Unit-I | Number System |
(i). Real Numbers | - More about rational and irrational numbers.
- Fundamental Theorem of Arithmetic – statements.
- Proofs of results, irrationality of 2, 3 etc. and decimal expansions of rational numbers in terms of terminating, non-terminating, recurring of decimals and vice versa.
- Properties of real numbers
- Introduction of logarithms
- Conversion of a number in exponential form to a logarithm tic form
- Properties of logarithms loga a =1; loga 1=0
- Laws of logarithms
- log xy = logx + logy;
- log x/y = logx – logy
- log xn = n log x
- Standard base of logarithms and usage
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(ii). Sets | - Sets and their representations: Empty set, Finite and infinite sets. Equal sets. Subsets, subsets of the set of real numbers (especially intervals with notations). Universal set and cardinality of sets.
- Venn diagrams : Union and intersection of sets. Difference of sets. Complement of a set. Disjoint sets.
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Unit-II | Algebra |
(i). Polynomials | - Zeros of a polynomial.
- The graph-based geometric interpretation of the zeros of cubic and quadratic polynomials.
- The relationship between a polynomial's zeros and coefficients, with an emphasis on quadratic polynomials.
- Statement and simple problems on division algorithm for polynomials with integral coefficients.
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(ii). 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 number of solutions.
- Using cross multiplication, substitution, and elimination to solve a pair of linear equations in two variables.
- Simple equation-related problems that can be reduced to linear equations.
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(iii). Quadratic Equations | - The quadratic equation ax2 + bx + c=0, (a 0), in standard form.
- Solving quadratic equations using the quadratic formula by factorization and completing the square (only for real roots).
- The association between the roots' nature and the discriminant.
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(iv). Progression | - Sequence and series
- Motivation for studying AP. Derivation of standard results of finding the nth term and sum of first n terms.
- Motivation for studying G.P.
- nth term of G.P.
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Unit-III | Trigonometry |
| (i) Trigonometry Introduction - Trigonometric ratios of an acute angle of a right-angled triangle i.e. sine, cosine, tangent, cosecant, cotangent.
- Motivate the ratios, whichever are defined at 00 and 900
- Values (with proofs) of the trigonometric ratios of 300, 450 and 600. Relationships between the ratios.
- Trigonometric Identities: Proof and applications of the identity sin2A+cos2A=1.
- 1+tan2A=sec2A
- cot2+1=cosec2
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(ii). | - Applications of trigonometry
- Angle of elevation, angle of depression
- Simple and daily life problems on heights and distances. Problems should not involve more than two right triangles and angles elevation/ depression.
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Unit-IV | Co-ordinate Geometry |
(i). | - Lines (In two-dimensions)
- Review the concepts of coordinate geometry done by the graphs of linear equations.
- Distance between two points i.e. p (x1, y1) and q (x2, y2)
- Section formula internal division of a line segment in the m:n.
- Area of a triangle on coordinate axis.
- Slope of a line joining two points.
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Unit-V | Geometry |
(i) | - Similar triangles
- Examples, definitions, and characteristics of similar triangles.
- The distinction between triangle congruency and triangle similarity.
- (Prove) The other two sides of a triangle are divided in the same ratio if a line drawn parallel to one side of a triangle intersects the other two sides in clearly defined points.
- (Motivate) A line is parallel to the third side of a triangle if it divides the first two sides of the triangle in the same ratio.
- (Motivate) If the corresponding sides of two triangles are proportionate, the corresponding angles are equal, and the triangles are comparable (AAA).
- (Motivate) If two triangles' corresponding sides are proportionate, their corresponding angles are equal, and the two triangles are similar (SSS), then the two triangles are similar.
- (Motivate) Two triangles are comparable if one of their angles is equal to another triangle's angle and the sides that include these angles are proportionate.
- (Prove) The ratio of the squares on the corresponding sides of two comparable triangles equals the ratio of the areas of the triangles.
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(ii) | - Construction
- Dividing a line segment utilizing the fundamental proportionality theorem.
- A triangle that, using the scale factor given, is comparable to the given triangle.
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(iii) | - (iii) Tangents and secants to a circle
- Tangents to a circle motivated by chords drawn from points coming 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.
- Segment of a circle made by the secant.
- Finding the area of the minor/ major segment of a circle.
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Unit-VI | Mensuration |
(i). | - Problems involving calculating the surface areas and volumes of mixtures of any two of the following: cubes, cuboids, spheres, hemispheres, and right circular cylinders/cones.
- Conversion-related difficulties, as well as other mixed challenges, including different types of metallic solids. (Problems with mixing more than two different substances at once should be taken.)
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Unit-VII | Data Handling |
(i). Statistics | - Revision of Mean, median and mode of ungrouped (frequency distribution) data.
- Understanding, the concept of Arithmetic Mean, Median and Mode for grouped (classified) data.
- The meaning and purpose of arithmetic Mean, Median and Mode
- Simple problems on finding Mean, Median and Mode for grouped / ungrouped data.
- Usage and different values and central tendencies through Ogives.
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(ii). Probability | - Concept and definition of Probability.
- Simple problems (day to day life situation) on single events simple using set notation.
- Concept of complimentary events.
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