SJ MathsTeacher Exam PreparationUP PGT Mathematics • Subject Code 08
Mathematics-PGT • Secondary Education • Subject Code 08

UP PGT Mathematics Syllabus 2026 & Study Tracker

Complete topic-wise UP PGT Mathematics tracker. Study pages live once under the reusable /mathematics/ master library, while this page preserves the exam-specific syllabus and marks topics common to both TGT and PGT.

16 tracker sections176 tracked topics67 TGT + PGT topicsShared /mathematics/ library

Shared Mathematics content, exam-specific syllabus

Actual notes stay under /mathematics/. This avoids duplicate theory when a topic appears in both TGT and PGT and also makes the library reusable for KVS, GIC and other exams later. No duplicate Topic Index table is added.

67TGT + PGT topics
109PGT Only
176Total tracked topics
Reflexive relation
PGT Only
/mathematics/relations-and-functions/reflexive-relation/
→
Symmetric relation
PGT Only
/mathematics/relations-and-functions/symmetric-relation/
→
Transitive relation
PGT Only
/mathematics/relations-and-functions/transitive-relation/
→
Equivalence relation
TGT + PGT
/mathematics/relations-and-functions/equivalence-relation/
→
Equivalence class
PGT Only
/mathematics/relations-and-functions/equivalence-class/
→
One-one functions
PGT Only
/mathematics/relations-and-functions/one-one-functions/
→
Onto functions
PGT Only
/mathematics/relations-and-functions/onto-functions/
→
Composite of functions
TGT + PGT
/mathematics/relations-and-functions/composition-of-functions/
→
Inverse of function
TGT + PGT
/mathematics/relations-and-functions/inverse-function/
→
Binary operations
PGT Only
/mathematics/relations-and-functions/binary-operations/
→
Types of matrices
TGT + PGT
/mathematics/algebra/matrices-and-determinants/matrices/types-of-matrices/
→
Transpose of a matrix
TGT + PGT
/mathematics/algebra/matrices-and-determinants/matrices/transpose/
→
Symmetric matrices
TGT + PGT
/mathematics/algebra/matrices-and-determinants/matrices/symmetric-matrices/
→
Skew-symmetric matrices
TGT + PGT
/mathematics/algebra/matrices-and-determinants/matrices/skew-symmetric-matrices/
→
Addition of matrices
TGT + PGT
/mathematics/algebra/matrices-and-determinants/matrices/addition/
→
Multiplication of matrices
TGT + PGT
/mathematics/algebra/matrices-and-determinants/matrices/multiplication/
→
Singular matrices
PGT Only
/mathematics/algebra/matrices-and-determinants/matrices/singular-matrices/
→
Non-singular matrices
PGT Only
/mathematics/algebra/matrices-and-determinants/matrices/non-singular-matrices/
→
Invertible matrices
PGT Only
/mathematics/algebra/matrices-and-determinants/matrices/invertible-matrices/
→
Properties of determinants
TGT + PGT
/mathematics/algebra/matrices-and-determinants/determinants/properties/
→
Adjoint of a square matrix
PGT Only
/mathematics/algebra/matrices-and-determinants/matrices/adjoint/
→
Inverse of a square matrix
PGT Only
/mathematics/algebra/matrices-and-determinants/matrices/inverse/
→
Consistency of system of linear equations
PGT Only
/mathematics/algebra/linear-equations/consistency/
→
Number of solutions of system of linear equations
PGT Only
/mathematics/algebra/linear-equations/number-of-solutions/
→
Solving linear equations in two variables
TGT + PGT
/mathematics/algebra/linear-equations/two-unknown-variables/
→
Solving linear equations in three variables
TGT + PGT
/mathematics/algebra/linear-equations/three-unknown-variables/
→
Theory of equations of degree ≥ 2
TGT + PGT
/mathematics/algebra/theory-of-equations/
→
Quadratic equation
TGT + PGT
/mathematics/algebra/theory-of-equations/quadratic-equation/
→
Arithmetic progression
TGT + PGT
