04/0901A/2022
Indraprastha INTERNATIONAL SCHOOL
Sector 10, Dwarka, New Delhi – 110075
Session: 2022-23
Periodical Assessment III
Mathematics (Set-A)
Class: IX Maximum Marks: 30
Date: 15.12.2022 Time Allowed: 1 Hour
General Instructions
• This question paper consists of 13 questions and 2 printed pages.
• All questions are compulsory.
• Write all the answers neatly and legibly.
• Marks for each question are indicated against it.
• Use of calculator is not permitted.
1. Find the value of the polynomial 5x – 4x2 + 3 at x = – 1. 1
2. If 3x + 2y = 12 and xy = 6, find the value of 9x2 + 4y2. 1
3. If x + 1 is a factor of polynomial ax3 + x2 – 2x + 4a – 9, then find the value of a. 2
4. Factorise : a3 – 2 √2 b 3 2
5. Solve using identity: 105 x 106. 2
6. Two opposite angles of a parallelogram are (3x – 2)° and ( 50 – x)°. Find the measure of each 2
angle of the parallelogram.
7. Factorise : 1 – 2ab – (a2 + b2). 2
8. If the polynomials ax3 + 4x2 + 3x – 4 and x3 – 4x + a leave the same remainder when divided 2
by (x – 3). Find the value of a.
9. One angle of a quadrilateral is 108° and remaining three angles are in the ratio 3:4:5, find the 2
measure of three angles.
10. Show that diagonals of a rhombus are perpendicular to each other. 3
11. Factorise : x3 –6 x2 + 11x – 6 . 3
12. Show that if diagonals of a quadrilateral are equal and bisects each other at right angle then it 4
is a square.
CASE STUDY
13. Read the following:
Rajshree is working from home. Her home office corner space shown below is minimalist in
style. The chair and table with trapezium shape legs has a contemporary look and a clear space
underneath.
Consider the trapezium ABCD in the figure in which AB is parallel to CD, AD = BC and
answer the following questions:
a. ∆ ABC ≌ ∆ BAD by which criterion?
1
b. If ∠D = 900 then what is the measure of ∠E?
1
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c. In figure if E is the midpoint of AD and a line is drawn through E is parallel to CD 2
intersecting BC at F, then show that F is midpoint of BC.
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