Madhya Pradesh Board Math Syllabus for Class 10


Madhya Pradesh Board Syllabus for Class 10 Math

Mathematics syllabus for class X_2007-08

Time: 3 hours
Total Marks: 100

 

Unit-1

(A) LINEAR EQUATIONS IN TWO VARIABLES :-

1.Linear equation in two variables system of linear equations

1. Graphically

2. Algebraic Method

(a) Elimination by Substitution

(b) Elimination by equating the coefficients

(c) Cross Multiplication.

(d) Transpose method of Vedic Mathematics.

3. Application of Linear equation in two variables in solving simple problems from different areas

12 Marks

19 periods

Unit-2

(A) POLYNOMIALS :-

 

 

 

 

 

 

 

 

 

 

 

 

(B) RATIONAL EXPRESSION

Zero of a Polynomial, Relationship between zero and Coefficients of a polynomial with particular reference to quadratic polynomials. Statements and Simple problems on division algorithm for polynomials with real Cofficients

Meaning, addition, subtraction and multiplication, factorization of cyclic order expressions. Introduction of Shridharachrya and his formula Method.

7 Marks

17 Periods

Unit-3

RATIO AND PROPORTION :-

Ratio and Proportion; Componendo, Dividendo, Alternendo, Invertendo etc, and their application

5 Marks

9 Periods

Unit-4

QUADRATIC EQUATIONS

(A) Meaning, its standard ax2 + bx + c = a =0 factorization method and formula method.

Discriminant of quadratic Equation and nature of roots

 

(B) Applications of quadratic equation. Different areas, solutions of equations that are reducible to quadratic equation. To factorize quadratic polynomial with the help of formula.

10 Marks

14 Periods

Unit-5

COMMERCIAL MATHS

(A) Compound Interest :- Rate of growth, depreciation, Conversion period not more than 4Year. (Rate should be 4%, 5% or 10%)

 

(B) Installments :- Installment, payments, Installment buying (Numbers of installment should not more than two in-case of buying) Only equal installment should be taken in case of payment thought equal installments not more than 3 installments should be taken.

 

(C) Income Tax :- Calculation of Income Tax for salaried class (Salary exclusive of H.R.A.)

 

(D) LOGARITHM :-

(i) Application in Mathematics use in compound Interest, increase in Population and depreciation

 

(ii) Use of Logarithm mensuration areas of rectangle, square, triangle, rhombus, trapezium which was taught in earlier classes (Simple Problems)

8 Marks

9 Periods

Unit-6

SIMILAR TRIANGLES

SIMILAR TRIANGLES-

 

(i) (Motivate) If a line is drawn Parallel to one side of a triangle, the other two sides are divided in the same ratio.

 

(ii) (Prove) If a line divide any two sides of a triangle in the same ratio, the line is parallel to the third side.

 

(iii) (Motivate) If in two triangles, the corresponding angle are equal, their corresponding sides are proportionate (axiom).

 

(iv) (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal (axiom).

 

(v) (Motivate) If two triangles are equiangular, the triangles are similar (axiom)

 

(vi) (Prove) If the corresponding sides of the two triangles are proportional, the triangle are similar.

 

(vii) (Prove) If one angle of a triangle is equal to one angle of the other and the sides including these angles are proportional the triangle are similar.

 

(viii) (Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangle on each side of the Perpendicular are similar to the whole triangle and to each other.

 

(ix) (Prove) The ratio of the areas of similar triangles is equal to the ratio of the squares of their corresponding sides.

 

(x) (a) (Motivate) In a right triangle, the square on the hypotenuse is equal to the sum of the square on the other two sides.

(b) (Motivate) In a triangle if the square of greatest side is equal to the sum of the square of the remaining two, the angle opposite to the greatest side is a right angle.

8 Marks

13 Periods

Unit-7

CIRCLES

CIRCLES :-

Definition of the angle made at the centre,
angle= arc/ radius angle =

(i) (Motivate) Two circles are Congruent if they have equal radii.

(ii) (Motivate) In a circle or two congruent circles, if are as are equal the angles subtended by the areas at the centre are equal and its converse (axiom)

 

(iii) (Motivate) If the areas of two congruent circles are equal their corresponding chords are equal and its converse.

 

(iv) (Prove) Perpendicular to a chord from the centre of a circle, bisects the chord and its converse.

 

(v) (Motivate) One and only one circle can be drawn through three non-collinear points.

 

(vi) (Motivate) Equal chord are Equidistant from the centre and Conversely if two chord are Equidistant from the centre, they are equal.

