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
What is the smallest prime number?
2.1
Write all factors of 48.
3.1
Is 57 a prime or composite number? Give reason.
4.1
What is the sum of first 5 prime numbers?
5.1
Using divisibility rule check if 2345 is divisible by 5.
6.1
What is the area of a triangle with base 10 cm and height 6 cm?
7.1
A square and a rectangle have the same perimeter of 40 cm. The rectangle has length 12 cm. Find the breadth of the rectangle.
8.1
What is the perimeter of a regular pentagon with side 8 cm?
9.1
If the area of a square is 144 sq cm what is its perimeter?
10.1
A room is 5 m long and 4 m wide. How many square tiles of side 50 cm are needed to cover the floor?
SECTION B
This section comprises 4 very short answer (VSA) type questions of 2 marks each.
11.2
Express 180 as a product of prime factors. Draw a factor tree and write in index notation.
12.2
Check divisibility of 7236 by 2, 3, 4, 6 and 9 using divisibility rules.
13.2
A rectangular park of length 60 m and breadth 40 m has a path of 2 m width running inside along its boundary. (a) Find the area of the path. (b) Find the cost of laying the path at Rs 80 per sq m.
14.2
The perimeter of a rectangle is 68 cm. Its length is 5 cm more than its breadth. (a) Find the length and breadth. (b) Find the area.
SECTION C
This section comprises 4 short answer (SA) type questions of 3 marks each.
15.3
The HCF of three numbers is 12 and their LCM is 1440. Two of the numbers are 48 and 60. (a) Find the third number using prime factorisation. (b) Verify that 12 is indeed the HCF. (c) Check that all three numbers are divisible by 12.
16.3
Verify Goldbach conjecture for 4 even numbers between 50 and 70. Also find: (a) twin prime pairs between 1 and 50. (b) prime numbers that are also palindromes below 100. (c) the only prime that is a triangular number below 20.
17.3
A composite figure consists of a rectangle of 8 cm x 5 cm with a square of side 3 cm cut from one corner. (a) Find the perimeter of the composite figure. (b) Find the area of the composite figure. (c) If the figure is to be painted at Rs 15 per sq cm find the cost.
18.3
A school playground is 80 m x 50 m. It has two rectangular flower beds each 10 m x 5 m and a circular fountain of radius 3 m. (a) Find the area of the playground. (b) Find the total area of flower beds. (c) Find the area of the fountain. Use pi=3.14. (d) Find the remaining area for playing. (e) If grass costs Rs 25 per sq m for the playing area find the total cost.
SECTION D
This section comprises 2 long answer (LA) type questions of 5 marks each.
19.5
Riya wants to fence her L-shaped garden. The garden can be seen as two rectangles: Rectangle 1 is 15 m x 8 m and Rectangle 2 is 6 m x 4 m joined at the corner. (a) Draw the L-shape and label dimensions. (b) Find the total area. (c) Find the perimeter of the L-shape. (d) If fencing costs Rs 120 per metre find the cost. (e) If she also wants to lay grass at Rs 40 per sq m find that cost.
20.5
(a) Find all prime numbers between 80 and 100. (b) Verify that each can be written as sum of two primes or explain why not. (c) Find LCM and HCF of 84, 90 and 120. (d) Three traffic lights change every 30, 45 and 60 seconds. If they change together at 10:00 AM when will they next change together? (e) How many times will they change together in one hour?
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