STAAR/EOC Comprehensive Review Packet

Transcription

1 Mathematics Department STAAR/EOC Comprehensive Review Packet Algebra I End of Course There are desks waiting to be filled with students, excited about getting an early start on learning! Algebra I End of Course

2 Name: Period: Date: CDs for the Band (Warm-Up) Bryan and his band want to record and sell CDs. There will be an initial setup fee of $250, and each CD will cost $5.50 to burn. 1. Write a function relating the total cost and the number of CDs burned. The Atlantis Curriculum Project, Module 18 EOC Review, WUSE

3 Chapter 1: Function Fundamentals Reuben learned in art class that a mosaic is made by arranging small pieces of colored material (such as glass or tile) to create a design. Reuben created a mosaic using tiles, then decided on a growing pattern and created a second and third mosaic. Reuben continued his pattern by building additional mosaics. He counted the number of tiles in each mosaic and then represented the data in multiple ways. He thinks he sees a relationship between the mosaic number and the total number of tiles in the mosaic. 1. Represent Reuben s data from the mosaics problem in at least three ways, including a general function rule, to determine the number of tiles in any mosaic. 2. Write a description of how your rule is related to the mosaic picture. Include a description of what is constant and what is changing as tiles are added. 3. How many tiles would be in the tenth mosaic? Use two different representations to show how you determined your answer. 4. Would there be a mosaic in Reuben s set that uses exactly 57 tiles? Explain your reasoning using at least one representation. 5. In Reuben s mosaic, there are 2 tiles in the center. How would the function rule change if the center of the mosaic contained 4 tiles instead? Explain your reasoning using two different representations. Functional Fundamentals 3

4 Name Period Date Jasmine s Art Class (Homework) Jasmine s art class was instructed to draw a picture that consisted of the geometric shape of their choice. Jasmine created a pattern using triangles. Using only the upward triangles in the pattern below answer the following questions. STAGE 1 STAGE 2 STAGE 3 1. Determine an expression that can be used to find the number of upward triangles at the nth stage of the pattern. 2. How many triangles would be needed for stages 55, 117 and 202? If Jasmine completed a drawing that consisted of 81 upward triangles, then at which stage must she be? The Atlantis Curriculum Project, Module 18 EOC Review, HWSE

5 Name Period Date What Comes Next? (Warm Up) From what you remember from Algebra 1, find the next item in each sequence. 1. John made $3 the first hour, $5 the second, $7 the third and $9 the fourth. How much will he make in the fifth hour? 2. What is next in this sequence? 17, 13, 9, 5 3. Dwayne has a wrench set with the socket sizes of 1, 1 2, 1 4, 1 8, 1 16 what would the next size be? The Atlantis Curriculum Project, Module 18 EOC Review, WUSE

6 Alicia Chapter 3: Interacting Linear Functions, Linear Systems Jerry, Alicia, Calvin, and Marisa wanted to test their cars gas mileage. Each person filled his or her car s gas tank to the maximum capacity and drove on a test track at 65 miles per hour until the car ran out of gas. The graphs given below show how the amount of gas in the cars changed over time. Jerry Volume of Gas (gallons) Calvin Marisa Time (hours) Whose car has the largest gas tank? Explain your reasoning. Whose car ran out of gas first? Explain your reasoning. Whose car traveled the greatest distance? How does knowing that they all traveled at 65 miles per hour help you know who traveled the greatest distance? Determine whose car gets the worst gas mileage. Describe how you used the graph to make your decision. How are Calvin s graph and Marisa s graph similar and how are they different in terms of the given situation? In terms of the given situation, how would the function rule that describes Marisa s graph compare to the function rule that describes Jerry s graph? In terms of the given situation, how would the function rule that describes Jerry s graph compare to the function rule that describes Alicia s graph? Jerry s graph intersects Marisa s graph. What does the point of intersection represent? After some automotive work, Jerry is now getting better gas mileage. How will this affect his graph? Interacting Linear Functions, Linear Systems 23

