50/2
SULIT 50/1
NAMA: _______________________________________________ TINGKATAN:
______________
TOPICAL TEST 4: ALGEBRAIC EXPRESSIONS III & ALGEBRAIC
FORMULAE
UJIAN TOPIKAL 4: UNGKAPAN ALGEBRA III & RUMUS ALGEBRA
This question paper consists of 40 questions. Answer all the
questions. For each question, choose only
one answer from the options A, B, C and D.
Kertas soalan ini mengandungi 40 soalan. Jawab semua soalan.
Bagi tiap-tiap soalan, pilih satu jawapan
daripada empat pilihan, iaitu A, B, C, dan D.
13xy(4 3y) =
A9xy 12xy2
B9xy + 12xy2
C 12xy + 9xy2
D12xy 9xy2
2(4x + y)(3x 2y) =
A12x2 5xy 2y2
B12x2 + 5xy 2y2
C 2x2 + 5xy 12y2
D2x2 5xy + 12y2
3Expand (3x 4)2.
Kembangkan (3x 4)2.
A9x2 + 24x 16
B9x2 24x + 16
C 6x2 18x 8
D6x2 + 18x + 8
4Simplify 2x 8xy.
Permudahkan 2x 8xy.
Ax(2 4y)
B2x(1 4y)
C2x(2 8y)
Dx(2 8xy)
5Factorise 2x2 32.
Faktorkan 2x2 32.
A(x 4)(x + 4)
B(x 8)(x + 8)
C2(x 8)(x + 8)
D2(x 4)(x + 4)
6Factorise p2 2pq + q2.
Faktorkan p2 2pq + q2.
A(p q)(p q)
B(p q)(p + q)
C (2p + q)(p + q)
D(2p q)
73x2 19x + 6 =
A(6x 1)(3x 1)
B(3x 1)(x 6)
C (3x 6)(x 1)
D(3x + 1)(6x 1)
8
57
23
bd
+
A
1415
6
bd
bd
+
C
12
5
bd
B
1415
6
dd
bd
+
D
12
23
bd
+
9
35
xx
xyyx
+=
--
A
2
x
xy
-
C
2
x
yx
-
B
8
x
xy
-
D
8
x
yx
-
10
(23)
3
24
a
aa
-
-=
A
13
2
a
a
-
C
13
4
a
a
-
B
43
2
a
a
+
D
43
4
a
a
+
11
22
13
xx
+=
-
A
(
)
2
241
3
x
x
+
+
B
2
82
33
x
xx
+
+
C
2
3
(x + 3)
D
2
62
33
x
xx
+
+
12
2
52
xy
x
-=
A
2
3
xy
B
2
52
xxy
xy
-
C
2
52
xy
xy
-
D
2
3
xy
xy
13
pqp
pqpq
+
=
--
A
(
)
2
pq
pq
+
-
C
22
1
pq
-
B
2
33
pq
pq
+
-
D
(
)
2
2
ppq
pq
+
-
14
55
26
xy
ab
-
+
(a + 3b) =
A
55
3
ab
+
B
515
26
xayb
ab
-
+
C
55
2
xy
-
D
22
55
218
xy
ab
-
+
15
mn
xy
+
5mn =
A
55
mn
xy
+
B
1
44
xmnymn
+
C
1
55
xy
+
D
()
5
mnxy
+
16
2
26
4
16
x
x
x
+
=
+
-
A
(
)
2
64
x
x
+
-
C
(
)
62
64
x
x
+
-
B
6
4
x
+
D
2
6
16
x
-
17
22
43
x
xy
xy
=
+
-
A
12
x
xy
-
C
4
3
xy
-
B
12
x
xy
+
D
(
)
4
3
xxy
-
18
36
mn
n
+
(m + 2n) =
A
4
2
n
B
3
n
C
2
mn
n
+
D
2
m
n
+
19(m 2)
2
6
4
m
-
=
A
6
n
C
6
2
m
-
B
6
n
D
6
2
m
+
20
2
2
612
3
6
ppq
q
qpq
-
=
-
A
2
2
p
pq
-
C
4
3
p
q
B
4
p
q
D
2
12
p
pq
-
21Which of the following is a constant?
