Al Qadr
Montessori, School & Academy
2nd Term Examination
MATHEMATICS SSC–I
Student Name: ______________________ Class: _____Pre 9th______
Date: _____________ Total Marks: __75__Obtain Marks: __________
Invigilator Sig
Subject Teacher Sig
Re-Checker Sig
Counter Checker Sig
SECTION – A (Marks 15)
Time allowed: 20 Minutes
Note: Section-A is compulsory. All parts of this section are to be answered on the question paper itself. It should be completed in the first 20 minutes and handed over to the Centre
Superintendent. Deleting/overwriting is not allowed. Do not use lead pencil.
(Section-A)
Q1.Choose the correct option.
(
1. The order of Matrix [𝟐 𝟏] is
a. 2 by 1
b. 1 by 2
c. 1 by 1
𝟐
2. Product of [𝒙 𝒚] [ ] is
−𝟏
a. [𝟐𝒙 + 𝒚] b. [𝒙 − 𝟐𝒚] c. [𝟐𝒙 − 𝒚]
𝟕
3. Write √𝒙 in exponential form
𝟏
b. x7
a. x
d. 2 by 2
d. [𝒙 + 𝟐𝒚]
𝟕
c. 𝒙𝟕
d. 𝒙𝟐
−𝟏
4.
𝟐𝟓 𝟐
(𝟏𝟔)
𝟓
a.
= _______
𝟒
𝟒
b. 𝟓
c.
−𝟓
d.
𝟒
5. Log mn can be written as
a. (Log m)n b. m logn
c. n log m
6. Logy x will be equal to ____
a.
𝒍𝒐𝒈𝒛 𝒙
𝒍𝒐𝒈𝒚 𝒛
𝒍𝒐𝒈 𝒛
b. 𝒍𝒐𝒈𝒙 𝒛
𝒚
𝒍𝒐𝒈 𝒙
c. 𝒍𝒐𝒈𝒛 𝒚
𝒛
−𝟒
𝟓
d. log (m n)
𝒍𝒐𝒈 𝒚
d. 𝒍𝒐𝒈𝒛 𝒙
𝒛
7. (𝟑 + √𝟐)(𝟑 − √𝟐) is equal to
a. 7
b. -7
c. -1
d. 1
8. What is the leading coefficient of polynominal 𝟑𝒙𝟐 + 𝟖𝒙 + 𝟓 ?
a. 2
b. 3
c. 5
d. 8
𝟑
𝟑
9. The factor of 𝟖𝒙 + 𝟐𝟕𝒚 are:
a. (𝟐𝒙 + 𝟑𝒚)(𝟒𝒙𝟐 − 𝟗𝒚𝟐 )
b. (𝟐𝒙 − 𝟑𝒚)(𝟒𝒙𝟐 − 𝟗𝒚𝟐 )
c. (𝟐𝒙 + 𝟑𝒚)(𝟒𝒙𝟐 − 𝟔𝒙𝒚 + 𝟗𝒚𝟐 ) d. (𝟐𝒙 − 𝟑𝒚)(𝟒𝒙𝟐 + 𝟔𝒙𝒚 + 𝟒𝒚𝟐 )
10. H.C.F of 𝒂𝟐 − 𝒃𝟐 and 𝒂𝟑 − 𝒃𝟑 is _____.
a. a + b
b. 𝒂𝟐 − 𝒂𝒃 + 𝒃𝟐
c. a - b
d. 𝒂𝟐 + 𝒂𝒃 + 𝒃𝟐
11. L.C.M x H.C.F= p(x)x q(x)
a. Two
b. Three
c. Four
d. None
12. The y-coordinate of a point is called :
a. Origin
b. x-coordinate
c. y-coordinate
13. Which of the following lines is parallel to y-axis?
a. x=0
b. x=-3
c. x=3
d. y=-3
14. Distance between points (0,0) and (1,1) is :
a. 0
b. 1
c. √𝟐
d. 2
15. A ___________ has two end points
a. Line
b. line segment
c. ray
d. angle
d. ordinate
/15)
SECTION – B (Marks 36)
i.
Simplify
−𝟐
−𝟏
(𝟐𝟒𝟑) 𝟑 (𝟑𝟐) 𝟓
√(𝟏𝟗𝟔)−𝟏
OR
𝟐
√
𝟏
(𝟐𝟏𝟔)𝟑 𝒙 (𝟐𝟓)𝟑
−𝟑
(𝟎. 𝟎𝟒) 𝟐
ii.
