Here you will know the latest examination pattern for CBSE Class 9 Maths. Question paper design has been explained in detail here.

CBSE Class 9th students must be preparing for their annual exams which will be held in 2020. All the students want to score good marks in their annual exams so that they may enter their board class all confidently and with full enthusiasm. For this students need to prepare for their upcoming annual exams in a planned and organised manner. They must have the right strategy so that they don’t miss any chance to score maximum marks in the exams.

Mathematics, for class 9 students, can be a little difficult subject to score good marks however, if they prepare methodically then they can easily obtain more than 90 marks in their Maths exam. Here, knowing the examination pattern can play a crucial role in planning the effective preparations for the exam. With the examination pattern, you get to know the scheme of assessment and format of question paper which are quite essential to structure the right plan for the exam preparation. We are providing here all the details of CBSE Class 9 Maths Examination Pattern which will help you plan your preparations for best results.

**CBSE Class 9 Maths Examination Pattern 2020**

CBSE Class 9 Maths Exam is of 100 marks out of which 80 marks are assigned to the theory paper and rest 20 marks are kept for internal assessment. Internal assessment will comprise following learning activities:

(i) Pen Paper Test and Multiple Assessment = 5+5 = 10 Marks

(ii) Portfolio = 05 Marks

(iii) Lab Practical (Lab activities to be done from the prescribed books) = 05 Marks

**CBSE Class 9 Maths Unit-Wise Weightage**

Class 9 Maths question paper in the annual exams will be prepared according to the unit-wise weightage distribution as prescribed by CBSE in the Class 9 Maths Syllabus for the current session. Below is given the list of units with their weightage for the annual exam 2020:

Units |
Unit Name |
Marks |

I |
NUMBER SYSTEMS | 08 |

II |
ALGEBRA | 17 |

III |
COORDINATE GEOMETRY | 04 |

IV |
GEOMETRY | 28 |

V |
MENSURATION | 13 |

VI |
STATISTICS & PROBABILTY | 10 |

Total |
80 |

Students should first prepare the units carrying more weightage and then move on to those with lower weightage. This ensures that they cover the important part first which enhances their confidence to perform well in the exam.

**CBSE Class 9th Mathematics Question Paper format and Blue Print for Annual Exam 2020**

Question paper format includes the type of questions and marks distribution in paper. This year, CBSE has made certain changes in the format of class 9 Maths question paper. According to the latest pattern, 25% of the questions in paper will be of objective type. Also the total number of question in paper is increased from 30 to 40.

CBSE Class 9 Maths question paper design will be as per the following scheme:

- The Maths question paper will comprise of a total of total 40 questions divided into four sections, viz., A, B, C and D.
- Section A will contain 20 questions of 1 mark each.
- Section B will contain 6 questions of 2 marks each.
- Section C will contain 8 questions of 3 marks each.
- Section D will contain 6 questions of 4 marks each.

Objective type questions may be asked in different formats like multiple choice type, fill in the blanks and short answer type questions. To prepare for all such questions, students must read the concepts given in the Class 9 Maths NCERT Book.

### CBSE Maths Syllabus for Class 9 2019-20

#### UNIT – I: NUMBER SYSTEMS

**REAL NUMBERS**

- 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 numbers 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 the learner to arrive at the general laws.)

#### UNIT – II: ALGEBRA

**POLYNOMIALS**

Definition of a polynomial in one variable, with examples and counter examples. 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.

Recall of algebraic expressions and identities. Verification of identities:

- (x + y + z)
^{2}= x^{2}+ y^{2}+ z^{2}+ 2xy + 2yz + 2zx - (x ± y)
^{3}= x^{3}± y^{3}± 3xy (x ± y) - x³ ± y³ = (x ± y) (x² ± xy + y²)
- x
^{3}+ y^{3}+ z^{3}– 3xyz = (x + y + z) (x^{2}+ y^{2}+ z^{2}– xy – yz – zx) and their use in factorization of polynomials.

**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. 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, including problems on Ratio and Proportion and with algebraic and graphical solutions being done simultaneously.

#### UNIT – III: COORDINATE GEOMETRY

**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

**INTRODUCTION TO EUCLID’S GEOMETRY**

History – Geometry in India and Euclid’s geometry. Euclid’s method of formalizing observed phenomenon into rigorous mathematics with definitions, common/obvious notions, axioms/postulates, and theorems. The five postulates of Euclid. Equivalent versions of the fifth postulate. Showing the relationship between axiom and theorem, for example:

- (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.

**LINES AND ANGLES**

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

**TRIANGLES**

- (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle are equal to any two sides and the included angle of the other triangle (SAS Congruence).
- (Prove) 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).
- (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).
- (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.
- (Prove) The angles opposite to equal sides of a triangle are equal.
- (Motivate) The sides opposite to equal angles of a triangle are equal.
- (Motivate) Triangle inequalities and relation between ‘angle and facing side’ inequalities in triangles.

**QUADRILATERALS**

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

**AREA**

Review the concept of area, recall area of a rectangle.

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

**CIRCLES**

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

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

**CONSTRUCTIONS**

- 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.

#### UNIT – V: MENSURATION

**AREAS**

Area of a triangle using Heron’s formula (without proof) and its application in finding the area of a quadrilateral.

**SURFACE AREAS AND VOLUMES**

Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones.

#### UNIT – VI : STATISTICS & PROBABILITY

**STATISTICS**

CBSE Class 9 Maths Syllabus: Introduction to Statistics: Collection of data, presentation of data – tabular form, ungrouped / grouped, 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.

**PROBABILITY**

History, Repeated experiments and observed frequency approach to probability.

The 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).

### INTERNAL ASSESSMENT: 20 Marks

- Periodical Test: 10 Marks
- Notebook Submission: 05 Marks
- Lab Practical (Lab activities to be done from the prescribed books): 05 Marks