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ISC Mathematics Class 12 Syllabus

ISC Physics Class 12 Syllabus

Reference books

## ISC Mathematics Class 12 Syllabus Stroke 396

The syllabus is divided into three sections: A, B and C. Section A is compulsory for all candidates. You have a choice of attempting questions from either Section B or Section C. There is one paper of three hours duration of 100 marks.

Section A (80 marks) consists of nine questions. You are required to answer Question 1 (compulsory) and five out of the rest of the eight questions.

In Section B/C (20 marks), you are required to answer two questions out of three from either Section B or Section C.

### 1. Determinants and Matrices

(i) Determinants

Order. Minors. Cofactors. Expansion. Properties of determinants. Simple problems using properties of determinants

Cramer's Rule

(ii) Matrices

Martin’s Rule

### 2. Boolean Algebra

Boolean algebra as an algebraic structure, principle of duality, Boolean function. Switching circuits, application of Boolean algebra to switching circuits.

### 3. Conics

As a section of a cone.

Definition of Foci, Directrix, Latus Rectum.

PS = ePL where P is a point on the conics, S is the focus, PL is the perpendicular distance of the point from the directrix.

(i) Parabola

(ii) Ellipse

(iii) Hyperbola

### 5. Calculus

(i) Differential Calculus

(ii) Integral Calculus

### 6. Correlation and Regression

Definition and meaning of correlation and regression coefficient. Coefficient of Correlation by Karl Pearson. Rank correlation by Spearman’s (Correction included). Lines of regression of x on y and y on x.

### 7. Probability

Random experiments and their outcomes. Events: sure events, impossible events, mutually exclusive events, independent events and dependent events. Definition of probability of an event. Laws of probability: addition and multiplication laws, conditional probability (excluding Baye’s theorem).

### 8. Complex Numbers

Argument and conjugate of complex numbers. Sum, difference, product and quotient of two complex numbers additive and multiplicative inverse of a complex number. Simple locus question on complex number; Triangle inequality. Square root of a complex number. Demoivre’s theorem and its simple applications. Cube roots of unity: 1,ω,ω2 ; application problems.

### 9. Differential Equations

Differential equations, order and degree. Solution of differential equations. Variable separable. Homogeneous equations and equations reducible to homogeneous form. Linear form

### 10. Vectors

Scalar (dot) product of vectors. Cross product - its properties - area of a triangle, collinear vectors. Scalar triple product - volume of a parallelopiped, co-planarity.

Proof of Formulae (Using Vectors)

Sine rule. Cosine rule Projection formula Area of a Δ = ½ ab sin C

### 11. Co-ordinate Geometry in 3-Dimensions

(i) Lines

Cartesian and vector equations of a line through one and two points. Coplanar and skew lines. Conditions for intersection of two lines. Shortest distance between two lines.

(ii) Planes

Cartesian and vector equation of a plane. Direction ratios of the normal to the plane. One point form. Normal form. Intercept form. Distance of a point from a plane. Angle between two planes, a line and a plane. Equation of a plane through the intersection of two planes

### 12. Probability

Baye’s theorem; theoretical probability distribution, probability distribution function; binomial distribution - its mean and variance.

### 13. Discount

True discount; banker's discount; discounted value; present value; cash discount, bill of exchange.

### 14. Annuities

Meaning, formulae for present value and amount; deferred annuity, applied problems on loans, sinking funds, scholarships. NOTE: Annuity due is required to be covered.

### 15. Linear Programming

Introduction, definition of related terminology such as constraints, objective function, optimization, isoprofit, isocost lines; advantages of linear programming; limitations of linear programming; application areas of linear programming; different types of linear programming (L.P.), problems, mathematical formulation of L.P problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimum feasible solution.

### 16. Application of derivatives in Commerce and Economics

Cost function, average cost, marginal cost, revenue function and break even point.

### 17. Index numbers and moving averages

Price index or price relative. Simple aggregate method. Weighted aggregate method. Simple average of price relatives. Weighted average of price relatives (cost of living index, consumer price index).

## ISC Physics Class 12 Syllabus

Paper I is of 3 hours duration and is divided into two parts.

Part I (20 marks): This part consists of compulsory short answer questions, testing knowledge, application and skills relating to elementary/fundamental aspects of the entire syllabus.

Part II (50 marks): This part is divided into three Sections A, B and C. There are six questions in Section A (each carrying 5 marks) and you are required to answer four questions from this Section. There are four questions in Section B (each carrying 5 marks) and you are required to answer three questions from this Section. There are four questions in Section C (each carrying 5 marks) and you are required to answer three questions from this Section. Therefore, you are expected to answer ten questions in Part II.

