SJ MathsTeacher Exam PreparationUP TGT Mathematics • Subject Code 07
Maths-TGT • Secondary Education • Subject Code 07

UP TGT Mathematics Syllabus 2026 & Study Tracker

Complete topic-wise UP TGT 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.

14 tracker sections190 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
123TGT Only
190Total tracked topics
Work and time
TGT Only
/mathematics/commercial-mathematics/work-and-time/
→
Speed and time
TGT Only
/mathematics/commercial-mathematics/speed-and-time/
→
Simple interest
TGT Only
/mathematics/commercial-mathematics/simple-interest/
→
Compound interest
TGT Only
/mathematics/commercial-mathematics/compound-interest/
→
Banking
TGT Only
/mathematics/commercial-mathematics/banking/
→
Taxation
TGT Only
/mathematics/commercial-mathematics/taxation/
→
Frequency distribution
TGT Only
/mathematics/statistics/frequency-distribution/
→
Pictorial representation of statistical data
TGT Only
/mathematics/statistics/pictorial-representation-of-data/
→
Measurement of central tendency
TGT Only
/mathematics/statistics/central-tendency/
→
Measurement of deflection
TGT Only
/mathematics/statistics/measurement-of-deflection/
→
Statistics of birth and death
TGT Only
/mathematics/statistics/birth-and-death-statistics/
→
Index
TGT Only
/mathematics/statistics/index-numbers/
→
Surds
TGT Only
/mathematics/algebra/surds/
→
Polynomials and factors of second-degree polynomials
TGT Only
/mathematics/algebra/polynomials/second-degree-polynomials-and-factors/
→
HCF of polynomials
TGT Only
/mathematics/algebra/polynomials/hcf-of-polynomials/
→
Linear equation of two unknown variables
TGT + PGT
/mathematics/algebra/linear-equations/two-unknown-variables/
→
Simultaneous equations of three unknown variables
TGT + PGT
/mathematics/algebra/linear-equations/three-unknown-variables/
→
Quadratic equation
TGT + PGT
/mathematics/algebra/theory-of-equations/quadratic-equation/
→
Logarithms
TGT Only
/mathematics/algebra/logarithms/
→
Ratios and proportions
TGT Only
/mathematics/algebra/ratios-and-proportions/
→
Number system
TGT Only
/mathematics/algebra/number-system/
→
Set operations
TGT Only
/mathematics/set-theory/set-operations/
→
Definition of determinants
TGT Only
/mathematics/algebra/matrices-and-determinants/determinants/definition/
→
Minors and cofactors
TGT Only
/mathematics/algebra/matrices-and-determinants/determinants/minors-and-cofactors/
→
Expansion of determinants up to order 3×3
TGT Only
/mathematics/algebra/matrices-and-determinants/determinants/expansion-up-to-3x3/
→
Properties of determinants
TGT + PGT
/mathematics/algebra/matrices-and-determinants/determinants/properties/
→
Cramer's rule for three simultaneous equations
TGT Only
/mathematics/algebra/matrices-and-determinants/determinants/cramers-rule/
→
Types of matrices
TGT + PGT
/mathematics/algebra/matrices-and-determinants/matrices/types-of-matrices/
→
Addition of matrices up to order 3×3
TGT + PGT
/mathematics/algebra/matrices-and-determinants/matrices/addition/
→
Multiplication of matrices up to order 3×3
TGT + PGT
/mathematics/algebra/matrices-and-determinants/matrices/multiplication/
→
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/
→
Solving simultaneous equations using inverse of matrix
TGT Only
/mathematics/algebra/matrices-and-determinants/matrices/solving-linear-equations-using-inverse/
→
Theory of equations
TGT + PGT
/mathematics/algebra/theory-of-equations/
→
Symmetric functions of roots
TGT Only
/mathematics/algebra/theory-of-equations/symmetric-functions-of-roots/
→
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/
