Geometry B. The University of Texas at Austin Continuing & Innovative Education K 16 Education Center 1

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1 Geometry B Credit By Exam This Credit By Exam can help you prepare for the exam by giving you an idea of what you need to study, review, and learn. To succeed, you should be thoroughly familiar with the subject matter before you attempt to take the exam. Every question that appears on the Credit by Exam/Examination for Acceleration is grounded in the knowledge and skills statements and student expectations within the state-mandated standards, the Texas Essential Knowledge and Skills (TEKS). It should be noted that an exam will not test every student expectation. However, it is important that students study and know the entire scope of the TEKS so that they can develop a complete understanding of the content. The s are a global exam grounded in the TEKS and are not designed to be a final exam for the University of Texas high school courses. You can view the TEKS for this exam online at Since questions are not taken from any one source, you can prepare by reviewing any of the state-adopted textbooks. About the exam The Credit By Exam consists of 50 multiple-choice questions that are worth 2 points each. You will be allowed 3 hours to take the exam and you will be allowed to use a graphing calculator. You will also be provided the Formula Sheet found in this. Materials Provided For paper-based exams, a formula sheet will be provided with your test. For computer-based exams, the proctor will provide to you a paper copy of the formula sheet immediately prior to testing. You will return the sheet after the exam. An example of the formula sheet follows. 1

2 Formula Sheet GEO B Perimeter: P = 2l + 2w or P = 2(l + w) Circumference: C = 2πr or C = πd Pythagorean Theorem: a 2 + b 2 = c 2 Pi (π) 3.14 or 22 7 Distance Formula: d = ( x 2 x 1 ) 2 + ( y 2 y 1 ) 2 Slope of a line: m = y y 2 1 x 2 x 1 Midpoint Formula: x 1 + x 2 2, y 1 + y 2 2 Quadratic Formula: x = b ± b2 4ac 2a ( ) Standard Form of an Equation: Ax + By Point-Slope Form of an Equation: y y 1 = m x x 1 Simple Interest Formula: I = prt Slope-Intercept Form of an Equation: y = mx + b When the vertex of an angle is outside of the circle, the measure of the angle formed is half of the difference of the intercepted arcs Special Circle Angles Vertical angles and their intercepted arcs: half of the sum of the arc measures is the measure of the angle Area Surface Area Rectangle: A = lw or A = bh Cube: SA = 6s 2 Triangle: A = 1 2 bh Cylinder (lateral): SA = 2πrh Trapezoid: A = 1 2 (b 1 + b 2 )h Cylinder (total): SA = 2πrh + 2πr 2 or SA = 2πr(h + r) Regular Polygon: A = 1 2 ap Cone (lateral): SA = πrl Circle: A = πr 2 Cone (total): SA = πrl + πr 2 or SA = π(l + r) Sector of a Circle: A = Volume Prism or cylinder: V = Bh Pyramid or cone: V = 1 3 Bh Sphere: V = 4 3 πr 3 m of arc 360 πr 2 Sphere: SA = 4πr 2 Trigonometry (Right Triangles) opposite side sin( B) = hypotenuse adjacent side cos( B) = hypotenuse opposite side tan( B) = adjacent side 2

3 GEO B Concepts and Objectives The bulleted list and sample questions below may not refer to all the material that will be in the exam. This list only provides additional information for some of the student expectations tested in the Geometry, Second Semester Credit by Exam. Ultimately, you should use the TEKS to guide your exam preparation. The second semester of Geometry focuses on dilations, similarity, similar triangle postulates, using similar triangles, the Pythagorean Theorem, special right triangles, right triangle trigonometry, properties of quadrilaterals, properties of circles, areas of plane figures, and three dimensional figures. For the exam, you should be able to use dilations to enlarge or reduce figures; create an accurate scale drawing of a figure given the original figure drawn on a grid and a scale factor; determine whether or not two figures are similar; use theorems and postulates to prove that two figures are similar; use a scale factor to determine the lengths of corresponding sides and the angle measures of corresponding vertices of a similar figure; use a proportional relationship to determine the length of a corresponding side of a similar figure; find the distance between two points and their midpoint, in two and three dimensions; use Pythagorean triplets to determine the missing lengths of the sides of a right triangle; apply the Pythagorean Theorem to solve problems; use what you know about right triangles and right triangles to determine the missing lengths of the sides of a right triangle; use the sine, cosine, and tangent ratios to determine the missing angles or the missing lengths of the sides of a right triangles; use the arithmetic Triangle Inequality Theorem to find a range of lengths for the missing side of a trangle; use the properties of quadrilaterals to calculate the lengths of missing parts of the figure; use the properties of quadrilaterals to sketch figures on a coordinate plane; use the properties of quadrilaterals to state relationships between the angles of a figure; use the properties of special parallelograms to solve problems; write the equation of a circle drawn on a coordinate plane, given the center and the radius, or given the endpoints of the diameter; identify tangent circles, secants, chords, tangent lines, radii, diameters, and external tangents of a drawing; use the properties of tangent lines, chords, secants, arcs, and central angles to solve problems; 3

4 GEO B find the circumference, area, sector area, and arc lengths of circles; find the areas of parallelograms, triangles, trapezoids, regular polygons, circles, and semicircles; use area formulas to find missing information about parallelograms, triangles, trapezoids, regular polygons, and circles; define the number of edges, vertices and faces for the following three dimensional figures: prism, cylinder, pyramid, and cone; describe the difference between right and oblique figures; describe the shape of the base and the plane sections created when prisms, cylinders, pyramids, and cones are cut parallel the base or perpendicular to the base; calculate the lateral area, surface area, and volume of prisms, cylinders, pyramids, cones, and spheres; use formulas for lateral area, surface area, and volume to calculate missing lengths associated with prisms, cylinders, pyramids, cones, and spheres; find the arithmetic and geometric mean of two numbers; construct top, side, and front views of specific figures; understand the relationship between the net of an object and the surface area of the object; use nets to construct three dimensional objects; find the distance between two sets of three-dimensional coordinates; identify a set of coordinates that represents a point lying on a sphere; write the equation of a sphere given the endpoints of the diameter; and, apply the relationships you know about similar figures to lengths, perimeters, areas, and volumes of three dimensional figures. Sample Questions These sample questions will give you a better idea of the types of questions you can expect on the Credit By Exam. These questions are provided to illustrate the format of the exam; they are not a duplicate of the actual exam. In order to be successful on the exam, you must study and review all of the concepts listed above. 4

5 GEO B Multiple-Choice This part of the sample exam contains 5 multiple-choice questions. Circle the letter of the correct response to each of the following questions. 1. Given that CD EF, what is the length of AE? A 3 B 9 C 11 D Given the center of a circle is at (2, 4) and one of the points on the circle is (5, 8), what is the length of the diameter of the circle? A 12 B 10 C 6 D 5 3. What is the equation of a circle with center of (4, 6) and radius of 5? A x 2 + y 2 = 25 B (x + 4) 2 + (y 6) 2 = 5 C (x 4) 2 + (y + 6) 2 = 5 D (x 4) 2 + (y + 6) 2 = The area of a decagon is 200. If the side of a decagon is 4, what is the length of its apothem? A 5 B 10 C 15 5

6 D 20 GEO B 5. What is the lateral area of a cylinder with height of 8 and base radius of 5? A 80π B 130π C 160π D 260π Answer Key Item Number Correct Answer 1 D 2 B 3 D 4 B 5 A 6