# HSSlive: Plus One & Plus Two Notes & Solutions for Kerala State Board

## Wednesday, June 29, 2022

Goa Board Class 9th Mathematics Syllabus 2022 PDF Download - GBSHSE has released the syllabus of Goa Board Class 9th Mathematics Syllabus 2022 along with the official notification on the official website - gbshse.info. The Goa Board Class 9th Mathematics 2022 Syllabus pdf comprises the subject-wise topics which will be asked in the class 9 Mathematics exam. Students of Goa State Board Class 9th Mathematics can download the syllabus PDF from this page.

## GBSHSE Class 9 Mathematics Syllabus 2022-23 PDF

Using the Goa Board Class 9th Mathematics Syllabus 2022 PDF, students can prepare their study schedule and exam preparation strategy. As the Goa Board exam date has been released, candidates can plan their schedule according to it, therefore, they can prepare their syllabus of Goa Board Class 9th Mathematics Exam 2022 accordingly. Along with the Goa Board Class 9th Mathematics 2022 syllabus, candidates can also check the official GBSHSE exam pattern and the previous year's GBSHSE Class 9th Mathematics question papers.

## Goa State Board Class 9th Mathematics Syllabus 2022 PDF Online

 Name of the Board Goa Board Name of the Grade 9 Subjects Mathematics Year 2022-23 Format PDF/DOC Provider hsslive.co.in Official Website gbshse.info

## How To Download Goa State Board Class 9th Mathematics Syllabus 2022 PDF Online?

1. Visit the official website - gbshse.info.
2. Look for GBSHSE Class 9th Mathematics Syllabus 2022.
3. Now check for Goa Board Class 9 Mathematics Syllabus 2022 PDF.

## Goa Board Class 9th Mathematics Syllabus 2022-23 PDF

Students of download the Goa Board Class 9th Mathematics Syllabus 2022-23 PDF online using the links provided below:

#### First Terminal Examination:

Chapter Name and Topics
Number System
1. Review of representation of natural numbers, integers, and 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. Operations on real numbers.
2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as, and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, viz. every point on the number line represents a unique real number.
3. Definition of nth root of a real number.
4. Rationalization (with precise meaning) of real numbers (and their combinations) where x and y are natural numbers and a and b are integers.
5. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learners to arrive at the general laws.)
Lines and Angles

1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180O 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 that are parallel to a given line are parallel.

5. (Prove) The sum of the angles of a triangle is 180O .

6. (Motivate) If a side of a triangle is produced, the exterior angle formed is equal to the sum of the two interior opposite angles.

Triangle

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. (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).

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. (RHS Congruence)

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.

Polynomial
• Definition of a polynomial in one variable, with examples and counterexamples. 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 ax2 + 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:
• and their use in the factorization of polynomials

1. (Prove) The diagonal divides a parallelogram into two congruent triangles. 2. (Motivate) In a parallelogram opposite sides are equal, and conversely.
3. (Motivate) In a parallelogram opposite angles are equal, and conversely.
4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides are parallel and equal.
5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely.
6. (Motivate) In a triangle, the line segment joining the midpoints of any two sides is parallel to the third side and in half of it and (motivates) its converse.
Constructions

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

#### Second Terminal Examination:

Chapter Name and Topics
Linear Equations in Two Variables

1. Recall 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, including problems on Ratio and Proportion and with algebraic and graphical solutions being done simultaneously
Areas of Parallelogram and Triangles

1. (Prove) Parallelograms on the same base and between the same parallels have equal areas.
2. (Motivate) Triangles on the same base (or equal bases) and between the same parallels are
equal in area.
Circles

Through examples, arrive at the definition of a circle and related concepts-radius, circumference, diameter, chord, arc, secant, sector, segment, subtended angle.
1. (Prove) Equal chords of a circle subtend equal angles at the centre and (motivate) its converse.
2. (Motivate) The perpendicular from the centre of a circle to a chord bisects the chord and conversely, the line is drawn through the centre of a circle to bisect a chord is perpendicular to the chord.
3. (Motivate) There is one and only one circle passing through three given non-collinear points. 4. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the centre (or their respective centres) and conversely.
5. (Prove) The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
6. (Motivate) Angles in the same segment of a circle are equal.
7. (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.
8. (Motivate) The sum of either pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.
Surface Areas and Volumes

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

Introduction to Statistics: Collection of data, presentation of data — tabular form, ungrouped / grouped, bar graphs, histograms (with varying base lengths), frequency polygons. Mean, median and mode of ungrouped data

## Key Benefits Of Solving Goa Board Class 9th Mathematics Syllabus 2022-23 PDF

There are several benefits of Goa Board Class 9th Mathematics Syllabus 2022 PDF

• It enhances the speed of solving questions and time management skills.
• It helps candidates to gain insight into the GBSHSE Class 9th Mathematics Syllabus 2022 PDF.
• Understand the type of questions and marking scheme.
• Helps in analyzing the preparation level.
• Gives an idea about the real exam scenario.
• Enhances exam temperament and boosts confidence.
• Gives an idea about the topics important for examination point of view.
• Goa State Board Class 9th Mathematics Syllabus 2022 PDF helps in understanding the Exam pattern and its level of difficulty.

## FAQ about GBSHSE Class 9th Mathematics Syllabus 2022 PDF

#### What is the Goa Board Class 9th Mathematics Syllabus 2022-23??

The Goa Board Class 9th Mathematics Syllabus 2022 PDF comprises the subject-wise topics which will be asked in the exam.

#### Is it necessary to go through the GBSHSE Class 9th Mathematics Syllabus 2022?

Candidates, if they want to score higher marks and stay ahead in the competition, should not ignore the syllabus. They should read the syllabus thoroughly. This will help in developing a strong preparation strategy and candidates will also gain valuable insights into the exam pattern, important chapters and topics, weightage of marks, objective of the entire course, etc.
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