→
Sum of series of squares
TGT Only
/mathematics/algebra/sequences-and-series/sum-of-squares/
→
Sum of series of cubes
TGT Only
/mathematics/algebra/sequences-and-series/sum-of-cubes/
→
Sum of natural numbers
TGT Only
/mathematics/algebra/sequences-and-series/sum-of-natural-numbers/
→
Permutations and combinations
TGT + PGT
/mathematics/algebra/permutations-and-combinations/
→
Binomial theorem
TGT + PGT
/mathematics/algebra/binomial-theorem/
→
Sum of exponential series
TGT + PGT
/mathematics/algebra/sequences-and-series/exponential-series/
→
Sum of logarithmic series
TGT + PGT
/mathematics/algebra/sequences-and-series/logarithmic-series/
→
Rules of set algebra
TGT Only
/mathematics/set-theory/set-algebra/
→
Equivalence relation
TGT + PGT
/mathematics/relations-and-functions/equivalence-relation/
→
Mapping
TGT Only
/mathematics/relations-and-functions/mapping/
→
Composition of mapping
TGT + PGT
/mathematics/relations-and-functions/composition-of-functions/
→
Inverse mapping
TGT + PGT
/mathematics/relations-and-functions/inverse-function/
→
Peano's postulates
TGT Only
/mathematics/set-theory/peanos-postulates/
→
Principle of mathematical induction
TGT Only
/mathematics/set-theory/mathematical-induction/
→
Group
TGT + PGT
/mathematics/abstract-algebra/groups/
→
Group homomorphism
TGT + PGT
/mathematics/abstract-algebra/groups/homomorphism/
→
Subgroup generated by subsets
TGT Only
/mathematics/abstract-algebra/groups/subgroup-generated-by-subsets/
→
Cyclic group
TGT + PGT
/mathematics/abstract-algebra/groups/cyclic-group/
→
Order of an element
TGT + PGT
/mathematics/abstract-algebra/groups/order-of-an-element/
→
Subgroup of cyclic group
TGT Only
/mathematics/abstract-algebra/groups/subgroup-of-cyclic-group/
→
Coset decomposition
TGT Only
/mathematics/abstract-algebra/groups/cosets/
→
Lagrange theorem
TGT + PGT
/mathematics/abstract-algebra/groups/lagrange-theorem/
→
Axioms of real numbers
TGT Only
/mathematics/real-analysis/real-numbers/axioms/
→
Countability of sets
TGT Only
/mathematics/real-analysis/countability/
→
Metric spaces
TGT Only
/mathematics/real-analysis/metric-spaces/
→
Neighbourhood
TGT Only
/mathematics/real-analysis/metric-spaces/neighbourhood/
→
Open sets
TGT Only
/mathematics/real-analysis/metric-spaces/open-sets/
→
Closed sets
TGT Only
/mathematics/real-analysis/metric-spaces/closed-sets/
→
Derived set
TGT Only
/mathematics/real-analysis/metric-spaces/derived-set/
→
Dense set
TGT Only
/mathematics/real-analysis/metric-spaces/dense-set/
→
Perfect set
TGT Only
/mathematics/real-analysis/metric-spaces/perfect-set/
→
Bolzano-Weierstrass theorem
TGT Only
/mathematics/real-analysis/bolzano-weierstrass-theorem/
→
General theorems on sets and sequences
TGT Only
/mathematics/real-analysis/general-theorems/
→
Real sequences
TGT Only
/mathematics/real-analysis/sequences/
→
Limit of sequences
TGT Only
/mathematics/real-analysis/sequences/limit-of-sequences/
→
Convergent sequences
TGT Only
/mathematics/real-analysis/sequences/convergent-sequences/
→
Divergent sequences
TGT Only
/mathematics/real-analysis/sequences/divergent-sequences/
→
Bounded sequences
TGT Only
/mathematics/real-analysis/sequences/bounded-sequences/
→
Monotonic sequences
TGT Only
/mathematics/real-analysis/sequences/monotonic-sequences/
→
Properties of convergent sequences
TGT Only
/mathematics/real-analysis/sequences/properties-of-convergent-sequences/
→
Cauchy sequence
TGT Only
/mathematics/real-analysis/sequences/cauchy-sequence/
→
Cauchy's theorem on limits
TGT Only
/mathematics/real-analysis/sequences/cauchy-theorem-on-limits/
→