• SECTION A
• 1. Electrostatics
• (i) Coulomb's law, S.I. unit of charge; permittivity of free space.
• (ii) Concept of electric field E = F/qo; Gauss' theorem and its applications.
• (iii) Electric dipole; electric field at a point on the axis and perpendicular bisector of a dipole; electric dipole moment; torque on a dipole in a uniform electric field.
• (iv) Electric lines of force.
• (v) Electric potential and potential energy; potential due to a point charge and due to a dipole; potential energy of an electric dipole in an electric field. Van de Graff generator.
• (vi) Capacitance of a conductor C = Q/V, farad; capacitance of a parallel-plate capacitor; C = ε0A/d. Capacitors in series and parallel combinations; effective capacitance and charge distribution. Energy stored
• (vii) Dielectrics (elementary ideas only); permittivity and relative permittivity of a dielectric (εr = ε/εo). Effects on pd, charge and capacitance. Electric polarisation.
• 2. Current Electricity
• (i) Mechanism of flow of current in metals, drift velocity and mobility of electrons, Ohm’s Law and its proof. Resistance and resistivity and their relation to drift velocity of electrons; description of resistivity and conductivity based on electron theory; effect of temperature on resistance, colour coding of resistance.
• (ii) Potential difference as the power supplied divided by the current. Ohm's law (V-I characteristics) and its limitations; Combinations of resistors in series and parallel; Electric energy and power.
• (iii) Electromotive force in a cell; internal resistance and back emf. Combination of cells in series, parallel and mixed grouping.
• (iv) Kirchoff's laws and their simple applications to circuits with resistors and sources of emf; Wheatstone bridge, metre-bridge and potentiometer; use to measure potential difference and for comparison of emf and determination of internal resistance of sources of current; use of resistors (shunts and multipliers) in ammeters and voltmeters.
• 3. Magnetism
• (i) Magnetic field B, definition from magnetic force on a moving charge; magnetic field lines; magnetic field and magnetic flux density; the earth's magnetic field and magnetic elements; Magnetic field of a magnetic dipole.
• (ii) Properties of dia, para and ferromagnetic substances; susceptibility and relative permeability, hysteresis.
• 4. Electromagnetism
• (i) Oersted's experiment; Biot-Savart law, the tesla; magnetic field near a long straight wire, at the centre of a circular loop, and at a point on the axis of a circular coil carrying current. Amperes circuital law and its application to obtain magnetic field due to a long straight wire and a solenoid.
• (ii) Force on a moving charge in a magnetic field; force on a current carrying conductor kept in a magnetic field; force between two long and parallel current carrying wires; definition of ampere based on the force between two current carrying wires. Cyclotron.
• (iii) A current loop as a magnetic dipole; magnetic dipole moment; torque on a current loop (magnetic dipole); moving coil galvanometer.
• (iv) Electromagnetic induction, magnetic flux and induced emf; Faraday's laws and Lenz's law, motional emf; eddy currents.
• (v) Mutual and self inductance: the henry. Growth and decay of current in LR and RC circuits (dc) (graphical approach), time constant. Transformer.
• (vi) Simple a.c. generators. Basic differences between a.c. and d.c.
• 5. Alternating Current Circuits
• (i) Change of voltage and current with time, phase; peak and rms values of voltage and current; their relation in sinusoidal case.
• (ii) Variation of voltage and current in a.c. circuits consisting of only a resistor, only an inductor and only a capacitor (phasor representation), phase lag and phase lead.
• (iii) The LCR series circuit: phasor diagram, expression for V or I; phase lag/lead; impedance of a series LCR circuit (arrived at by phasor diagram); Special cases for RL and RC circuits.
• (iv) Power P associated with LCR circuit = ½VoIo cosφ =VrmsIrms cosφ = Irms2R; power absorbed and power dissipated; choke coil (choke and starter); electrical resonance; bandwidth of signals and Q factor; oscillations in an LC circuit (ω = 1/√LC).
• #### SECTION B

