.
a(sin  +
1
cos ).
2
B.
a(sin  +
1
sin ).
2
C.
1
1
a(
+
).
2 cos
sin 
D.
1
1
a(
+
).
cos
2 sin 
18. In the figure, AB // DC.
A.
( p  q) sin 50o
.
2 sin 70o
B.
( p  q) sin 70o
.
2 sin 50o
C.
( p  q) sin 70o
.
sin 60o
D
C
A
P
S
a

B
Q
C
R
AB = q and DC = p. BC =
A
q
B
70o
D
50o
p
C
F.4 Summer Holiday Assignment – Multiple Choice
Page
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( p  q) sin 70
.
sin 50o
o
D.
19. In ABC, AB = 2, AC = 3 and sin B =
A.
C.
9
.
13
B.
1
.
2
D.
3
, then cos2C =
4
1
.
4
A
3
.
4
B
20. In the figure, BD:DC =
A.
B.
C.
D.
1.
B
D
C
Application of trigonometry
In the figure, A and B are the positions of two boats. The bearing of B from A is
B. N65E.
D. S15E.
In the figure, the bearing of B from A is
A. 005.
C. 095.
3.
C
A
sin C : sin B.
cos C : cos B.
tan C : tan B.
sin B : sin C.
A. N25E.
C. S25E.
2.
3
2
B.
D.
055.
170.
A tree of 5 m tall has a shadow of length 12 m long. Find the angle of elevation of the sun
F.4 Summer Holiday Assignment – Multiple Choice
Page
18 / 24
correct to the nearest degree.
A. 23
B. 25
C. 45
D. 67
4. In the figure, the bearings of two cars A and B from a town T are 040 and 100 respectively. B
is 200 m and at a bearing of 140 from A. Find the distance of B from T.
A. 200 m
5.
B.
200 sin 50
m
sin 80
C.
200 sin 80
m
sin 60
D.
200 sin 70
m
sin 80
If the true bearing of A from B is 140, then the compass bearing of B from A is
A. N50E.
B. N40W.
C. S40E.
D. S50W.
6.
In the figure, the angle of elevation of B from P is
10. If AB : BC = 2 : 1, then the angle of elevation of A
from P is
A.
B.
C.
D.
20.
27.9.
30.
32.9.
F.4 Summer Holiday Assignment – Multiple Choice
Page
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7. In the figure, the compass bearings of A and B
from P are N50W and S25W respectively.
If PA = 60 m and PB = 50 m, then AB =
A. 67.4 m.
B. 81.4 m.
C. 82.9 m.
D. 87.5 m.
8. In the figure, PC is a building standing on the ground
AB. The angles of depression of A and B from P are 25
and 35 respectively. If AB = 20 m, then PC =
9.
A.
20 tan 25 tan 35
m.
tan 35 o  tan 25
B.
tan 35  tan 25
m.
20 tan 25 tan 35
C.
20 tan 25  tan 35
m.
tan 35  tan 25
D.
20 tan 25 tan 35
m.
tan 35  tan 25
The figure shows a triangular prism.  and  are the
inclinations of DC and AC with the plane BCFE
respectively. Which of the following is true?
A.
3
sin   sin 
5
B.
sin  
3
sin 
4
C.
sin  
4
sin 
5
D.
sin  
4
sin 
5
10. Refer to the figure in question 5, which of the following lines on the plane ABCD has the least
value of slope?
A. AB
B. AC
C. DC
D. PA, where P is the mid-point of BC.
F.4 Summer Holiday Assignment – Multiple Choice
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11. The figure shows a rectangular block with AB = 6 cm,
AE = 8 cm and AD = 10 cm. Which of the following angles
is the greatest?
A. Angle between the planes ACGE and BCGF.
B. Angle between the planes EBCH and BCGF.
C. Angle between the planes ABFE and BCGF.
D. Angle between the planes DHFB and ABFE.
12. A mosquito flies in a rectangular box from A to G.
Find the shortest distance.
A. 10 2 cm
B. 2 74 cm
C. 8 5 cm
D. 8 10 cm
13. In the figure, the height of the vertical flagstaff PO is
A. 9 m.
C.
9 3 m.
B.
9 2 m.
D.
18 m.
14. The figure shows a vertical rectangular wall of 2 m high and 6 m long. If the sun shines from
S45E with an angle of elevation of 60, find the area of the shadow of the wall on the ground.
F.4 Summer Holiday Assignment – Multiple Choice
A.
2 3 m2
B.
4 3 m2
C.
6 m2
D.
2 6 m2
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The figure shows a cube. Which of the following angles is/are equal to AFH?
I
CHF
15.
II DGE
III BGH
A. I only
B. II only
C. III only
D. I and II only
16.
In the figure, ABCD is a rectangular plane inclined at an acute angle to the horizontal
plane ABEF. AF, BF, EF and EB are the projections of AD, BD, CD and CB on the plane
ABEF respectively. Which of the following angles is NOT a right angle?
A.
B.
C.
D.
CEB
DCB
DFB
FBE
F.4 Summer Holiday Assignment – Multiple Choice
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17. In the figure, CD is a vertical pole and the points A, B, C lie on a horizontal ground. If AB =
2 3 , CAB = 60, ABC = 30 and the angle of elevation of D from B is 45o, find CD.
A.
2 3
B.
3 2
C.
3 3
D. 3
18. A door ABCD is opened through an angle of 60 to ABEF. The door is 1 m wide and 2 m high.
If CAE = , find cos .
A.
5
10
B.
5
5
C.
1
10
D.
9
10
F.4 Summer Holiday Assignment – Multiple Choice
19. The figure shows a regular tetrahedron with side 6 cm.
M is the mid-point of VC. Find the angle between
the line AB and the base VBC.
A.
B.
C.
D.
48.7
50.8
51.8
54.7
20. In the figure, VA is a vertical tower with height 60 m
standing on the horizontal plane ABC.
Find the angle of elevation of V from B.
A.
B.
C.
D.
31.3
33.3
37.5
41.5
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F.4 Summer Holiday Assignment – Multiple Choice
Page
24 / 24
Answer of the multiple choice
Factorization and miscellaneous
1
2
3
4
5
6
7
8
9
10
D
C
A
A
C
D
D
A
A
D
11
12
13
14
15
16
17
18
19
20
A
B
D
C
B
B
C
B
A
A
Function and graphs
1
2
3
4
5
6
7
8
9
10
A
B
A
D
D
B
C
D
D
A
11
12
13
14
15
16
17
18
19
20
B
C
B
C
A
C
C
B
C
A
Equation of straight line
1
2
3
4
5
6
7
8
9
10
A
A
D
B
D
C
D
C
B
A
11
12
13
14
15
16
17
18
19
20
D
D
B
D
C
A
A
D
D
A
Trigonometry
1
2
3
4
5
6
7
8
9
10
B
C
A
C
D
B
A
D
D
B
11
12
13
14
15
16
17
18
19
20
A
B
A
D
B
D
C
C
D
C
Application of Trigonometry
1
2
3
4
5
6
7
8
9
10
B
D
A
C
B
B
D
A
D
C
11
12
13
14
15
16
17
18
19
20
C
A
C
D
D
D
D
D
D
A