Dear Student: Congratulations on being placed in the GSE Accelerated Analytic Geometry B/Advanced Algebra class for the 0-09 school year! This is a fast-paced and rigorous college-preparatory math course that includes substantial work with the skills and concepts presented in each lesson. The course emphasizes more complex applications and challenging exercises than students might be exposed to in the traditional high school Geometry and Advanced Algebra courses. You will be required to think, to apply what you know in new and different situations, and to use problem-solving skills. The course is one in which the concepts from the beginning lessons build upon one another and are essential to the mastery of the material that will be encountered later in the semester. In order to be successful, you must have strong foundational math skills and be consistent with your homework and study habits. It is our hope that you will not only learn the major concepts of this course but that you will also become more independent in your learning and study habits, skills that you will need to be successful in future honorslevel and AP courses. It is your responsibility to be the best student you can be! Because of the pace of our curriculum, we will not be able to spend time in class reviewing skills that were presented in the pre-requisite courses. This packet represents a brief review of some of those topics that will be an important foundation for this course. This assignment will not be graded. You are responsible for this material. A basic skills test will be given the first week of school. Prerequisite Skills Basic math skills (order of operation, fractions, decimals, percent) Linear functions and their characteristics,write and graph the function Linear equations Shape, domain, range, equation and characteristics of parent functions Operations with polynomial expressions Factoring polynomial expressions Properties of exponents Geometry of circles (properties and theorems) Similarity and Congruency Area, Surface Area and Volume of plain figures and solids If you have any difficulties with this assignment, please find additional problems for practice and mastery. It is highly recommended that all problems are answered without the use of a calculator. I. Simplifying expression with exponents.. a a a. (( ) ). g h ( g ). m m. ap r k ap 6. k a b 7. 7 a b. r s r s b a 9. a b a 0. 7x 6 x x a. x a 0 m x y z. x y z
II. Solving Equations.. 7 ( x ) x 9. x x. Solve for y: 6(x + ) = (y + ) III. Evaluate the function. 6. f ( x) x x ; f ( ) 7. x g ( x) ; g ( ) x IV. Simplify the expression.. (9x ) ( x) 9. ( x )( x ) 0. ( x ) V. Radicals: Simplify the following.. 7.. 60.. 6 6. 0 7. b 0b 90b. a b cd VI. Solve the inequalities and sketch the solutions on a number line. 9. x orx x 0. ( x ) 7 and x (x ). ( x ) VII. Functions and Graphs.. Graph the parent functions: (a) linear (b) exponential (b = ). For each function below: graph, state x and y intercepts, domain, and range (a) y x (b) y x (c) y x. For the function y x, (a) State the y-intercept (b) State the end behavior of the graph. What are the domain and range for the function f ( x) 6 x 6. Write the function modeled by this table: x f ( x) 7
7. Describe the transformation from the parent f x ( x) graph represented by f ( x) x. What is the average rate of change over the interval [, ] for each equation? What type of model is represented by each equation: (a) f ( x) x (b) f ( x) x VIII. Writing equation in point-slope form using the given information 9. A line passing through (6,) with slope. 0. A line passing through (-,) and (7,). A line perpendicular to the graph of x y and passes through (-,0). A line that is perpendicular to f ( x) x and passes through the point (, 7).. A line that is parallel to f ( x) x and passes through the point (,-).. A horizontal line that contains the point (, 7).. A vertical line that contains the point (-, -). 6. A line with that contains the point (, ) and has an x-intercept of -. 7. A line with a slope of and a y-intercept of. 6 IX. Graph to solve the system y x. y x X. Solve the system algebraically 0. x y 6 6x 9y 9. x y 7 x y. x 6y 7x 0y. Write the pair of inequalities shown in the graph.
