Study Guide for Benchmark #1 Window of Opportunity: March 4-11
|
|
- Catherine Short
- 5 years ago
- Views:
Transcription
1 Study Guide for Benchmark #1 Window of Opportunity: March -11 Benchmark testing is the department s way of assuring that students have achieved minimum levels of computational skill. While partial credit is given on the other tests in this course, on the benchmark tests you are expected to demonstrate that you can do basic computations carefully and accurately. This benchmark covers skills that are considered prerequisite for this course, and computations that have been covered in the first two chapters of this course. To pass a benchmark test, you must get 17 (or more) of 0 points. If you pass on the first attempt, your score will be recorded as 100%. (So strive to pass on the first attempt...) If you do not pass the benchmark test on your first attempt, your score will initially be recorded as 0%. You can replace this 0% with a better grade by retaking the benchmark once or twice within the windowof-opportunity. You are encouraged to meet with either me or Ed to go over problems that are giving you difficulty. If you pass the Benchmark on a re-take, the score of 0% that was originally recorded will be changed to the average of your scores on your two or three attempts. If you re-take a benchmark but do not pass it within three attempts or by the due date, your score will be changed to the average of your scores together with a 0%. Each Benchmark grade will contribute 5% to your overall grade for the course. This test will have ten basic computational problems. You may not u use a calculator while you are working on the benchmark. If you pass the benchmark on your first attempt, I will record your grade as 100%. If you do not pass on your first attempt, you may meet with me or Ed to go over your mistakes and demonstrate that you have done some additional study. If you pass on a re-take, your grade will be recorded as the average of your scores on each attempt. If you do not pass the benchmark in three attempts or by March 11, your score will be recorded as the average of your scores together with 0. So the idea is to do as well as you can on your first attempt, and to make sure that you do pass by March 11. The first attempt will take place in class on March th. It will be the last 30 minutes of class. You will receive your exams back the following Tuesday. If you do not pass the first time, it will be on you to discuss with me when you will re-take the exam outside of class. If you do not then you will receive a score of 0% for the assessment. if you have an unexcused absence on the day of the in-class attempt on a benchmark assessment, you will not be allowed any additional attempts. This benchmark will have two problems from basic algebra, two from coordinate geometry, two from trigonometry, and four problems from symbolic computation of the derivative.
2 Basic Algebra ( problems) You should be able to demonstrate the following skills: Simplify arithmetic or algebraic expressions using correct order of operations and rules for working with exponents. Evaluate a given function, f(x), at particular values, such as x = 5, x = t + h, or x = g(t). Use rules of exponents to evaluate or simplify an algebraic equation. Remember: A negative exponent denotes a reciprocal, and a fractional exponent denotes a root. So what is 5 3? Calculate the sum or product of polynomials. Solve a linear equation for a specified value of x or y. Given an equation of the form y = f(x) = Ax n or y = f(x) = Ae bx, you should be able to take logs of both sides of the equation, and simplify the resulting expression. Coordinate Geometry ( problems) You should be able to demonstrate the following skills: Plot points in the coordinate plane using rectangular coordinates. Find the slope of a straight line given its graph, its algebraic expression, or a set of point which lie on the line. Use the slopes to determine whether two lines are parallel, perpendicular, or neither. Remember: Parallel lines have the same slope. If two lines are perpendicular, the product of their slopes will be 1. Find the equation of a line given two points, or a point and the slope of the line. Find the length and the midpoint of a line segment. Sketch the graph of a line given its equation, its slope and one point, or two points. You should know and be able to use formulas for area of a square, rectangle, triangle, and circle; volume of a rectangular box or right circular cylinder, perimeter of a polygon, and circumference of a circle. Trigonometry ( problems) You should be able to demonstrate the following skills: Use the Pythagorean Theorem to find the length of the third side of a right triangle, given the lengths of any two sides. Use the two standard triangles ( and ) to find the values of the six trigonometric relationships for the angles in the two standard triangles.
3 You should know the six trigonometric relationships: sine, cosine, tangent, cotangent, secant, and cosecant. Given a right triangle with lengths of any two of the sides indicated, you should be able to find the sine, cosine, or tangent of each of the angles. Given the sine, cosine, or tangent of an angle, you should be able to sketch a triangle and calculate the other trigonometric values of that angle. Convert between degrees and radians. In particular, you should know the radian measures for angles of 0, 30, 5, 60, 90, 180, 70, and 360. Use the unit circle to find the sine, cosine, or tangent of angles in the second, third, and fourth quadrants that are related to the angles in the two standard triangles. In particular, you should be able to find the sine, cosine or tangent of 0, 30, 5, 60, 90, 10, 135, 150, 180, 70, and 360. Symbolic computation of the Derivative ( problems - see Sections.3 and. of our text) You should be able to take the derivative of the following kinds of functions, where a, b, and c denote constants: Constant functions:f(x) = π, f(x) = 5,(or f(x) = any other constant) Linear functions: f(x) = ax + b (any linear function) Polynomial functions: f(x) = ax + bx + c (or any polynomial) Power functions: f(x) = ax n (any power function) The power could be negative, such as f(x) = a x = ax 1 Constant multiple rule: f(x) = c g(x) For example, f(x) = c (ax + bx + π) f(x) = b x (an exponential function) f(x) = e x (a special exponential function) Sum rule: functions formed by taking the sum of simpler functions For example: f(x) = x + x + ln()
4 Sample Questions for this Benchmark Be sure to review the sample questions from the Study Guide for the Quiz you took during the first week of class. In addition to those questions, the following questions are questions similar in nature to what you can expect. 1. Write the expression x 3 in the form x n.. Write an expression for the cube root of x 5 in the form x n. 3. Write the expression 1 x 3 in the form x n.. Write the expression x x 7 in the form x n. What do fractional exponents mean? What do negative exponents mean? 5. If g(x) = 3x, find an expression for g( 7). 6. If g(x) = 3x, find an expression for g(x + 5). 7. If g(x) = 3x, find an expression for g(π). 8. If g(x) = 3x, find an expression for g (cos (5)). 9. If g(x) = 3x, find an expression for g ( cos ( π )). Although you are not expected to evaluate cos(5) by hand, you should be able to evaluate the cosine or sine of 0, π 6, π, π 3, π, π, π without using a calculator. 10. Find the slope of the line which passes through the point (3, 5) and goes through the origin. 11. Find the equation of the line which passes through the point (3, 5) and goes through the origin. 1. Find the length of the line segment from the point (3, 5) to the origin. 13. Find the midpoint of the line segment from the point (3, 5) to the origin. 1. Find the slope of the line which passes through the points (3, 5) and ( 3, 8). 15. Find the equation of the line which passes through the points (3, 5) and ( 3, 8). 16. Find the length of the line segment from (3, 5) to ( 3, 8). 17. Find the midpoint of the line segment from (3, 5) to ( 3, 8). 18. Find the slope of the line which passes through the points (3, 5) and (3, ). 19. Find the equation of the line which passes through the points (3, 5) and (3, ). 0. Find the length of the line segment from (3, 5) to (3, ). 1. Find the midpoint of the line segment from (3, 5) to (3, ).. Does the line from (, 5) to (, 8) pass through the origin? How do you know?
