Series RTEQ.P. Code 38/1/1
Roll No.
RTE LEARN · CBSE PATTERN 2026–27
MATHEMATICS
Periodic Test 1
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
Write a quadratic polynomial whose zeroes are 3 and −3.
2.1
Find the sum of the zeroes of the cubic polynomial 2x³ − 6x² + x − 5.
3.1
What is the maximum number of zeroes a polynomial of degree 5 can have?
4.1
Write the degree of the polynomial x²(x − 1)(x + 2).
5.1
Is √x + 3 a polynomial in x? Give a reason.
6.1
Is 1 a prime number, a composite number, or neither? Give a reason.
7.1
Find the exponent of 5 in the prime factorisation of 7500.
8.1
Is (3 + √5)(3 − √5) rational or irrational?
9.1
The product of two numbers is 1800 and their HCF is 6. Find their LCM.
10.1
Find the HCF of 24 and 40.
SECTION B
This section comprises 4 very short answer (VSA) type questions of 2 marks each.
11.2
If −2 is a zero of the polynomial 2x² + kx − 6, find k.
12.2
Find the zeroes of 6x² − 7x + 2.
13.2
Show that 9 × 11 × 13 + 13 is a composite number.
14.2
Find the HCF and LCM of 70 and 196 using prime factorisation.
SECTION C
This section comprises 4 short answer (SA) type questions of 3 marks each.
15.3
If α and β are the zeroes of 3x² − 4x + 1, find the value of α² + β² and of 1/α² + 1/β².
16.3
If α and β are the zeroes of x² − 5x + k and α − β = 1, find the value of k.
17.3
Ram, Shyam and Kiran take 12, 16 and 18 minutes respectively to complete one round of a circular track. If they start together from the same point and in the same direction, after how many minutes will they meet again at the starting point?
18.3
Find the HCF and LCM of 1260 and 7350 by prime factorisation, and verify that HCF × LCM = product of the two numbers.
SECTION D
This section comprises 2 long answer (LA) type questions of 5 marks each.
19.5
Find the zeroes of 2x² − 3x − 2 and verify the relationship between the zeroes and the coefficients. Hence form a quadratic polynomial whose zeroes are the squares of the zeroes of 2x² − 3x − 2.
20.5
Prove that √3 is irrational. Hence show that 2 + 5√3 is irrational.
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