TNPSC Maths Notes and Questions: Free Study Material, Formulas & Practice Sets

Maths is one of the most scoring sections in TNPSC exams, yet many aspirants skip it out of fear. The good news is that the questions are based on Class 10 level concepts. With the right TNPSC Maths Notes, a set of core formulas and regular practice, you can secure almost full marks in this section.

In this blog, you will find topic-wise TNPSC Maths Study Material, important formulas, shortcut tricks, TNPSC Maths Questions with answers, and a smart preparation strategy. Whether you are preparing for Group 4, Group 2, Group 2A or Group 1, these notes will help you.

Why TNPSC Maths Notes Matter

• Maths and mental ability questions are formula-based, so marks are easy to secure if you revise well.
• The syllabus is limited and of Class 10 standard.
• Accuracy and speed improve quickly with short notes and daily practice.
• It can be the difference between qualifying and missing the cut-off.

TNPSC Maths Notes 2026 – Download Free PDF

Download the TNPSC Maths Notes 2026 PDF to revise important formulas, concepts, and problems for the exam. The free PDF will be available for download soon.

TNPSC Maths Notes 2026: Important Formulas and Shortcuts

1. Number System

• Sum of first n natural numbers = n(n + 1) / 2
• Sum of first n odd numbers = n²
• Sum of first n even numbers = n(n + 1)
• Divisibility by 3: sum of digits divisible by 3. By 9: sum of digits divisible by 9. By 11: difference of sum of odd and even place digits is 0 or a multiple of 11.

2. HCF and LCM

• HCF × LCM = Product of two numbers
• HCF of fractions = HCF of numerators / LCM of denominators
• LCM of fractions = LCM of numerators / HCF of denominators

3. Percentage

• Percentage = (Value / Total) × 100
• If a number increases by x% and then decreases by x%, net change = −x²/100 %
• Successive change of a% and b% = a + b + (ab/100) %

4. Ratio and Proportion

• If a : b = c : d, then ad = bc
• Mean proportion of a and b = √(ab)
• Third proportional of a and b = b²/a

5. Average

• Average = Sum of observations / Number of observations
• Average speed (equal distance) = 2xy / (x + y)
• Average of first n natural numbers = (n + 1) / 2

6. Profit and Loss

• Profit % = (Profit / Cost Price) × 100
• Loss % = (Loss / Cost Price) × 100
• Selling Price = Cost Price × (100 + Profit%) / 100
• Discount % = (Discount / Marked Price) × 100

7. Simple and Compound Interest

• Simple Interest = (P × R × T) / 100
• Compound Amount = P (1 + R/100)ⁿ
• Compound Interest = Amount − Principal
• CI − SI for 2 years = P (R/100)²

8. Time and Work

• If A does a work in x days and B in y days, together they take xy / (x + y) days
• Work = Rate × Time
• Efficiency is inversely proportional to the time taken

9. Time, Speed and Distance

• Speed = Distance / Time
• km/h to m/s: multiply by 5/18. m/s to km/h: multiply by 18/5
• Train crossing a pole: Time = Length of train / Speed
• Relative speed (same direction) = difference of speeds. Opposite direction = sum of speeds.

10. Mensuration

• Area of rectangle = l × b. Perimeter = 2(l + b)
• Area of triangle = ½ × base × height
• Area of circle = πr². Circumference = 2πr
• Volume of cylinder = πr²h. Volume of cone = ⅓πr²h. Volume of sphere = 4/3 πr³
• Curved surface area of cylinder = 2πrh

11. Algebra and Probability

• (a + b)² = a² + 2ab + b²
• (a − b)² = a² − 2ab + b²
• a² − b² = (a + b)(a − b)
• Probability = Number of favourable outcomes / Total number of outcomes

TNPSC Maths Questions with Answers – Online Practice Set

Q1. What is the HCF of 36 and 48?

(a) 6

(b) 12

(c) 18

(d) 24 Answer: (b) 12

Q2. Find the LCM of 12, 15 and 20.