/mathematics/algebra/sequences-and-series/arithmetic-progression/
→
Geometric progression
TGT + PGT
/mathematics/algebra/sequences-and-series/geometric-progression/
→
Harmonic progression
TGT + PGT
/mathematics/algebra/sequences-and-series/harmonic-progression/
→
Permutations and combinations
TGT + PGT
/mathematics/algebra/permutations-and-combinations/
→
Binomial theorem
TGT + PGT
/mathematics/algebra/binomial-theorem/
→
Exponential series
TGT + PGT
/mathematics/algebra/sequences-and-series/exponential-series/
→
Logarithmic series
TGT + PGT
/mathematics/algebra/sequences-and-series/logarithmic-series/
→
Limit of a function
TGT + PGT
/mathematics/calculus/differential-calculus/limit-of-a-function/
→
Continuity of a function
TGT + PGT
/mathematics/calculus/differential-calculus/continuity/
→
Differentiability of a function
PGT Only
/mathematics/calculus/differential-calculus/differentiability/
→
Derivative of composite function
PGT Only
/mathematics/calculus/differential-calculus/derivative-of-composite-function/
→
Rolle's theorem
TGT + PGT
/mathematics/calculus/differential-calculus/rolles-theorem/
→
Lagrange mean value theorem
PGT Only
/mathematics/calculus/differential-calculus/lagrange-mean-value-theorem/
→
Cauchy mean value theorem
PGT Only
/mathematics/calculus/differential-calculus/cauchy-mean-value-theorem/
→
Maclaurin's series
PGT Only
/mathematics/calculus/differential-calculus/maclaurin-series/
→
Taylor's series
PGT Only
/mathematics/calculus/differential-calculus/taylor-series/
→
L'Hospital's rule
PGT Only
/mathematics/calculus/differential-calculus/lhospital-rule/
→
Successive differentiations
PGT Only
/mathematics/calculus/differential-calculus/successive-differentiation/
→
Leibnitz theorem
PGT Only
/mathematics/calculus/differential-calculus/leibnitz-theorem/
→
Equation of tangent and normal
TGT + PGT
/mathematics/calculus/differential-calculus/tangent-and-normal/
→
Maxima and minima
TGT + PGT
/mathematics/calculus/differential-calculus/maxima-and-minima/
→
Increasing functions
PGT Only
/mathematics/calculus/differential-calculus/increasing-functions/
→
Decreasing functions
PGT Only
/mathematics/calculus/differential-calculus/decreasing-functions/
→
Methods of integration
PGT Only
/mathematics/calculus/integral-calculus/methods-of-integration/
→
Integration by parts
TGT + PGT
/mathematics/calculus/integral-calculus/integration-by-parts/
→
Integration by substitution
TGT + PGT
/mathematics/calculus/integral-calculus/integration-by-substitution/
→
Integration using partial fractions
TGT + PGT
/mathematics/calculus/integral-calculus/partial-fractions/
→
Definite Integral
TGT + PGT
/mathematics/calculus/integral-calculus/definite-integral/
→
Definite integration as a limit of sum
PGT Only
/mathematics/calculus/integral-calculus/definite-integral-as-limit-of-sum/
→
Properties of definite integrals
PGT Only
/mathematics/calculus/integral-calculus/properties-of-definite-integrals/
→
Evaluation of definite integrals
PGT Only
/mathematics/calculus/integral-calculus/evaluation-of-definite-integrals/
→
Area under simple curves
PGT Only
/mathematics/calculus/integral-calculus/applications/area-under-curves/
→
Riemann integration
PGT Only
/mathematics/calculus/integral-calculus/riemann-integration/
→
Order of differential equations
TGT + PGT
/mathematics/calculus/differential-equations/order/
→
Degree of differential equations
TGT + PGT
/mathematics/calculus/differential-equations/degree/
→
Formation of differential equations
PGT Only
/mathematics/calculus/differential-equations/formation/
→
First-order first-degree differential equations
TGT + PGT
/mathematics/calculus/differential-equations/first-order-first-degree/