Cauchy criterion of convergence
TGT Only
/mathematics/real-analysis/sequences/cauchy-criterion/
→
Limit of real-valued functions
TGT + PGT
/mathematics/calculus/differential-calculus/limit-of-a-function/
→
Continuity of real-valued functions
TGT + PGT
/mathematics/calculus/differential-calculus/continuity/
→
Left-hand and right-hand limits
TGT Only
/mathematics/real-analysis/functions/left-and-right-hand-limits/
→
Properties of continuous functions
TGT Only
/mathematics/real-analysis/functions/properties-of-continuous-functions/
→
Types of discontinuity
TGT Only
/mathematics/real-analysis/functions/types-of-discontinuity/
→
Rolle's theorem
TGT + PGT
/mathematics/calculus/differential-calculus/rolles-theorem/
→
Circular measurement
TGT Only
/mathematics/trigonometry/circular-measurement/
→
Trigonometric ratios of special angles
TGT Only
/mathematics/trigonometry/special-angles/
→
Trigonometric ratios of sum and difference
TGT Only
/mathematics/trigonometry/sum-and-difference/
→
Trigonometric ratios of factors and multiples
TGT Only
/mathematics/trigonometry/factors-and-multiples/
→
Trigonometric identities
TGT Only
/mathematics/trigonometry/trigonometric-identities/
→
Trigonometric equations
TGT + PGT
/mathematics/trigonometry/trigonometric-equations/
→
Solution of triangle
TGT + PGT
/mathematics/trigonometry/solution-of-triangles/
→
Radii and Properties of Circumcircle, Incircle and Excircle
TGT Only
/mathematics/trigonometry/triangle-circles/radii-and-properties/
→
Inverse circular functions
TGT + PGT
/mathematics/trigonometry/inverse-circular-functions/
→
General Properties of Inverse Circular Functions
TGT Only
/mathematics/trigonometry/inverse-circular-functions/general-properties/
→
Addition of complex numbers
TGT Only
/mathematics/complex-numbers/addition/
→
Multiplication of complex numbers
TGT Only
/mathematics/complex-numbers/multiplication/
→
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/
→
Height and distance
TGT + PGT
/mathematics/trigonometry/height-and-distance/
→
Exponential functions of a complex variable
TGT Only
/mathematics/complex-numbers/complex-functions/exponential-functions/
→
Circular functions of a complex variable
TGT Only
/mathematics/complex-numbers/complex-functions/circular-functions/
→
Hyperbolic functions of a complex variable
TGT Only
/mathematics/complex-numbers/complex-functions/hyperbolic-functions/
→
Separation into real and imaginary parts
TGT Only
/mathematics/complex-numbers/separation-real-and-imaginary-parts/
→
Baudhayana-Pythagoras theorem and its expansion
TGT Only
/mathematics/geometry/baudhayana-pythagoras-theorem/
→
Circle and sector of circle
TGT Only
/mathematics/geometry/circle-and-sector/
→
Arc and chord of circle
TGT Only
/mathematics/geometry/arc-and-chord/
→
Tangent line of circle
TGT Only
/mathematics/geometry/tangent-to-circle/
→
Alternate sector and angle
TGT Only
/mathematics/geometry/alternate-sector-and-angle/
→
Segments of chord and formed rectangle
TGT Only
/mathematics/geometry/chord-segments-and-rectangle/
→
Congruence of linear and planar shapes
TGT Only
/mathematics/geometry/congruence/
→
Cartesian plane
TGT Only
/mathematics/coordinate-geometry/two-dimensional/cartesian-plane/
→
Homogeneous equation of second degree and pair of straight lines
TGT Only
/mathematics/coordinate-geometry/two-dimensional/pair-of-straight-lines/
→
Equation of bisectors
TGT Only
/mathematics/coordinate-geometry/two-dimensional/angle-bisectors/
→
Angle between straight lines
TGT Only
/mathematics/coordinate-geometry/two-dimensional/angle-between-lines/
→
Angle Between Angle Bisectors