7 1. 3u + z = 15 u + 2z = 10 Linear Systems (A) Solve each system of equations. 5. 2a + 2x = 18 a + 3x = u + 6y = 32 u + 3y = a + 2v = 32 6a + 6v = c + 4u = 33 6c + 3u = b + v = 13 b + v = u + v = 18 5u + 2v = a + 5u = 17 2a + u = 9 Math-Drills.com

8 Name Date Period Rocket Launch (Warm Up) The Fireworks Extravaganza in Denton, Texas, is a 4 th of July fireworks display set to music. If a rocket (firework) is launched with an initial velocity of 39.2 meters per second at a height of 1.6 meters above the ground, the equation h = 4.9t t represents the rocket s height h in meters after t seconds. According to the picture below, when will the rocket explode and at what height? Adapted from Glencoe Algebra I 2007, page 465 (Get Ready for the Lesson)

9 Golfing The height, h (in feet), of a golf ball depends on the time, t (in seconds), it has been in the air. Sarah hits a shot off the tee that has a height modeled by the velocity function f(h)= 16t t. 1. Sketch a graph and create a table of values to represent this function. How long is the golf ball in the air? 2. What is the maximum height of the ball? How long after Sarah hits the ball does it reach the maximum height? 3. What is the height of the ball at 3.5 seconds? Is there another time when the ball is at this same height? 4. At approximately what time is the ball 65 feet in the air? Explain. 5. Suppose the same golfer, Sarah, hit a second ball from a tee that was elevated 20 feet above the fairway. What effect does this have on the values in your table? Write a function that describes the new path of the ball. Sketch the new relationship between height and time on your original graph. Compare and contrast the graphs. Quadratic Functions 257

10 Name Period Date Applications of Quadratic Functions (Homework) Use the finite difference method to determine whether or not the following set of data tables models a quadratic, linear function, neither x y x y x y x Y x y x Y The Atlantis Curriculum Project, Module 18 EOC Review, HWSE

11 Name Period Date 7. The graph of the function P below models rock concert income. a) Use the graph to approximate P(20)? b) Identify the domain and range from the graph above. c) Using the graph, determine the coordinates of the maximum or minimum. The Atlantis Curriculum Project, Module 18 EOC Review, HWSE

12 Name Date Period The Gateway Arch (Warm Up) The shape of the Gateway Arch in St. Louis, Missouri, is a catenary curve. It resembles a parabola with the equation h = x x , where h is the height in feet and x is the distance from one base in feet. What is the equation of the axis of symmetry? What is the distance from one end of the arch to the other? What is the maximum height of the arch? Adapted from Glencoe Algebra I 2007, page 470

13 Chapter 4: Quadratic Functions A biologist was interested in the number of insect larvae present in water samples of various temperatures. He collected the following data: Temperature (C ) Population Make a scatterplot of the data. Given the function y = ax 2 + bx + c, where b is 75, experiment with values of a and c to fit a quadratic function to your plot Write a verbal description of the relationship between the larvae population and the temperature of the water samples. What do the x- and y-intercepts mean? At what water temperature is the larvae population greatest? The water sample is considered to be mildly contaminated but does not need to be treated if the larvae population is 300 or less. At what temperatures is the larvae population 300 or less? Explain. Suppose that testing shows virtually no larvae present at 0 4. C, and the model for this situation is the function y = 1.5x(x 50). How does this function compare with the original function? How well does it appear to fit the data? Quadratic Functions 29