Antara yang berikut, manakah pemalar?
AThe number of days in a week.
Bilangan hari dalam satu minggu.
BThe number of motorcycles on a road in a day.
Bilangan motosikal di jalan raya dalam satu hari.
CThe number of passengers of a bus in a day.
Bilangan penumpang bagi satu bas dalam satu hari.
DThe height of students in a class.
Ketinggian pelajar dalam satu kelas.
22Which of the following is a variable?
Antara yang berikut, manakah pemboleh ubah?
AThe number of days in the month of June.
Bilangan hari dalam bulan Jun.
BThe length of a piece of A4 paper.
Panjang sekeping kertas A4.
CThe time taken to have a dinner.
Masa yang diambil untuk makan malam.
DThe sum of interior angles in a square.
Hasil tambah sudut pedalaman dalam segi empat sama.
23P is the number of sunny days in April. The possible value of
P is
P ialah bilangan hari cerah dalam bulan April. Nilai yang
mungkin bagi P ialah
A2
B5
C 18
D31
24Given that 3x = 5y + 1, then y =
Diberi 3x = 5y + 1, maka y =
A
31
5
x
+
C
31
5
x
-
B
151
5
x
+
D
151
5
x
-
25Given that
5()
xy
y
+
= 2, then y =
Diberi
5(xy)
y
+
= 2, maka y =
A
5
7
xC
5
3
x
B
4
7
xD
5
7
x
26Given that
6
5
x
xy
-
= 6, then y =
Diberi
6x
5xy
-
= 6, maka y =
A3x
B4x
C5x
D6x
27Given that x = xy2 + 9, then y =
Diberi x = xy2 + 9, maka y =
Ax + 3C
9
1
x
-
Bx 3D1
3
x
28Given that
4
3
x
y
-
= 2, therefore y =
Diberi
x4
3y
-
= 2, maka y =
A
4
4
x
-
C
4
6
x
-
B
4
12
x
-
D
22
2
4
6
x
-
29Express L as the subject of the formula
2
2
3
mn
L
= 4.
Ungkapkan L sebagai perkara dalam bentuk
2
2
3mn
L
= 4.
A3m2n 4
B
2
2
3
4
mn
C
2
3
mn
L
D
2
3
4
mn
30Given that p =
2
qr
+ r2, p = 5 and r = 1, find the value of q.
Diberi p = 2
qr
+ r2, p = 5 dan r = 1, cari nilai q.
A2C4
B3D9
31Find the value of n in the formula,
m =
2
2
n
n
+
-
if m = 3.
Cari nilai n bagi rumus, m =
2n
2n
+
-
jika m = 3.
A1C4
B2D6
32Given that m =
1
2
-
and n = 3, then
2
3
n2 16m3n =
Diberi m =
1
2
dan n = 3, maka
2
3
n2
16m3n =
A0C12
B6D18
33Given that p =
4
xy
, p = 20 and y = 2, find the value of x.
Diberi p =
4xy
, p = 20, dan y = 2, cari nilai x.
A40C60
B50D70
34Given that
1
a
=
1
b
+
1
c
, express b in terms of a and c.
Diberi
111
abc
=+
, ungkapkan b dalam
sebutan a dan c.
Ab =
ac
ca
-
Cb =
1
ca
+
Bb =
ac
ca
+
Db =
1
ca
-
35Given that a2 = b2 + 2bc, find the value of c if a = 2 and b =
4.
Diberi a2 = b2 + 2bc, cari nilai c jika a = 2 dan b = 4.
A0.5C1.5
B0.5D1.5
36The perimeter of a rectangle is x cm and the width is y cm. If
the area of the rectangle is 56 cm2, express x in terms of y.
