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NEET / State Class 12 Board (e.g. ISC) Mathematics Syllabus
The Mathematics syllabus for NEET / State Class 12 Board (e.g. ISC) in full: 4 chapters, 14 topics and 33 sub-topics, every one listed below, plus 50 Mathematics flashcards with answers.
Mathematics syllabus: all 4 chapters
Expand any chapter to see its topics and sub-topics.
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Relations and Functions
3 topics- Types of Relations and Functions
- Reflexive, symmetric, transitive and equivalence relations
- One-one, onto and bijective functions
- Composition of functions and invertible functions
- Inverse Trigonometric Functions
- Domain, range and principal value branches
- Properties and identities of inverse trigonometric functions
- Binary Operations and Algebra of Functions
- Binary operations and their properties
- Types of Relations and Functions
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Algebra and Calculus I
3 topics- Matrices and Determinants
- Operations on matrices; symmetric and skew-symmetric
- Determinants, minors, cofactors and properties
- Adjoint, inverse and solution of linear equations
- Continuity and Differentiability
- Continuity, differentiability and chain rule
- Derivatives of implicit, parametric and logarithmic functions
- Rolle's and Lagrange's mean value theorems
- Applications of Derivatives
- Rate of change and approximations
- Increasing and decreasing functions; tangents and normals
- Maxima and minima
- Matrices and Determinants
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Integral Calculus
4 topics- Indefinite Integrals
- Integration by substitution and partial fractions
- Integration by parts and special integrals
- Definite Integrals
- Fundamental theorem and properties of definite integrals
- Definite integral as limit of a sum
- Applications of Integrals
- Area under simple curves and between curves
- Differential Equations
- Order, degree and formation of differential equations
- Variable separable and homogeneous equations
- Linear differential equations
- Indefinite Integrals
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Vectors, 3D Geometry and Probability
4 topics- Vectors
- Scalar and vector products
- Scalar triple product and applications
- Three-Dimensional Geometry
- Direction cosines and equation of a line
- Equation of a plane; angle between lines and planes
- Shortest distance between two lines
- Probability
- Conditional probability and multiplication theorem
- Bayes' theorem and total probability
- Random variables and binomial distribution
- Linear Programming
- Formulation of LPP and graphical solution
- Feasible region, optimal solution and constraints
- Vectors
NEET / State Class 12 Board (e.g. ISC) Mathematics flashcards — 50 questions with answers
What is a reflexive relation on a set A?
A relation R on A is reflexive if (a, a) belongs to R for every element a in A.
Define a symmetric relation.
A relation R on A is symmetric if (a, b) in R implies (b, a) in R for all a, b in A.
Define a transitive relation.
A relation R on A is transitive if (a, b) in R and (b, c) in R together imply (a, c) in R.
What is an equivalence relation?
A relation that is reflexive, symmetric, and transitive simultaneously.
When is a function f: A to B called one-one (injective)?
When f(x1) = f(x2) implies x1 = x2; distinct elements of A have distinct images.
When is a function called onto (surjective)?
When every element of the codomain B has at least one pre-image in A, i.e. range = codomain.
What is a bijective function?
A function that is both one-one (injective) and onto (surjective); it has an inverse.
What is the principal value range of sin inverse x?
[-pi/2, pi/2], with domain [-1, 1].
What is the principal value range of cos inverse x?
[0, pi], with domain [-1, 1].
What is the principal value range of tan inverse x?
(-pi/2, pi/2), with domain all real numbers.
State the identity relating sin inverse x and cos inverse x.
sin inverse x + cos inverse x = pi/2, for x in [-1, 1].
What is tan inverse x + cot inverse x equal to?
pi/2, for all real x.
Define a binary operation on a set A.
A binary operation * on A is a function from A x A to A, assigning to each ordered pair (a, b) a unique element a * b in A.
When is a binary operation * commutative?
When a * b = b * a for all a, b in the set.
What is the identity element for a binary operation *?
An element e such that a * e = e * a = a for every a in the set.
What is the inverse of an element a under operation * with identity e?
An element b such that a * b = b * a = e.
When is a binary operation * associative?
When (a * b) * c = a * (b * c) for all a, b, c in the set.
What is a symmetric matrix?
A square matrix A for which A transpose = A, i.e. a_ij = a_ji.
What is a skew-symmetric matrix?
A square matrix A for which A transpose = -A; its diagonal elements are all zero.
State the condition for two matrices to be multipliable (A times B).