14 Name Period Date Open Parachute (Homework) 1. The formula d = 0.05s s estimates the minimum distance d in feet for a car traveling s miles per hour. If a car stops in 200 feet, how long did it take to stop? 2. A marine biologist observes a dolphin jumping in and out of the water. After several observations, the marine biologist estimates the height h path of the dolphin when jumping to be h = -0.53t x 46 after t seconds. At what time will the dolphin exit the water? Enter the water? Approximate answers to nearest tenth. 3. Ignoring wind resistance, the distance d in feet that a parachutist falls in t seconds can be estimated using the formula d = 16t 2. If a parachutist jumps from an airplane and falls for 1100 feet before opening the parachute, how many seconds pass before the parachute is opened? 4. A computer graphics animator would like to make a realistic simulation of a tossed ball. The animator wants the balls to follow the parabolic trajectory represented by the parabolic trajectory represented by the quadratic equation h = -0.3t 2 + 5t + 7, where h is height in feet and t is time in seconds. If the animator wants the ball thrown up from a window that is 7 feet off the ground, how long will it take the ball to land on the ground? The Atlantis Curriculum Project, Module 18 EOC Review, HWSE

15 Name Period Date Quadratic Function (Warm Up) 1. The factors of a polynomial are (x + 10) and (x 2). Using algebra tiles, determine the standard form for this polynomial. Standard Form: The Atlantis Curriculum Project, Module 18 EOC Review, WUSE.docx, page 1 of 1

16 Name: Period: Date: The Marvel of Medicine (Exponential Function) A doctor prescribes a dosage of 500 milligrams of medicine to treat an infection. Each hour following the initial dosage, the concentration decreases by 20% from the preceding hour. 1. Complete the table showing the amount of medicine remaining after each hour. Number of Hours Number of Milligrams Process Number of Milligrams 2. Using symbols and words describe the functional relationship in this situation. Discuss the domain and range of the function rule and of the problem situation. Does this situation represent exponential growth or exponential decay? Explain your reasoning. 3. Describe how to determine the amount of medicine left in the body after 10 hours. 4. When will the amount reach 60 milligrams? Explain how you know. 5. Why would it be important for the patient to repeat the dosage after a prescribed number of hours? The Atlantis Curriculum Project, Module 18 EOC Review, FISE.docx, Page 1 of 1

17 Name Period Date Exponential Growth and Decay (Homework) A.11C The students is expected to analyze data and represent situations involving exponential growth and decay using [concrete] models, tables, graphs, or algebraic methods. Supporting Standard Identify if each situation represents exponential growth or exponential decay and justify your answer. Then write the exponential growth or exponential decay functions that best represents the situation and use the function to find the indicated value. 1) Juan deposited $300 in a savings account. The account earns a 3% annual interest. Write the exponential function that models this situation, assuming that he does not make any other deposits or withdrawals in the account. What would be the amount in his account after 5 years? 2) A bacteria culture grows at a rate of 18% each day. Today, there are 500 bacteria. Write the exponential function that models that situation. After how many years will the bacteria reached ) Rudy bought a Honda accord for $13,500. If the value of the car depreciated by 18% each year, what exponential equation models this situation? After how many years will the value of the car be 5000? The Atlantis Curriculum Project, Module 18 EOC Review, HWSE.docx, page 1 of 2

18 Name Period Date 4) Earl bought a coat from Macy s Store using his credit card for $150. His credit card charges a 1.50% interest each month. Write the exponential function that represents this situation if he does not make any monthly payments. How much money will he owe after 7 months? 5) The bird population in a forest is about 2500 and decreasing at a rate of 3% per year. Write the exponential function that will determine the amount of birds, B, after t, years. Determine how the amount of birds after 10 years. 6) Johnny borrowed $40,000 from her mother in law with a yearly interest of 3%. Write the exponential function can use used to find the amount he owes, A, after t, years? Johnny plans to pay the amount in 3 years with the interest. What is the amount he will need to pay in 3 years? The Atlantis Curriculum Project, Module 18 EOC Review, HWSE.docx, page 2 of 2

19 Name Period Date Exponential Function (Warm Up) 1. Grant invests his $300 at a bank that offers 5% compounded annually. Write the exponential function, m (t), for this situation when m is for the amount of money Grant has in the bank after investing, and t is for the number of years of investing. Between how many years does Grant need to keep his investment at the bank if his goal is to have a minimum of $500? 2. Rosa purchased a new SUV that costs $27,000. Her car depreciates at a rate of 15% every year. Write an equation that represents this situation. What is Rosa s SUV value after 6 years? The Atlantis Curriculum Project, Module 18 EOC Review, WUSE.docx, page 1 of 1

