MR. LUPINACCI'S CLASSROOM

FINAL EXAM INFO:

 

 

Regarding the final exam:  You should review all of your notes from second semester. The exam is only based on second semester. However, there is some basic information that carries over from first semester that it is assumed you will remember (isosceles triangles, straight angles, etc.)

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This PDF file contains some practice problems: 

(The numbering is out of order - don't ask, just go with it.) 

 

The solutions are linked below.

 

 

Problem #8, 9, and 12 are a little difficult, so I probably won't ask anything that difficult on the final, but they are worth studying because they have valuable information that I am likely to use in a similar, but easier, problem. 

 

 

I want to be REALLY CLEAR about something:  The problems on the review sheets are NOT the only problems you need to know. For example, we did a bunch of problems based on the Power Theorems (p. 464).  There aren't any of those problems on the review sheet, but OF COURSE you should study those kinds of problems. The best thing to do is to look through your notes and look at the kinds of problems we did in class - that will be a good indication of the kinds of problems to expect on the final.  

 

Here are important concepts:

 

-  know how to factor and solve quadratic equations using the Zero Product Property (for example:   x^2 - 13x + 40 = 0).

 

-  know special right triangle relationships.

-  be able to solve triangles using SohCahToa. 

 

-  be able to draw accurate diagrams based on descriptions.

 

-  understand what it means for a polygon to be inscribed or circumscribed with a circle.

 

-  know the area formulas for polygons, including regular polygons and how to find the apothem.

 

-  know the angle bisector theorem.

 

-  be able to simplify radical expressions, rationalize denominators, and add, subtract, multiply and divide radicals.

 

-  know isosceles and equilateral triangles.

 

-  use the circle theorems to find missing angles, arcs and lengths of segments (chords, secants, and tangents). 

 

-  use the geometric mean to solve sides of triangles. 

 

-  use the geometric means proportions to prove the Pythagorean Theorem - this is simply an algebraic proof and you don't have to justify your statements with reasons. A version of this proof can be found on p. 359, where you would need to state the equivalent of statements 4 - 8, but NOT the reasons. We did a similar version in class, that proof should be in your notes. THIS IS NOT Euclid's proof , which we demonstrated in class. 

 

-  in one or two sentences, you should be able to describe the basic definition of Pi in terms of circumference and diameter. 

 

-  you MUST know the formulas for the VOLUME of a PYRAMID, a CYLINDER, and a CONE. 

 

There will NOT be any proofs on the final exam (with the exception of the algebraic proof of the Pythagorean Theorem described above).

 

While this exam focuses on second semester, it will be a good idea to review some of the particularly important definitions from first semester, such as perpendicular bisectors, as they may be included in problems from this semester. Included in this are the basic properties of the important quadrilaterals that we have studied: parallelogram, rectangle, rhombus, square, kite, trapezoid. You do not need to memorize any of these things, but you should re-familiarize yourself with these basic shapes and how they work. 

 

Also, questions from the tests that you took from the semester are a good review, as well as looking over homework problems that we spent time on in class. Along with the background information that is necessary to solve these problems, you should also review the strategies that were developed to solve the problems. 

 

OK, have fun.