Evaluate
𝟎. 𝟎𝟕𝟗𝟐𝟏 𝒙 (𝟏𝟖. 𝟗𝟗)𝟐
√
(𝟓. 𝟕𝟗)𝟒 𝒙 𝟎. 𝟗𝟒𝟕𝟒
OR
(𝟒𝟑𝟖)𝟑 √𝟎.𝟎𝟓𝟔
(𝟑𝟖𝟖)𝟐
iii.
Simplify
𝟏
𝟏
𝟐
𝟒
−
− 𝟐
− 𝟒
𝒙−𝟏
𝒙+𝟏 𝒙 +𝟏 𝒙 −𝟏
OR
𝒙+𝟏
𝒙−𝟏
𝟒𝒙
𝟒𝒙
⌈
−
− 𝟐
⌉+ 𝟒
𝒙−𝟏
𝒙+𝟏 𝒙 + 𝟏
𝒙 −𝟏
iv.
𝟒𝒙
𝟓
𝟏𝟔𝒙𝟐
𝟐𝟓
Find the Product ( 𝟓 − 𝟒𝒙)(
𝟐𝟓
+ 𝟏𝟔𝒙𝟐 + 𝟏)
OR
𝟐
√𝟓+√𝟑
v.
+
𝟏
-
𝟑
√𝟑+√𝟐 √𝟓+√𝟐
Factorize
(𝒙𝟐 − 𝟓𝒙 + 𝟔)(𝒙𝟐 + 𝟓𝒙 + 𝟔)-2𝒙𝟐
OR
vi.
(𝒙 + 𝟒)(𝒙 − 𝟓)(𝒙 + 𝟔)(𝒙 − 𝟕) −504
H.C.F by division Method
𝒙𝟒 + 𝒙𝟑 − 𝟐𝒙𝟐 + 𝒙 − 𝟑 , 𝟓𝒙𝟑 + 𝟑𝒙𝟐 − 𝟏𝟕𝒙 + 𝟔
OR
Find the Square root of expression
𝟒𝒙𝟐 𝟖𝒙
𝟏𝟐𝒚 𝟗𝒚𝟐
+
+
𝟏𝟔
+
+ 𝟐
𝒚𝟐
𝒚
𝒙
𝒙
vii. Solve the equation
𝟐𝒙
𝟐
𝟓
−𝟓
= −
𝒙 ≠
𝟐𝒙 + 𝟓
𝟑 𝟒𝒙 + 𝟏𝟎
𝟐
OR
viii.
𝟐𝒙
𝟐
𝟐𝟑 + 𝟑
ix.
In isosceles
(𝟓𝒙 − 𝟒) >
−𝟏
(𝟖𝒙 +
𝟑
𝟕)
PQR shown in the figure , find the value of x and y .
P
X
10cm
6 cm
Q
R
Y
SECTION-C (24Marks)
x.
In the
ABC as shown in the figure , m
ACB = 90 o and CD
AB Find lengths a , h and b if m BD = 5 mints and m AD = 7 mints
D
5
7
B
a
h
A
C
b
xi.
xii.
Show that the diagonals of the parallelogram having vertices A(1, 2) B (4 , 2) C (-1 , -3) and D(-4 , -3) bisect each other.
OR
Show whether or not the points with vertices ( -1, 1)(5 , 4) (2 , -2) and (-4 , 1) form a square?
Note: Attempt ALL questions. Each question carries (08) marks.
i.
ii.
iii.
The length of a rectangle is 8 times its width The perimeter of the rectangle is 250 cm. Find the dimensions of the rectangle.
OR
The length of a rectangle is 6 cm less then 3 times its width. The perimeter of the rectangle is 140 cm. Find the dimensions of the rectangle. By
using inverse method
𝒙+𝟑
𝒙𝟐 − 𝟑𝒙 + 𝟐
𝒙+𝟐
𝒙+𝟏
+ 𝒙𝟐 −𝟒𝒙 + 𝟑 + 𝒙𝟐 − 𝟓𝒙 + 𝟔
x ≠ 1, 2 , 3
OR
iv.
v.
vi.
𝒙+𝟑
𝟐𝒙𝟐 + 𝟗𝒙 + 𝟗
𝟏
𝒙+𝟏
+ 𝟐(𝟐𝒙−𝟑) + 𝟒𝒙𝟐 −𝟗
In a right angled triangle the square of the length of hypotenuse is equal to the sum of the square of the lengths of the other two sides.
OR
Show that the points M (-1 , 4) N (-5 , 3) P (1 , -3) and Q ( 5, -2) are vertices of a parallelogram and also find the mid points of each side of
parallelogram