• 6. Wave Optics
• (i) Complete electromagnetic spectrum from radio waves to gamma rays; transverse nature of electromagnetic waves, Huygen's principle; laws of reflection and refraction from Huygen's principle.
• (ii) Conditions for interference of light, interference of monochromatic light by double slit; Young’s double slit experiment, measurement of wave length.
• (iii) Single slit Fraunhofer diffraction (elementary explanation).
• (iv) Plane polarised electromagnetic wave (elementary idea), methods of polarisation of light. Brewster's law; polaroids.
• 7. Ray Optics and Optical Instruments
• (i) Reflection of light by spherical mirrors.
• (ii) Refraction of light at a plane interface, Snell's law; total internal reflection and critical angle; total reflecting prisms and optical fibres.
• (iii) Refraction through a prism, minimum deviation and derivation of relation between n, A and δmin.
• (iv) Refraction at a single spherical surface (relation between n1, n2, u, v and R); refraction through thin lenses (lens maker's formula and formula relating u, v, f, n, R1 and R2); lens formula, combined focal length of two thin lenses in contact. Combination of lenses and mirrors [Silvering of lens excluded] and magnification. Spherical aberration.
• (v) Dispersion; dispersive power; pure and impure spectrum; Scattering of light. Chromatic aberration.
• (vi) Simple microscope; Compound microscope and their magnifying power.
• (vii) Simple astronomical telescope (refracting and reflecting), magnifying power and resolving power of a simple astronomical telescope.
• (viii) Human Eye, Defects of vision and their correction.
• ### SECTION C

• 8. Electrons and Photons
• (i) Photo electric effect, quantization of radiation; Einstein's equation; threshold frequency; work function; stopping potential; energy and momentum of a photon. Determination of Planck’s Constant.
• (ii) Wave particle duality, De Broglie equation, phenomenon of electron diffraction (qualitative only).
• 9. Atoms
• (i) Charge and size of nuclei (α-particle scattering); atomic structure; Bohr's postulates; radii of Bohr orbits for hydrogen atom; energy of the hydrogen atom in the nth state; line spectra of hydrogen and calculation of ΔE and f for different lines.
• (ii) Production of X-rays; maximum frequency for a given tube potential. Characteristic and continuous X -rays. Moseley’s law.
• 10. Nuclei
• (i) Atomic masses; Isotopes, Isobars and Isotones; unified atomic mass unit u and its value in MeV; composition and size of nucleus; mass defect and binding energy. Energy - mass equivalence.
• (ii) Radioactivity: nature and radioactive decay law, half-life, mean life and decay constant. Nuclear reactions.
• 11. Nuclear Energy
• (i) Nuclear fission; chain reaction; principle of operation of a nuclear reactor.
• (ii) Nuclear fusion; thermonuclear fusion as the source of the sun's energy.
• 12. Semiconductor Devices
• (i) Energy bands in solids; energy band diagrams for distinction between conductors, insulators and semi-conductors - intrinsic and extrinsic; electrons and holes in semiconductors.
• (ii) Junction diode; depletion region; forward and reverse biasing, V-I characteristics; half wave and a full wave rectifier; solar cell, LED and photodiode. Zener diode.
• (iii) Junction transistor; npn and pnp transistors; current gain in a transistor and transistor as an amplifier in common emitter mode (only circuit diagram and qualitative treatment); transistor as a switch; oscillator.
• (iv) Elementary idea of discreet and integrated circuits, analogue and digital signals. Logic gates (symbols; working with truth tables; applications and uses) - NOT, OR, AND, NOR, NAND. Combination of gates.
• 13. Communication Systems
• Propagation of electromagnetic waves in the atmosphere, sky and space wave propagation, need for modulation, amplitude and frequency modulation, bandwidth of signals, bandwidth of transmission medium, basic elements of a communication system (block diagram only).

## Reference books

 Reference Books for Class 12- ISC Board Subject Name of the Book Author Publishers Mathematics 1. ISC Mathematics Book I For Class XI O P Malhotra S Chand & Company Ltd. S K Gupta Anubhuti Gangal 2. Understanding ISC Mathematics Class XI M. L. Aggrawal Arya Publication Chemistry 1. Nootan ISC Chemistry Class XI Dr H.C. Srivastava Nageen Prakashan Pvt. Ltd 2. Reference Book: I.S.C.Practical Chemistry Volume-1 For Class XI Pitambar Publication Company S. P. Sharma & Dr Ajaya Baboo 1. Srijan Biology for ISC Schools Class 11 Dr. Veer Bala Rastogi Srijan Publications Biology 2. 2. Srijan ISC Biology Lab Manual Class 11 Dr. Veer Bala Rastogi Srijan Publications Physics Nootan ISC Physics For Class XI Kumar Mittal Nageen Prakashan