→
Singular solutions
PGT Only
/mathematics/calculus/differential-equations/singular-solutions/
→
Linear differential equations with constant coefficients
PGT Only
/mathematics/calculus/differential-equations/linear-with-constant-coefficients/
→
Homogeneous differential equations
PGT Only
/mathematics/calculus/differential-equations/homogeneous-differential-equations/
→
General equation of second degree in two variables
PGT Only
/mathematics/coordinate-geometry/two-dimensional/general-second-degree/
→
Classification as pair of straight lines
TGT + PGT
/mathematics/coordinate-geometry/two-dimensional/general-second-degree/pair-of-straight-lines-condition/
→
Classification as circle
TGT + PGT
/mathematics/coordinate-geometry/two-dimensional/general-second-degree/circle-condition/
→
Classification as parabola
TGT + PGT
/mathematics/coordinate-geometry/two-dimensional/general-second-degree/parabola-condition/
→
Classification as ellipse
TGT + PGT
/mathematics/coordinate-geometry/two-dimensional/general-second-degree/ellipse-condition/
→
Classification as hyperbola
TGT + PGT
/mathematics/coordinate-geometry/two-dimensional/general-second-degree/hyperbola-condition/
→
Equation of tangents
TGT + PGT
/mathematics/coordinate-geometry/two-dimensional/conics/tangent/
→
Equation of normals
TGT + PGT
/mathematics/coordinate-geometry/two-dimensional/conics/normal/
→
Common tangents to two conics
PGT Only
/mathematics/coordinate-geometry/two-dimensional/conics/common-tangents/
→
Pair of tangents
TGT + PGT
/mathematics/coordinate-geometry/two-dimensional/conics/pair-of-tangents/
→
Chord of contact
PGT Only
/mathematics/coordinate-geometry/two-dimensional/conics/chord-of-contact/
→
Vectors and scalars
PGT Only
/mathematics/vectors-and-three-dimensional-geometry/vectors/vectors-and-scalars/
→
Unit vectors
TGT + PGT
/mathematics/vectors-and-three-dimensional-geometry/vectors/unit-vector/
→
Direction cosines and ratios of a vector
TGT + PGT
/mathematics/vectors-and-three-dimensional-geometry/vectors/direction-cosines/
→
Multiplication of a vector by scalar
PGT Only
/mathematics/vectors-and-three-dimensional-geometry/vectors/scalar-multiplication/
→
Dot product of vectors
TGT + PGT
/mathematics/vectors-and-three-dimensional-geometry/vectors/dot-product/
→
Cross product of vectors
TGT + PGT
/mathematics/vectors-and-three-dimensional-geometry/vectors/cross-product/
→
Simple applications of dot and cross products
TGT + PGT
/mathematics/vectors-and-three-dimensional-geometry/vectors/applications-of-dot-and-cross-products/
→
Direction cosines and ratios of line joining two points
PGT Only
/mathematics/vectors-and-three-dimensional-geometry/three-dimensional/direction-cosines-line-joining-two-points/
→
Cartesian equation of a straight line
PGT Only
/mathematics/vectors-and-three-dimensional-geometry/three-dimensional/cartesian-equation-of-line/
→
Vector equation of a straight line
PGT Only
/mathematics/vectors-and-three-dimensional-geometry/three-dimensional/vector-equation-of-line/
→
Coplanar lines
PGT Only
/mathematics/vectors-and-three-dimensional-geometry/three-dimensional/coplanar-lines/
→
Skew lines
PGT Only
/mathematics/vectors-and-three-dimensional-geometry/three-dimensional/skew-lines/
→
Shortest distance between two lines
PGT Only
/mathematics/vectors-and-three-dimensional-geometry/three-dimensional/shortest-distance-between-lines/
→
Cartesian equation of a plane
PGT Only
/mathematics/vectors-and-three-dimensional-geometry/three-dimensional/cartesian-equation-of-plane/
→
Vector equation of a plane
PGT Only
/mathematics/vectors-and-three-dimensional-geometry/three-dimensional/vector-equation-of-plane/
