NCERT Solutions
Class 12 Applied Mathematics
8 chapters · 16 important questions · Updated 2025-26
Numbers, Quantification and Numerical Applications
Covers modular arithmetic, successive discounts, partnership, time and work, time and distance, and Boats and Streams — all in the context of applied numericals.
Key Topics
Important Questions
Two partners invest in ratio 3:5 for 4 months and 6 months respectively. Find their profit sharing ratio.
A boat travels 36 km upstream and returns in 8 hours. Speed of stream is 3 km/h. Find speed of boat.
Algebra
Covers matrices (addition, scalar multiplication, multiplication, transpose) and determinants (calculation, properties, inverse of 2×2 and 3×3 matrices, solving linear equations using Cramer's rule).
Key Topics
Important Questions
Find the inverse of the matrix [[2,3],[1,4]] and use it to solve the system of equations.
Using Cramer's rule, solve: 2x + y = 5 and 3x − 2y = 4.
Calculus
Covers limits (standard results), continuity, differentiation of log and exponential functions, and applications of derivatives in business — marginal cost, marginal revenue, maxima and minima of cost and profit functions.
Key Topics
Important Questions
A company's cost function is C(x) = x³ − 6x² + 15x + 5. Find the marginal cost at x = 4 and determine whether cost is minimum or maximum.
Find dy/dx for y = x² · eˣ · log x.
Probability Distributions
Covers random variables, expected value and variance, Bernoulli trials, Binomial distribution (mean = np, variance = npq), and introduction to normal distribution.
Key Topics
Important Questions
A coin is tossed 8 times. Find P(exactly 3 heads) using Binomial distribution.
For a binomial distribution with n = 10 and p = 0.4, find mean and variance.
Index Numbers and Time-Based Data
Covers construction of index numbers (Laspeyre's, Paasche's, Fisher's), Consumer Price Index, time series analysis, and trend by moving averages.
Key Topics
Important Questions
Calculate Laspeyre's, Paasche's and Fisher's index numbers from the given price and quantity data.
Calculate 3-year moving averages for the given time series data and identify the trend.
Financial Mathematics
Covers compound interest, effective rate of interest, EMI calculation, annuities (present value and future value), sinking funds, linear depreciation, and reducing balance method.
Key Topics
Important Questions
Find the EMI for a loan of ₹5,00,000 at 12% per annum for 5 years.
A machine costing ₹2,00,000 depreciates at 20% per annum on reducing balance. Find its value after 3 years.
Linear Programming
Covers formulation of linear programming problems, graphical method (feasible region, corner points), and application to maximisation (profit) and minimisation (cost) problems in business.
Key Topics
Important Questions
A manufacturer makes two products. Formulate and solve the given LPP graphically to maximise profit.
Identify the feasible region and find the maximum value of Z = 5x + 4y subject to given constraints.
Inferential Statistics
Covers population vs sample, types of sampling (random, stratified, systematic), sampling distributions, Central Limit Theorem, confidence intervals, and basic hypothesis testing (z-test, t-test).
Key Topics
Important Questions
A sample of 100 students has mean score 72 with SD 10. Construct a 95% confidence interval for the population mean.
Distinguish between census and sample survey. What are the advantages of sampling?
Frequently Asked Questions
Is NCERT enough for CBSE Class 12 Applied Mathematics board exam?
Yes. CBSE board exams are designed entirely around NCERT. 80–90% of questions in the Class 12 Applied Mathematics paper are directly based on NCERT concepts — sometimes reworded, never from outside NCERT. Completing all 16 important questions listed here is the minimum you need.
How to study NCERT Class 12 Applied Mathematics for board exams?
Go chapter-by-chapter. Read the chapter first, then attempt the important questions without looking at answers. Check your answer structure — CBSE gives marks per point, so structure matters as much as content. For 5-mark answers: brief intro + 4–5 numbered points with keywords + conclusion.
Which chapters are most important in Class 12 Applied Mathematics for CBSE boards?
Chapters with the most long-answer (5-mark) important questions carry the most marks in the board paper. Look at which chapters here have the highest question count — those are the ones CBSE has historically focused on. Don't skip any chapter, but spend extra time on these.
How many questions come from NCERT in CBSE Class 12 Applied Mathematics exam?
Nearly all 16 questions in the Class 12 Applied Mathematics board paper are rooted in NCERT. The exact question may be reworded, but the concept, definition, or formula always comes from the NCERT textbook. Practicing these 16 important questions covers the vast majority of what can be asked.