5 3. Does the line from (3, 5) to ( 6, 10) pass through the origin? How do you know?. Find the equation of a line which passes through the point (3, 5), and is perpendicular to the line y = x. 5. Is the line y = 5x + [parallel to, perpendicular to, neither parallel nor perpendicular to] the line x + 5y = 0? Explain. 6. Is the line y = 5x + [parallel to, perpendicular to, neither parallel nor perpendicular to] the line 5y 10x = 0? How do you know? 7. Find an angle whose tangent is If sin(t) = a, find an expression for cos(t) in terms of a. Hint: Sketch a triangle which has an angle whose sine is a. 9. If sin(t) = a, find an expression for sec(t). 30. Evaluate (find the exact value of ) sin ( π ). (Remember: While taking the benchmark, you may not use a calculator. You should be able to answer questions like this using the unit circle and the two standard triangles.) 31. Evaluate cos ( π 3 ). 3. Evaluate tan ( π ). 33. Evaluate cos(π). 3. If an equilateral triangle has sides of length 3 units, what are the lengths of its altitude and its base? 35. If an equilateral triangle has sides of length 3 units, what is its area? 36. How many feet of fencing are needed to enclose a field which is 76 yards wide and 50 yards long? 37. A rectangular box has a volume of 600 cubic inches, and is 8 inches high. If the length is three times the width, what are the dimensions [length, width, height] of the box? 38. A rectangular box has a volume of 600 cubic inches, and is 8 inches high. If the length is three times the width, what is the surface area of the box? 39. What is the volume of a cylinder if its diameter and its height are both 3 inches? 0. What is the total surface area of a cylinder (including its top, bottom, and curved side) if its diameter and its height are both 3 inches? 1. Take the natural log of both sides of the equation y = 5e 3x, and simplify the resulting expression.. Use logs to transform the equation y = f(x) = 5x 3 to a linear equation. What is the slope of the resulting equation?
6 3. Use logs to transform the equation y = f(x) = 7x n to a linear equation. Is the resulting equation a semi-log equation or a log-log equation?. Consider the equation y = f(x) = 3e x. Transform this equation by taking the natural log on both sides of the equation. What is the slope of the transformed equation? 5. Find the derivative of the function y = f(x) = 3x Find the derivative of the function y = f(x) = 5x x Find the derivative of the function y = f(x) = 3x n 8. Find the derivative of the function y = f(x) = x 9. Find the derivative of the function y = f(x) = Find the derivative of the function y = f(x) = π 51. Find the derivative of the function y = f(x) = x 5. Find the derivative of the function y = f(x) = e x 53. Find the derivative of the function y = f(x) = 3 x + 5x 5. Find the derivative of the function y = f(x) = (5x x + 7) 55. Find the derivative of the function y = f(x) = 3x n + x 1 x Find the derivative of the function y = f(x) = x Find the derivative of the function y = f(x) = ln(5) 58. Find the derivative of the function y = f(x) = π x 59. Find the derivative of the function y = f(x) = x 3 x + 5x 60. Find the derivative of the function y = f(x) = 15e x 61. Find the derivative of the function y = f(x) = 3x x 15 x 6. Find the derivative of the function y = f(x) = 5x x Find the derivative of the function y = f(x) = 3x Find the derivative of the function y = f(x) = 65. Find the derivative of the function y = f(x) = 15(π x ) 66. Find the derivative of the function y = f(x) = πx 3 + x 67. Find the derivative of the function y = f(x) = 3 x + x Find the derivative of the function y = f(x) = e x + 7x 1 x
7 Answer Key for Benchmark Study Questions 1. x 3. x x 3. x 3 5. g( 7) = g(x + 5) = 3(x + 5) = 3x + 30x g(π) = 3π 8. g(cos(5)) = 3cos (5) 9. g ( cos ( π )) = 3 0 = m = y = 5 3 x = ( 3, 5 ) 1. m = = y = 1 x (3 ( 3) + (5 8) = 5 = 3 5 ( ) ( 3), 5+8 = ( 0, 13 ) 18. The slope is undefined because the line is vertical. 19. x = 3 0. (3 3) + (5 ( )) = 9 = 7 ( ) , 5+( ) = ( 3, 3 ). It does not because the slope of the line containing these two points is 3, so the function is decreasing and passes through points in the first quadrant. In order to pass through the origin, it would have to have a positive slope in order to pass through points in the first quadrant. 3. The slope of the line containing these points is 5 3 and the slope of the line from the origin to the point (3, 5) is also 5 3 (see question 10). So, this line does indeed pass through the origin.