(a) 30

(b) 60

(c) 90

(d) 120 Answer: (b) 60

Q3. What is 25% of 480?

(a) 100

(b) 110

(c) 120

(d) 130

Answer: (c) 120

Q4. If the ratio of two numbers is 3 : 5 and their sum is 64, find the larger number.

(a) 24

(b) 32

(c) 36

(d) 40

Answer: (d) 40

Q5. The average of 5 numbers is 24. If one number is removed, the average becomes 22. Find the removed number.

(a) 28

(b) 30

(c) 32

(d) 34

Answer: (c) 32

Q6. An article bought for ₹500 is sold for ₹600. Find the profit percentage.

(a) 15%

(b) 20%

(c) 25%

(d) 30%

Answer: (b) 20%

Q7. Find the simple interest on ₹4,000 at 5% per annum for 3 years.

(a) ₹500

(b) ₹600

(c) ₹700

(d) ₹800

Answer: (b) ₹600

Q8. A can do a piece of work in 10 days and B in 15 days. In how many days can they finish it together?

(a) 5

(b) 6

(c) 7

(d) 8

Answer: (b) 6 days

Q9. A train 150 m long passes a pole in 10 seconds. What is its speed in km/h?

(a) 45

(b) 54

(c) 60

(d) 72

Answer: (b) 54 km/h (150/10 = 15 m/s; 15 × 18/5 = 54)

Q10. Find the area of a circle with radius 7 cm. (π = 22/7)

(a) 144

(b) 154

(c) 164

(d) 174

Answer: (b) 154 cm²

Q11. Find the next number in the series: 2, 6, 12, 20, 30, ?

(a) 36

(b) 40

(c) 42

(d) 48

Answer: (c) 42 (differences increase by 2: 4, 6, 8, 10, 12)

Q12. A die is thrown once. What is the probability of getting an even number?

(a) 1/6

(b) 1/3

(c) 1/2

(d) 2/3

Answer: (c) 1/2

Q13. If a² + b² = 50 and ab = 7, find (a + b)².

(a) 60

(b) 62

(c) 64

(d) 66

Answer: (c) 64

Q14. What is the compound interest on ₹10,000 at 10% per annum for 2 years?

(a) ₹2,000

(b) ₹2,100

(c) ₹2,200

(d) ₹2,400

Answer: (b) ₹2,100

Q15. The sum of the first 20 natural numbers is:

(a) 190

(b) 200

(c) 210

(d) 220

Answer: (c) 210

TNPSC Maths Previous Year Questions: Why You Should Solve Them

Solving TNPSC Maths Previous Year Questions shows you which topics repeat most often. Percentage, profit and loss, time and work, average, simple interest and number series appear regularly. Solve at least the last 5 years of papers for your exam, and note the topics where you lose marks.

How to Prepare TNPSC Maths: Smart Strategy

1. Learn the formulas first. Make a one-page formula sheet and revise it daily.
2. Start with easy topics. Percentage, average, ratio and profit and loss give quick marks.
3. Learn shortcuts. Use short tricks to save time in the exam.
4. Practice every day. Solve 20 to 25 questions daily with a timer.
5. Take mock tests. Attempt full-length tests to improve speed and accuracy.
6. Revise mistakes. Keep a notebook of errors and revisit it weekly.
7. Study Tamil and GS alongside. Maths should take only a small part of your daily schedule.

Tips to Score Full Marks in TNPSC Aptitude Questions

• Do not spend more than one minute on a single question.
• Use option elimination when you are stuck.
• Learn squares up to 30, cubes up to 15 and tables up to 20.
• Memorise common fractions and their percentage values (1/8 = 12.5%, 1/6 = 16.67%).
• Check units carefully (km/h, m/s, days, hours).

Practice TNPSC Maths on the Entri App

Reading notes is only half the job. On the Entri app, you can:

• Access TNPSC Maths Notes and study material in simple language
• Practice topic-wise TNPSC Maths Questions
• Take free mock tests and previous year question papers
• Track your progress and fix weak areas
• Join live classes by expert mentors

Download the Entri app today and start your TNPSC preparation.