Chapter Test Class IX: Real Numbers and Compound Interest

COMPLETE MCQ MATHEMATICS ASSESSMENT - Prime Maths

Full Marks: 32

Time: 55 minutes

Format: All Multiple Choice Questions

Group A [4 × 1 = 4]

Select the correct option in each case.

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.

Complete MCQ Mathematics Assessment - Irrationals & Compound Interest | For Class IX | © Prime Maths - 9038126497

ICSE Quadratic Equations Questions 2013 - 2025 | Class X Mathematics

ICSE Quadratic Equations

2013-2025 | Class X Mathematics

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Ace Your ICSE Class 10 Maths Board 2026: The Ultimate 50-Question Mock Test

 

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?

1. Full Syllabus Coverage: We test your grasp on GST, Banking, Shares, Algebra, Geometry, Mensuration, Trigonometry, and Statistics.

2. Time Management: With 50 questions, this quiz simulates the pressure of the real exam hall.

3. Instant Feedback: No waiting for a teacher to grade it. Click "Submit" and get your score immediately.

4. 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.

Questions: 50 Pass Score: 40%

Question 1 of 50

Results

Score: 0/50 (0%)

Practice quiz for ICSE Class 10 Maths Pre-Board Exam 2026. © Prime Maths

CBSE Maths Pre-Board Exam 2026: Top 50 MCQs with Interactive Test

 

About This Practice Quiz

This collection covers essential topics from the CBSE Class 10 Maths syllabus, including Number Systems, Polynomials, Coordinate Geometry, Trigonometry, Circles, Probability, and more. The questions have been carefully selected to reflect the types of problems you'll encounter in your board examination.

📊 Quiz Features:

• 50 carefully curated MCQs

• Instant scoring and feedback

• Progress saving (your answers are saved automatically)

• Performance analysis after submission

• No login required

Additional Resources for Preparation

• NCERT Solutions: Solve all NCERT exercises thoroughly

• Sample Papers: Practice with CBSE sample papers

• Formula Sheets: Create topic-wise formula revision sheets

• Important Questions: Focus on frequently asked questions from each chapter

Remember: The key to scoring well in Mathematics is consistent practice and clear conceptual understanding. Use this quiz as a tool to identify your strengths and weaknesses, then focus your study efforts accordingly.

Happy studying and all the best for your pre-board exams!

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.

Questions: 50 Pass Score: 60%

Question 1 of 50

Results

Score: 0/50 (0%)

Practice quiz for CBSE Class 10 Maths Pre-Board Exam 2026. © PRIME MATHS

Trigonometry, Probability and Statistics 90 Difficult Problems CBSE, ICSE Class X

 

📘 Mastering Trigonometry, Probability & Statistics for Class X CBSE & ICSE Boards

Board exams are around the corner, and three chapters that always carry high weightage in Class X Mathematics are Trigonometry, Probability, and Statistics. These topics not only appear every year but also form the base for higher classes.

To help you practice effectively, here’s a comprehensive 90-question problem sheet covering all major types of problems that can be asked in your board exams.

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🔹 Why Focus on These Topics?

• Trigonometry: Around 8–10 marks every year (Identities, Heights & Distances).

• Probability: 4–6 marks, usually simple but tricky MCQ-type.

• Statistics: 8–10 marks (Mean, Median, Mode, Graphs, Ogive, Histogram).

That means almost 25% of your math exam comes directly from these three chapters!

---

🟦 1. Trigonometry Section (Q.1–30, 71–90)

This section begins with basic identities and proofs like:

• Proving trigonometric identities (Q.1–20).

• Higher-level simplifications involving sec, tan, and cot (Q.21–30).

• Word problems on Heights & Distances (Q.71–90), including angles of elevation, depression, aeroplane problems, and applications with towers and buildings.

👉 Tip: Always draw a rough figure in height & distance problems; 50% of the solution comes just from a correct diagram.

---

🟩 2. Probability Section (Q.31–50)

The probability section has a mix of dice, coins, cards, and real-life examples:

• Simple dice problems (Q.31–33, 37–38).

