Section A – Numbers, Quantification and Numerical Applications
This section builds the foundation of Applied Mathematics. It introduces students to different number systems such as decimal and binary numbers, and explains how computers use the binary system (base 2). Students learn how to convert numbers from decimal to binary and vice versa, and how to perform binary operations like addition, subtraction, multiplication, and division.
The section also covers indices, logarithms, and antilogarithms, including laws of exponents and properties of logarithms. Students understand concepts like characteristic and mantissa and learn how logarithms simplify complex calculations.
Another major part of this section is numerical applications, which includes practical topics such as clock problems, calendar calculations (odd days and leap years), time and work, time and distance, and seating arrangements. These topics develop logical reasoning and real-life mathematical problem-solving skills.
Practice Questions (Section A)
Convert the decimal number 45 into binary form and explain the steps clearly.
Find the angle between the hour and minute hands of a clock at 5:40.
Section B – Algebra and Mathematical Reasoning
This section focuses on algebraic thinking and logical development. It includes topics such as:
Sets and Relations, where students learn about types of sets, operations on sets, and relations between elements.
Sequences and Series, including arithmetic progressions and basic pattern recognition.
Permutations and Combinations, which help students understand counting principles and arrangement problems.
Mathematical Reasoning, which develops logical statements, implications, and truth values.
This section strengthens analytical ability and prepares students for higher mathematical applications in finance, data science, and competitive exams.
Students not only solve equations but also learn how to interpret patterns and logically justify mathematical statements.
Practice Questions (Section B)
Find the number of different arrangements possible using the letters of the word “MATH”.
If the first term of an arithmetic progression is 5 and the common difference is 3, find the 10th term.
Section C – Calculus, Probability, Statistics and Financial Mathematics
This section introduces students to advanced applied concepts that connect mathematics with real-world applications.
Calculus introduces limits and basic differentiation concepts.
Probability teaches how to calculate the likelihood of events.
Descriptive Statistics includes mean, median, mode, variance, and data interpretation.
Basics of Financial Mathematics explains interest, annuities, EMI calculations, and investment mathematics.
Coordinate Geometry deals with straight lines and geometric representation of equations.
This section is especially important for students interested in commerce, economics, finance, actuarial science, and data analytics. It connects classroom mathematics to banking, business, and statistical analysis.
Practice Questions (Section C)
Calculate the compound interest on ₹10,000 at 8% per annum for 2 years.
Find the probability of getting a head when a fair coin is tossed three times.