20 Name: Period: Date: Music and Mathematicians (Inverse Variation) A.11B The student is expected to analyze data and represent situations involving inverse variation using [concrete] models, tables, graphs, or algebraic method. Supporting Standard Stringed instruments, like violins and guitars, produce different pitches of a musical scale depending on the length of the string and the frequency of the vibrating string. When under equal tension, the frequency of the vibrating string varies inversely with the string length. 1. Complete the table to find the string lengths for a C-major scale. Round your answers to the nearest whole number. Pitch C D E F G A B C Frequency (cycles/sec) String Length (mm) Describe how the values of the frequency change in relation to the string length. 3. Make a scatterplot of your data. Describe the graph. Chapter 5: Inverse Variations, Exponential Functions, and Other Function 4. Find a function that models this variation. The Atlantis Curriculum Project, Module 18 EOC Review, FISE.docx, Page 1 of 2

21 Name: Period: Date: Music and Mathematicians (Inverse Variation) A.11B The student is expected to analyze data and represent situations involving inverse variation using [concrete] models, tables, graphs, or algebraic method. Supporting Standard Stringed instruments, like violins and guitars, produce different pitches of a musical scale depending on the length of the string and the frequency of the vibrating string. When under equal tension, the frequency of the vibrating string varies inversely with the string length. 1. Complete the table to find the string lengths for a C-major scale. Round your answers to the nearest whole number. Pitch C D E F G A B C Frequency (cycles/sec) String Length (mm) Describe how the values of the frequency change in relation to the string length. 3. Make a scatterplot of your data. Describe the graph. Chapter 5: Inverse Variations, Exponential Functions, and Other Function 4. Find a function that models this variation. The Atlantis Curriculum Project, Module 18 EOC Review, FITE.docx, Page 1 of 4

22 Name Period Date y = k x Inverse Variation (Homework) y = k x A.11B The student is expected to analyze data and represent situations involving inverse variation using [concrete] models, tables, graphs, or algebraic method. Supporting Standard 1) CHEMISTRY Boyle s Law states that when a sample of gas is kept at a constant temperature, the volume varies inversely with the pressure exerted on it. Write an equation for Boyle s Law that expresses the variation in volume V as a function of pressure P. 2) ASTRONOMY Astronomers can use the brightness of two light sources, such as stars, to compare the distances from the light sources. The intensity or brightness, of light I is inversely proportional to the square of the distance from the light source d. 3) If y varies inversely as x and y = 2 when x = 25, find x when y = 40. 4) If y is inversely proportional to x and y = 4 when x = 12, find y when x = 5. 5) PHYSICAL SCIENCE The illumination produced by a light source varies inversely as the square of the distance from the source. The illumination produced 5 feet from the light source is 80 foot-candles. Find the illumination produced 8 feet from the same source. 6) ELECTRICITY The resistance in ohms, of a certain length of electric wire varies inversely as the square of the diameter of the wire. If a wire 0.04 centimeter in diameter has a resistance of 0.60 ohm, what is the resistance of a wire of the same length and material that is 0.08 centimeters in diameter. The Atlantis Curriculum Project, Module 18 EOC Review, HWSE.doc, page 1 of 2

23 Name Period Date 7) SOUND: The sound produced by a string inside a piano depends on its length. The frequency of a vibrating string varies inversely as its length. Write an equation that represents the relationship between the frequency f and length l. 8) Determine whether the data in each table represents an inverse variation. If it does, find the constant of variation an inverse variation equation. 9) If r is inversely proportional to s, and r = ½ when s = ¾, find the constant of variation. 10) If w varies inversely as z, and z = 3 and w = 40, find the constant of variation. The Atlantis Curriculum Project, Module 18 EOC Review, HWSE.doc, page 2 of 2