 

(vii) (Prove) Angle subtended by an arc at the centre is twice the angle subtended at any other point on the circle.

 

(viii) (Prove) Angle subtended in a semi circle is a right angle and its converse.

 

(ix) (Prove) Angles in the same segment of the circle are equal.

 

(x) If the angles subtended at two points on the same side of the line segment are equal, then all the four points are con-cyclic.

 

(xi) (Motivate) Equal chords subtend Equal angles at the centre and is converse.

(xii) (Prove) The sum of the either pair of the opposite angles of a cyclic quadrilateral is 180 °

 

CONVERSE :- (Prove)

 

If a pair of opposite angles of a quadrilateral is supplementary, the quadrilateral is cyclic.

 

(xiii) (Prove) Tangent drawn to a circle at any point is perpendicular to the radius through the point of contact.

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

 

(xv) (Motivate) If two chords of a circle Intersect internally or

externally then the rectangle formed by the two parts of one chord is equal in area to the rectangle formed by the two parts of the other.

 

(xvi) (Prove) If PAB is a secant to a circle inter sectional it at A and

B and PT is a tangent, then PA x PB = PT2

 

(xvii) (Motivate) If a line to touches a circle and from the point of contact a chord is drawn, the angles which this chord makes with the given line are equal respectively to the angles formed in the corresponding alternate segments and the converse.

(xviii) (Prove) If two circles touch each other internally or externally, the point of contact lies on the line Joining their centres. (Concept of common tangents to two circles should be given.) Information only for the (Motivate) theorem and proof for (Prove) theorem's are required.

 

10 Marks

19 Periods

Unit-8

CONSTRUCTIONS

(i) Constructions of Cir-cum circle and in circle of a triangle.

 

(ii) To construct a triangle if its base and angle opposite to it is given altitude or median is given.

 

(iii) To construct a Cyclic quadrilateral if its one vertical angle is right angle.

 

(iv) Construction of triangles and quadrilaterals Similar to the given figure as per the given scale factor.

5 Marks

11 Periods

Unit-9

TRIGONOMETRY

Trigonometrical functions Trigonometrical identities

Sin2θ + Cos2θ = 1

1 + tan2θ = Sec2θ

1 + Cot2θ = Cosec2θ

Proving simple identities based on the above trigonometrical ratios of complementary angle.

Sin(90-θ) = Cosθ

Cos(90-θ ) = sinθ

tan (90-θ )= Cotθ

Cosec(90- θ ) = Secθ

Sec(90-θ ) = Cosecθ

Cot(90-θ ) = tanθ

Simple problem based on above.

 

16 Periods

Unit-10

HEIGHTAND DISTANCE

Simple problem based on heights and distances based on angles 30°, 45°, 60° Only

5 Marks

9 Periods

Unit-11

MENSURATION

(i) Area of Circle :- Area of circle, area of sector of a circle.

 

(ii) Cube and cuboid :- Concept of cube cuboid and its four walls, diagonal, surface area and volume.

 

(iii) Cylinder Cone and Sphere - Cylinder, Hollow cylinder, sphere, spherical shell, cone surface areas, whole surface area and volumes.

 

(iv) Frustum of a cone, Problem involving converting one type of metallic solid in to another and other mixed problems. Problems with combination of not more than two different solids be taken.

Note :- Use Vedic Mathematics Methods for Calculating Problems of Commercial Maths and mensuration (See Vedic Methods in Mathematics Index)

10 Marks

19 Periods

Unit-12

STATISTICS & PROBABILITY

(A) STATISTICS :-

Mean, Median and Mode. living index problems related to cost of living index (only).

 

(B) PROBABILITY :-

Classical definition of Probability Connection with Probability as given in Class IX Simple Problems on Single events, not using set notation.

10 Marks

13 Periods

 

Appendix-

1. Proof in Mathematics


Further discussion on, concept of statement, proof and argument further illustrations, of deductive proof with complete arguments using simple results from arithmetic, algebra and geometry. Simple theorems of the Given ...... and assuming .... prove ..... "Training of using only the given facts (irrespective of their truths) to arrive at the required conclusion. Explanation of converse, negation constructing converses and negations of given results statements.

2. Mathematical Modeling

Reinforcing the concept of mathematical modeling using simple examples of models where some constraints are ignored Estimating probability of occurrence of certain events and estimating averages may be considered. Modeling fair installments payments, using only simple interest and future value (use of AP)

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