TGT Only
/mathematics/coordinate-geometry/two-dimensional/angle-between-angle-bisectors/
→
Standard equation of circle
TGT Only
/mathematics/coordinate-geometry/two-dimensional/conics/circle/
→
Standard equation of parabola
TGT Only
/mathematics/coordinate-geometry/two-dimensional/conics/parabola/
→
Standard equation of ellipse
TGT Only
/mathematics/coordinate-geometry/two-dimensional/conics/ellipse/
→
Standard equation of hyperbola
TGT Only
/mathematics/coordinate-geometry/two-dimensional/conics/hyperbola/
→
Parametric equations of conics
TGT Only
/mathematics/coordinate-geometry/two-dimensional/conics/parametric-equations/
→
Condition for second-degree equation to represent pair of straight lines
TGT + PGT
/mathematics/coordinate-geometry/two-dimensional/general-second-degree/pair-of-straight-lines-condition/
→
Condition for second-degree equation to represent circle
TGT + PGT
/mathematics/coordinate-geometry/two-dimensional/general-second-degree/circle-condition/
→
Condition for second-degree equation to represent parabola
TGT + PGT
/mathematics/coordinate-geometry/two-dimensional/general-second-degree/parabola-condition/
→
Condition for second-degree equation to represent ellipse
TGT + PGT
/mathematics/coordinate-geometry/two-dimensional/general-second-degree/ellipse-condition/
→
Condition for second-degree equation to represent hyperbola
TGT + PGT
/mathematics/coordinate-geometry/two-dimensional/general-second-degree/hyperbola-condition/
→
Conics using transformation of origin
TGT Only
/mathematics/coordinate-geometry/two-dimensional/conics/transformation-of-origin/
→
Conics using transformation of coordinate axes
TGT Only
/mathematics/coordinate-geometry/two-dimensional/conics/transformation-of-axes/
→
Tangent to conics
TGT + PGT
/mathematics/coordinate-geometry/two-dimensional/conics/tangent/
→
Normal to conics
TGT + PGT
/mathematics/coordinate-geometry/two-dimensional/conics/normal/
→
Condition for a Line to be Normal to a Conic
TGT Only
/mathematics/coordinate-geometry/two-dimensional/conics/normal-condition/
→
Section of conic by bisecting line
TGT Only
/mathematics/coordinate-geometry/two-dimensional/conics/section-by-bisecting-line/
→
Condition for tangent in limiting position
TGT Only
/mathematics/coordinate-geometry/two-dimensional/conics/tangent-limiting-position/
→
Parametric equation of tangent
TGT Only
/mathematics/coordinate-geometry/two-dimensional/conics/parametric-tangent/
→
Pair of tangents from a point to conics
TGT + PGT
/mathematics/coordinate-geometry/two-dimensional/conics/pair-of-tangents/
→
Condition for a line to be tangent
TGT Only
/mathematics/coordinate-geometry/two-dimensional/conics/tangent-condition/
→
Standard polar equation of conics
TGT Only
/mathematics/coordinate-geometry/two-dimensional/conics/polar-equation/
→
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/
→
Differentiation of algebraic functions
TGT Only
/mathematics/calculus/differential-calculus/algebraic-functions/
→
Differentiation of trigonometric functions
TGT Only
/mathematics/calculus/differential-calculus/trigonometric-functions/
→
Differentiation of exponential functions
TGT Only
/mathematics/calculus/differential-calculus/exponential-functions/
→
Differentiation of logarithmic functions
TGT Only
/mathematics/calculus/differential-calculus/logarithmic-functions/
→
Tangent and normal
TGT + PGT
/mathematics/calculus/differential-calculus/tangent-and-normal/
→
Maxima and minima of function of one variable
TGT + PGT
/mathematics/calculus/differential-calculus/maxima-and-minima/
→
Tracing of simple curves
TGT Only
