# Mathematics Class 9 Term-I Syllabus 2022

The syllabus consists of six units: (i) Number Systems (ii) Algebra (iii) Coordinate Geometry (iv) Geometry (v) Mensuration (vi) Statistics and Probability.

### Exam Structure

 Units Marks I Number Systems 8 II Algebra 5 III Coordinate Geometry 4 IV Geometry 13 V Mensuration 4 VI Statistics and Probability 6 Total 40

### Unit I: Number Systems

1. REAL NUMBERS

Review of representation of natural numbers, integers, rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real numbers.

1. Examples of non-recurring / non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as √2, √3 and their representation on the number line.
2. Rationalization (with precise meaning) of real numbers of the type 1/(a+b√x) and 1/(√x+√y) (and their combinations) where x and y are natural number and a and b are integers.
3. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.)

### Unit II: Algebra

2. LINEAR EQUATIONS IN TWO VARIABLES

Recall of linear equations in one variable. Introduction to the equation in two variables.

Focus on linear equations of the type ax + by + c = 0. Explain that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line. Graph of linear equations in two variables. Examples, problems from real life with algebraic and graphical solutions being done simultaneously.

### Unit III: Coordinate Geometry

3. COORDINATE GEOMETRY

The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting points in the plane.

### Unit IV: Geometry

4. LINES AND ANGLES

1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° and the converse.
2. (Prove) If two lines intersect, vertically opposite angles are equal.
3. (Motivate) Results on corresponding angles, alternate angles, interior angles when a transversal intersects two parallel lines.
4. (Motivate) Lines which are parallel to a given line are parallel.
5. (Prove) The sum of the angles of a triangle is 180°.
6. (Motivate) If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.

5. TRIANGLES

1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence).
2. (Motivate) Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence).
3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).
4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle.
5. (Prove) The angles opposite to equal sides of a triangle are equal.
6. (Motivate) The sides opposite to equal angles of a triangle are equal.
7. (Motivate) Triangle inequalities and relation between 'angle and facing side' inequalities in triangles.

### Unit V: Mensuration

6. HERON'S FORMULA

Area of a triangle using Heron's formula (without proof)

### Unit VI: Statistics and Probability

7. STATISTICS

Introduction to Statistics: Collection of data, presentation of data - tabular form, ungrouped / grouped, bar graphs, histograms.