8 . The line perpendicular to the line y = x has a slope of 1. So, we have y = x + b, and using the point (3, 5), we see that the equation we seek is y = x The equation x + 5y = 0 can be put into slope-intercept form to become y = 1 5x +. Since this line has a slope of 1 5 and the first line has a slope of 5, these lines are perpendicular. 6. The equation 5y 10x = 0 can be rewritten as y = x +. We have different slopes that are not negative reciprocals of each other, so the lines are neither parallel or perpendicular. 7. We know from our reference angles that tan ( π ) = 1. Since we want an angle whose tangent is 1, however, we need an angle in quadrant or. Since we are not asked for the arctangent, which would restrict the domain, both answers are necessary here and so the angles we want are π and 3π. 8. If we draw a right triangle, we see that sin(t) = a gives that the length of the opposite side from angle t is of length a as compared to the hypotenuse of length 1. If we apply the Pythagorean Theorem, we get that the length of the adjacent side is 1 a. So, cos(t) = 1 a. 9. Since sec(t) = 1 1 cos(t), we have that sec(t) =. 1 a 30. sin ( ) π = cos ( ) π 3 = 1 3. tan ( π ) = cos (π) = 1 3. The base is 3 units long. To find the length of the altitude, we need to set up a right triangle with the legs being half the base and the height being the altitude, and the hypotenuse as one of the sides of the equilateral triangle. We have to solve the Pythagorean Theorem to find the length of the other leg. 3 = a + 3 a = 9 9 a = 7 a = 3 3 ( 35. Using the base and altitude lengths from the past problem, we have that A = 1 ) (3) 3 3 = 9 3 square units. 36. The perimeter of the field is field is (76) + (50) = 5 yards. But, the problem asked for how many feet of fencing is required, so we need 3(5) = 756 feet of fencing.
9 37. The height is given the be 8 inches. The volume is 600 cubic inches, so the area of the base is = 75 square inches. Since length is three times the width, if the width is x inches, then the length is 3x inches and by solving A = 3x(x) = 75, we see that x = 5 and therefore the length is 15 inches and the width is 5 inches. 38. Using the dimensions we found in the last problem, the surface area is given by S = A B +P B h where A B is the area of the base and the perimeter of the base is given by P B. This gives S = 75 + (0)8 = 70 square inches 39. V = πr h We are given that the diameter is 3 inches, so the radius has a length of 3 inches. So, we have V = π ( ) 3 3 = 7 cubic inches. 0. S = πr + πrh. Using the dimensions from the last question, we have S = π ( 3 ) + π ( ) 3 (3) = 9π + 9π square inches. 1. We are working with y = f(x) = 5e 3x.. Here we are working with y = f(x) = 5x 3. y = 5e 3x ln(y) = ln(5e 3x ) ln(y) = ln(5) + ln(e 3x ) ln(y) = ln(5) + 3x y = 5x 3 ln(y) = ln(5x 3 ) ln(y) = ln(5) + ln(x 3 ) ln(y) = ln(5) + 3ln(x) The slope of this transformed linear equation is Here, we work on y = f(x) = 7x n. This is a log-log equation.. Here we are working on y = f(x) = 3e x. y = 7x n ln(y) = ln(7x n ) ln(y) = ln(7) + nln(x) y = 3e x ln(y) = ln(3e x ) ln(y) = ln(3) + ln(e x ) The slope of this transformed equation is. ln(y) = ln(3) + x
10 5. f (x) = 3 6. f (x) = 10x 7. f (x) = 3nx n 1 8. f (x) = x 9. f (x) = f (x) = f (x) = ln() x 5. f (x) = e x 53. f (x) = 3 + 0x 3 x 5. f (x) = 0x f (x) = 3nx n 1 + ln() x + 3 x 56. f (x) = 1 x 57. f (x) = f (x) = π x 59. f (x) = ln() x + 6 x 3 + 0x f (x) = 15e x 61. f (x) = x + 15 x 6. f (x) = 10x 63. f (x) = 5x 1 6. f (x) = f (x) = 15 ln(π)π x 66. f (x) = 3πx f (x) = ln(3) 3 x + 3x 68. f (x) = e x x
Math 121: Calculus 1 - Fall 2013/2014 Review of Precalculus Concepts
Introduction Math 121: Calculus 1 - Fall 201/2014 Review of Precalculus Concepts Welcome to Math 121 - Calculus 1, Fall 201/2014! This problems in this packet are designed to help you review the topics
More informationMath 121: Calculus 1 - Fall 2012/2013 Review of Precalculus Concepts
Introduction Math 11: Calculus 1 - Fall 01/01 Review of Precalculus Concepts Welcome to Math 11 - Calculus 1, Fall 01/01! This problems in this packet are designed to help you review the topics from Algebra
More informationA. Incorrect! For a point to lie on the unit circle, the sum of the squares of its coordinates must be equal to 1.
