Analytic Geometry Grade 10 Notes

[Do Kieu]

Itcovers some important topics such as midpoints and distance, parallel and perpendicular lines on the coordinate plane, dividing line segments, distance between the line and a point, and so on. The study of analytic geometry is important as it gives the knowledge for the next level of mathematics. It is the traditional way of learning the logical thinking and the problem solving skills. In this article, let us discuss the terms used in the analytic geometry, formulas, Cartesian plane, analytic geometry in three dimensions, its applications, and some solved problems.

Analytic geometry is that branch of Algebra in which the position of the point on the plane can be located using an ordered pair of numbers called as Coordinates. This is also called coordinate geometry or the Cartesian geometry. Analytic geometry is a contradiction to the synthetic geometry, where there is no use of coordinates or formulas. It is considered axiom or assumptions, to solve the problems. But in analytic geometry, it defines the geometrical objects using the local coordinates. It also uses algebra to define this geometry.

To understand how analytic geometry is important and useful, First, We need to learn what a plane is? If a flat surface goes on infinitely in both the directions, it is called a Plane. So, if you find any point on this plane, it is easy to locate it using Analytic Geometry. You just need to know the coordinates of the point in X and Y plane.

As there are several boxes in every column and rows, but only one box has the point x, and we can find its location by locating the intersection of row and column of that box. There are different types of coordinates in analytical geometry. Some of them are as follows:

The most well-known coordinate system is the Cartesian coordinate to use, where every point has an x-coordinate and y-coordinate expressing its horizontal position, and vertical position respectively. They are usually addressed as an ordered pair and denoted as (x, y). We can also use this system for three-dimensional geometry, where every point is represented by an ordered triple of coordinates (x, y, z) in Euclidean space.

In the case of cylindrical coordinates, all the points are represented by their height, radius from z-axis and the angle projected on the xy-plane with respect to the horizontal axis. The height, radius and the angle are denoted by h, r and θ, respectively.

In spherical coordinates, the point in space is denoted by its distance from the origin ( ρ), the angle projected on the xy-plane with respect to the horizontal axis (θ), and another angle with respect to the z-axis (φ).

To locate a point: We need two numbers to locate a plane in the order of writing the location of X-axis first and Y-axis next. Both will tell the single and unique position on the plane. You need to compulsorily follow the order of the points on the plane i.e., the x coordinate is always the first one from the pair. (x, y).

Using the Cartesian coordinates, we can define the equation of a straight lines, equation of planes, squares and most frequently in the three dimensional geometry. The main function of the analytic geometry is that it defines and represents the various geometrical shapes in the numerical way. It also extracts the numerical information from the shapes.

In three-dimensional space, we consider three mutually perpendicular lines intersecting in a point O. these lines are designated coordinate axes, starting from 0, and identical number scales are set up on each of them.

Analytic geometry is widely used in the fields such as Engineering and Physics. Also, it is widely used in the fields such as space science, rocket science, aviation, space flights and so on. Analytical geometry has made many things possible like the following:

CALCULATOR: You are required to have a graphing calculator. The instructor will support the TI series: specifically TI-83, TI-84. There will be some quizzes and parts of exams that the student is expected to complete without the use of a calculator.

CONTENT: Continuation of MAC 2311. Logarithmic, Exponential, hyperbolic, and inverse trigonometric functions, techniques of integration, partial fractions, area, trapezoid and Simpson's rules, volume, work; analytic geometry; Taylor approximations; sequences and series; polar representation of complex numbers. This is a General Education course.

CLASS STRUCTURE: The class will be mostly run in a lecture style format though the instructor encourages discussions and questions concerning the material. Some days will be used for collaborative efforts. Please feel free to come to office hours if you have additional questions about the homework.

ATTENDANCE POLICY: Regular attendance is expected. If a student misses a class meeting it is his/her responsibility to obtain the class notes either from another student or from the instructor during regularly scheduled office hours. However, the latter usually means the student will be given the sections that were covered. If a student misses 4 classes, the instructor has the right to drop the student's course grade by one letter grade. If a student misses 8 classes, the instructor has the right to drop the student's course grade by two letter grades, etc. All exams will be taken as scheduled, unless prior arrangementsare made with at least 48 hours of advance notice. I, and only I, have the right to agree to giving a makeup exam.

