Reader's Digest: Want to know the ins and outs of CBSE Class 11 Applied Maths Coordinate Geometry 2024? Read this blog to learn the concept, project topics, syllabus, weightage & prep tips!
Exciting news for CBSE students! The board has announced 'Applied Maths' as a fresh subject addition. Now, you might wonder, "What's the big deal?"
Even though you might have studied Coordinate Geometry in your regular Maths lessons, the approach in Applied Maths takes a whole new turn.
Diving into the syllabus, Coordinate Geometry consists of three sub-topics. First, we have the "Straight Lines," which forms the foundational pillar.
Next is the "Conic Sections," which focuses on circles and parabolas, offering a fascinating perspective on curves. And lastly, for those with a knack for visualizing beyond the 2D realm, there's an "Introduction to Three-Dimensional Geometry."
Here's a quick fact: out of the entire CBSE Class 11 Applied Maths blueprint, Coordinate Geometry hold a weightage of 5 marks, neatly spread across 15 periods.
CBSE recommends the ever-reliable NCERT as your go-to guide for Applied Maths Coordinate Geometry to aid you in this mathematical journey.
This blog aims to provide you with invaluable insights into this subject, covering key aspects such as:
Basics of CBSE Applied Maths Coordinate Geometry: Discover the foundations and significance of this subject, exploring its unique approach to Coordinate Geometry.
Pros of Studying CBSE Class 11 Applied Maths Coordinate Geometry: Understand Applied Maths's practical applications and real-world relevance in various fields.
CBSE Class 11 Applied Maths Coordinate Geometry Syllabus 2024: Get a detailed syllabus overview, including the topics you'll encounter and their weightage.
Project Topics for CBSE Class 11 Applied Maths Coordinate Geometry 2024:Explore exciting project topics to enhance your understanding of Coordinate Geometry while making connections to real-life scenarios.
Most Important Topics for Class 11 Applied Maths Coordinate Geometry 2024: Identify the core concepts and chapters that deserve your attention.
Best Strategy to Solve CBSE Applied Maths Coordinate Geometry Class 11 Questions: Discover effective strategies to tackle problems, ensuring your success in this subject.
What is Coordinate Geometry in CBSE Class 11 Applied Maths?
Coordinate Geometry, often called analytic geometry or Cartesian geometry, is a branch of mathematics that employs algebraic equations to represent and analyze geometric figures on a coordinate plane.
In this, geometric figures such as points, lines, and curves are represented using coordinates and algebraic equations.
The coordinate system is typically the Cartesian coordinate system, which utilizes two perpendicular lines called axes (the x-axis representing the horizontal direction and the y-axis representing the vertical direction) to define a point uniquely in a plane using a pair of numerical coordinates.
To better understand the concept of coordinate geometry, consider the simple example of a point in a plane.
In the Cartesian coordinate system, a point is an ordered pair of numbers represented P (x,y), where x is the distance of the point from the y-axis (called the x-coordinate or abscissa), and y is the distance from the x-axis (called the y-coordinate or ordinate).
For instance, the point P (3,2) represents a point 3 units to the right of the y-axis and 2 units above the x-axis. This systematic approach allows for a seamless blend of algebra and geometry, facilitating the study of figures and spaces' shapes, sizes, and properties using algebraic methods.
What are the Benefits of Studying CBSE Class 11 Applied Maths Coordinate Geometry?
This subject is designed to develop significant mathematical skills and methods needed in other subject areas. Topics covered in two years aim to enable students to use mathematical knowledge in business, economics and social sciences.
It aims to promote appreciation of mathematical power and simplicity for its countless applications in diverse fields.
It will help you understand essential mathematical and statistical tools and their applications in commerce (business/ finance/economics) and social sciences.
Model real-world experiences/problems into mathematical expressions using numerical/algebraic/graphical representation.
To make sense of the data by organizing, representing, interpreting, analyzing, and making meaningful inferences from the real-world situations
To develop logical reasoning skills and apply the same in simple problem-solving
To reinforce mathematical communication by formulating conjectures, validating logical arguments, and testing hypothesis
To make connections between Mathematics and other disciplines.
CBSE Class 11 Applied Maths Coordinate Geometry Syllabus 2024
In class 11 coordinate geometry, you will study only three topics: Straight Lines, Conic sections (Circles and parabolas), and Introduction to Three - Dimensional Geometry. The coordinate geometry holds a weightage of 13 marks in the CBSE class 11 Applied Maths subject.
The table below shows the CBSE class 11 Applied Maths Coordinate Geometry Syllabus:
Explanation of Topics
Find the slope and equation of a line in various form
Find the angle between the two lines
Find the perpendicular from a given point on a line
Find the distance between two parallel lines
Gradient of a line
Equation of line: Parallel to axes, point-slope form, two-points form, slope intercept form, intercept form
Application of the straight line in the demand curve related to economic problems
Define a circle
Find different forms of equations of a circle
Solve problems based on applications of circle
Circle as a locus of a point in a plane
Equation of a circle in standard form, central form, diameter form and general form
Introduction to Three-Dimensional Geometry
Define parabola and related terms
Define eccentricity of a parabola
Derive the equation of a parabola
A parabola as a locus of a point in a plane.
Equation of a parabola in standard form:
Focus, Directrix, Axis, Latus rectum, Eccentricity
Application in a parabolic reflector, beam supported by wires at the end of the support, girder of a railway bridge, etc.
What are the Most Important Topics for CBSE Class 11 Applied Maths Coordinate Geometry 2024?
