HP LEET Syllabus 2025: Check Subject/Chapters-Wise Syllabus PDF Here

Unit 1: Number System

Real Number

Euclid’s division lemma, Fundamental Theorem of Arithmetic-statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of results irrationality of √2 , √3 , √5 , decimal expansions of rational numbers in terms of terminating non-terminating recurring decimals.

Unit 2: Algebra

Polynomials

Zeros of a polynomial, Relationship between zeros and coefficients of a polynomial with particular reference to quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real coefficients.

Pair of Linear Equations in Two Variables

Pair of linear equations in two variables. Geometric representation of different possibilities of solutions inconsistency. Algebraic conditions for a number of solutions. Solution of pair of linear equations in two variables algebraically by substitution, by elimination and by cross multiplication. Simple situational problems must be included. Simple problems on equations reducible to linear equations may be included.

Quadratic Equations

Standard form of a quadratic equation ax2 +bx+c = 0, (a≠0). Solution of the quadratic equations (only real roots) by factorization and by completing the square, i.e. by using the quadratic formula. Relationship between discriminant and nature of roots. Problems related to day-to-day activities to be incorporated.

Arithmetic Progression

Motivation for studying AP. Derivation of standard results of finding the nth term and sum of first ‘n’ terms

Unit 3: Trigonometry

Trigonometric Ratios

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios, whichever are defined at 00 & 900. Values (with proofs) of the trigonometric ratios of 300, 450, & 600. Relationships between the ratios.

Trigonometric Identities

Proof and applications of the identity sin² A + Cos² A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.

Heights and Distances

Simple and believable problems on heights and distances. Problems should not involve more than two right triangle. Angles of elevation/ depression should be only 30^o, 45^o, 60^o.

Unit 4: Coordinate Geometry

Lines (In two-dimensions)

Review the concepts of coordinate geometry done earlier including graphs of linear equations. Awareness of geometrical representation of quadratic polynomials. Distance between two points and section formula (internal). Area of a triangle.

Unit: 5 Geometry

Triangles

Definitions, examples, counter examples of similar triangles.

Circles

Tangents to a circle motivated by chords, drawn from points coming closer and closer and closer to the point.

(Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.

(Prove) The lengths of tangents drawn from an external point to a circle are equal.

Constructions

Division of line segment in a given ratio (internally).

Tangent to a circle from a point outside it.

Construction of a triangle similar to a given triangle.

Unit 6: Mensuration

Areas of plane figures

The area of a circle; area of sectors and segments of a circle. Problems bases on the areas and perimeter/ circumference of the above said plane figures. (In calculating the area of a segment of a circle, problems should be restricted to the central angle of 60^o, 90^o, & 120^o only. Plane figures involving triangles, simple quadrilaterals and circle should be taken).

Surface areas and volumes

Problems in finding surface areas and volumes of combinations of any two of the following cubes, cuboids, spheres, hemispheres and right circular cylinders/cones. Frustum of a cone.

Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with a combination of not more than two different solids be taken)

Unit 7: Statistics and Probability

Statistics

Mean, Median, and Mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.

Probability

The classical definition of probability. Connection with probability as given in class IX. Simple problems on single events, not using set notation.

Electricity

1. Electric Current and circuit

2. Electric potential and potential difference

3. Ohm’s Law

4. Series and Parallel combination of resistors

5. Heating Effect of Electric Current

6. Electric Power

7. Inter relation between P,V,I and R.

Magnetic Effects of Electric Current

1. Magnetic field and field lines

2. Magnetic field due to a current a) Straight conductor b) Circular loop c) Solenoid

3. Fleming’s Right Hand Thumb Rule

4. Left Hand Rule

5. Electric Motor, Electromagnetic Induction

6. Electric Generator and Domestic Electric Circuit

Light- Reflection and refraction

1. Reflection of light

2. Spherical Mirrors: Concave and convex

3. Image Formation with Ray diagrams.

4. Mirror Formula and Magnification

5. Refraction of light through Glass Slab and lenses (convex and concave) and Image formation by lenses.

6. Lens formula and Magnification

7. Uses of Mirrors and Lenses

8. Power of Lens.

The Human Eye and the Colorful World

1. The Human Eye.

2. Power of Accommodation

3. Defects of Vision and Their correction

4. Refraction of Light Through Prism

5. Dispersion of light and scattering of light

6. Atmospheric Refraction a) Twinkling of Stars b) Tyndall Effect

Sources of Energy

1. Different forms of Energy.

2. Leading to different Sources of Human use: Fossil fuels, solar energy, biogas, wind water and tidal energy.

3. Renewable and Non-renewable sources.

Management of Natural Resources.

1. Conservation and Judicious use of natural resources.

2. Forests and Wildlife

3. Stakeholders and sustainable management

4. Dams and Water Harvesting

5. Cool and Petroleum.

Chemical Reaction and Equations

1. Chemical Equations

2. Types of Chemical Reactions a) Combination Reaction b) Decomposition Reaction c) Displacement Reaction d) Double Displacement Reaction e) Oxidation and Reduction

3. Effect of oxidation Reaction in Everyday life a) Corrosion and b) Rancidity

Acids, Bases and Salts

1) General Properties (physical and chemical properties) of acids, bases and salts with examples and their uses.

2) PH scale and Importance of PH in Everyday life.

Metals and Non-metals

1) Physical and Chemical Properties of Metals and Non-Metals

2) Reactivity Series

3) Metal and Non-Metal Reactions

4) Occurrence of Metals and their extraction

5) Corrosion of Metals and Prevention of corrosion

Carbon and its Compounds

1) Bonding in carbon- the covalent Bond.

2) Saturated and Unsaturated Carbon Compounds.

3) Nomenclature of Carbon Compounds.

4) Chemical Properties of Carbon Compounds

5) Some Important carbon Compounds Ethanol and Ethanoic Acid. (only properties)

6) Soaps and Detergents: Cleaning action of Soaps (Micelles Formation)

Periodic Classification of Elements

1) Early attempts at the classification of Elements a) Dobereiner’s Triads b) Newlands law of octaves c) Mendeleev’s Periodic Table

2) The Modern Periodic Table.

3) Trends in the Modern Periodic Table.

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