Name Summer Assignment for College Credit Math Courses
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1 Name Summer Assignment for College Credit Math Courses To: All students enrolled in Pre-AP PreCalculus and Dual Credit PreCalculus at El Campo High School College math classes utilizes skills and concepts you learned in previous math courses such as solving equations, working with algebraic expressions, and factoring. If you are unable to apply these skills, this course will be difficult. Therefore, this summer assignment is a review of previously learned concepts you need in order to be successful in college math. This assignment is due on the first day of school and will count as one daily grade. Be sure to show your work on every problem in the space provided, write neatly, and circle your final answer. In addition, you will be tested on the topics covered in this packet during the second week of school. This test will be a major grade. Before the assessment, you will have the opportunity to ask questions about the summer assignment in class. Below are website resources and a reference sheet that have full instructions on the reviewed skills in this assignment. If you are unsure how to attempt these problems, please consult the resources. If you have any questions regarding this packet, please dhamman@ecisd.org or msandoval@ecisd.org.. RESOURCES This is a free online tutorial video series that includes over 30 full algebra lessons for students and teachers. This site offers lessons and worksheets on many algebra concepts. Free SAT, ACT AP prep as well as video instruction in Algebra, Geometry, Trig/PreCalc, and Calculus Helps to understand basic math and algebra, as well as advanced math topics like calculus and statistics. This site provides detailed solutions for actual math textbook homework problems in many popular textbooks. Grades 6 through Calculus. (free trial). Interactive Mathematics provides free, online math explanations and examples ranging in topics from basic algebra to advanced calculus. Free SAT/ACT Prep. Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. Math planet is an online community where one can study math for free. This site offers fun and challenging lessons and activities for students in high school, including resources in algebra, geometry, and statistics and materials to use with computer programs, such as Java and the geometer s Sketchpad. All sites provide FREE SAT prep available to students. Purplemath's algebra lessons are written with the student in mind. These lessons emphasize the practicalities rather than the technicalities, demonstrating dependable techniques, warning of likely "trick" questions, and pointing out common mistakes. Free resource for math review material from Algebra to Differential Equations! The perfect study site for high school, college students and adult learners. Get help to do your homework, refresh your memory, prepare for a test, etc.
2 REFERENCE SHEET Distance Formula: d Midpoint Formula: ( x, y) Slope Formula: Quadratic Formula: Standard form of a line: x x y x x 1 y1 y, 1 1 y m Ax + By = C y x b x y x Quadratic Standard form: A x + Bx + C = b 4ac a equilateral triangle = (1/4) (3) a triangle given SAS = (1/) a b sin C triangle given a,b,c = [s(s-a)(s-b)(s-c)] when s = (a+b+c)/ (Heron's formula) regular polygon = (1/) n sin(360 /n) S when n = # of sides and S = length from center to a corner Volumes cube = a 3 rectangular prism = a b c Slope Intercept form: y = mx + b irregular prism = b h Point-slope form: y y 1 = m(x x 1 ) Pythagorean Theorem: Applications involving distance (d), speed/rate (r), and time (t). d rt a b c cylinder = b h = r h pyramid = (1/3) b h cone = (1/3) b h = 1/3 sphere = (4/3) r 3 r h Areas ellipsoid = (4/3) pi r 1 r r 3 square = a rectangle = ab parallelogram = bh trapezoid = h/ (b 1 + b ) Surface Areas cube = 6 a prism: (lateral area) = perimeter(b) L circle = pi r ellipse = pi r 1 r (total area) = perimeter(b) L + b sphere = 4 r triangle = (1/) b h
3 Name DUAL CREDIT PRECALCULUS AND PRE-AP PRECALCULUS SUMMER ASSIGNMENT Complete the following. Show work in a clear manner. Clearly indicate your final answer. Have this assignment completed and ready to turn in on the first day of school. Identify the domain and range. Tell whether the relation is a function. 1. (-1, 5), (-3, ), (, 0), (1, ). (-4, 3), (-4, -1), (-, 4), (0, ) Graph the following functions on the graph at the end of this paper. Clearly label x and y axis, any intercepts, and any minimum or maximum. 3. y = x 4 4. y = x 5. f(x) = 3 6. x = 7 7. y = x y = (x + 1) 4 9. y = x x + 4, if x < f(x) = { x + 9, if x 1 x +, if x > f(x) = { x +, if x 1 Evaluate the function for the given value of x. 1. f(x) = 3x 11; f(0) 13. f(x) = x 4; f(1) 14. f(x) = 6 x; f( 5)
4 Evaluate the function for the given value of x. x + 1, if x > 1 f(x) = { x, if x 1 3x +, if x < 5 g(x) = { x, if x g(5) 16. g( ) 17. f(3) Simplify x x 4 y a 8 b 5 3 3a b 4. ( x3 y x (y z 4 ) ) i 1 i
5 Simplify the following exponential expressions. 7. 4a 3 b 3a 4 b 3 8. x 5 x x 0 y z 3 4 Evaluate the following logarithms. 30. log log log 5 1 Solve for x. 33. log x + 1 log 16 = log x+ = ( 1 7 )x = 7 x 9 Determine the slope of a line that goes through the two given points. 36. (1, 5), (-3, 4) 37. (5, -), (5, -4) Write the equation of the line that passes through the given two points. Write your answer in point-slope form and slope-intercept form. 38. (, 5), (4, -1) 39. (-, 1), (4, 7)
6 Use slope intercept form to write the following equations. 40. A line perpendicular to y = x+4 and passing through (6., -). 5 Identify the parent function, sketch the graph and identify any transformations. 41. f(x) = x g(x) = x h(x) = x Factor completely the following. 44. x + x x + 6x x 8x x 3 x 9x x x 4 16x + 64
7 Solve the following equations x = 9x 51. (x + 1)(x 5) = x 16x 7 = x + 7 = x x+ x 1 = x x+5 Solve the following systems of equations. 55. y = 4 3x 6y= y=x x+5y=0 57. { x y + z = 4x y + z = 3 x 3y + z = 7
8 Let f(x) = x 1 and g(x) = x. Perform the indicated operation and state the domain. 58. f(g(x)) 59. g(f(x)) 60. f(f(x)) Simplify the following rational expressions. 61. y 81 y x 3 4x x+3 x +6x x +x 3 x+ x +x x x 0 x+6 5x+15 x x x 1 3x x Write a function H(t) that represents the distance between a runner and the finish line, in meters, after t seconds if he starts 10 kilometers from the finish line and runs at a rate of 5 meters per second.
9 68. Rupert s Rent-a-Car will rent you a car for $55 per day with no mileage charge. Mark s Mobilesfor-Rent will rent you a car for $34 per day plus 15 cents per mile beyond the first 100 miles. For what number of miles is the total cost of a one-day rental the same for both rental companies? 69. Chad is standing on the roof of his apartment building when he throws a ball straight upward over the edge. The ball is 55 feet above the ground when he lets it go. The quadratic equation that models the path of the ball is p(t) = 16t + 4t How long does it take for the ball to hit the ground? 70. The chart below show the first, second, and third place finishes, and the total points earned by each of three schools competing in a track meet. How many points is a first place finish in an event worth? School 1 st nd 3 rd Total ECHS BCHS LCHS
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