→
Angle between two lines
PGT Only
/mathematics/vectors-and-three-dimensional-geometry/three-dimensional/angle-between-two-lines/
→
Angle between two planes
PGT Only
/mathematics/vectors-and-three-dimensional-geometry/three-dimensional/angle-between-two-planes/
→
Angle between line and plane
PGT Only
/mathematics/vectors-and-three-dimensional-geometry/three-dimensional/angle-between-line-and-plane/
→
Distance of a point from a plane
PGT Only
/mathematics/vectors-and-three-dimensional-geometry/three-dimensional/distance-point-from-plane/
→
Intersection of two lines
PGT Only
/mathematics/vectors-and-three-dimensional-geometry/three-dimensional/intersection-of-two-lines/
→
Intersection of a line and plane
PGT Only
/mathematics/vectors-and-three-dimensional-geometry/three-dimensional/intersection-line-and-plane/
→
Intersection of two planes
PGT Only
/mathematics/vectors-and-three-dimensional-geometry/three-dimensional/intersection-of-two-planes/
→
Sphere
TGT + PGT
/mathematics/coordinate-geometry/three-dimensional/sphere/
→
Cone
TGT + PGT
/mathematics/coordinate-geometry/three-dimensional/cone/
→
Cylinder
TGT + PGT
/mathematics/coordinate-geometry/three-dimensional/cylinder/
→
Group and examples
TGT + PGT
/mathematics/abstract-algebra/groups/
→
Subgroups
PGT Only
/mathematics/abstract-algebra/groups/subgroups/
→
Group homomorphism
TGT + PGT
/mathematics/abstract-algebra/groups/homomorphism/
→
Group isomorphism
PGT Only
/mathematics/abstract-algebra/groups/isomorphism/
→
Properties of homomorphism
PGT Only
/mathematics/abstract-algebra/groups/properties-of-homomorphism/
→
Order of an element
TGT + PGT
/mathematics/abstract-algebra/groups/order-of-an-element/
→
Cyclic group
TGT + PGT
/mathematics/abstract-algebra/groups/cyclic-group/
→
Symmetric group Sn
PGT Only
/mathematics/abstract-algebra/groups/symmetric-group-sn/
→
Lagrange theorem
TGT + PGT
/mathematics/abstract-algebra/groups/lagrange-theorem/
→
Fermat's theorem
PGT Only
/mathematics/abstract-algebra/groups/fermats-theorem/
→
Applications of Fermat's theorem
PGT Only
/mathematics/abstract-algebra/groups/fermats-theorem/applications/
→
Normal subgroups
PGT Only
/mathematics/abstract-algebra/groups/normal-subgroups/
→
Fundamental theorem of homomorphism
PGT Only
/mathematics/abstract-algebra/groups/fundamental-theorem-of-homomorphism/
→
Ring with examples
PGT Only
/mathematics/abstract-algebra/rings/ring-and-examples/
→
Field with examples
PGT Only
/mathematics/abstract-algebra/fields/field-and-examples/
→
Vector space with examples
PGT Only
/mathematics/linear-algebra/vector-spaces/
→
Subspace
PGT Only
/mathematics/linear-algebra/vector-spaces/subspace/
→
Linear dependence
PGT Only
/mathematics/linear-algebra/vector-spaces/linear-dependence/
→
Linear independence
PGT Only
/mathematics/linear-algebra/vector-spaces/linear-independence/
→
Basis of a vector space
PGT Only
/mathematics/linear-algebra/vector-spaces/basis/
→
Dimension of a vector space
PGT Only
/mathematics/linear-algebra/vector-spaces/dimension/
→
Quotient space
PGT Only
/mathematics/linear-algebra/vector-spaces/quotient-space/
→
Linear sum of subspaces
PGT Only
/mathematics/linear-algebra/vector-spaces/linear-sum/
→
Direct sum of subspaces
PGT Only
/mathematics/linear-algebra/vector-spaces/direct-sum/
→
Linear transformation
PGT Only
/mathematics/linear-algebra/linear-transformations/
→
Kernel of linear transformation
PGT Only
/mathematics/linear-algebra/linear-transformations/kernel/
→
Image of linear transformation
PGT Only
/mathematics/linear-algebra/linear-transformations/image/
→
Rank of linear transformation
PGT Only
/mathematics/linear-algebra/linear-transformations/rank/