Algebra - Problem Drill 19: Basic Trigonometry - Right Triangle No. 1 of 10 1. Which of the following points lies on the unit circle? (A) 1, 1 (B) 1, (C) (D) (E), 3, 3, For a point to lie on the unit circle,
More informationMath 121: Calculus 1 - Winter 2012/2013 Review of Precalculus Concepts
Introduction Math 11: Calculus 1 - Winter 01/01 Review of Precalculus Concepts Welcome to Math 11 - Calculus 1, Winter 01/01! This problems in this packet are designed to help you review the topics from
More informationFunctions and their Graphs
Chapter One Due Monday, December 12 Functions and their Graphs Functions Domain and Range Composition and Inverses Calculator Input and Output Transformations Quadratics Functions A function yields a specific
More informationNAME: DATE: CLASS: AP CALCULUS AB SUMMER MATH 2018
NAME: DATE: CLASS: AP CALCULUS AB SUMMER MATH 2018 A] Refer to your pre-calculus notebook, the internet, or the sheets/links provided for assistance. B] Do not wait until the last minute to complete this
More informationAP CALCULUS SUMMER WORKSHEET
AP CALCULUS SUMMER WORKSHEET DUE: First Day of School, 2011 Complete this assignment at your leisure during the summer. I strongly recommend you complete a little each week. It is designed to help you
More informationPart I: SCIENTIFIC CALCULATOR REQUIRED. 1. [6 points] Compute each number rounded to 3 decimal places. Please double check your answer.
Chapter 1 Sample Pretest Part I: SCIENTIFIC CALCULATOR REQUIRED 1. [6 points] Compute each number rounded to 3 decimal places. Please double check your answer. 3 2+3 π2 +7 (a) (b) π 1.3+ 7 Part II: NO
More informationSpring 06/MAT 140/Worksheet 1 Name: Show all your work.
Spring 06/MAT 140/Worksheet 1 Name: Show all your work. 1. (4pts) Write two examples of each kind of number: natural integer rational irrational 2. (12pts) Simplify: ( a) 3 4 2 + 4 2 ) = 3 b) 3 20 7 15
More informationThe American School of Marrakesh. AP Calculus AB Summer Preparation Packet
The American School of Marrakesh AP Calculus AB Summer Preparation Packet Summer 2016 SKILLS NEEDED FOR CALCULUS I. Algebra: *A. Exponents (operations with integer, fractional, and negative exponents)
More informationTrigonometry.notebook. March 16, Trigonometry. hypotenuse opposite. Recall: adjacent
Trigonometry Recall: hypotenuse opposite adjacent 1 There are 3 other ratios: the reciprocals of sine, cosine and tangent. Secant: Cosecant: (cosec θ) Cotangent: 2 Example: Determine the value of x. a)
More informationSection 6.2 Trigonometric Functions: Unit Circle Approach
Section. Trigonometric Functions: Unit Circle Approach The unit circle is a circle of radius centered at the origin. If we have an angle in standard position superimposed on the unit circle, the terminal
More informationPrentice Hall Geometry (c) 2007 correlated to American Diploma Project, High School Math Benchmarks
I1.1. Add, subtract, multiply and divide integers, fractions and decimals. I1.2. Calculate and apply ratios, proportions, rates and percentages to solve problems. I1.3. Use the correct order of operations
More informationLone Star College-CyFair Formula Sheet
Lone Star College-CyFair Formula Sheet The following formulas are critical for success in the indicated course. Student CANNOT bring these formulas on a formula sheet or card to tests and instructors MUST
More informationMath Level 2. Mathematics Level 2
Math Reference Information THE FOLLOWING INFORMATION IS FOR YOUR REFERENCE IN ANSWERING SOME OF THE SAMPLE QUESTIONS. THIS INFORMATION IS ALSO PROVIDED ON THE ACTUAL SUBJECT TEST IN MATHEMATICS LEVEL.
More informationREQUIRED MATHEMATICAL SKILLS FOR ENTERING CADETS
REQUIRED MATHEMATICAL SKILLS FOR ENTERING CADETS The Department of Applied Mathematics administers a Math Placement test to assess fundamental skills in mathematics that are necessary to begin the study
More information4 The Trigonometric Functions
Mathematics Learning Centre, University of Sydney 8 The Trigonometric Functions The definitions in the previous section apply to between 0 and, since the angles in a right angle triangle can never be greater
More informationSolutions to Final Review Sheet. The Math 5a final exam will be Tuesday, May 1 from 9:15 am 12:15 p.m.
Math 5a Solutions to Final Review Sheet The Math 5a final exam will be Tuesday, May 1 from 9:15 am 1:15 p.m. Location: Gerstenzang 1 The final exam is cumulative (i.e., it will cover all the material we
More informationMath Review for AP Calculus
Math Review for AP Calculus This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet
More informationMath Prep for Statics
Math Prep for Statics This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular
More informationWelcome to AP Calculus!!!
Welcome to AP Calculus!!! In preparation for next year, you need to complete this summer packet. This packet reviews & expands upon the concepts you studied in Algebra II and Pre-calculus. Make sure you
More information( ) 2 + 2x 3! ( x x ) 2
Review for The Final Math 195 1. Rewrite as a single simplified fraction: 1. Rewrite as a single simplified fraction:. + 1 + + 1! 3. Rewrite as a single simplified fraction:! 4! 4 + 3 3 + + 5! 3 3! 4!
More informationCopyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 2/10
Prep for Calculus This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (281 topics + 125 additional topics) Real
More informationCourse Catalog. Pre-calculus Glynlyon, Inc.