The number of columns of A must equal the number of rows of B.
Show the other 30 Mathematics flashcards
What is the property (AB) transpose in terms of A transpose and B transpose?
(AB) transpose = B transpose times A transpose.
What is a singular matrix?
A square matrix whose determinant is zero; it has no inverse.
Give the formula for the inverse of a matrix A.
A inverse = (1 / det A) times adj A, valid when det A is not zero.
What does adj A times A equal?
adj A times A = A times adj A = (det A) times I.
How is the area of a triangle with vertices (x1,y1), (x2,y2), (x3,y3) found using determinants?
Area = (1/2) times the absolute value of the determinant of rows [x1 y1 1], [x2 y2 1], [x3 y3 1].
State the condition for a function f to be continuous at x = c.
f is continuous at c if the limit of f(x) as x approaches c equals f(c) (and both exist and are finite).
What is the derivative of sin inverse x?
1 / sqrt(1 - x squared), for |x| < 1.
What is the derivative of tan inverse x?
1 / (1 + x squared).
State the chain rule for differentiation.
If y = f(g(x)), then dy/dx = f'(g(x)) times g'(x).
State the product rule for differentiation.
d/dx (u v) = u times (dv/dx) + v times (du/dx).
State Rolle's Theorem.
If f is continuous on [a,b], differentiable on (a,b), and f(a) = f(b), then there exists c in (a,b) with f'(c) = 0.
State the Mean Value Theorem (Lagrange).
If f is continuous on [a,b] and differentiable on (a,b), there exists c in (a,b) with f'(c) = (f(b) - f(a)) / (b - a).
How do you determine where a function is increasing?
A function is increasing on an interval where its derivative f'(x) > 0 (and non-decreasing where f'(x) >= 0).
What is the second derivative test for a local maximum at x = c?
If f'(c) = 0 and f''(c) < 0, then f has a local maximum at c.
What is the integral of 1/x dx?
ln|x| + C.
What is the integral of sec squared x dx?
tan x + C.
State the formula for integration by parts.
Integral of u dv = u v minus integral of v du.
What is the integral of 1 / (1 + x squared) dx?
tan inverse x + C.
State the Fundamental Theorem of Calculus (evaluation form).
The definite integral of f from a to b equals F(b) - F(a), where F is an antiderivative of f.
What is the property: integral from a to b of f(x) dx in terms of f(a + b - x)?
Integral from a to b of f(x) dx = integral from a to b of f(a + b - x) dx.
When does the integral from -a to a of f(x) dx equal zero?
When f is an odd function, i.e. f(-x) = -f(x).
How is the area between a curve y = f(x) and the x-axis from a to b found?
Area = integral from a to b of |f(x)| dx.
What is the order of a differential equation?
The order of the highest derivative appearing in the equation.
What is the degree of a differential equation?
The power of the highest order derivative when the equation is polynomial in derivatives (free of radicals/fractions in them).
What is the integrating factor for the linear ODE dy/dx + P(x) y = Q(x)?
I.F. = e raised to the integral of P(x) dx.
What is the formula for the dot (scalar) product of vectors a and b?
a dot b = |a| |b| cos(theta), where theta is the angle between them.
What does the cross product magnitude |a x b| represent geometrically?
It equals |a| |b| sin(theta), the area of the parallelogram formed by a and b.
What is the direction-cosine identity for a line?
l squared + m squared + n squared = 1, where l, m, n are the direction cosines.
State the multiplication theorem of probability (conditional form).
P(A and B) = P(A) times P(B given A) = P(B) times P(A given B).
State Bayes' Theorem for events with prior P(E_i).
P(E_i given A) = [P(E_i) P(A given E_i)] divided by the sum over j of P(E_j) P(A given E_j).
NEET / State Class 12 Board (e.g. ISC) Mathematics FAQ
What is in the NEET / State Class 12 Board (e.g. ISC) Mathematics syllabus?
NEET / State Class 12 Board (e.g. ISC) Mathematics is split into 4 chapters: Relations and Functions, Algebra and Calculus I, Integral Calculus and Vectors, 3D Geometry and Probability. Together they contain 14 topics and 33 sub-topics.
How many chapters are in NEET / State Class 12 Board (e.g. ISC) Mathematics?
4 chapters, containing 14 topics and 33 sub-topics. The largest chapter is Integral Calculus, with 4 topics.
Are there flashcards for NEET / State Class 12 Board (e.g. ISC) Mathematics?
Yes — a 50-card Mathematics deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.