PreAP Algebra I Problems for the First Semester Exam

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1 This is not a semester exam, but problems that you could use on a semester exam that are similar to some of the problems from the unit quizzes 1. Stephanie left home at 8:30 and rode her bicycle at a steady rate until 11:00. She traveled much faster must she ride to make it back home by 1:00? 3 A. 1 miles per hour 4 B. 7 miles per hour 3 C. 8 miles per hour 4 D. E miles per hour miles per hour miles. How 2. Suppose you see the two summer jobs advertised below. To earn the same amount of money at both jobs, how much will you need to sell in a week? A. $5 B. $50 C. $250 D. $500 E. $2500 Cellular Phone Sales Position $150 per week + 20% commission Stereo Sales Position $200 per week + 10% commission 3. A high school marching band consists of woodwind and brass musicians in a ratio of 7 to 3. There are 50 woodwind and brass players in the band. How many woodwinds are there? A. 7 B. 15 C. 17 D. 35 E. 50 Algebra I Semester Exam Questions Page 1

2 4. Suppose your class receives $1,084 for selling 205 packages of greeting cards c and gift wrap w. Gift wrap costs $4 per package and greeting cards cost $10 per package. Which system below could be solved to find how many packages of gift wrap and greeting cards were sold? A. B. C. D. E w+ 10c= 4w+ 10c= w+ 205c= 10w+ 4c= Which of the following graphs shows the solution to the given system of equations? 3x 5y = 6 6x+ 2y = 24 Algebra I Semester Exam Questions Page 2

3 6. Alamo Junior High s student council is trying to earn money selling balloon bouquets. The price they will charge includes the cost of the balloons and a delivery fee. The equation that represents this situation is y = 1.25x + 2, where x, represents the number of balloons ordered and y represents the total price. (a) Identify the slope and the y-intercept and explain the meaning of each relative to the problem situation. (b) Sketch a graph of the equation, y = 1.25x + 2. Be sure to label the axes with correct units. (c) How much would a student pay to have a dozen balloons delivered? (d) If a student has $34, what is the maximum number of balloons he can have delivered? (e) If the student council raises the price of balloons to $150 each, how will this affect the graph? Algebra I Semester Exam Questions Page 3

4 7. Frank s Auto Zone charges $125 for parts and $ 75 per hour of labor for a certain repair. Gracie s Engine Works charges a flat fee of $275 for the same job. (a) Write two equations, one for each shop, that represent the total charge, C, in terms of the repair time, r. (b) Graph the system of equations from part (a). Label each line with its equation. (c) After how many hours would the charge at each shop be the same? Verify the answer algebraically (d) Frank decides to change his hourly rate so that his total charge for a three hour repair job will be the same as Gracie s. What hourly rate should he charge if the cost of parts is still $125? Show the work that supports your answer. (e) A customer wants to have a two-hour repair job done for which the parts will cost $125. Using Frank s new charge equation from part 9d), how much will a customer save by having the repair work done at Frank s instead of at Gracie s? Algebra I Semester Exam Questions Page 4

5 8. Danh rides his bicycle along a straight road starting from home at t = 0 minutes. For the first eight minutes, Danh s speed, in miles per minute, is modeled by the piecewise linear function whose graph is provided. s Danh s Speed t s speed in miles per minute time in minutes t (a) How fast is Danh riding when t = 1 minute? Include units in the answer. (b) What is the equation for Danh s speed between 0 and 2 minutes? What is the equation for Danh s speed between 5 and 6 minutes? (c) The equation for Danh s speed between 7 and 8 minutes is s = 0.1( t 7) where s is the speed in miles per minute and t is the time in minutes. How fast is Danh riding when t = 7.2 minutes? (d) Since the area between the speed function and the t-axis represents the distance that Danh travels, how far does Danh ride during the first four minutes? Include units in the answer. (e) Danh decreases his speed at a constant rate from t = 8 minutes to t = 12 minutes so that his speed at t = 12 minutes will be 0 miles per minute. On the graph provided on the first page, extend the speed function to include this new information. Mark each grid point that lies on the new portion of the speed function. How much farther will Danh travel in this time period. Algebra I Semester Exam Questions Page 5

6 Use the following information to answer questions A water tank collects and stores water used for gardening. At any given time, water may be flowing into or out of the tank. The graph shows the volume of water in the tank, in gallons, over a period of 12 hours. During which time interval is the volume of water in the tank decreasing the fastest? A. 2 to 4 hours B. 4 to 5 hours C. 5 to 6 hours D. 6 to 10 hours E. 10 to 12 hours 10. Which of the following is the piecewise function for the graph on the time interval 0 t 5? 60 0 t A. 5( t 4) t 4 20( t 4) t t B. 5( t 2) t 4 10( t 4) t 5 60t 0 t C. 5( t 2) t 4 20( t 5) t 5 t t D. 5( t 4) t 4 20( t 4) t 5 + t 60 0 t E. 5t t 4 10t t 5 Algebra I Semester Exam Questions Page 6

7 11. For 0 t 5, at what time is the volume of water in the tank 45 gallons? A. 3 hours B hours C. 4.5 hours D. 5 hours E. 6.5 hours 12. At what time does the volume of water in the tank change from increasing to decreasing? A. 2 hours B. 4 hours C. 5 hours D. 6 hours E. 10 hours Algebra I Semester Exam Questions Page 7

8 13. Buford is a town that began in 1970 with 20 people and has increased by 2.5% a year. (a) Write an equation that would represent its population over t years. (b) Sketch a graph of the population including the initial population, one other point and the end behavior. Label the axis properly with units. 14. A Chevrolet Camaro initially costs $45,250 dollars and depreciates (goes down in value) by 14% each year. (a) Write an equation that gives the value for the car after t years. (b) Sketch a graph of the value of the car including the initial value, one other point and the end behavior. Label the axis properly with units. Algebra I Semester Exam Questions Page 8

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