CBSE Class 9

The Central Board of Secondary Education (CBSE) is one of the most prestigious and preferred educational boards in India. It aims to provide a holistic and healthy education to all its learners so that students can get adequate space to develop mentally and physically. CBSE is known for its comprehensive syllabus and well structured exam pattern which helps students to get a detailed idea about the entire curriculum. There are around 20,102 schools under the board which follows the NCERT curriculum.

The CBSE Class 9 can be called as the foundation for higher classes and thus it is very important for students to learn the topics thoroughly. For example, if a student takes up science after their board exams, topics like mechanics and waves, etc. would also be included in higher classes. So, learning the topics properly from an early stage is very crucial. The curriculum is designed in a way that the students learn and develop their sense of individuality which naturally shapes their future. The guidelines for CBSE Class 9 are issued by the board and the NCERT. So, the schools affiliated to the CBSE board follows the NCERT syllabus. It is important that subjects like science and maths are learnt properly by understanding each concept and topic as these topics would be included in higher standards. For proper preparation, knowing the syllabus is very important along with solving various sample questions.

Unit No. | Unit |
---|---|

Lesson 1 | Number systems |

Lesson 2 | Polynomials |

Lesson 3 | Coordinate geometry |

Lesson 4 | Linear equations in two variables |

Lesson 5 | Introduction to euclid's geometry |

Lesson 6 | Lines and angles |

Lesson 7 | Triangles |

Lesson 8 | Quadrilaterals |

Lesson 9 | Areas of parallelograms and triangles |

Lesson 10 | Circles |

Lesson 11 | Constructions |

Lesson 12 | Heron’ s formula |

Lesson 13 | Surface areas and volumes |

Lesson 14 | Statistics |

Lesson 15 | Probability |

Unit No. | Unit | Marks |
---|---|---|

I | Number Systems | 08 |

II | Algebra | 17 |

III | Coordinate Geometry | 04 |

IV | Geometry | 28 |

V | Mensuration | 13 |

VI | Statistics and Probability | 10 |

Total | 80 |

- Review of representation of natural numbers, integers, rational numbers on the number line. Representation of terminating / non-terminating recurring decimals, on the number line through successive magnification. Rational numbers as recurring/terminating decimals.
- 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. Explaining that every real number is represented by a unique point on the number line and conversely, every point on the number line represents a unique real number.
- Existence of √x for a given positive real number x (visual proof to be emphasized).
- Definition of nth root of a real number.
- 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.
- 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.)

Coefficients of a polynomial, terms of a polynomial and zero
polynomial. Degree of a polynomial. Constant, linear, quadratic and
cubic polynomials. Monomials, binomials, trinomials. Factors and
multiples. Zeros of a polynomial. Motivate and State the Remainder
Theorem with examples. Statement and proof of the Factor Theorem.
Factorization of ax^{2} + bx + c, a ≠ 0 where a, b and c
are real numbers, and of cubic polynomials using the Factor Theorem.

Focus on linear equations of the type ax+by+c=0. Prove 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.

The Cartesian plane, coordinates of a point, notations, plotting points in the plane.

- (Axiom) 1. Given two distinct points, there exists one and only one line through them.
- (Theorem) 2. (Prove) Two distinct lines cannot have more than one point in common.

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

- 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).
- 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).
- Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).
- 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.
- The angles opposite to equal sides of a triangle are equal.
- (The sides opposite to equal angles of a triangle are equal.
- Triangle inequalities and relation between 'angle and facing side' inequalities in triangles.

- The diagonal divides a parallelogram into two congruent triangles.
- In a parallelogram opposite sides are equal, and conversely.
- In a parallelogram opposite angles are equal, and conversely.
- A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.
- In a parallelogram, the diagonals bisect each other and conversely.
- In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and (motivate) its converse.

Review concept of area, recall area of a rectangle.

- Parallelograms on the same base and between the same parallels have the same area.
- Triangles on the same (or equal base) base and between the same parallels are equal in area.

Through examples, arrive at definitions of circle related concepts, radius, circumference, diameter, chord, arc, secant, sector, segment subtended angle.

- Equal chords of a circle subtend equal angles at the center and (motivate) its converse.
- The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.
- There is one and only one circle passing through three given non-collinear points.
- Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely.
- The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
- Angles in the same segment of a circle are equal.
- If a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle.
- The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.

- Construction of bisectors of line segments and angles of measure 60°, 90°, 45° etc., equilateral triangles.
- Construction of a triangle given its base, sum/difference of the other two sides and one base angle.
- Construction of a triangle of given perimeter and base angles.

Area of a triangle using Heron's formula and its application

Surface areas and volumes of cubes, cuboids, spheres and right circular cylinders/cones.

Introduction to Statistics: bar graphs, histograms (with varying base lengths), frequency polygons, qualitative analysis of data to choose the correct form of presentation for the collected data. Mean, median, mode of ungrouped data.

Focus is on empirical probability. (A large amount of time to be devoted to group and to individual activities to motivate the concept; the experiments to be drawn from real - life situations, and from examples used in the chapter on statistics).

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