• Coin toss problems (Q.39–40).

• Playing cards (Q.35, Q.48).

• Real-world word problems with marbles, ice creams, tickets, etc.

👉 Tip: Always remember

$$P(E) = \frac{\text{Favourable Outcomes}}{\text{Total Outcomes}}$$

and carefully check whether the problem is "or" (union) or "and" (intersection) type.

---

🟥 3. Statistics Section (Q.51–70)

This section covers:

• Mean, Median, Mode (Q.51–59, Q.67–69).

• Ogives & Histograms (Q.60–64).

• Word problems with real-life data (Q.65–70).

👉 Tip:

• Use step-deviation method for quicker calculation of mean.

• Median = value of $\frac{N}{2}$-th observation (learn how to locate it correctly in cumulative frequency tables).

• For graphs, label your axis neatly—marks are often lost for presentation.

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📌 How to Use This Problem Sheet?

1. Start with Trigonometric Identities → They sharpen algebraic manipulation skills.

2. Move to Probability → These are quick, scoring questions.

3. Finish with Statistics → Practice graphs separately for neatness and accuracy.

4. Solve at least 10 questions daily from the sheet.

5. Time yourself as if in an exam.

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🌟 Final Words

This 90-question sheet is a perfect revision package for Class X boards. If you can solve these confidently, you’ll be exam-ready for all tricky variations.

📌 Pro Tip: Practice without looking at the answers first, then cross-check.

💡 Consistency is the key—solve 3–5 questions every day and revise formulas daily.

CHAPTER TEST - ICSE MATHEMATICS - Probability, Quadratic Equations, Factorisation, and Trigonometry:

 "TEST – ICSE MATHEMATICS - X", which covers topics in Probability, Quadratic Equations, Factorisation, and Trigonometry:

🧮 Topics Covered

• Probability:

  • Calculating probabilities based on card draws and coin tosses.
  • Real-life scenarios like games and playing cards used to frame questions.

• Quadratic Equations:

  • Solving quadratic equations.
  • Finding conditions for real and equal roots.
  • Application-based problems involving area and tile dimensions.

• Factorisation:

  • Using factor theorem to find unknown coefficients.
  • Polynomial division and complete factorisation.

• Trigonometry:

  • Proving identities involving cotangent, tangent, sine, cosine, secant, and cosecant.
  • Complex expressions simplified to standard trigonometric identities.

📝 Sample Questions

• Probability of winning different prizes based on number card properties.
• Proving trigonometric identities like: [ \frac{(\cot A + \tan A - 1)(\sin A + \cos A)}{\sin^3 A + \cos^3 A} = \sec A \cdot \csc A ]
• Solving and factorising polynomials such as: [ 2x^3 - 7x^2 + kx - 2 \quad \text{(given that } x - 2 \text{ is a factor)} ]
• Finding the value of ( x ) in a tile-based floor problem.
• Probability of drawing a specific card from a reduced deck.

⏱️ Format

• Total Marks: 40
• Duration: 1 hour 30 minutes
• Each question is marked individually, ranging from 1 to 4 marks.

HARDER PROBLEMS FOR CLASSES VIII- X Algebra

This collection is designed for secondary school students (Classes VIII–X) preparing for Math Olympiads and competitive exams. It brings together a variety of challenging algebra problems that go beyond routine textbook exercises and test deeper understanding, creativity, and problem-solving skills.

👉 Key Features of the Set

• Classical Identities – Problems based on famous results such as Sophie Germain’s identity.

• Equation Manipulation – Creative use of algebraic transformations and substitutions.

• Inequalities & Rationalization – Strengthening algebraic reasoning with proofs and simplifications.

• Number Theory Links – Problems connecting algebra with concepts of divisibility and composite numbers.

• Summations & Series – Telescoping series and rational number expansions.

• Olympiad Flavor – Each problem is selected to stimulate lateral thinking and develop advanced techniques.

This set not only sharpens algebraic manipulation but also trains students to recognize patterns, symmetry, and hidden structures in problems—an essential skill for Olympiads and higher-level mathematics.