Series RTEQ.P. Code 12/1/-1
Roll No.
RTE LEARN · CBSE PATTERN 2026–27
MATHEMATICS
Periodic Test 3
Time allowed : 1½ HoursMaximum Marks : 40
General Instructions :
Read the following instructions carefully and follow them :
(i)This question paper contains 20 questions. All questions are compulsory.
(ii)This question paper is divided into four sections – A, B, C and D.
(iii)In Section A, Question numbers 1 to 10 carry 1 mark each.
(iv)In Section B, Question numbers 11 to 14 are very short answer (VSA) type questions carrying 02 marks each.
(v)In Section C, Question numbers 15 to 18 are short answer (SA) type questions carrying 03 marks each.
(vi)In Section D, Question numbers 19 to 20 are long answer (LA) type questions carrying 05 marks each.
(vii)Draw neat figures wherever required. Take π = 22/7 wherever required, if not stated.
(viii)Use of calculators is not allowed.
SECTION A
This section comprises 10 questions of 1 mark each.
1.1
A number is divisible by 9 if and only if what is divisible by 9?
2.1
What is the digital root of a number that is exactly divisible by 9?
3.1
What are mathematical statements about a digit puzzle where each letter represents exactly one digit called?
4.1
State the distributive property of multiplication over addition.
5.1
What is the expansion of (a+b)² (Identity 1A)?
6.1
What is the expansion of (a-b)² (Identity 1B)?
7.1
What is the expansion of (a+b)(a-b) (Identity 1C)?
8.1
In algebra, what are terms with the same letter-numbers called?
9.1
To check divisibility by 11, what do you alternately add and subtract?
10.1
Who gave the first explicit statement of the distributive property?
SECTION B
This section comprises 4 very short answer (VSA) type questions of 2 marks each.
11.2
Find the smallest multiple of 9 with no odd digits.
12.2
Solve the cryptarithm UT × 3 = PUT. Find U, T, and P.
13.2
Expand (6x + 5)² using Identity 1A.
14.2
Using Identity 1C, calculate 98 × 102.
SECTION C
This section comprises 4 short answer (SA) type questions of 3 marks each.
15.3
If 48a23b is a multiple of 18, find all possible pairs of values for a and b.
16.3
Determine if this statement is Always/Sometimes/Never true with justification: "The sum of a multiple of 6 and a multiple of 9 is a multiple of 3."
17.3
Expand (a+b)(a²+2ab+b²) fully, combining like terms.
18.3
Find the mistake and correct it: (a+2)(b+4) = ab + 8.
SECTION D
This section comprises 2 long answer (LA) type questions of 5 marks each.
19.5
Find a number that leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 4, and a remainder of 4 when divided by 5. What is the smallest such number, and why?
20.5
A square of sidelength 65 is split into a 60×60 square, a 5×5 square, and two 60×5 rectangles. Using Identity 1A, prove that 65² = 3600 + 600 + 25 = 4225, and explain the geometric reasoning.
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