Syllabus:
1. REAL NUMBERS
Euclid’s Division Lemma – HCF and LCM – Fundamental Theorem of Arithmetic – Rational and irrational numbers – Proofs of irrationality – Decimal expansion of rational numbers – Introduction to logarithms – Conversion between exponential and logarithmic forms – Laws and properties of logarithms.
2. POLYNOMIALS
Zeroes of linear, quadratic and cubic polynomials – Relationship between zeroes and coefficients – Division algorithm for polynomials – Biquadratic polynomials – Applications of polynomial equations.
3. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
Graphical representation of solutions – Consistent and inconsistent systems – Algebraic methods including substitution and elimination – Situational and word problems – Equations reducible to linear equations in two variables.
4. QUADRATIC EQUATIONS
Standard form of quadratic equations – Solutions by factorization – Completing the square – Quadratic formula – Discriminant and nature of roots – Real-life applications and word problems.
5. PROGRESSIONS
Sequences and series – Arithmetic Progressions (AP) – Finding the nth term – Sum of n terms – Geometric Progressions (GP) – Finding the nth term of a GP – Applications of progressions.
6. TRIGONOMETRY
Trigonometric ratios of acute angles – Sine, cosine, tangent, cosecant, secant and cotangent – Values of trigonometric ratios for 30°, 45° and 60° – Trigonometric identities – Complementary angles – Angle of elevation and depression – Heights and distances – Applications in surveying and real-life situations.
7. COORDINATE GEOMETRY
Distance formula – Section formula – Area of a triangle using coordinates – Slope of a line – Applications in geometry and graphing.
8. SIMILAR TRIANGLES AND CIRCLES
Similarity criteria (AAA, SSS, SAS) – Basic proportionality theorem – Areas of similar triangles – Pythagoras theorem and converse – Tangents to circles – Properties of tangents – Segments of circles – Construction of tangents from external points.
9. SURFACE AREAS AND VOLUMES
Surface areas and volumes of combinations of cubes, cuboids, cylinders, cones, spheres and hemispheres – Conversion of one solid into another – Practical problems involving volume and capacity.
10. STATISTICS AND PROBABILITY
Mean, median and mode for grouped and ungrouped data – Frequency distributions – Ogives and cumulative frequency curves – Probability of simple events – Complementary events – Applications of probability in everyday situations.
