Math Review for Test 3

Transcription

1 Math Review for Test 3 When: Friday, December 3. Where: In class What is covered: Chapters 5,, 8, and 9 (sections that were covered in class, i.e..4, 8.5 are NOT included) What to bring: Picture ID, scantron form (same form that you use for poppers), pencil, eraser, calculator (optional). Test 3 is a multiple choice test. How to study: Study the class notes, solve all the problems we solved in class. Go over the homework problems. If you have time, I also suggest solving the eercises in the review part -at the end of the chapters. Below I provided some practice problems for you. This is not a complete list, studying only these problems is not enough! What is covered Chapter 5 You need to be able to: You need to know how to work with proportions, how to find an unknown in a proportion, how to find the geometric mean of two numbers. If I say these 3 sides (or angles) are in the ratio 2:3:4, then the sides are 2, 3 and 4. Use the given information to solve for. You need to know the definition of similarity, how to write down similarity, how to get a proportion from a given similarity. If two triangles are similar, and I give some of the sides, you need to be able to find the missing sides by using the proportion. You need to know the reasons to give to prove two triangles are similar (AA, SSS, SAS). You can use CSSTP or CASTC as a reason to prove that corresponding sides of similar triangles are proportional, or corresponding angles are congruent. You have to know the Pythagorean theorem and how to use it to find the missing sides. Also, know how to understand if a given triangle is right, acute or obtuse (check a 2 + b 2 >, <, or = c 2 ). If I give you a right triangle with an altitude (of the hypotenuse), you need to be able to use the geometric mean to find the altitude, or the legs. (Altitude is the geometric mean of the parts you get, leg is the geometric mean of the part net to it and all of the hypotenuse) Know how to find the missing sides of the special triangles ( and ). Chapter Terms: Circle, radius, perimeter, chord, arc, minor arc, major arc, central angle, inscribed angle, tangent, point of tangency, secant. Facts: The measure of the whole circle is 30 0, of the semicircle is The measure of the central angle is same as the measure of the arc you get from its arms, and the measure of the inscribed angle is half of the measure of the arc.

2 Know the formulas about the line segments when 2 chords intersect inside the circle (part*part) or when 2 secants intersect outside the circle (whole*eterior), or when a secant and a tangent intersects. Know the fact: if you draw two tangent lines to a circle from a fied eterior point, then the line segments you get are congruent. You need to be able to: Find the angle formed by two intersecting lines (2 secants, 2 chords, a tangent and a secant ). Chapter 8 You need to be able to: Find the area and perimeter of a triangle, rectangle, square, regular polygon, apothem, radius and length of a side of a regular polygon using or right triangle, circumference and area of a circle. Find the area of a shaded region by adding or subtracting areas of two polygons. Chapter 9 You need to be able to: Find the lateral area, surface area, and volume of a prism, pyramid, right cylinder, right circular cone and sphere. Also how to find the slant height in case of pyramids and cones. 1. Find the eact value of Find the eact value of Find the eact value of

3 4. Find the eact value of Find the eact value of. 45 X 45. Find the eact value of Find the eact value of. X 8 8. Find the area of the figure below.

4 Find the area of the shaded area Find the area of a trapezoid with bases of 7 and 12 and a height of Find the apothem, perimeter and area of a regular heagon whose sides are Find the apothem, perimeter and area of an equilateral triangle with sides of Find the perimeter and the area of a square whose length of apothem is 5.

5 12. Find the value of in the circle below Find the value of Find the AE given DE = 5, BE = 1 and CE = Find the value of in circle C below. C 3 7

6 1. Given PR = 5, PS = 2, find SQ. 17. Given: MNP ~ QRS, m M = 5, m R =82, MN = 9, QR =, RS = 7, MP = 12 Find: m N, m P, NP, QS 18. If mab = 85 and mbc = 30, then find mbe, mcd, mead. A B T C E D

7 19. Find, y and z: z y Find and y if ST is parallel to UV. R S 10 T U y V 21. The measures of two complementary angles are in ratio 1:5. Find the measure of each angle. 22. Reduce to its simplest form: 12 20, 5 3, 24.

8 23. Solve for : = Determine the type of triangle if the lengths of it s sides are: 4, 5, 7;,7,8; 9, 12, 15; 3,4, Find the Lateral Area, Total Area, and Volume of the cylinder with radius 5 and altitude. 2. Find the slant height of the cone with the radius 3 and the altitude. 27. Suppose that the perimeter of a quadrilateral is 70 and the lengths of the sides are in ratio 2:3:4:5. Find the measure of each side. 28. Find the apothem, perimeter and area of an equilateral triangle with sides of 18.

9 29. Find the slant height, and the volume of the regular square pyramid if each side of the base is 8m and altitude is 5m. 5m 8m 8m 30. Find the eact area of the shaded region (equilateral triangle is inscribed in a circle of radius ). 31. Find the length of a 0 72 arc in a circle whose circumference is 45 π.