Course Catalog Pre-calculus 2016 Glynlyon, Inc. Table of Contents COURSE OVERVIEW... 1 UNIT 1: RELATIONS AND FUNCTIONS... 1 UNIT 2: FUNCTIONS... 1 UNIT 3: TRIGONOMETRIC FUNCTIONS... 2 UNIT 4: CIRCULAR
More information1. Trigonometry.notebook. September 29, Trigonometry. hypotenuse opposite. Recall: adjacent
Trigonometry Recall: hypotenuse opposite adjacent 1 There are 3 other ratios: the reciprocals of sine, cosine and tangent. Secant: Cosecant: (cosec θ) Cotangent: 2 Example: Determine the value of x. a)
More informationCollege Algebra with Trigonometry
College Algebra with Trigonometry This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (556 topics + 614 additional
More informationCoach Stones Expanded Standard Pre-Calculus Algorithm Packet Page 1 Section: P.1 Algebraic Expressions, Mathematical Models and Real Numbers
Coach Stones Expanded Standard Pre-Calculus Algorithm Packet Page 1 Section: P.1 Algebraic Expressions, Mathematical Models and Real Numbers CLASSIFICATIONS OF NUMBERS NATURAL NUMBERS = N = {1,2,3,4,...}
More informationDirections: This is a final exam review which covers all of the topics of the course. Please use this as a guide to assist you in your studies.
MATH 1113 Precalculus FINAL EXAM REVIEW irections: This is a final exam review which covers all of the topics of the course. Please use this as a guide to assist you in your studies. Question: 1 QI: 758
More informationCourse Outline and Objectives. MA 1453 Precalculus with Graphing Calculators
Effective Fall 2011 Course Outline and Objectives MA 1453 Precalculus with Graphing Calculators TEXT: Precalculus, 5 th Edition, by Faires and DeFranza ISBN 978-0-8400-6862-0 NOTE: A graphing calculator
More informationMATH 32 FALL 2012 FINAL EXAM - PRACTICE EXAM SOLUTIONS
MATH 3 FALL 0 FINAL EXAM - PRACTICE EXAM SOLUTIONS () You cut a slice from a circular pizza (centered at the origin) with radius 6 along radii at angles 4 and 3 with the positive horizontal axis. (a) (3
More informationAP Calculus Summer Assignment Summer 2017 Expectations for Summer Assignment on the first day of the school year.
Summer 07 Expectations for Summer Assignment This packet is to be submitted to your Calculus BC teacher on the first day of the school year. All work must be shown in the packet OR on separate paper attached
More informationCurriculum Catalog
2017-2018 Curriculum Catalog 2017 Glynlyon, Inc. Table of Contents PRE-CALCULUS COURSE OVERVIEW...1 UNIT 1: RELATIONS AND FUNCTIONS... 1 UNIT 2: FUNCTIONS... 1 UNIT 3: TRIGONOMETRIC FUNCTIONS... 2 UNIT
More informationPrecalculus Review. Functions to KNOW! 1. Polynomial Functions. Types: General form Generic Graph and unique properties. Constants. Linear.
Precalculus Review Functions to KNOW! 1. Polynomial Functions Types: General form Generic Graph and unique properties Constants Linear Quadratic Cubic Generalizations for Polynomial Functions - The domain
More informationPART ONE: Solve algebraically and check. Be sure to show all work.
NAME AP CALCULUS BC SUMMER ASSIGNMENT 2017 DIRECTIONS: Each part must be completed separately on looseleaf. All work should be shown and done in a neat and precise manner. Any questions pertaining to the
More informationAlgebra 2. Curriculum (384 topics additional topics)
Algebra 2 This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs.
More information= = =
. D - To evaluate the expression, we can regroup the numbers and the powers of ten, multiply, and adjust the decimal and exponent to put the answer in correct scientific notation format: 5 0 0 7 = 5 0
More informationNew Rochelle High School Geometry Summer Assignment
NAME - New Rochelle High School Geometry Summer Assignment To all Geometry students, This assignment will help you refresh some of the necessary math skills you will need to be successful in Geometry and
More informationAlgebra II/Geometry Curriculum Guide Dunmore School District Dunmore, PA
Algebra II/Geometry Dunmore School District Dunmore, PA Algebra II/Geometry Prerequisite: Successful completion of Algebra 1 Part 2 K Algebra II/Geometry is intended for students who have successfully
More informationThe Other Trigonometric
The Other Trigonometric Functions By: OpenStaxCollege A wheelchair ramp that meets the standards of the Americans with Disabilities Act must make an angle with the ground whose tangent is or less, regardless
More informationCorrelation of 2012 Texas Essential Knowledge and Skills (TEKS) for Algebra I and Geometry to Moving with Math SUMS Moving with Math SUMS Algebra 1
Correlation of 2012 Texas Essential Knowledge and Skills (TEKS) for Algebra I and Geometry to Moving with Math SUMS Moving with Math SUMS Algebra 1 ALGEBRA I A.1 Mathematical process standards. The student
More informationPre AP Algebra. Mathematics Standards of Learning Curriculum Framework 2009: Pre AP Algebra
Pre AP Algebra Mathematics Standards of Learning Curriculum Framework 2009: Pre AP Algebra 1 The content of the mathematics standards is intended to support the following five goals for students: becoming
More informationCorrelation of WNCP Curriculum to Pearson Foundations and Pre-calculus Mathematics 10
Measurement General Outcome: Develop spatial sense and proportional reasoning. 1. Solve problems that involve linear measurement, using: SI and imperial units of measure estimation strategies measurement
More informationMathematics, Algebra, and Geometry
Mathematics, Algebra, and Geometry by Satya http://www.thesatya.com/ Contents 1 Algebra 1 1.1 Logarithms............................................ 1. Complex numbers........................................
