Grade 7 Maths Ncert Textbook Pdf
Nga Sagastume
NCERT solutions for class 9 maths comprise the analysis and explanation of all the problems covered by the NCERT textbook for 9th grade. The solutions are provided in a detailed manner to ensure that students can understand concepts as they go through them. These class 9 maths NCERT solutions are prepared by some of the most accomplished experts in the field of Mathematics.
Class 9th Maths NCERT Solutions are extremely helpful for students preparing for CBSE exams and state or national competitive tests such as Olympiads. The CBSE examinations follow the structure provided by the NCERT textbooks. Additionally, CBSE NCERT solutions for class 9 maths help in getting students ready to face class 10th and the corresponding board exams.
Practicing these class 9 maths NCERT solutions can help students to increase their theoretical skills and practical knowledge. The solutions to all NCERT class 9 maths sums are available for free pdf download. You can find tips and tricks included with the solutions. The links to these pdf solutions are given below.
As a student, you must indulge in constant revision and practice all the solutions. Thus, revisiting the above-mentioned links periodically is a must. Start by attempting the questions in the NCERT book and then have a look at these class 9th maths NCERT solutions. You can download the NCERT textbook given below and begin your learning journey.
NCERT solutions for class 9 maths chapter 1 number systems help students amass the tools required to identify rational and irrational numbers, locate real numbers on a number line, and convert a real number to its decimal form. The solutions to this chapter also give students a good understanding of simplifying expressions using certain identities and laws of exponents.
Topics Covered: NCERT solutions for class 9 maths cover questions based on rationalizing the denominator, the rules of exponentiation, identities applied to positive real numbers, expanding a real number into its decimal form, and vice versa.
NCERT solutions for class 9 maths chapter 2 polynomials help students form the basics of polynomials that will be used in higher classes. Students learn about the types of polynomials in one variable, degree and zeros of a polynomial, the remainder theorem, factorization of polynomials, and the application of algebraic identities.
Topics Covered: Factorization of different polynomials using the splitting method and factor theorem, finding the remainder of a polynomial, applying algebraic identities to simplify sums, and determining the zeros of a polynomial.
NCERT solutions for class 9 maths chapter 3 coordinate geometry help students to get a grasp on how to describe the position of an object using coordinates and explanation of the cartesian system. It acts as a foundation for further chapters that require students to use their knowledge to solve geometrical problems.
Topics Covered: Determining the x and y coordinates of a point in a cartesian plane, identifying quadrants, locating an object, and expressing it in the form of coordinates are the topics under class 9 maths NCERT solutions.
Class 9 maths NCERT solutions chapter 3 gives a brief overview of the definition of the origin, how to use the horizontal x-axis and vertical y-axis to pinpoint the position of an object. It also helps students determine what quadrant does a point lies in depending upon the signs of the coordinates.
NCERT solutions for class 9 maths chapter 4 linear equations in two variables introduce students to a linear equation in two variables by helping them understand the concepts behind it. The solutions include solving linear equations, graphical representation methods, and the depiction of parallel lines.
Linear equations are one of the most important chapters covered in class 9 maths NCERT solutions. The following are a few tips that can help you power through these solutions quickly and efficiently.
Topics Covered: Finding solutions to a linear equation by substituting values, representing a linear equation in two variables graphically, and how to write the equation of lines parallel to the x-axis.
Total Questions: Chapter 4 linear equations in two variables have a total of 16 questions. 8 require students to carefully think and attempt the problem, 5 are moderate and 4 are easy sums.
Class 9 maths NCERT solutions chapter 6 lines and angles give students an understanding of the basic definitions of various terms that are used in geometry. Students learn about the different types of angles, pairs of angles, transversals, parallel lines, angle sum property of triangles, and axioms associated with these concepts.
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Topics Covered: Adjacent angles, vertically opposite angles, linear pairs of angles, alternate angles, corresponding angles, parallel lines, and transversal are topics falling under Class 9 maths NCERT solutions. In addition to this, problems based on the angle sum property of a triangle are also included in these solutions.
NCERT solutions for class 9 maths chapter 7 triangles are a fantastic way for students to learn about the congruence of triangles using the SAS, SSS, ASA, RHS criteria. Several properties of triangles along with concepts on the inequality of triangles also fall under the scope of this chapter.
Topics Covered: Questions based on applying properties of triangles, proving the congruence of two triangles using different methods, and theorems on the inequality of triangles are the topics covered.
In this chapter, students learn about the SSS, SAS, ASA, and RHS congruence criteria. Students can get a good grasp on properties of triangles such as sides opposite to equal angles are equivalent, the sum of any two sides of a triangle is greater than the third side, and so on. Thus, after studying this chapter students can master the basic concepts of a triangle.
NCERT solutions for class 9 maths chapter 8 quadrilaterals comprise questions that teach students about the different types of quadrilaterals such as squares, rhombuses, rectangles, parallelograms, and their properties.
Topics Covered: Angle sum property of quadrilaterals, properties of a parallelogram, square, and rhombus that depend upon different factors such as length of diagonals, the measure of sides, etc. It also includes the mid-point theorem.
Class 9 maths NCERT solutions chapter 9 areas of parallelograms and triangles include various theorems that help to simplify finding the area of complex parallelograms as well as triangles, properties to find the area of triangles divided by a median, and area of planar regions.
Topics Covered: Topics covered incorporate questions on finding the area of two or more triangles and parallelograms with the same base between the same parallels, determining the area of triangles that are split by a median as well as the area of congruent figures.
Total Questions: Chapter 9 areas of parallelograms and triangles have a total of 31 questions. 8 questions belong to an optional exercise with a high difficulty level, 14 are intermediate and 9 are simple sums.
NCERT solutions for class 9 maths chapter 10 circles build a foundation for students by introducing them to the various terms related to circles. Students get the opportunity to build their knowledge base on properties of chords, the angle subtended by chord and arc, perpendicular to a point, the distance of a chord from the center as well as cyclic quadrilaterals.
Topics Covered: NCERT solutions class 9 maths encompass topics such as angles subtended by a chord at a point, perpendiculars dropped from the center to a chord, and how to calculate the distance of equal chords from the center. Other discussions include angles subtended by an arc of the circle, cyclic quadrilaterals, and their attributes.
NCERT solutions for class 9 maths chapter 11 constructions will teach students how to precisely use geometrical instruments for basic constructions. Students learn to construct different angles, perpendicular bisectors, and triangles with a few given restraints.
Topics Covered: Constructing an angle from a ray, bisector of a given angle, and techniques to construct triangles when certain constraints such as the perimeter are mentioned, are the topics explained in this chapter.
After studying NCERT solutions class 9 maths chapter 11 students will be adept at using a ruler and compass to bisect a given angle, construct angles of discrete values, draw the perpendicular bisector of a line segment, and building triangles.
Class 9 maths NCERT solutions chapter 13 surface areas and volumes introduce students to the concepts required to find the total surface areas, lateral or curved surface areas, and volumes of different shapes. The concepts and formulas in this chapter are very important as they form the basis of topics covered in higher education.
Class 9 maths NCERT solutions chapter 14 statistics provide an in-depth analysis of problems that are based on the collection and presentation of data for analytical purposes, graphical representation of data using different types of graphs, and measures of central tendency. This chapter enables students to develop their calculation speed and visualization skills.
Topics Covered: Representation of data in the form of frequency tables and drawing inferences from them, plotting data points using bar graphs, histograms, and frequency polygons, finding the mean, median, and mode of the given data.