→
Nullity of linear transformation
PGT Only
/mathematics/linear-algebra/linear-transformations/nullity/
→
Rank-nullity theorem
PGT Only
/mathematics/linear-algebra/linear-transformations/rank-nullity-theorem/
→
Composite of linear transformations
PGT Only
/mathematics/linear-algebra/linear-transformations/composition/
→
Singular linear transformations
PGT Only
/mathematics/linear-algebra/linear-transformations/singular/
→
Non-singular linear transformations
PGT Only
/mathematics/linear-algebra/linear-transformations/non-singular/
→
Transpose of a linear transformation
PGT Only
/mathematics/linear-algebra/linear-transformations/transpose/
→
Matrix of a linear transformation
PGT Only
/mathematics/linear-algebra/linear-transformations/matrix-of-transformation/
→
Scalar fields
PGT Only
/mathematics/vector-calculus/scalar-fields/
→
Vector fields
PGT Only
/mathematics/vector-calculus/vector-fields/
→
Gradient
PGT Only
/mathematics/vector-calculus/gradient/
→
Divergence
PGT Only
/mathematics/vector-calculus/divergence/
→
Curl
PGT Only
/mathematics/vector-calculus/curl/
→
Vector identities
PGT Only
/mathematics/vector-calculus/vector-identities/
→
Directional derivatives
PGT Only
/mathematics/vector-calculus/directional-derivatives/
→
Line integral
PGT Only
/mathematics/vector-calculus/line-integral/
→
Surface integral
PGT Only
/mathematics/vector-calculus/surface-integral/
→
Volume integral
PGT Only
/mathematics/vector-calculus/volume-integral/
→
Green's theorem
PGT Only
/mathematics/vector-calculus/greens-theorem/
→
Gauss-divergence theorem
PGT Only
/mathematics/vector-calculus/gauss-divergence-theorem/
→
Stokes' theorem
PGT Only
/mathematics/vector-calculus/stokes-theorem/
→
Simple applications of vector integration theorems
PGT Only
/mathematics/vector-calculus/applications/
→
Equilibrium of a body under three forces
TGT + PGT
/mathematics/mechanics/statics/equilibrium-under-three-forces/
→
Coplanar forces
PGT Only
/mathematics/mechanics/statics/coplanar-forces/
→
Equilibrium under a system of coplanar forces
PGT Only
/mathematics/mechanics/statics/equilibrium-of-coplanar-force-system/
→
Centre of gravity
TGT + PGT
/mathematics/mechanics/statics/centre-of-gravity/
→
Common catenary
TGT + PGT
/mathematics/mechanics/statics/common-catenary/
→
Properties of common catenary
PGT Only
/mathematics/mechanics/statics/common-catenary/properties/
→
Moment of inertia
PGT Only
/mathematics/mechanics/statics/moment-of-inertia/
→
Projectile motion in vertical plane under gravity
TGT + PGT
/mathematics/mechanics/dynamics/projectile-motion/
→
Work, power and energy
PGT Only
/mathematics/mechanics/dynamics/work-power-and-energy/
→
Radial and transverse velocity and acceleration
TGT + PGT
/mathematics/mechanics/dynamics/radial-and-transverse-motion/
→
Tangential and normal velocity and acceleration
TGT + PGT
/mathematics/mechanics/dynamics/tangential-and-normal-motion/
→
Central orbits
PGT Only
/mathematics/mechanics/dynamics/central-orbits/
→
Trigonometric equations
TGT + PGT
/mathematics/trigonometry/trigonometric-equations/
→
Properties of triangles
TGT + PGT
/mathematics/trigonometry/solution-of-triangles/
→
Inverse circular functions
TGT + PGT
/mathematics/trigonometry/inverse-circular-functions/
→
Height and distance
TGT + PGT
/mathematics/trigonometry/height-and-distance/
→
Complex numbers
PGT Only
/mathematics/complex-numbers/
→
De Moivre's theorem
TGT + PGT
/mathematics/complex-numbers/de-moivres-theorem/
→
Applications of De Moivre's theorem
TGT + PGT
/mathematics/complex-numbers/de-moivres-theorem/applications/
→
No matching Mathematics topic found.
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