More informationPreCalculus Honors Curriculum Pacing Guide First Half of Semester
Unit 1 Introduction to Trigonometry (9 days) First Half of PC.FT.1 PC.FT.2 PC.FT.2a PC.FT.2b PC.FT.3 PC.FT.4 PC.FT.8 PC.GCI.5 Understand that the radian measure of an angle is the length of the arc on
More informationPreCalculus. Curriculum (447 topics additional topics)
PreCalculus This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs.
More informationMonroe Township High School Mathematics Department
To: AP Calculus AB Re: Summer Project 017 Date: June 017 Monroe Township High School Mathematics Department To help begin your study of Calculus, you will be required to complete a review project this
More informationOne of the powerful themes in trigonometry is that the entire subject emanates from a very simple idea: locating a point on the unit circle.
2.24 Tanz and the Reciprocals Derivatives of Other Trigonometric Functions One of the powerful themes in trigonometry is that the entire subject emanates from a very simple idea: locating a point on the
More informationPrecalculus Summer Assignment 2015
Precalculus Summer Assignment 2015 The following packet contains topics and definitions that you will be required to know in order to succeed in CP Pre-calculus this year. You are advised to be familiar
More informationPrentice Hall: Algebra 2 with Trigonometry 2006 Correlated to: California Mathematics Content Standards for Trigonometry (Grades 9-12)
California Mathematics Content Standards for Trigonometry (Grades 9-12) Trigonometry uses the techniques that students have previously learned from the study of algebra and geometry. The trigonometric
More informationDear Future CALCULUS Student,
Dear Future CALCULUS Student, I am looking forward to teaching the AP Calculus AB class this coming year and hope that you are looking forward to the class as well. Here a few things you need to know prior
More information2014 Summer Review for Students Entering Algebra 2. TI-84 Plus Graphing Calculator is required for this course.
1. Solving Linear Equations 2. Solving Linear Systems of Equations 3. Multiplying Polynomials and Solving Quadratics 4. Writing the Equation of a Line 5. Laws of Exponents and Scientific Notation 6. Solving
More informationEXPLORE Score 9 th Grade. English College Algebra Mathematics Social Sciences Reading
Working with Your Curriculum in Mathematics and the ACT College & Career Readiness Standards T h i s d o c u m e n t p r o v i d e s y o u a n e x a m p l e o f h o w y o u r c u r r i c u l u m i n m
More informationSTAAR STANDARDS ALGEBRA I ALGEBRA II GEOMETRY
STANDARDS ALGEBRA I ALGEBRA II GEOMETRY STANDARDS ALGEBRA I TEKS Snapshot Algebra I (New TEKS 2015-16) Mathematical Process Standards A.1 Mathematical process standards. The student uses mathematical processes
More information9-12 Mathematics Vertical Alignment ( )
Algebra I Algebra II Geometry Pre- Calculus U1: translate between words and algebra -add and subtract real numbers -multiply and divide real numbers -evaluate containing exponents -evaluate containing
More informationDear Future CALCULUS Student,
Dear Future CALCULUS Student, I am looking forward to teaching the AP Calculus AB class this coming year and hope that you are looking forward to the class as well. Here a few things you need to know prior
More informationDESK Secondary Math II
Mathematical Practices The Standards for Mathematical Practice in Secondary Mathematics I describe mathematical habits of mind that teachers should seek to develop in their students. Students become mathematically
More informationAP CALCULUS SUMMER WORKSHEET
AP CALCULUS SUMMER WORKSHEET DUE: First Day of School Aug. 19, 2010 Complete this assignment at your leisure during the summer. It is designed to help you become more comfortable with your graphing calculator,
More informationCrash Course in Trigonometry
Crash Course in Trigonometry Dr. Don Spickler September 5, 003 Contents 1 Trigonometric Functions 1 1.1 Introduction.................................... 1 1. Right Triangle Trigonometry...........................
More informationMLC Practice Final Exam
Name: Section: Recitation/Instructor: INSTRUCTIONS Fill in your name, etc. on this first page. Without fully opening the exam, check that you have pages through. Show all your work on the standard response
More informationAP Calculus AB Summer Math Packet
Name Date Section AP Calculus AB Summer Math Packet This assignment is to be done at you leisure during the summer. It is meant to help you practice mathematical skills necessary to be successful in Calculus
More informationA) 13 B) 9 C) 22 D) log 9
Math 70 Exam 2 Review Name Be sure to complete these problems before the review session. Participation in our review session will count as a quiz grade. Please bring any questions you have ready to ask!
