Mathematics

This unit related to Mathematics has 5 chapters to learn

Number and Quantity

This unit related to Mathematics has 2 chapters to learn

Geometry - II

This unit related to Mathematics has 4 chapters to learn

Geometry - III

Algebra

Functions

Statistics and Probability

This unit related to Mathematics has 1 chapters to learn

Geometry - I

Mathematics Textbook of Competency Based Questions for Class IX

Mathematics Textbook of Competency Based Questions for Class X

THINK ABOVE AND BEYOND  MATHEMATICS PRACTICE BOOKS

Operations on Rational Expressions: Illustrations

Tangent to Standard Parabola in Slope Form

Tangents to a Circle From an External Point

Addition and Subtraction of Rational Expressions

Application of Logarithm: Illustration 2

Multiplication of Rational Expressions

Concept of Reflection in Geometry

Condition for Tangency to a Circle

The Volume of Hollow Solids: Cylinder and Sphere

Graph of Sine Function and Its Characteristics

Standard Equation of a Hyperbola

Magnitude of a Vector: Formula and Examples

Volume of a Prism Using Scalar Triple Product

Parallel Lines: Illustrations

Tangent to the Ellipse at a Given Point

Condition of Tangency of Line to a Hyperbola

Neighbourhood of a Point

Tangent to a Standard Parabola at a Given Point

The Intersection of a Line and a Circle

Reduction of Rational Expression

Equal Arcs

Unit Circle in Trigonometry

Triangle Construction With Base, Angle & Median

Triangle Construction With Base, Angle & Altitude

Roots of the Quadratic Equation: Illustration

Family of Straight Lines: Example

Theorem on Perpendicular Bisectors of a Triangle

Construction of Transverse Common Tangents

Period of Trigonometric Functions: Example

Logarithm: Illustration

Construction of an Incircle of a Triangle

Construct Triangle Equal to the Area of Quadrilateral

Finding Nature of Roots Using Coefficients

Trigonometric Functions: Illustration

Construction of Circumcircle of a Triangle

Application of Vectors in Geometry: Illustration

Values of the Symmetric Expression of the Roots

The Standard Equation of a Circle

Probability: Illustration

Formation of Quadratic Equation

Construction of Incircle of a Triangle

Graph of Logarithmic Function

AAS Criteria for Congruence of Triangles: Example

Solution of Quadratic Equation: Perfect Square Method

Division of Line Segment into Equal Parts

Angle Between Two Planes in Vector Form

Translation: Geometrical Figures

Graphing Quadratic Function: Standard Form

Construction: Parallel Lines

HCF of Monomials

Parallel Lines: Construction

Graphing Quadratic Function: Vertex Form

Symmetry in Real Life

Converse of Consecutive Interior Angles Theorem

Sum and Product of the Roots of Quadratic Equation

Various Tools in a Geometry Box

Validating Statements Using Direct Method

Solving System of Linear Equations using Matrices

Multiplying Two Monomials

Multiplication of Three or More Monomials

Counter Example Method for Validity of a Statement

Calculation of Compounded Amount

Parallelograms Formed by Four Points

Ruler and Compass Constructions

Construction of Angles Using Protractor

General Term in a Multinomial Expansion

Distance Between Two Parallel Lines in 3D

Areas of Similar Triangles

Distance of a Point From a Plane

Applications of Section Formula

Angle Sum Property of a Quadrilateral

Trigonometric Ratios of Complementary Angles

Section Formula in Three-Dimensional Space

Number of Distinct Terms in a Multinomial Expansion

Deriving the Multinomial Theorem

The Shortest Distance Between Two Skew Lines

Linear Programming: Manufacturing Problem

Uses of Straight Lines

Representation of Distance in Various Units

Litres to Millilitres

Variance and Standard Deviation for Ungrouped Distribution

Derivative of Functions in Parametric Form

Derivatives of Exponential and Logarithmic Functions

Finding Inverse by Elementary Transformations

Elementary Operations or Transformations of a Matrix

Properties of Binary Operations

Equivalence Relations and Equivalence Classes

Uses of Lines

Half of the Whole and Half of a Half

Perimeter and Area of a Closed Shape

Oblique Sketches

Nets for Building 3D Shapes

Speedometer and Odometer

Mean Deviation About Mean and Median for Ungrouped Data

Discrete Frequency Stats: Mean, Variance, SD

Linear Programming: Diet Problem

Linear Programming Problem: Graphical Method

Mean Deviation, Its Merits, and Demerits

How Are 3d Solids Different From 2d Shapes?

Different Views of 3D Solids

Modeling with Geometry

The Complex Number System

This chapter consists of topics like Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another etc.

Linear, Quadratic, and Exponential Models

This chapter consists of topics like Use units as a way to understand problems and to guide the solution of multi step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays etc.

Quantities

This chapter consists of topics like Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method etc.

Reasoning with Equations and Inequalities

This chapter consists of topics like Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real. etc.

This chapter consists of topics like Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle etc.

Trigonometric Functions

This chapter consists of topics like Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions etc.

Creating Equations

This chapter consists of topics like Understand statistics as a process for making inferences about population parameters based on a random sample from that population parameters based on a random sample from that population etc.

Making Inferences and Justifying Conclusions

This chapter consists of topics like Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation etc.

Expressing Geometric Properties with Equations

This chapter consists of topics like Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments etc.

Geometric Measurement and Dimension

This chapter consists of topics like Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle etc.

Circle

This chapter consists of topics like Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc etc.

Congruence

This chapter consists of topics like Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. etc.

The Real Number System

This chapter consists of topics like Verify experimentally the properties of dilations given by a center and a scale factor: a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor etc.

Similarity, Right Triangles, and Trigonometry

This chapter consists of topics like Represent data with plots on the real number line (dot plots, histograms, and box plots) etc.

Interpreting Categorical and Quantitative Data

This chapter consists of topics like Apply concepts of density based on area and volume in modeling situations etc.

This chapter consists of topics like Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”) etc.

Conditional Probability and the Rules of Probability

This chapter consists of topics like Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system etc.

Arithmetic with Polynomials and Rational Expressions

This chapter consists of topics like Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions etc.

Using Probability to Make Decisions

This chapter consists of topics like Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context. b. Combine standard function types using arithmetic operations. c. Compose functions. etc.

Building Functions

This chapter consists of topics like Recognize vector quantities as having both magnitude and direction.Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes etc.

Vector and Matrix Quantities

This chapter consists of topics like Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x) etc.

Interpreting Functions

This chapter consists of topics like Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. etc.

Seeing Structure in Expressions

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