Perimeter bagi sebuah segi empat tepat ialah x cm dan lebarnya
ialah y cm. Jika luas segi empat tepat itu ialah 56 cm2, ungkapkan
x dalam sebutan y.
Ax = 3y +
56
y
C x = 2y +
56
y
Bx = 2y +
112
y
Dx = 3y +
112
y
37There are p blue marbles in a container. The number of yellow
marbles in the container is
1
3
that of the blue marbles while the number of green marbles is 5
more than yellow marbles. If the total number of marbles in the
container is x, then the formula for x is
Terdapat p guli biru dalam sebuah bekas. Bilangan guli kuning
dalam bekas itu adalah
1
3
daripada guli biru manakala bilangan guli hijau adalah lima kali
lebih banyak daripada bilangan guli kuning. Jika jumlah bilangan
guli dalam bekas itu ialah x, maka rumus bagi x ialah
A
5
3
p + 5C
5
6
p + 5
B6
2
3
pD
5
3
p 5
38In Diagram 1, ABCE is a rectangle.
Dalam Rajah 1, ABCE ialah sebuah segi empat tepat.
Diagram 1 Rajah 1
Given that area of the shaded region is 30 cm2, express x in
terms of y.
Diberi luas kawasan berlorek ialah 30 cm2, ungkapkan x dalam
sebutan y.
A
2
y
C
4
y
B8yD4y
39Diagram 2 is made up of an isosceles triangle and a
rectangle.
Rajah 2 terdiri daripada sebuah segi empat tepat dan sebuah segi
tiga sama kaki.
Diagram 2 Rajah 2
The perimeter of the whole diagram is p cm. Express p in terms
of x, y and z.
Perimeter seluruh rajah itu ialah p cm. Ungkapkan p dalam
sebutan x, y, dan z.
Ap = 3(2x + 3y + 2z)
Bp = 2(2z + 5x + 6y)
Cp = 2(3z + 5x + y)
Dp = 3(3z + 5x + y)
40In Diagram 3, PQRS is a square.
Dalam Rajah 3, PQRS ialah sebuah segi empat sama.
Diagram 3 Rajah 3
QTR is a semicircle of radius j cm. The formula for the area, x
cm2, of the shaded region is. (Use =
22
7
)
QTR ialah sebuah semibulatan dengan jejari j cm. Rumus bagi
luas, x cm2, bagi kawasan berlorek ialah (Guna =
22
7
)
A2
3
7
j2C7
3
7
j2
B3
1
2
j2D8
1
2
j2
1Expand the following expressions.
Kembangkan ungkapan yang berikut.
(a)h(4 + i)
(b)
1
4
(8x + 12y 4ab)[3 marks]
[3 markah]
2Expand the following expressions.
Kembangkan ungkapan yang berikut.
(a)(2 + x)(x + y)
(b)(4y 4x)( + 4x)[3 marks]
[3 markah]
3State the highest common factor (HCF) of 8x2y2, 4x2 and
12xy2.[2 marks]
Nyatakan faktor sepunya terbesar (FSTB) 8x2y2, 4x2, dan 12xy2.[2
markah]
4Factorise completely the following expressions.
Faktorkan selengkapnya ungkapan yang berikut.
(a)15x2y + 10xy2
(b)12y2 + 13y 4[3 marks]
[3 markah]
5Factorise completely the following algebraic expressions.
Faktorkan selengkapnya ungkapan yang berikut.
(a)16x2 36
(b)15x2 3y2[3 marks]
[3 markah]
6Simplify each of the following.
Permudahkan ungkapan yang berikut.
(a)
612
3
x
-+
(b)
2
31
91
y
y
-
-
[3 marks]
[3 markah]
7Express the following as a single fraction in its simplast
form.
Ungkapkan yang berikut sebagai pecahan tunggal dalam bentuk
termudah.
(a)
25
32
x
yxy
+
(b)
(
)
5
1
21
aa
a
a
-
+
+
[3 marks]
[3 markah]
8Simplify
22
8
6
xy
x
xy
-
-
.[2 marks]
Permudahkan
22
xy
8x
xy6
-
-
.[2 markah]
9Simplify each of the following.