More informationSummer Work Packet for MPH Math Classes
Summer Work Packet for MPH Math Classes Students going into AP Calculus AB Sept. 018 Name: This packet is designed to help students stay current with their math skills. Each math class expects a certain
More informationFall 09/MAT 140/Worksheet 1 Name: Show all your work. 1. (6pts) Simplify and write the answer so all exponents are positive:
Fall 09/MAT 140/Worksheet 1 Name: Show all your work. 1. (6pts) Simplify and write the answer so all exponents are positive: a) (x 3 y 6 ) 3 x 4 y 5 = b) 4x 2 (3y) 2 (6x 3 y 4 ) 2 = 2. (2pts) Convert to
More informationGeometry Honors Summer Packet
Geometry Honors Summer Packet Hello Student, First off, welcome to Geometry Honors! In the fall, we will embark on an eciting mission together to eplore the area (no pun intended) of geometry. This packet
More informationMath Prep for College Physics
Math Prep for College Physics This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (190 topics + 52 additional
More informationMath 005A Prerequisite Material Answer Key
Math 005A Prerequisite Material Answer Key 1. a) P = 4s (definition of perimeter and square) b) P = l + w (definition of perimeter and rectangle) c) P = a + b + c (definition of perimeter and triangle)
More informationSUMMER MATH PACKET. Geometry A COURSE 227
SUMMER MATH PACKET Geometry A COURSE 7 MATH SUMMER PACKET INSTRUCTIONS Attached you will find a packet of exciting math problems for your enjoyment over the summer. The purpose of the summer packet is
More informationCHAPTER 6. Section Two angles are supplementary. 2. Two angles are complementary if the sum of their measures is 90 radians
SECTION 6-5 CHAPTER 6 Section 6. Two angles are complementary if the sum of their measures is 90 radians. Two angles are supplementary if the sum of their measures is 80 ( radians).. A central angle of
More informationSummer Review for Students Entering AP Calculus AB
Summer Review for Students Entering AP Calculus AB Class: Date: AP Calculus AB Summer Packet Please show all work in the spaces provided The answers are provided at the end of the packet Algebraic Manipulation
More informationVirginia Unit-Specific Learning Pathways. Grades 6-Algebra I: Standards of Learning
BUI L T F O VIR R G INIA 2014 2015 Virginia -Specific Learning Pathways Grades 6-Algebra I: Standards of Learning Table of Contents Grade 6...3 Grade 7...6 Grade 8...9 Algebra I... 11 Grade 6 Virginia
More informationMilford Public Schools Curriculum. Department: Mathematics Course Name: Precalculus Level 1
Milford Public Schools Curriculum Department: Mathematics Course Name: Precalculus Level 1 UNIT 1 Unit Description: Students will construct polynomial graphs with zeros and end behavior, and apply limit
More informationWAYNESBORO AREA SCHOOL DISTRICT CURRICULUM PRE-CALCULUS (June 2014)
WAYNESBORO AREA SCHOOL DISTRICT CURRICULUM PRE-CALCULUS (June 2014) COURSE NAME: Pre-Calculus UNIT: Chapter 1 NO. OF DAYS: KEY LEARNING (S): UNIT ESSENTIAL QUESTIONS: What methods are used to solve equations
More informationMath 370 Exam 2 Review Name
Math 70 Exam 2 Review Name Be sure to complete these problems before the review session. 10 of these questions will count as a quiz in Learning Catalytics. Round 1 will be individual. Round 2 will be in
More informationAlbertson AP Calculus AB AP CALCULUS AB SUMMER PACKET DUE DATE: The beginning of class on the last class day of the first week of school.
Albertson AP Calculus AB Name AP CALCULUS AB SUMMER PACKET 2015 DUE DATE: The beginning of class on the last class day of the first week of school. This assignment is to be done at you leisure during the
More informationBemidji Area Schools Outcomes in Mathematics Analysis 1. Based on Minnesota Academic Standards in Mathematics (2007) Page 1 of 5
Understand the concept of function, and identify important features of functions and other relations using symbolic and graphical methods where appropriate. 9..1.1 9..1. 9..1.3 9..1.4 9..1.5 9..1.6 9..1.7
More informationCalculus: Early Transcendental Functions Lecture Notes for Calculus 101. Feras Awad Mahmoud
Calculus: Early Transcendental Functions Lecture Notes for Calculus 101 Feras Awad Mahmoud Last Updated: August 2, 2012 1 2 Feras Awad Mahmoud Department of Basic Sciences Philadelphia University JORDAN
More informationName: for students entering. Algebra 2/Trig* For the following courses: AAF, Honors Algebra 2, Algebra 2
Name: Richard Montgomery High School Department of Mathematics Summer Math Packet for students entering Algebra 2/Trig* For the following courses: AAF, Honors Algebra 2, Algebra 2 (Please go the RM website
More informationJUST THE MATHS SLIDES NUMBER 3.1. TRIGONOMETRY 1 (Angles & trigonometric functions) A.J.Hobson
JUST THE MATHS SLIDES NUMBER 3.1 TRIGONOMETRY 1 (Angles & trigonometric functions) by A.J.Hobson 3.1.1 Introduction 3.1.2 Angular measure 3.1.3 Trigonometric functions UNIT 3.1 - TRIGONOMETRY 1 - ANGLES
More informationNumbers Content Points. Reference sheet (1 pt. each) 1-7 Linear Equations (1 pt. each) / Factoring (2 pt. each) /28
Summer Packet 2015 Your summer packet will be a major test grade for the first nine weeks. It is due the first day of school. You must show all necessary solutions. You will be tested on ALL material;
More informationAP CALCULUS Summer Assignment 2014
Name AP CALCULUS Summer Assignment 014 Welcome to AP Calculus. In order to complete the curriculum before the AP Exam in May, it is necessary to do some preparatory work this summer. The following assignment
More informationLyman Memorial High School. CP Pre-Calculus Prerequisite Packet. Name:
Lyman Memorial High School CP Pre-Calculus Prerequisite Packet 018 Name: Dear Pre-Calculus Student, Within this packet you will find mathematical concepts and skills covered in Algebra I, II and Geometry.
