Math Syllabus for NIFT - Detailed

Snapshot

Topic	Subtopics
Number System	Types of numbers, Number operations
HCF & LCM	Finding HCF and LCM
Percentage	Percentage calculations, Profit and Loss, Discounts
Simple & Compound Interest	Interest calculations
Ratio & Proportion	Ratios, Proportions, Direct and Inverse Proportions
Profit and Loss	Apply concepts in advanced applications
Averages	Mean, Weighted Average, Alligation
Time & Work	Work and Time, Pipes and Cisterns
Time & Distance	Speed, Time, Distance, Trains, Boats and Streams, Races
Set Theory	Sets, Venn Diagrams
Probability	Probability calculations
Algebra	Algebraic expressions, Polynomials, Equations, Inequalities
Geometry	Angles, Triangles, Circles, Geometric Shapes

Number System

Types of numbers: Integers, Whole numbers, Natural numbers, Even numbers, Odd numbers, Prime numbers, Composite numbers, Co-prime numbers.
Number operations: Representing rational numbers, finding the unit's digit in a product, finding the number of zeros in any factorial.
- Sample Questions:
  1. Find a number which lies between 700 and 800, and which is perfectly divisible by 10, 12, and 18.
  2. Find the greatest number of 3 digits which is exactly divisible by 2, 3 and 4.
  3. A man was employed on the promise that he will be paid the highest wages per day. The contract money to be paid was ̀ 185. He was finally paid 111. For how many days did he actually work?

HCF & LCM

Finding HCF and LCM of numbers.
- Sample Questions:
  1. Find the greatest number which after dividing 13, 17 and 23 leaves the same remainder in each case.
  2. Find the greatest common factor of: 12a²bc³, 3ab²c, 2a²bc², 6ab⁴

Percentage

Understanding percentage as a fraction of 100.
Calculations involving percentages, profit and loss, discounts.
- Sample Questions:
  1. In an examination, 80% of the students passed in English, 85% in Mathematics and 75% in both English and Mathematics. If 40 students failed in both the subjects, find the total number of students.
  2. In an election between two candidates, the candidate who gets 30% of the votes polled is defeated by 15000 votes. Find the number of votes polled by the winning candidate.
  3. The price of an article is first increased by 20% and later on it is decreased by 25% due to reduction in sales. Find the net percentage change in the final price of the article.

Profit & Loss

Understanding concepts of Cost Price (CP), Selling Price (SP), Marked Price (MP), Discount.
Calculating profit percentage, loss percentage, discounts, marked price.
- Sample Questions:
  1. A T.V. when sold for 4600 fetches a profit of 15%. Find the cost price of the TV.
  2. A man sells two houses for Rs. 536800 each. On one he gains 10% and on the other he loses 10%. Find his gain or loss percent in the whole transaction.
  3. A trader marks his product 30% above the cost price and gives a 10% discount to his customers. What is his actual profit%?

Simple & Compound Interest

Understanding the difference between Simple Interest and Compound Interest.
Calculations involving principal, rate of interest, time period, and interest amount.

Ratio & Proportion

Simplifying ratios, finding equivalent ratios.
Types of ratios: duplicate ratio, triplicate ratio, sub-duplicate ratio, sub-triplicate ratio.
Solving problems involving proportions, direct and inverse proportions.
- Sample Questions:
  1. Divide 1458 into two parts in the ratio 2 : 7.
  2. Find three numbers in the ratio of 1 : 2 : 3, so that the sum of their squares is equal to 504.
  3. If 15 toys cost Rs. 234, what do 35 toys cost?
  4. The ratio of income of two persons is 9 : 7 and the ratio of their expenditure is 4 : 3. If each of them saves Rs. 200 per month, find their monthly incomes.
  5. The incomes of A and B are in the ratio 3 : 2 and their expenditures are in the ratio 5 : 3. If each saves 1000, then B's income is

Averages

Calculating average (mean) of a set of data.
Weighted average calculation.
Averages related to speed and mixtures.
Concept of Alligation.
- Sample Questions:
  1. The average weight of 4 men is increased by 3 kg when one of them who weighs 120kg is replaced by another man. What is the weight of the new man?
  2. The average of 25 results is 18. The average of first twelve of them is 14 and that of the last twelve is 17. Find the thirteenth result.
  3. A train travels from A to B at the rate of 20 km per hour and from B to A at the rate of 30 km/hr. What is the average rate for the whole journey?
  4. In what proportion must rice at `3.10 per kg be mixed with rice at 3.60 per kg, so that the mixture be worth ̀ 3.25 per kg?
  5. A trader has 50 kg of rice, a part of which he sells at 10% profit and the rest at 5% loss. He gains 2% on the whole. What is the quantity sold at 10% gain?

Time & Work

Understanding the relationship between time, work, and efficiency.
Calculating the time required to complete a task based on individual or combined work rates.
Problems involving pipes and cisterns.
- Sample Questions:
  1. A can do a piece of work in 10 days while B alone can do it in 15 days. In how many days both working together can finish the work?
  2. 12 men can do a work in 15 days. After 5 days, 3 men left the work. In how many more days will the work be finished?
  3. Two pipes can fill a cistern in 14 hours and 16 hours respectively. A third pipe can empty the full cistern in 8 hrs. If all the pipes are opened together in the empty tank, how much time will be needed to make the tank full?

Time & Distance

Understanding the relationship between speed, time, and distance.
Calculating speed, time, or distance based on the other two variables.
Problems involving trains, boats and streams, and races.
- Sample Questions:
  1. A car travels 150 km in 3 hours. What is its speed?
  2. Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. How long will it take them to cross each other?
  3. A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.

Set Theory

Key concepts: Universal set, Union, Intersection, Null Set, Cardinal Number.
Solving problems related to sets and Venn diagrams.
- Sample Questions:
  1. In a coaching institute, 40 students are selected in banking exam coaching, 30 students selected in SSC exam coaching and 20 students selected in both the examinations coaching. How many students are there in the institute? How many students are selected (i) in banking exam coaching only (ii) in SSC exam coaching only?
  2. 65% of students in a class like cartoon movies, 70% like horror movies and 75% like war movies. What is the smallest % of students liking all the three types of movies?
  3. Percentage of those who like sweets and chocolates but not milkshakes is
  4. Percentage of passes in all subjects is
  5. The number of students who like only English is greater than the number of students who like only G.K. by

Probability

Calculating the probability of events.
- Sample Questions:
  1. 100 employees appeared for two levels of an interview. 60 passed the first, 50 passed the second and 30 passed both the levels. Find the probability that an employee selected at random has failed in both the levels of the interview.
  2. From a pack of 52 cards, two are drawn at random. Find the chance that one is a knave and the other a queen.
  3. Three balls numbered 2, 4 and 8 are put into a bag and a ball is drawn at random. What is the probability that the ball drawn is a prime number?
  4. 20 balls are marked 1 to 20. One ball is drawn at random. Find the probability that it is marked with a number multiple of 5 or 7.

Algebra

Basic concepts: Algebraic expressions, Polynomials, Equations, Inequalities.
Operations: Addition, subtraction, multiplication, and division of polynomials.

Geometry

Concepts related to angles, triangles, circles, and other geometric shapes