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PERIODIC TEST

Periodic Test 2

40marks
20questions
33%to pass
3checks left

Solve every question in your notebook, then upload clear photos of every page. AI checks them like a CBSE examiner, with step marks. Pass with 33% to complete this test.

Series RTEQ.P. Code 70/-1/-1
Roll No.

RTE LEARN · CBSE PATTERN 2026–27

MATHEMATICS

Periodic Test 2

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.
Is √49 rational or irrational?
1
2.
Does 3/40 have a terminating decimal? If so, write it.
1
3.
Evaluate (−6) × (−9).
1
4.
Express 0.777… (7 repeating) as a fraction.
1
5.
Find one rational number between 1/3 and 1/2.
1
6.
Expand (y − 4)².
1
7.
Using an identity, find 98².
1
8.
Factor 4a² − 25b².
1
9.
What is the coefficient of ab in the expansion of (a + b + c)²?
1
10.
Write the factorised form of x³ + y³.
1

SECTION B

This section comprises 4 very short answer (VSA) type questions of 2 marks each.

11.
Express 0.2333… (only the 3 repeating) as a fraction.
2
12.
Given that √2 is irrational, show that 3 + √2 is irrational.
2
13.
Factor 6x² − x − 2.
2
14.
Using an identity, find 997².
2

SECTION C

This section comprises 4 short answer (SA) type questions of 3 marks each.

15.
Express 3.142424… (42 repeating) as a fraction in lowest terms.
3
16.
Simplify (a³ − b³)/(a² − b²), assuming a ≠ ±b.
3
17.
A rectangular pool is 5 m longer than it is wide and has area 84 m². Find its dimensions.
3
18.
Find five rational numbers between 1/6 and 2/5.
3

SECTION D

This section comprises 2 long answer (LA) type questions of 5 marks each.

19.
a + b + c = 7, ab + bc + ca = 14 and abc = 8. Find (a) a² + b² + c², (b) a³ + b³ + c³ − 3abc, (c) a³ + b³ + c³. (d) Check your answers using the numbers 1, 2 and 4.
5
20.
(a) Prove that √5 is irrational. (b) Hence show that 2 + √5 is irrational.
5

✦ ✦ ✦

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Q11 · 2/2Full marks. Correct method and the final answer is clearly stated.
Q12 · 1/2Right approach, but one step of working is missing. Show every step to get full marks.
Q13 · 2/2Well explained, with correct units and a neat diagram.
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