More informationMath Section 4.3 Unit Circle Trigonometry
Math 10 - Section 4. Unit Circle Trigonometry An angle is in standard position if its vertex is at the origin and its initial side is along the positive x axis. Positive angles are measured counterclockwise
More informationChapter 2 Polynomial and Rational Functions
SECTION.1 Linear and Quadratic Functions Chapter Polynomial and Rational Functions Section.1: Linear and Quadratic Functions Linear Functions Quadratic Functions Linear Functions Definition of a Linear
More informationFall 2013 Hour Exam 2 11/08/13 Time Limit: 50 Minutes
Math 8 Fall Hour Exam /8/ Time Limit: 5 Minutes Name (Print): This exam contains 9 pages (including this cover page) and 7 problems. Check to see if any pages are missing. Enter all requested information
More informationMath Exam 02 Review
Math 10350 Exam 02 Review 1. A differentiable function g(t) is such that g(2) = 2, g (2) = 1, g (2) = 1/2. (a) If p(t) = g(t)e t2 find p (2) and p (2). (Ans: p (2) = 7e 4 ; p (2) = 28.5e 4 ) (b) If f(t)
More informationCandidates are expected to have available a calculator. Only division by (x + a) or (x a) will be required.
Revision Checklist Unit C2: Core Mathematics 2 Unit description Algebra and functions; coordinate geometry in the (x, y) plane; sequences and series; trigonometry; exponentials and logarithms; differentiation;
More informationIntegrated Math II. IM2.1.2 Interpret given situations as functions in graphs, formulas, and words.
Standard 1: Algebra and Functions Students graph linear inequalities in two variables and quadratics. They model data with linear equations. IM2.1.1 Graph a linear inequality in two variables. IM2.1.2
More informationFor all questions, answer choice E. NOTA" means none of the above answers is correct.
For all questions, answer choice " means none of the above answers is correct. 1. The sum of the integers 1 through n can be modeled by a quadratic polynomial. What is the product of the non-zero coefficients
More informationBrunswick School Department Honors Geometry Unit 6: Right Triangles and Trigonometry
Understandings Questions Knowledge Vocabulary Skills Right triangles have many real-world applications. What is a right triangle? How to find the geometric mean of two numbers? What is the Pythagorean
More informationREVIEW PACKET. Classical Academy High School Algebra 2 Readiness Assessment
Classical Academy High School Algebra 2 Readiness Assessment REVIEW PACKET - Spring 2012 Student Name: _ Algebra 2 Readiness Assessment REVIEW PACKET Math Success is the Goal! In working with our Classical
More informationContent Guidelines Overview
Content Guidelines Overview The Pearson Video Challenge is open to all students, but all video submissions must relate to set of predetermined curriculum areas and topics. In the following pages the selected
More informationb = 2, c = 3, we get x = 0.3 for the positive root. Ans. (D) x 2-2x - 8 < 0, or (x - 4)(x + 2) < 0, Therefore -2 < x < 4 Ans. (C)
SAT II - Math Level 2 Test #02 Solution 1. The positive zero of y = x 2 + 2x is, to the nearest tenth, equal to (A) 0.8 (B) 0.7 + 1.1i (C) 0.7 (D) 0.3 (E) 2.2 ± Using Quadratic formula, x =, with a = 1,
More informationMIDTERM 2 REVIEW: ADDITIONAL PROBLEMS. 1 2 x + 1. y = + 1 = x 1/ = 1. y = 1 2 x 3/2 = 1. into this equation would have then given. y 1.
MIDTERM 2 REVIEW: ADDITIONAL PROBLEMS ) If x + y =, find y. IMPLICIT DIFFERENTIATION Solution. Taking the derivative (with respect to x) of both sides of the given equation, we find that 2 x + 2 y y =
More informationMATH II CCR MATH STANDARDS
RELATIONSHIPS BETWEEN QUANTITIES M.2HS.1 M.2HS.2 M.2HS.3 M.2HS.4 M.2HS.5 M.2HS.6 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents
More informationSummer Packet Greetings Future AP Calculus Scholar,
Summer Packet 2017 Greetings Future AP Calculus Scholar, I am excited about the work that we will do together during the 2016-17 school year. I do not yet know what your math capability is, but I can assure
More informationAlgebra III INSTRUCTIONAL PACING GUIDE (Days Based on 90 minutes)
EA, IA, PC-1. Connect algebra and trigonometry with other branches of mathematics. EA, IA, PC-1.7 G-1. G-1.8 G-1.9 Understand how to represent algebraic and trigonometric relationships by using tools such
More informationOverall Description of Course Trigonometry is a College Preparatory level course.
Radnor High School Course Syllabus Modified 9/1/2011 Trigonometry 444 Credits: 1 Grades: 11-12 Unweighted Prerequisite: Length: Year Algebra 2 Format: Meets Daily or teacher recommendation Overall Description
More information(b) x = (d) x = (b) x = e (d) x = e4 2 ln(3) 2 x x. is. (b) 2 x, x 0. (d) x 2, x 0
1. Solve the equation 3 4x+5 = 6 for x. ln(6)/ ln(3) 5 (a) x = 4 ln(3) ln(6)/ ln(3) 5 (c) x = 4 ln(3)/ ln(6) 5 (e) x = 4. Solve the equation e x 1 = 1 for x. (b) x = (d) x = ln(5)/ ln(3) 6 4 ln(6) 5/ ln(3)
More informationSection 6.2 Notes Page Trigonometric Functions; Unit Circle Approach
Section Notes Page Trigonometric Functions; Unit Circle Approach A unit circle is a circle centered at the origin with a radius of Its equation is x y = as shown in the drawing below Here the letter t
More informationFUNCTIONS AND MODELS
1 FUNCTIONS AND MODELS FUNCTIONS AND MODELS 1.6 Inverse Functions and Logarithms In this section, we will learn about: Inverse functions and logarithms. INVERSE FUNCTIONS The table gives data from an experiment
More information