Solved Problems: Indian Statistical Institute (ISI), Chennai Mathematical Institute (CMI), IIT-JEE Main & Advance, and Olympiads (RMO/INMO).
Entrance Exam Solutions: Solved Problems for ISI B.Math/B.Stat, CMI, JEE (IIT), Olympiads, and CBSE/ISC/ICSE Mathematics Board Papers.
Practice Problems and Chapter Test on various topics for CBSE, ICSE, Madhyamik, HS and ISC students
Master the Art of Factorisation with 39 Progressive Problems
Factorisation Overview
What is Factorisation?
Factorisation is the process of breaking down algebraic expressions into simpler components called "factors" that, when multiplied together, give the original expression.
Worksheet Structure
Problems 1-10: Basic factorisation
Problems 11-20: Difference of squares
Problems 21-30: Grouping techniques
Problems 31-39: Challenge mastery
How to Use This Worksheet:
1. Work through problems one by one using the slides.
2. Try to solve before clicking "Next".
3. Use the list below to jump to specific questions.
1. At present the population of a village is P and if the rate of increase of population per year be 2r%, the population after n years will be
(a)
\( P \left( 1 + \frac{r}{100} \right)^n \)
(b)
\( P \left( 1 + \frac{r}{50} \right)^n \)
(c)
\( P \left( 1 + \frac{r}{100} \right)^{2n} \)
(d)
\( P \left( 1 - \frac{r}{100} \right)^n \)
2. A person deposited Rs. 100 in a bank and received Rs. 121 after two years, the rate of compound interest is
(a)
10%
(b)
20%
(c)
5%
(d)
10.5%
3. \(\sqrt{5} - 3 = 2\) is
(a)
A rational number
(b)
A natural number
(c)
Equal to zero
(d)
An irrational number
4. Which of the following rational numbers have a terminating decimal expression?
(a)
\( \frac{125}{441} \)
(b)
\( \frac{77}{210} \)
(c)
\( \frac{15}{1600} \)
(d)
\( \frac{129}{2^2 \times 5^2 \times 7^2} \)
Group B [4 × 2 = 8]
All questions converted to multiple choice format.
1. To prove that \( 3\sqrt{7} \) is not a rational number, which approach is correct?
(a)
Assume \(3\sqrt{7}\) is rational, then \(\sqrt{7} = \frac{a}{3b}\) where a, b are integers, which implies \(\sqrt{7}\) is rational - a contradiction
(b)
Assume \(3\sqrt{7}\) is rational, then \(\sqrt{7} = \frac{a}{b}\) where a, b are integers with no common factors - leads to contradiction as 7 divides a²
(c)
Since \(\sqrt{7}\) is irrational and 3 is rational, their product must be rational
(d)
\(3\sqrt{7}\) can be written as \(\sqrt{63}\), and since 63 is not a perfect square, it's rational
2. If a sum of money doubles itself at certain rate compounded annually in n years, in how many years will the sum become four times of itself?
(a)
n years
(b)
2n years
(c)
3n years
(d)
n² years
3. Using the formula of simple interest, the amount at the end of 2nd year for a sum P at the compound interest rate of r% per annum is:
(a)
\( P \left(1 + \frac{r}{100}\right)^2 \)
(b)
\( P \left(1 + \frac{2r}{100}\right) \)
(c)
\( P \left(1 + \frac{r}{50}\right) \)
(d)
\( P + \frac{2Pr}{100} \)
4. Which of the following is an irrational number between 2 and 3?
(a)
2.5
(b)
\( \sqrt{4} \)
(c)
\( \sqrt{5} \)
(d)
\( \sqrt{9} \)
Group C [5 × 4 = 20]
All questions converted to multiple choice format. For questions with "OR", both parts are included as separate options.
1. The expression \( \left( 3 + 2\sqrt{5} \right)^2 \) is:
(a)
Irrational because it simplifies to \( 29 + 12\sqrt{5} \), which is a sum of rational and irrational
(b)
Rational because it equals \( 49 \)
(c)
Irrational because \( \sqrt{5} \) is irrational
(d)
Rational because it simplifies to \( 29 + 12\sqrt{5} \) and \( 12\sqrt{5} \) is rational
2. If p is a prime number, \( \sqrt{p} \) is:
(a)
Always rational
(b)
Always irrational
(c)
Rational if p is even, irrational if p is odd
(d)
Irrational except when p = 4
3. After rationalizing the denominator, \( \frac{1}{3-2\sqrt{2}+\sqrt{5}} \) simplifies to:
(a)
\( \frac{3+2\sqrt{2}-\sqrt{5}}{2} \)
(b)
\( \frac{3-2\sqrt{2}+\sqrt{5}}{12} \)
(c)
\( \frac{3+2\sqrt{2}-\sqrt{5}}{12} \)
(d)
\( \frac{3-2\sqrt{2}-\sqrt{5}}{4} \)
OR
The simplest value of \( \frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}} + \frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}} \) is:
(e)
2
(f)
5
(g)
10
(h)
\( \frac{10}{\sqrt{21}} \)
4. If simple interest and compound interest on a certain sum for two years are Rs. 8400 and Rs. 8652 respectively, then:
(a)
Rate = 5%, Sum = Rs. 80,000
(b)
Rate = 6%, Sum = Rs. 70,000
(c)
Rate = 8%, Sum = Rs. 60,000
(d)
Rate = 10%, Sum = Rs. 50,000
5. In how many years will Rs. 50000 amount to Rs. 60500 at 10% compound interest per annum?
(a)
1 year
(b)
2 years
(c)
3 years
(d)
4 years
OR
The height of a tree increases at 20% yearly. If present height is 28.8m, its height 2 years before was:
(e)
20 m
(f)
22 m
(g)
24 m
(h)
26 m
Assessment Results
Your Score: 0/32
Group A
0/4
4 × 1 mark questions
Group B
0/8
4 × 2 mark questions
Group C
0/20
5 × 4 mark questions
Question-wise Results:
Note: For questions with "OR" options, only one part needs to be answered. If you answer both, only the first selected option is considered.
The countdown to the ICSE 2026 Board Exams has officially begun. As you navigate through the Special Intensive Revision period, nothing beats the confidence of knowing you are ready.
At Prime Maths, we believe that practice isn't just about solving problems—it's about simulation. That is why we have curated this comprehensive 50-mark MCQ Mock Test. Designed strictly according to the latest ICSE syllabus, this test covers every critical chapter, from Commercial Mathematics to Probability.
Why Take This Mock Test?
Full Syllabus Coverage: We test your grasp on GST, Banking, Shares, Algebra, Geometry, Mensuration, Trigonometry, and Statistics.
Time Management: With 50 questions, this quiz simulates the pressure of the real exam hall.
Instant Feedback: No waiting for a teacher to grade it. Click "Submit" and get your score immediately.
Identify Weak Spots: Find out instantly if you need to revise Circles or if you've already mastered Matrices.
Instructions
Total Questions: 50
Time Recommended: 90 Minutes
Passing Score: 40% (But aim for 90%!)
Note: Keep a notebook and pen ready. Do not guess! Solve the problems on paper before selecting your option.
📊 Quiz Features:
50 carefully curated MCQs
Instant scoring and feedback
Progress saving (your answers are saved automatically)
Performance analysis after submission
No login required
ICSE Maths Pre-Board 2026 Quiz
Test your knowledge with these 50 MCQs
PRIME MATHS
Instructions: Select one answer per question. Click "Submit" at the end to see your score.