/mathematics/calculus/differential-calculus/tracing-of-curves/
→
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/
→
Area between curves
TGT Only
/mathematics/calculus/integral-calculus/applications/area-between-curves/
→
Volume of cylinder, cone and sphere by integration
TGT Only
/mathematics/calculus/integral-calculus/applications/volumes/
→
Surface area of cylinder, cone and sphere by integration
TGT Only
/mathematics/calculus/integral-calculus/applications/surface-areas/
→
Order of differential equation
TGT + PGT
/mathematics/calculus/differential-equations/order/
→
Degree of differential equation
TGT + PGT
/mathematics/calculus/differential-equations/degree/
→
General solution of first-order first-degree differential equation
TGT + PGT
/mathematics/calculus/differential-equations/first-order-first-degree/
→
Position vector of ordered pair and ordered triad
TGT Only
/mathematics/vectors-and-three-dimensional-geometry/vectors/position-vector/
→
Displacement vector
TGT Only
/mathematics/vectors-and-three-dimensional-geometry/vectors/displacement-vector/
→
Free vector
TGT Only
/mathematics/vectors-and-three-dimensional-geometry/vectors/free-vector/
→
Unit vector
TGT + PGT
/mathematics/vectors-and-three-dimensional-geometry/vectors/unit-vector/
→
Modulus of vector
TGT Only
/mathematics/vectors-and-three-dimensional-geometry/vectors/modulus/
→
Direction cosines of vector
TGT + PGT
/mathematics/vectors-and-three-dimensional-geometry/vectors/direction-cosines/
→
Composition of vectors
TGT Only
/mathematics/vectors-and-three-dimensional-geometry/vectors/composition-of-vectors/
→
Composition of Force Vectors
TGT Only
/mathematics/vectors-and-three-dimensional-geometry/vectors/composition-of-vectors/force/
→
Composition of Velocity Vectors
TGT Only
/mathematics/vectors-and-three-dimensional-geometry/vectors/composition-of-vectors/velocity/
→
Composition of Acceleration Vectors
TGT Only
/mathematics/vectors-and-three-dimensional-geometry/vectors/composition-of-vectors/acceleration/
→
Difference of two vectors
TGT Only
/mathematics/vectors-and-three-dimensional-geometry/vectors/difference-of-vectors/
→
Relative velocity
TGT Only
/mathematics/vectors-and-three-dimensional-geometry/vectors/relative-velocity/
→
Scalar product of two vectors
TGT + PGT
/mathematics/vectors-and-three-dimensional-geometry/vectors/dot-product/
→
Vector product of two vectors
TGT + PGT
/mathematics/vectors-and-three-dimensional-geometry/vectors/cross-product/
→
Applications of Dot and Cross Products — Work and Moment of Force
TGT + PGT
/mathematics/vectors-and-three-dimensional-geometry/vectors/applications-of-dot-and-cross-products/
→
Triple product of vectors
TGT Only
/mathematics/vectors-and-three-dimensional-geometry/vectors/triple-product/
→
Equilibrium of a body under three forces
TGT + PGT
/mathematics/mechanics/statics/equilibrium-under-three-forces/
→
Lami's theorem
TGT Only
/mathematics/mechanics/statics/lamis-theorem/
→
Rules of triangle
TGT Only
/mathematics/mechanics/statics/rules-of-triangle/
→
Trigonometrical theorem
TGT Only
/mathematics/mechanics/statics/trigonometrical-theorem/
→
Resolution into two perpendicular forces
TGT Only
/mathematics/mechanics/statics/resolution-of-forces/
→
General conditions of equilibrium
TGT Only
/mathematics/mechanics/statics/general-conditions-of-equilibrium/
→
Centre of gravity
TGT + PGT
/mathematics/mechanics/statics/centre-of-gravity/
→
Common catenary
TGT + PGT
/mathematics/mechanics/statics/common-catenary/
→
No matching Mathematics topic found.
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