CBSE Class 12

Mathematics

13 units · 92 topicsInternal 20Exam 80

Prep tip

Calculus carries 35 of the 80 marks. Write every step, because CBSE marks the method. Learn the standard integrals, check each integral by differentiating your answer, and draw the figure for every area, 3D and linear programming question.

Suggested order: Unit I, then II, then III, then IV, then V, then VI, then VII, then VIII, then IX, then X, then XI, then XII, and XIII last.

Units

Unit I0 of 6 read

Relations and functions

6 sheets · about 55 min reading

Relations, and reflexive relations8 min Symmetric relations7 min Transitive relations8 min Equivalence relations and equivalence classes12 min One-one (injective) functions9 min Onto (surjective) and bijective functions11 min

Unit II0 of 5 read

Inverse trigonometric functions

5 sheets · about 44 min reading

What an inverse trigonometric function is8 min Domains of the inverse trigonometric functions8 min Ranges and principal value branches9 min Finding principal values10 min Graphs of inverse trigonometric functions9 min

Unit III0 of 8 read

Matrices

8 sheets · about 70 min reading

Matrices: notation and order7 min Types of matrices and equality of matrices8 min Addition, subtraction and scalar multiplication8 min Multiplication of matrices11 min AB ≠ BA, and zero products8 min Transpose of a matrix7 min Symmetric and skew symmetric matrices11 min Invertible matrices and the uniqueness of the inverse10 min

Unit IV0 of 7 read

Determinants

7 sheets · about 66 min reading

Determinant of a square matrix10 min Minors and cofactors8 min Area of a triangle using determinants8 min Adjoint of a square matrix9 min Inverse of a square matrix10 min Consistency of a system and the number of solutions9 min Solving linear equations using the inverse of a matrix12 min

Unit V0 of 9 read

Continuity and differentiability

9 sheets · about 83 min reading

Continuity of a function10 min Differentiability and its link with continuity10 min Chain rule: derivative of a composite function8 min Derivatives of inverse trigonometric functions9 min Derivatives of implicit functions8 min Exponential and logarithmic functions and their derivatives10 min Logarithmic differentiation10 min Derivatives of functions in parametric form9 min Second order derivatives9 min

Unit VI0 of 8 read

Applications of derivatives

8 sheets · about 79 min reading

Rate of change of quantities10 min Increasing and decreasing functions9 min Finding where a function increases or decreases10 min Maxima and minima: local and absolute values9 min First derivative test10 min Second derivative test10 min Absolute maximum and minimum on a closed interval9 min Maxima and minima in real-life problems12 min

Unit VII0 of 9 read

Integrals

9 sheets · about 94 min reading

Integration as the reverse of differentiation9 min Integration by substitution11 min Special integrals: 1/(x² ± a²), 1/(a² − x²) and their square roots9 min Integrals with ax² + bx + c in the denominator12 min Integration by partial fractions11 min Integration by parts11 min Integrals of √(a² − x²), √(x² ± a²) and √(ax² + bx + c)9 min Definite integrals and the fundamental theorem of calculus10 min Properties of definite integrals12 min

Unit VIII0 of 5 read

Application of integrals

5 sheets · about 49 min reading

Area under a curve: the idea and the method10 min Area under lines10 min Area under circles10 min Area under parabolas10 min Area under ellipses9 min

Unit IX0 of 7 read

Differential equations

7 sheets · about 70 min reading

What a differential equation is6 min Order and degree of a differential equation9 min General and particular solutions9 min Solving by separating the variables12 min Homogeneous differential equations12 min Linear equations: dy/dx + Py = Q12 min Linear equations: dx/dy + P₁x = Q₁10 min

Unit X0 of 9 read

Vectors

9 sheets · about 84 min reading

Scalars, vectors and position vectors8 min Types of vectors8 min Addition of vectors9 min Multiplying a vector by a scalar8 min Components of a vector9 min Direction cosines and direction ratios of a vector9 min Position vector of a point dividing a segment9 min Scalar (dot) product12 min Vector (cross) product12 min

Unit XI0 of 7 read

Three dimensional geometry

7 sheets · about 64 min reading

Direction cosines and direction ratios of a line8 min Direction cosines and ratios of a line joining two points7 min Vector equation of a line9 min Cartesian equation of a line10 min Angle between two lines10 min Skew lines: intersecting, parallel or skew?8 min Shortest distance between two lines12 min

Unit XII0 of 6 read

Linear programming

6 sheets · about 53 min reading

What linear programming is8 min Constraints, objective function and optimisation6 min Feasible and infeasible regions (bounded or unbounded)10 min Feasible solutions, optimal solutions and corner points7 min Graphical method: the corner point method12 min Unbounded regions and problems with no solution10 min

Unit XIII0 of 6 read

Probability

6 sheets · about 58 min reading

Conditional probability10 min Properties of conditional probability7 min Multiplication theorem on probability9 min Independent events10 min Partition of a sample space and total probability10 min Bayes' theorem12 min

How the 100 marks split

Internal · Periodic tests10

Internal · Mathematics activities (record, test and viva)10

End-semester exam80

Total100

The usual internal split. Your college may differ.Practise a model paper