HOMEWORK: There is a link on the webpage for the list of HW problems. At the beginning of the semester each student will be assigned a card (e.g. King of hearts). At the beginning of almost every class I will be randomly selecting 5-7 cards and will collect HW from those 5-7 students. The HW will be collected, graded, and returned. Sometimes HW will simply be checked for completion.

EXAM SCHEDULE: There will be many quizzes (announced or unannounced), three tests, and a final examination. The three tests will take place during the regurlarly scheduled class time on the following dates unless otherwise noted. The final exam will also be scheduled as follows.

DateDayEvent September 19th Thursday Test 1 October 22nd Tuesday Test 2 November 21st Thursday Test 3 December 10th Tuesday 10:30am-1:00pmFinal ExamEach test/exam will be cummulative and knowledge of previous material is essential. The quizzes will cover material since the previous quiz. This does include the possibility of problems on the quiz covering topics that were assigned in the HW due that day.I will try to be as straightforward as possible with regards to the material covered over the quizzes, tests, and exam.

EVALUATION: Throughout the course the student will have opportunities to gain and lose points; losing means a student might earn negative points. The most common examples of gaining points (but not limited to) are through the homeworks, quizzes, three tests, extra-credit problems, class participation and attendance, and a final exam. The most common examples of losing points (but not limited to) are not taking a quiz or test, not turning in a project, poor class participation, or an unsatisfactory attendance record. At the end of the semester if the student's (net) point total is greater than or equal to 90% of the total possible number of points, then the student will have earned an A. The rest of the grades are as follows 80%-90% B, 70%-80% C, 60%-70% D, below 60% F.

For a general sense of the course (this is an approximation): each test will be worth 16%, the final exam 30%, attendance and participation 7%, quizzes 10%, HW 5%. However, this assumes that the student has attempted all of the HW assignments. The percentage for HW is variable depending on how much a student does. If a student has a poor HW record, then HW will be worth up to 14%, with the other percentages dropped appropriately. The same goes for a student's attendance record.The official gradebook will be kept by the instructor. Canvas will not be used for offical grade-keeping.

POLICY ON ACCOMMODATIONS: In compliance with the Americans with Disabilities Act Amendments Act (ADAAA), students who require reasonable accommodations due to a disability to properly execute coursework must register with Student Accessibility Services (SAS) and follow all SAS procedures. SAS has offices across three of FAUs campuses -- Boca Raton, SU 131 (561-297-3880); in Davie, LA 131 (954-236-1222); in Jupiter and all Northern Campuses, SR 111F (561-799-8585). Disability services are available for students on all campuses. For more information, please visit SAS website at Counseling and Psychological Services (CAPS) Center: Life as a university student can be challenging physically, mentally and emotionally. Students who find stress negatively affecting their ability to achieve academic or personal goals may wish to consider utilizing FAUs Counseling and Psychological Services (CAPS) Center. CAPS provides FAU students a range of services individual counseling, support meetings, and psychiatric services, to name a few offered to help improve and maintain emotional well-being. For more information, go to CODE OF ACADEMIC INTEGRITY POLICY STATEMENT:Students at Florida Atlantic University are expected to maintain the highest ethical standards. Academic dishonesty is considered a serious breach of these ethical standards, because it interferes with the university mission to provide a high quality education in which no student enjoys an unfair advantage over any other. Academic dishonesty is also destructive of the university community, which is grounded in a system of mutual trust and places high value on personal integrity and individual responsibility. Harsh penalties are associated with academic dishonesty. For more information, see University Regulation 4.001 and the WHC Academic Honor Code at -code.php.Collaboration and the Honor Code: You are expected to adhere to the Honor Code (see HC Honor Code and FAU Honor Code).DISCLAIMER: The instructor reserves the right to change/alter/add/delete any statement from this syllabus in hopes of creating a more enjoyable/equitable course.

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