Permudahkan setiap ungkapan yang berikut.
(a)
57
66
bca
c
(b)
4221
36
xx
y
--
[4 marks]
[4 markah]
10Express
63
3
416
y
xxy
-
-
as a single fraction in its simplest form.
[3 marks]
Ungkapkan
63y
3
4x16xy
-
-
sebagai pecahan tunggal dalam bentuk termudah.[3 markah]
11Determine whether each of the following quantities is a
variable or constant.
Tentukan sama ada setiap kuantiti yang berikut ialah pemboleh
ubah atau pemalar.
(a)The price of 1 kg of fish
Harga bagi 1 kg ikan
(b)The number of seconds in a week[4 marks]
Bilangan saat dalam satu minggu[4 markah]
12Pei Voon bought x Mathematics books for RM30 each and y
Science books for RM28 each. She paid a total of RMz for her
purchase. Write a formula relating x, y and z.[3 marks]
Pei Voon telah membeli x buku Matematik dengan RM30 setiap satu
dan y buku Sains dengan RM28 setiap satu. Dia membayar jumlah RMz
bagi pembeliannya. Tulis satu rumus yang melibatkan x, y, dan z.[3
markah]
13There are m boxes of candles containing 28 candles each box
and another 5 boxes containing n candles each box. 20 of those
candles are red and the rest are white. Write a formula for w, to
show the number of white candles in terms of m and n.[3 marks]
Terdapat m kotak lilin yang mengandungi 28 batang lilin dalam
setiap kotak dan lima kotak yang mengandungi n batang lilin bagi
setiap kotak. 20 daripada lilin-lilin itu berwarna merah dan
selebihnya berwarna putih. Tulis satu rumus, W, yang menunjukkan
bilangan lilin putih dalam sebutan m dan n.[3 markah]
14Given that a2 = b2 + c2, express b in terms of a and c.[2
marks]
Diberi a2 = b2 + c2, ungkapkan b dalam sebutan a dan c.[2
markah]
15Given that 4x + 7 = 3(5 2y), express y in terms of x.
[3 marks]
Diberi 4x + 7 = 3(5 2y), ungkapkan y dalam sebutan x.[3
markah]
16Given 4m 4(5 + n) = 8, write a formula with n as the subject
of the formula.[3 marks]
Diberi 4m 4(5 + n) = 8, tulis satu rumus dengan n sebagai
perkara rumus.[3 markah]
17In Diagram 1, D is the midpoint of BC.
Dalam Rajah 1, D ialah titik tengah BC.
Diagram 1 Rajah 1
Express x in terms of y and z.[3 marks]
Ungkapkan x dalam sebutan y dan z.[3 markah]
18Given that x =
42
3
yz
+
, express z in terms of x and y.
[3 marks]
Diberi x =
4y2z
3
+
, ungkapkan z dalam sebutan x dan y.[3 markah]
19Given that p(3 + q) = 3r pq,
Diberi p(3 + q) = 3r pq,
(a)express p in terms of q and r,
ungkapkan p dalam sebutan q dan r,
(b)calculate the value of p if q = 2 and r = 3.[4 marks]
hitungkan nilai p jika q = 2 dan r = 3.[4 markah]
20Given that p =
4
8
rq
+
, express q as the subject of the formula.
[3 marks]
Diberi p =
4
r8q
+
, ungkapkan q sebagai perkara rumus.[3 markah]
50/2
MATEMATIK
KERTAS 2
1 jam 45 minit
50/2
This paper consists of 20 questions. Answer all the questions.
Write your answers clearly in the space provided in this question
paper and show your working. The calculator is not allowed to be
used.
Kertas soalan ini mengandungi 20 soalan. Jawab semua soalan.
Tuliskan jawapan dalam ruang yang disediakan dan tunjukkan jalan
kerja. Kalkulator tidak boleh digunakan.
6 SULIT
www.smkti.com@201025 SULIT
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