Algebra 1 B Semester Exam Review

Transcription

1 Algebra 1 B 014 MCPS

2 Residual: Difference between the observed (actual) value and the predicted (regression) value Slope-Intercept Form of a linear function: f m b Forms of quadratic functions: Verte Form: f a h k Standard Form: f a b c Factored Form: f d e Quadratic Formula: If 4 a b c 0, then b b ac a Zero-Product Property: If ab 0, then a 0 or b 0 Pythagorean Theorem: In a right triangle, a b c, where a and b are the lengths of the legs, and c is the length of the hypotenuse. Distance between two points, y and, y : y y y 1 y1 y : y1 Slope of a line containing two points, and, 1 MCPS Page 1

3 Unit 3 1. Ms. Tran looks at the scores on her first Algebra 1 test. They are listed below: 99, 45, 88, 68, 77, 73, 81, 76, 66, 79, 81, 74, 81, 41, 91, 94, 68 She cannot decide how to display these scores, so she makes two different displays. a. Make a bo plot of the data Test Scores b. Make a histogram of the data. Use the intervals shown for your display. Frequency Test Scores c. Use your displays to describe the data. You should use measures of central tendency, variability and distribution in your description. MCPS Page

4 . The following bo plots show the distributions of test scores for two math classes. a. From the list below, circle which ones you can NOT determine from the bo plots. median mean range interquartile range individual scores quartiles distribution (skewness) the number of test scores b. Based on what you know about bo plots, which class performed better on the test? Give at least two reasons for your answer. c. Which data set has greater variability? Justify your answer. 3. Make a sketch of the following types of frequency distributions. Skewed left Skewed right Normal MCPS Page 3

5 4. Look at a scatterplot and the line of best fit below. y A residual for a value of is the difference between the observed value of y and the predicted (regression) value of y on the line of best fit. a. What is the residual when 3? b. What is the residual when 6? c. What is the residual when 9? 5. a. In the 1980 s it was found that the correlation coefficient between the amount of ice cream sold and the number of crimes in New York City was.97. Does this mean that an increase in ice cream sales causes an increase in the number of crimes? Eplain your reasoning. b. Give another eample of two variables that might have a high correlation coefficient, but the change in one of the variables does NOT cause a change in the other. MCPS Page 4

6 6. Sammy is interested in the number of visitors that will come to the beach as a function of the temperature. Below is the data and a scatterplot that Sammy has collected. Temperature (t) Visitors V t Visitors At the Beach Temperature o F a. What is the relationship between the temperature and the number of visitors to the beach? b. Circle the value that best describes the value of r, the linear correlation coefficient. Justify your answer. r 1 r.89 r.76 r.05 This item continues on the net page. MCPS Page 5

7 Continuation of item 6 from the previous page. Here are the results of finding the line of best fit on a calculator. LinReg y = a + b a = 3 b = 56 r =.8944 c. What is the slope of the line of best fit? What is its meaning in the contet of this situation? d. What is the y-intercept of the line of best fit? What is its meaning in the contet of this situation? e. What does your line of best fit predict for a temperature of 88 degrees? f. What is the residual at a temperature of 88 degrees? Residual: Difference between the observed (actual) value and the predicted (regression) value g. According to your regression line, at what temperature will there be no visitors at the beach? Eplain how you determined your answer. MCPS Page 6

8 7. A carnival game kept track of the ages and what type of prize, if any, that people won at the game. The results are shown in the table below. Children Adults Total No Prize Small Prize Big Prize Total a. Of the children who played, what fraction won a big prize? b. What fraction of the small prize winners were adults? c. What fraction of the total number of players were children? d. The percent of children who won a small prize was (less than/equal to/greater than) the percent of adults who won no prize. 8. Montgomery County middle and high school students were asked if school should start later in the day. Here is some information about the responses. Yes No Total Middle School 30 High School 5 50 Total 350 Complete the table. MCPS Page 7

9 Unit 4, Topic 1 For items 9 through 11, classify each function below as linear, eponential, or quadratic. Use mathematics to justify your answers. 9. y y y A rectangle has a length that is 6 inches longer than its width. If w represents the width, write an epression, in terms of w, for the area of the rectangle. 13. A rectangle has a length that is 4 inches shorter than its width. If w represents the width, write an epression, in terms of w, for the area of the rectangle. MCPS Page 8

10 14. A rectangle shown below has a perimeter of 40 inches. Its width is 5 inches. 5 What is the area of the rectangle? 15. A rectangle shown below has a perimeter of 30 feet. Its width is w feet. w What is the area of the rectangle? (the area should be an epression in terms of the variable w) For items 16 through 18, a function of time is given. In each item, determine the average rate of change on the given interval. Give the units for your answer. 16. Time (seconds) Distance (feet) Average speed on the interval : Units: MCPS Page 9

