12th Maths Important 1 Mark Questions Chapter Wise (Samacheer Kalvi)

The one-mark section of the Class 12 Maths public exam is the most predictable part of the paper. The concepts repeat, the phrasing repeats, and almost all of it is drawn from the book back MCQs and previous year questions. If you know what gets asked, you can lock down this section well before the exam.

Below is a chapter-by-chapter map of what the one-markers actually test.

Unit 1: Applications of Matrices and Determinants

• Rank of a matrix from its order and row echelon form
• Properties of the adjoint: the determinant of adj A in terms of det A
• Condition for a system to be consistent or inconsistent
• Inverse of a two by two matrix and singular matrix conditions

Nearly all of these are one-step once you know the property. Memorise the relationship between det(adj A) and det A for a matrix of order n, because it appears almost every year in some form.

Unit 2: Complex Numbers

• Powers of i and sums of four consecutive powers
• Modulus of a product or quotient
• Principal argument, especially in the second and third quadrants
• Cube roots of unity and the identity that they sum to zero
• Locus questions: which curve does a given modulus condition describe

This chapter is the highest-yield one-mark chapter in the whole syllabus. The full set is worked out on the Complex Numbers solved MCQ page.

Unit 3: Theory of Equations

• Relations between roots and coefficients
• Number of positive and negative roots by Descartes rule of signs
• Nature of roots of a reciprocal equation

Unit 4: Inverse Trigonometric Functions

• Principal value branches, which differ for each function
• Domain and range questions phrased as "which of the following is defined"
• Sum and difference identities for inverse tangent

The single most common error here is quoting the range of one inverse function when the question asks about another. Write all six ranges on one card and revise that card, not the chapter.

Unit 5: Two Dimensional Analytical Geometry II

• Eccentricity of a conic from its standard equation
• Length of the latus rectum
• Condition for a line to be a tangent to a given conic
• Identifying the conic from the general second degree equation

Unit 6: Applications of Vector Algebra

• Scalar triple product and its geometric meaning as a volume
• Condition for three vectors to be coplanar
• Angle between two planes or between a line and a plane
• Shortest distance between skew lines

Unit 7: Applications of Differential Calculus

• Conditions for increasing and decreasing functions
• Points of inflection and the second derivative test
• Statement conditions for Rolle theorem and the mean value theorem

Questions here often ask which hypothesis fails for a given function on a given interval, so know the conditions as precisely as the conclusions.

Unit 8: Differentials and Partial Derivatives

• Euler theorem for homogeneous functions
• Degree of a homogeneous function
• Approximation of a small change using differentials

Unit 9: Applications of Integration

• Properties of definite integrals, especially the even and odd function property
• Gamma function values
• Reduction formula results for powers of sine and cosine

The even and odd property turns several questions into an instant zero, and it is a favourite of paper setters.

Unit 10: Ordinary Differential Equations

• Order and degree of a given differential equation
• Number of arbitrary constants in the general solution
• Identifying whether an equation is variable separable, homogeneous or linear
• Integrating factor of a linear first order equation

Degree questions are a trap when the equation contains radicals or fractional powers. Clear those first, then read off the degree.

Unit 11: Probability Distributions

• Mean and variance of the binomial distribution
• Conditions a function must satisfy to be a probability density function
• Cumulative distribution function properties

Unit 12: Discrete Mathematics

• Closure, associativity, identity and inverse for a given binary operation
• Whether a given set forms a group under an operation
• Truth tables, tautology and contradiction
• Converse, inverse and contrapositive of a statement

This chapter is almost pure definition recall, which makes it the fastest chapter in the syllabus to secure marks in.

How to revise the one-mark section

Do not revise it by reading. Revise it by testing. Take a chapter, do twenty MCQs against a timer, and mark yourself honestly. Anything you got wrong goes in a single-page mistakes list. In the last week, that page is your entire revision for this section.

You can take a timed chapter test for any of these units on the Class 12 Maths practice section, choosing your own question count and timer.