| A1A1: Algebra | - Order, equality and types of matrices; A = ½(A + A′) + ½(A − A′)
- Addition, scalar and matrix multiplication; AB ≠ BA in general
- Determinants of 2 × 2 and 3 × 3 matrices, |AB| = |A||B|, |kA| = kⁿ|A|
- A⁻¹ = adj A / |A|, (AB)⁻¹ = B⁻¹A⁻¹; solving AX = B as X = A⁻¹B
- Skew-symmetric matrix
- Singular matrix
- Adjoint
| Ch 3–4 |
|---|
| A1A1: Calculus | - First and second derivatives of standard and composite functions
- Sign of f′(x) for increasing and decreasing intervals; critical points
- First and second derivative tests; absolute extrema on a closed interval
- Simple optimisation word problems
- Critical point
- Local maximum
- Second derivative test
| Ch 5–6 |
|---|
| A1A1: Integration and applications | - Standard integrals of xⁿ, 1/x, eˣ and trigonometric functions
- Substitution and simple algebraic manipulation
- Definite integrals via the fundamental theorem
- Area bounded by a simple curve, such as a parabola, and a line
- Antiderivative
- Definite integral
- Area under a curve
| Ch 7–8 |
|---|
| A1A1: Differential equations | - Order as the highest derivative; degree defined only when the equation is a polynomial in derivatives
- Separating variables and integrating both sides
- Using an initial condition to find the particular solution
- Order
- Degree
- Variable separable
| Ch 9 |
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| A1A1: Probability | - P(E) = favourable outcomes ÷ total outcomes for coins, dice and cards
- Complementary events P(not E) = 1 − P(E)
- P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
- Sample space
- Complementary event
| Ch 13 (basics from Class 11 Ch 14) |
|---|
| A1A1: Linear programming | - Plotting constraints and shading the feasible region
- Corner point method for maximum and minimum
- Infeasible problems and unbounded regions
- Feasible region
- Corner point
- Optimal solution
| Ch 12 |
|---|
| B1 IRelations and functionsSection A1 + B1: Mathematics | - Reflexive, symmetric, transitive and equivalence relations; equivalence classes
- One-one (injective), onto (surjective) and bijective functions
- Domains and principal-value ranges of sin⁻¹, cos⁻¹, tan⁻¹ and the others
- Principal values such as sin⁻¹(sin 2π/3) = π/3 and graphs of inverse functions
- Equivalence relation
- Bijection
- Principal value branch
| Ch 1–2 |
|---|
| B1 IIAlgebraSection A1 + B1: Mathematics | - Matrix operations; non-zero 2 × 2 matrices with a zero product
- Minors, cofactors and expansion of 3 × 3 determinants
- Area of a triangle = ½|determinant of vertices|
- |adj A| = |A|ⁿ⁻¹, |kA| = kⁿ|A|, A(adj A) = |A|I
- Consistency: unique solution if |A| ≠ 0; checking (adj A)B when |A| = 0
- Cofactor
- Adjoint
- Consistent system
| Ch 3–4 |
|---|
| B1 IIICalculusSection A1 + B1: Mathematics | - Chain rule, implicit, logarithmic and parametric differentiation; second derivatives
- Rate of change, increasing and decreasing functions, maxima and minima
- Integration by substitution, partial fractions and parts; standard algebraic forms
- Definite-integral properties such as ∫₀ᵃ f(x) dx = ∫₀ᵃ f(a − x) dx
- Areas under lines, circles, parabolas and ellipses
- Variable-separable, homogeneous and linear equations dy/dx + Py = Q with integrating factor
- Parametric derivative
- Integration by parts
- Integrating factor
- Definite-integral properties
| Ch 5–9 |
|---|
| B1 IVVectors and 3D geometrySection A1 + B1: Mathematics | - Position vectors, unit vectors, direction cosines (l² + m² + n² = 1)
- Section formula and collinearity
- Dot product a·b = |a||b| cos θ and projection
- Cross product, |a × b| as parallelogram area and half of it as triangle area
- Vector and Cartesian equations of a line, angle between lines, shortest distance between skew lines
- Direction cosines
- Cross product
- Skew lines
| Ch 10–11 |
|---|
| B1 VLinear programmingSection A1 + B1: Mathematics | - Decision variables, constraints, non-negativity and objective function
- Corner point method; checking unbounded regions with an extra half-plane
- Multiple optimal solutions along an edge
- Objective function
- Bounded region