XI. Geometry. Find the missing sides (given the right triangle). In the circle, solve for x and y. AD and FB pass circle. through the center of the. Given the following triangle, identify (a) sin B (b) cos A (c) tan B 6. Find the area of the triangle 7. A sphere has volume equal to 6 cubic feet. If the length of the radius of this sphere is tripled, then what is the volume of this new sphere?. A cylinder with a height of 6 meters has a volume of 9 cm. Find the diameter of one of the bases of the cylinder. 9. The base of a pyramid is a square with side lengths of ft. If the height of the pyramid is ft, then find its volume. 60. What is the volume of a right circular cone whose base has a diameter of and whose height is 6? 6. M is the midpoint of RS. Given the coordinates of R (-, 0) and M (, ), what are the coordinates of S? 6. What is the distance from E (9, -) to F (-, -)? 6. Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints A (,-) and B (6,). 6. What is the area of triangle ABC? 6. What is the perimeter of triangle ABC? (round answer to nearest whole unit)
XII. Modeling: 66. Carla and Ken are both electricians. Carla charge $ for a service call, plus $ per hour. Ken charges $ for a service call, plus $0 per hour. If they work the same number of hours and are paid the same amount of money, how many hours did they work? 67. Eva has earned points prior to the 00-point semester test in her math class. To get an A for the semester, she must earn at least 60 points. What is the minimum number of points she can score on the test and still get an A. 6. The perimeter of a football field is 00 feet. The length of the field is 0 feet less than times the width. What are the dimensions of the field? mv 69. The tension caused by a wave moving along a string is found using the formula T. If m is the mass of L the string in grams, L is the length of the string in centimeters, and v is the velocity of the wave in centimeters per second, what is the unit of the tension of the string, T? 70. Write the expression for the area of a rectangle if its width is 6 units less than its length. 7. Kevin ran at a rate of km/h. Convert his speed to meters per minute. 7. The ratio of students to faculty members in a high school is :. If there are 0 faculty members, how many students are there? 7. The area of a rectangle was sq. cm. Every dimension was multiplied by a scale factor and the new area was.7 sq. cm. What was the scale factor? 7. A tree casts a shadow. ft long at the same time that a nearby -foot-tall pole casts a shadow.7 feet long. Write and solve a proportion to find the height of the tree. 7. Bruce owns a business that produces widgets. He must bring in more in revenue than he pays out in costs in order to turn a profit. It costs $0 in labor and materials to make each of his widgets. His rent each month for his factory is $000. He sells each widget for $. How many widgets does Bruce need to sell each month to make the minimum profit? 76. A shop sells one-pound bags of peanuts for $ each and three-pound bags for $ each. If 9 bags are purchased for a total cost of $6, how many three-pound bags were purchased? 77. Jasmine and her sister are saving to buy MP players. Jasmine has $0 and plans to save $0 per week. Her sister has $0 and plans to save $7 per week. How many weeks will it take for Jasmine to have more money saved than her sister? 7. The average of Cindy s three test scores must be greater than 70 for her to pass the class. She got a 76 on the last test. She got the same score on her first and second test. She passed the class. What scores could she have gotten on the first two tests?
Answers:. a.. g h. 6. r 0 x y. a. z 7. b. s r s r 9. m. b a a 0.. 0 = 0 (infinitely many solutions).. y x 7 6. f ( ) 7. f ( ). 9x 0 x 9. x x 0. x 0x. 7. 6. x.. 6 6. 7. b 0. a bd abc 9. x or x 0. x and x. x. (a) (b). (a) x-int. (-/, 0); y-int. (0, ); Domain: x ; Range: y (b) x-int. (., 0); y-int. (0. -); Domain: x ; Range: y (, ) (c) x-int. none; y-int. 0, ; Domain: x ; Range: y (, ). (a) y-int. (0, -) (b) x, y ; x, y. Domain: x ; Range: y 6. f ( x) x 7. unit up and units right. (a) rate of change =, exponential growth; (b) rate of change =, linear 9. 9 y x 0. y x. y x. y x. y x 7. y 7. x 6. 6 y x 7. y x 6
. 9. 0. no solution. 7,. y x y x. b. x =, y =. (a) sin B ; (b) cos A ; (c) tan B 6. Area sin0 units 7. R ft, R new 9 ft, V new 97 ft. Diameter = cm 9. V 676 ft 60. V 9 units 6. M (,0) 6. diameter 0 6 6. y x 6. A units 6. P units 66. +x = + 0x, x = hours 67. 77 points 6. width = 60 feet; length = 60 feet gramcm 69. sec 60 70. A l( l 6) 7. m min 7. 6 7. 00 7. 6. ft 7. x 67 76. -pound bags =, -pound bags = 6 77. w 0 7. x 67