Evaluate Polynomials Using Algebraic Identities | Problems, Online Practice, Tests, Worksheets, Quizzes, Assignments | Class 9 | NCERT (CBSE and ICSE)

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Class 9
Polynomials
Evaluate Polynomials Using Algebraic Identities

Class 9

1. Number Systems

1.1. Rational and Irrational Numbers

1.1.1. Understand the Concept

1.1.2. Find Rational Numbers Between Given Rational Numbers

1.1.3. Without Actual Division Identify Terminating Decimals

1.1.4. Relate Rational Numbers and Decimals

1.1.4.1. Express Rational Numbers as Terminating and Recurring Decimals

1.1.4.2. Express Terminating Decimals as Fractions

1.1.4.3. Express Recurring Decimals as Fractions

1.1.5. Represent Irrational Numbers on the Number Line

1.1.6. Find Irrational Numbers Between Given Rational Numbers

1.1.7. Identify Rational and Irrational Numbers

2. Real Numbers

2.1. Operations on Real Numbers

2.1.1. Addition and Subtraction of Real Numbers

2.1.2. Multiplication and Division of Real Numbers

2.2. Rationalization of Real Numbers

2.3. Exponents of Real Numbers

3. Polynomials

3.1. Identify Polynomial Expressions

3.2. Identify the Degree of a Polynomial

3.3. Identify Coefficients in a Polynomial

3.4. Evaluate Polynomials

3.5. Zeros of a Polynomial

3.6. Square of Binomials

3.7. Remainder Theorem

3.8. Factor Theorem

3.9. Factorization of Polynomials

3.9.1. Factorization by Taking out the Common Factor

3.9.2. Factorization by Grouping

3.9.3. Factoring the Difference of Two Squares

3.9.4. Factorization of Quadratic Polynomials

3.9.5. Factorization Using the Identity for Square of a Trinomial

3.9.6. Factorization of Sum or Difference of Cubes

3.9.7. Factorization of Degree 3 Polynomials

3.10. Polynomials in Equations

3.11. Evaluate Polynomials Using Algebraic Identities

4. Coordinate Geometry

4.1. Understand the Terms Related to Coordinate Geometry

4.2. Identify the Coordinates of a Point on the Cartesian Plane

4.3. Identify the Coordinates of the Points on the X-axis, Y-axis, and the Origin

4.4. Identify the Quadrant of a Point

4.5. Draw the Graphs of Linear Equations

4.6. Higher Order Thinking Skills (HOTS) Related to the Cartesian Plane

5. Linear Equations in Two Variables

5.1. Verify a Solution to a Linear Equation in Two Variables

5.2. Find the Unknown Variable When the Equation of the Line and Several Conditions are Given

5.3. Draw Graph of Linear Equations and Find the Unknown Variable

5.4. Draw Graph of Some Special Type of Linear Equations

5.5. Word Problems

6. Introduction to Euclid's Geometry

6.1. Understanding Points, Line Segments, Rays, Lines, and Planes

6.2. Euclid's Axioms and Postulates

6.3. Parallel, Concurrent and Intersecting Lines

7. Lines and Angles

7.1. Understand the Concept of Angles and Terms Related to Angles

7.2. Interior and Exterior Points of an Angle

7.3. Categorize Angles on the Basis of Their Measures

7.4. Angles Around a Point

7.5. Complementary and Supplementary Pairs of Angles

7.6. Adjacent Angles, Vertically Opposite Angles, and Linear Pair of Angles

7.7. Parallel Lines, Transversal, and Angles Formed

8. Triangles

8.1. Classification of Triangles on the Basis of its Sides and Angles

8.2. Theorems and Problems Related to Side and Angle Measures of Triangles

8.3. Congruence of Triangles

8.3.1. Congruence: Understand the Meaning

8.3.2. Criteria for Congruence of Triangles

8.3.3. Problems Related to Congruence of Triangles

8.4. Inequalities in a Triangle

9. Quadrilaterals

9.1. Understand the Concept of Quadrilaterals and Related Terms

9.2. Theorems and Problems Related to the Angles of a Quadrilateral

9.3. Theorems and Problems Related to Parallelograms

9.4. Intercept Theorem and Midpoint Theorem

9.4.1. Intercept Theorem (Thales Theorem, or Basic Proportionality Theorem) and Related Problems

9.4.2. Midpoint Theorem and Related Problems

10. Areas of Parallelograms and Triangles

10.1. Area of a Triangle

10.2. Area of a Parallelogram

11. Circles

11.1. Terms Related to Circles

11.2. Theorems and Problems Related to Chord Properties of Circles

11.3. Theorems and Problems Related to Angles Subtended by Arcs/Chords

11.4. Theorems and Problems Related to Cyclic Quadrilaterals

11.5. Problems Related to Circumcircles and In-circles

12. Constructions

12.1. Bisector of a Line Segment

12.2. Construction of Angles

12.3. Construction of Triangles

13. Heron's Formula

13.1. Area of a Triangle Using Heron's Formula

14. Surface Areas and Volumes

14.1. Volume and Surface Area of Cuboids and Cubes

14.2. Volume and Surface Area of Cylinders

14.3. Volume and Surface Area of Circular Cones

14.4. Volume and Surface Area of Spheres, Hemispheres and Spherical Shells

14.5. Mixed Problems on Volume and Surface Area

15. Statistics

15.1. Frequency Distribution of an Ungrouped Data

15.2. Cumulative Frequency Table of an Ungrouped Data

15.3. Bar Graph

15.3.1. Drawing Bar Graphs

15.3.2. Interpreting Bar Graphs

15.4. Histogram

15.4.1. Histogram When the Frequency Distribution is Exclusive

15.4.2. Histogram When the Frequency Distribution is Inclusive

15.4.3. Histogram When the Class Intervals are of Unequal Size

15.5. Frequency Polygons

15.5.1. Frequency Polygons when the Frequency Distribution is Exclusive

15.5.2. Frequency Polygons when the Frequency Distribution is Inclusive

15.6. Histograms and Frequency Polygons on a Single Graph

15.7. Mean, Median, and Mode

15.7.1. Mean

15.7.1.1. Arithmetic Mean of Numerical Data

15.7.1.2. Word Problems on Mean

15.7.2. Median

15.7.2.1. Median of Numerical Data

15.7.2.2. Median of Discrete Series

15.7.3. Mode

15.7.3.1. Mode of Ungrouped Data

15.7.3.2. Empirical Formula for Calculating Mode

16. Probability

16.1. Calculate Probability for Events in Random Experiments

17. Miscellaneous Topics

17.1. Measuring Areas of Quadrilaterals

17.1.1. Area of a Quadrilateral

17.1.2. Area of a Parallelogram

17.1.3. Area of a Rhombus

17.1.4. Area of a Trapezium

17.1.5. Area of a Quadrilateral Using Heron's Formula

17.1.6. Application of Results on Area of Polygonal Regions

Class 9 NCERT (CBSE and ICSE) Evaluate Polynomials Using Algebraic Identities

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