- Corner point method
| Ch 12 |
|---|
| B1 VIProbabilitySection A1 + B1: Mathematics | - P(A | B) = P(A ∩ B)/P(B) and the multiplication rule
- Independent events: P(A ∩ B) = P(A)P(B)
- Total probability over a partition of the sample space
- Bayes' theorem for 'which bag or machine' problems
- Conditional probability
- Independent events
- Bayes' theorem
| Ch 13 |
|---|
| B2 INumbers and numerical applicationsSection A1 + B2: Applied Mathematics | - a mod n, modular addition and multiplication; a ≡ b (mod n) when n divides a − b
- Rule of alligation: cheaper : dearer = (dearer − mean) : (mean − cheaper)
- Downstream speed = b + s, upstream = b − s
- Pipes and cisterns using work per unit time; races with head starts
- Numerical inequalities and comparing situations
- Congruence modulo
- Alligation
- Upstream speed
| CBSE Applied Maths syllabus, Unit I: Numbers & Quantification |
|---|
| B2 IIAlgebraSection A1 + B2: Applied Mathematics | - Types of matrices; writing data in matrix form
- Singular and non-singular matrices, |AB| = |A||B|
- Inverse using cofactors; (AB)⁻¹ = B⁻¹A⁻¹, (A′)⁻¹ = (A⁻¹)′
- Cramer's rule and the inverse method for non-homogeneous systems
- Matrix method
- Non-singular matrix
- Cofactor
| CBSE Applied Maths syllabus, Unit II: Algebra |
|---|
| B2 IIICalculusSection A1 + B2: Applied Mathematics | - Parametric and implicit derivatives; rates of change
- Marginal cost MC = dC/dx and marginal revenue MR = dR/dx
- Maxima and minima for cost, revenue and profit
- Integration by substitution, partial fractions and parts (non-trigonometric)
- Consumer surplus = ∫₀^x₀ D(x) dx − p₀x₀; producer surplus = p₀x₀ − ∫₀^x₀ S(x) dx
- Order, degree, formation and simple solutions of differential equations
- Marginal revenue
- Consumer surplus
- Equilibrium price
| CBSE Applied Maths syllabus, Unit III: Calculus |
|---|
| B2 IVProbability distributionsSection A1 + B2: Applied Mathematics | - Probability distribution of a discrete random variable; E(X) = Σ x p(x)
- Var(X) = E(X²) − [E(X)]²
- Binomial P(r) = ⁿCᵣ pʳ qⁿ⁻ʳ, mean np, variance npq
- Poisson conditions, P(X = x) = λˣ e^(−λ) / x!, mean = variance = λ
- Normal curve properties and Z = (X − μ)/σ
- Expectation
- Binomial distribution
- Standard normal variate
| CBSE Applied Maths syllabus, Unit IV: Probability Distributions |
|---|
| B2 VTime-based dataSection A1 + B2: Applied Mathematics | - Components: secular trend, seasonal, cyclical and irregular variation
- Moving-average method of measuring trend
- Least-squares straight-line trend y = a + bx and estimating future values
- Secular trend
- Seasonal variation
- Moving average
| CBSE Applied Maths syllabus, Unit VI: Time-Based Data |
|---|
| B2 VIInferential statisticsSection A1 + B2: Applied Mathematics | - Population versus sample; simple and systematic random sampling
- Parameter (population) versus statistic (sample); limits of generalising
- Central Limit Theorem and sampling distributions (conceptual)
- Null and alternative hypotheses, degrees of freedom n − 1, t = (x̄ − μ)/(s/√n)
- Parameter
- Null hypothesis
- Degrees of freedom
| CBSE Applied Maths syllabus, Unit V: Inferential Statistics |
|---|
| B2 VIIFinancial mathematicsSection A1 + B2: Applied Mathematics | - Present value of a perpetuity = R/i; sinking fund versus savings account
- Bond value as the present value of coupons plus redemption value
- EMI by flat-rate and reducing-balance methods
- CAGR = (final/initial)^(1/n) − 1 versus simple annual growth rate
- Straight-line depreciation = (cost − residual value) ÷ useful life
- Perpetuity
- Sinking fund
- CAGR
- Residual value
| CBSE Applied Maths syllabus, Unit VII: Financial Mathematics |
|---|
| B2 VIIILinear programmingSection A1 + B2: Applied Mathematics | - Decision variables, constraints, objective function and non-negativity
- Formulating manufacturing, diet and transportation problems with up to three constraints
- Graphical solution and corner point method; infeasible and unbounded cases
- Decision variable
- Non-negativity constraint
- Infeasible region
| CBSE Applied Maths syllabus, Unit VIII: Linear Programming |
|---|