From the syllabus for CBSE Class 11 Applied Maths Coordinate Geometry 2024, here are the most important topics:
Gradient (Slope) of a Line: Understanding the concept of slope is foundational to many other topics in coordinate geometry. Almost all the other concepts related to straight lines are built upon understanding the slope.
Equation of Line: Different forms of the equation of a line are crucial. These forms include:
Angle between Two Lines: This helps in understanding the relative position of two lines, which can further assist in topics like the condition for lines to be parallel or perpendicular.
Applications in Economics: Applying straight lines in demand curves related to economic problems is vital, especially if students are keen on understanding real-life applications.
Equation of a Circle: Knowing the different forms of equations of a circle, such as the standard form, central form, diameter form, and general form, is fundamental. These equations provide insights into the properties and applications of circles in various scenarios.
Applications of Circle: This would give an understanding of circles' real-life significance and applicability.
Introduction to Three-Dimensional Geometry:
Basics of Parabola: Understanding the definition and characteristics of a parabola, such as its focus, directrix, axis, and latus rectum, is essential. Knowing how to derive its standard equation helps solve various problems.
The eccentricity of Parabola: The eccentricity defines the shape of a conic section, and in the case of a parabola, it is always 1. Understanding this is important for problems related to the properties and applications of parabolas.
Real-life Applications of Parabola: Concepts become more ingrained when students understand their real-world applications. Topics like the use of parabolic reflectors in satellite dishes, the shape of girders in railway bridges, and beams supported by wires give practical insights.
CBSE Class 11 Applied Maths Coordinate Geometry Solved Sample Questions
To help you understand the type of questions asked in the exam, we have provided some sample questions for your reference here.
CBSE Applied Maths Coordinate Geometry on Circles
Q1) How are the points (0, 1), (3, 1) and (1, 3) situated with respect to the circle x 2 + y 2 – 2x – 4y + 3 = 0?
Answer: To check the position of a point to a circle, substitute the point in the circle equation.
For (0,1): 02+12−0−4(1)+3=002+12−0−4(1)+3=0 So, the point lies on the circle.
For (3,1) and (1,3), substituting them in the equation, we get values greater than 0. So, they lie outside the circle.
Q2) Obtain the equation of the circle orthogonal to both the circles x 2 + y 2 + 3x – 5y + 6 = 0 and 4x 2 + 4y 2 – 28x + 29 = 0 and whose centre lies on the line 3x + 4y + 1 = 0.
Answer: The given problem requires detailed calculation using the properties of orthogonal circles and the conditions they satisfy.
Q3) The chords of contact of the pair of tangents drawn from each point on the line 2x + y = 4 to the circle x 2 + y 2 = 1 pass through a fixed point.
Answer: Using the T = 0 condition, the chord of contact for the tangents from any point (h, k) to the given circle is ℎ+xy=1hx+ky=1
Class 11 Applied Maths Coordinate Geometry Questions on Straight Lines
Q1) Find the equation of the straight line, which makes an angle of 15° with the positive direction of the x-axis and cuts an intercept of length 4 on the negative direction of the y-axis.
Given that the line makes an angle of 15° with the positive direction of the x-axis, we have tan(θ)=tan(15°)tan(θ)=tan(15°). The slope m of the line is the value of tan(θ).
Using the value of tan(15°)=2−3tan(15°)=2−√ 3 (you can use trigonometric identities or a calculator), m=2−√ 3
The line cuts an intercept of length 4 on the negative direction of the y-axis, so the y-intercept c=-4.
Using the slope-intercept form y=mx+c, y=(2−√ 4)x−4. That is the required equation of the line.
In conclusion, introducing Applied Maths as a subject in CBSE Class 11 brings a fresh perspective to Coordinate Geometry. This blog highlights the essential aspects of this subject, including its syllabus, weightage, benefits, and key concepts.
Here are the key takeaways:
Applied Maths Coordinate Geometry focuses on three main topics: Straight Lines, Conic Sections, and Introduction to Three-Dimensional Geometry.
Straight Lines cover concepts like slope, equations in various forms, angles between lines, and real-world applications in economics.
Conic Sections delve into circles and their equations, emphasizing their applications.
Introduction to Three-Dimensional Geometry introduces parabolas, their equations, eccentricity, and practical applications.
Projects can enhance understanding, exploring historical aspects and real-world applications of these concepts.
To excel in this subject, students should focus on mastering fundamental concepts, practising regularly, and visualizing problems graphically.
Frequently Asked Questions
Should I take applied maths in class 11?
Which Mathematics subject is harder? The pure one or the applied one?
What are the topics students will study in CBSE class 11 Applied mathematics coordinate geometry?
What is the weightage of coordinate geometry topic?
What is the importance of studying CBSE Class 11 Applied Maths Coordinate Geometry?
What topics are covered in the CBSE Class 11 Applied Maths Coordinate Geometry syllabus for 2024?
How much weightage does Coordinate Geometry hold in CBSE Class 11 Applied Maths 2024?
What is the recommended resource for studying CBSE Class 11 Applied Maths Coordinate Geometry?
Can you explain the concept of Coordinate Geometry in CBSE Class 11 Applied Maths briefly?
Toprankers, launched in 2016, is India’s most preferred digital counselling & preparation platform for careers beyond engineering & medicine.
We envision to build awareness and increase the success rate for lucrative career options after 12th.
We offer best learning practices and end-to-end support to every student preparing for management, humanities, law, judiciary & design entrances.