11 17. Number of Bacteria y Average rate of bacteria growth on the interval : Units: Time (hours) 18. d t 500t t t in minutes, d t in kilometers Average speed on the interval : Units: MCPS Page 10

12 19. The number of weeds on a lawn can be written as the function W d 5d 60 represents the number of days since spring started. a. Is the rate of change of this function constant? Eplain your answer., where d b. What is the constant rate of change? c. What are the units for the rate of change? MCPS Page 11

13 0. Jack is inventing a variation on bowling. Here are the first four rows of pins. 1 row rows 3 rows 4 rows Let P r represent the total number of pins in r rows. a. Complete the table based on the total number of pins. Number of Rows (r) Total Number of Pins P r b. What type of function is represented by the table above? c. Eplain why you chose that type of function. d. Write a function for P r. The function can either be eplicit or recursive. e. Jack decides that he will have 1 rows of pins. What is the total number of pins that he will need? MCPS Page 1

14 1. Look at the pattern of dots below. Figure 1 Figure Figure 3 Figure 4 Let D n be a function that represents the number of dots in figure number n. a. Complete the table below. Figure number (n) Number of Dots D n b. Which type of function: linear, quadratic, or eponential, is represented by the table? Give a reason for your answer. c. Write the function rule for D n. The rule can be eplicit or recursive. d. How many dots will be in Figure 9? Show how you determined your answer. MCPS Page 13

15 Unit 4, Topic In the table below, a square is shown in the first column. The second column tells what change is made to the length of each side of the square. In the third column, write the AREA of the new square in two different ways. Original Square Change to each side of the original square. Add 3 AREA of the NEW square, written in two different ways 3. Subtract 7 4. Multiply by 4 5. Multiply by, then add 5 6. Multiply by 9, then subtract 1 For items 7 through 9, fill in the number that completes the square MCPS Page 14

16 30. The graph below represents y. y Look at the graphs, labeled I, II, III, and IV below. I y II y III y IV y Match the equations listed below with the graphs I, II, III, and IV above. 1 a. y b. y c. y 5 d. y MCPS Page 15

17 For items 31 through 34, write two equivalent quadratic functions for each representation. 31. y 3. A quadratic parent function f whose graph is translated to the right 4 units and up 5 units. O f f For items 35 and 36, write one equation for the function represented. y O f MCPS Page 16

18 For items 37 and 38, sketch the graph of the function, then give the information requested. f y Verte: Line of Symmetry: -intercepts: y-intercept: Domain: O Range: Interval on which Interval on which is increasing: is decreasing: 38. f 3 8 y Verte: Line of Symmetry: -intercepts: y-intercept: Domain: O Range: Interval on which is increasing: Interval on which is decreasing: MCPS Page 17

19 For items 39 through 4, add or subtract as indicated For items 43 through 48, multiply as indicated MCPS Page 18

20 For each rectangle below, determine the perimeter and the area. The area should be written as a trinomial Perimeter Area as a trinomial Perimeter Area as a trinomial For items 51 through 55, the area of a rectangle is given. Factor the epression as the product of two binomials to find its side lengths. 51. Area: Area: Area: Area: Area: Factor: Factor: MCPS Page 19

21 Unit 4, Topic 3 For items 58 through 60, use your calculator to graph the function, then state the number of real zeros. 58. f f f Jack kicked a football. The height, htin feet, of the ball after t seconds is given by the quadratic function ht 16t 64t. a. After how many seconds does the ball hit the ground? Show how you determined your answer. b. Does the ball reach its maimum height at t seconds? Show how you determined your answer. MCPS Page 0

22 6. An animal makes a leap into the air. A function for the height ht, in meters, of the animal above the ground after t seconds is given by ht 5t 1.5t. a. How long is the animal in the air? Show how you determined your answer. b. What is the animal s maimum height? Show how you determined your answer. MCPS Page 1

23 63. In your own words, what is the zero-product property? For items 64 through 69, solve the equation using any method MCPS Page

24 70. A farmer plants apple trees. The total number of apples can be represented by the function At 300t 5t, where t is the number of trees that he plants. a. Sketch the graph of A t 300t 5t on the coordinate plane below. Show the points where t 0,10, 0,30, 40,50, t b. The farmer wants to be able to harvest at least 4000 apples. Solve the inequality 300t 5t c. What is the meaning of your solution in the contet of this situation? MCPS Page 3

25 71. The equations y 4 5 and y 7 on the coordinate plane below. y O a. What are the solutions to the equation 4 5 7? b. What are the solutions to the inequality 4 5 7? MCPS Page 4

26 For items 7 and 73, determine the side of the right triangle marked For items 74 and 75, the lengths of 3 sides of a triangle are given. Determine whether the triangle is a right triangle. 74. Lengths are 1, 16, and Lengths are, 3, and 4 MCPS Page 5

27 On the coordinate plane below, three line segments are shown, with their coordinates. y O For items 76 and 77, find the distance between each pair of points , and 6, ,3 and,9 MCPS Page 6