[CLA notes : Pay close attentions to the hatch marks on the graph.]

[CLA notes 2 : It is possible to guess the answers but the usual practice of the day was for the students to submit the work needed to arrive at the answer as well as the answers. Try to formally write out all the steps needed to arrive definitively at the answer.]
[CLA notes : Every bit of information reveals something important about the two circles. Be careful and be thorough in examination of the problem and expect the work involved to be made up of
multiple parts. ] [CLA notes : Another straight forward problem. If you consider the properties involved, you can
easily note that there is a simple way to solve this problem. ] [CLA note : A relatively straight forward problem that can be solved in multiple ways. It would be
good to practice all the different ways.] [CLA note : If you remember the distance formula and the Pythagorean Theorem , this problem is
solvable. Remember to give as much details to the shape of the path of the point P ] When most people talk about the test for college admission, they usually mention SAT general test or ACT. After that, they may mention AP exams. Seldom have you heard people talk about SAT Subject tests, yet many universities have departments that require at least one SAT subject test to be submitted when applying. So, why does any department even requires a SAT subject test scores when there are AP exams?
There are crucial differences between AP and SAT subject test which make it necessary for any college applicants to carefully consider how they will approach them, both. AP exam is very demanding and students typically get only one shot at the test. The students can try multiple times at a SAT subject test, and unlike AP, they have much more freedom to choose when to take the subject test. Furthermore, a student need not be enrolled in an AP class to adequately prepare for a SAT subject test, thus it offers a great alternative to those who seek to limit the number of AP courses they will take, in order to not overburden themselves. Unlike AP exams, SAT subject test mostly requires knowledge obtainable by the end of Junior years for most high school students. This is important for college application as most students will be taking the AP courses during their Senior years, thus they won’t be able to use the AP Exam scores to bolster their college application. SAT subject tests may be the best way to demonstrate a student’s college readiness to an admission officer. It also is worth noticing the difference in the frequency of the perfect scores. The AP exam is in 5 points maximum scale, and in many tests, more than 20% of the students report a “perfect” 5/5 in the AP exam. In contrast, SAT subject test is in 800 points maximum scale, and in the majority of the tests, less than 5% of the students get the 800/800. In subjects like Literature and Chemistry, it might be harder to get an 800 in SAT subject test compared to 5 in AP exam. The college admission officers know well what the distributions of the scores are, thus will not consider 5/5 from AP in the same light as 800/800 in SAT subject tests. In many ways, SAT subject tests are just as useful in preparing for college as AP courses. AP courses expose students to materials normally taught at the college. Since students have to learn many year worths of high school materials as well as college materials in a single year, the students are not expected to know everything there is in an AP Exam. Recent released information says a student can get 5/5 mark in AP while receiving less than 70% of the maximum possible scores in an AP Exam(If more details are desired, click here). To get an 800 in any SAT Subject Tests, you need at to receive at least 80% of maximum RAW score in any test, and this is a score where you get 1/4 of points deducted for wrong guess, thus you usually have to answer more than 90% of the questions correctly. If AP exams test how much college materials a student already knows, SAT subject tests examine how completely a student knows the high school materials. To further illustrate the difference between these two test achievements, consider the following. A student with AP score of 5 may impress his/her college professor with knowing something already, but may also disappoint them by not knowing what the college professor assumed everyone should already know before arriving at his class. A student with SAT subject score of 800 might not know the college subject material in advance, but will not disappoint the professors by failing to answer something professors consider to be fundamental. Someone with AP Score of 5 may fluctuate wildly in test scores for the college course of similar content, while someone with SAT subject test score of 800 will likely perform steadily and adequately, provided that both students put efforts similar to other students in the same course. In college, more advanced the course becomes, more important the knowledge of the fundamentals. Even if SAT Subject Test score didn’t help a student enough to get the student get admitted into a college program of their choice, it will help them graduate from whatever college program they enter. At the minimum, preparing for SAT Subject tests will minimize a student’s need to take a “remedial class” after entering a college, thus improve his chance of graduating within 4 years, saving great amount of money for everyone. On top of everything said above, SAT Subject Test is a great way to bolster one’s college application, and also a way to cover up for a mistake. For example, if someone scored mere 3/5 on AP Chemistry, he can try to cover it up with a score of 780/800 on SAT chemistry subject test. Also, consider following scenario. Put yourself as someone in charge of admission for an Electrical Engineering Department. On one hand, you have a straight A student with 2200 on SAT General Test, has 5/5 in AP Calculus BC, but no other AP scores since he is taking them in Senior years, and also no other SAT subject Test scores. On the other hand, you have a student who has high school grades distributed between B+ to A+, with 1800 on SAT General ( 510 on Reading and Writing, 780 on Math ), but has 750 or above in SAT Subject tests in Math Level II, Chemistry, Physics, Biology, and World History , and 5/5 on AP Physics B ( the non-calculus one) and a 5/5 on AP Calculus AB during his junior year . The first student did what is expected of a typical student, but his application just doesn’t have that “engineering flavor”. The second student must be a math/science geek whose difficulty with English interfered with his grades, and this probably have denied him a chance to take better AP courses as well. Despite that 400 point difference in SAT General Test, and some deficit in GPA, an admission officer for an Engineering department will take a very good look at the second students, and may often pick him instead of the first student. The comparative ease at which a student may prepare and take SAT Subject test makes it a crucial part of the plan for the college admission process. It is a test that is easy to take, and one that can be taken often. While it is a hard test to receive a perfect score, very good score will bolster any student’s college application. Even if the student don’t end up with score that may help them in college application, the work that goes into preparing for these tests will help them during their college life and probably long afterward as well. Therefore, every student should try to master at least one of these SAT subject tests every year after reaching 9th grade. If they do, they will be rewarded well, sooner or later. [CLA note : A good problem to refresh your memory about angles, triangles, circles, and chords.
Try following link : http://www.clisnotes.com/math/geometry/circles/arcs-and-chords ] [CLA note : As many would have guessed, this is a counting problems about choosing three dots.
Think very carefully about how many lines you can draw on the picture that will pass through at least three dots.] |
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