ALGEBRA 1 Workbook. Common Core Standards Edition

Transcription

1 ALGEBRA 1 Workbook Common Core Standards Edition

2

3 ALGEBRA 1 Workbook Common Core Standards Edition Published by TOPICAL REVIEW BOOK COMPANY P. O. Box 328 Onsted, MI EXAM PAGE Reference Sheet...i Test Test Test June August January Correlation of Standards...53

4

5 ALGEBRA 1 Test 1 Part I Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. For each question, write on the space provided the numeral preceding the word or expression that best completes the statement or answers the question What are the values of x in the equation x(x 6) = 4(x + 6)? (1) { 6, 6} (2) { 12, 2} (3) { 2, 12} (4) { 6, 0, 6} 1 2. Which of ordered pairs is not a function? (1) {(0, 9),(9, 0),(1, 2),(3, 4)} (3) {(2, 3),(3, 4),(4, 5),(5, 6)} (2) {(0, 1),( 1, 0),(1, 2),(3, 2)} (4) {(2, 3),(2, 4),(4, 5),(4, 6)} 2 3. If f(x) = 3x 4 + 2, find f( 10). (1) 28 (2) 34 (3) 36 (4) What is the value of the 1 st quartile in the data set below? Scores on a math quiz: 65, 90, 100, 72, 88, 55, 73 (1) 65 (2) 73 (3) 90 (4) What is the length of the missing side of the quadrilateral shown if the perimeter is 5x 2 + 2x + 1? 2x 2 + x 1 4x 2 3x 2 5x? (1) 4x 2 6x + 2 (3) 4x 2 + 8x + 4 (2) 4x 2 + 6x + 2 (4) 4x 2 + 8x What is the product of (x + 1) and (2x 2 + 3x 1)? (1) 2x 2 + 5x 2 x 1 (3) 2x 3 + 3x 2 + 3x + 1 (2) 2x 3 + 5x 2 + 2x 1 (4) 2x 3 + 3x 2 3x Which graph is a correct representation of the function f(x) = 3 x? (1) (2) (3) (4) 7 8. A sequence has an initial value of 10 and each term is twice the previous term. Which function models this sequence? (1) a(n) = 10(2) n (3) a(n) = n (2) a(n) = 10(2) n 1 (4) a(n) = (n 1) 8

6 2 ALGEBRA 1 Test 1 9. How can b 2 + 9b + 14 be re-written? (1) (b + 7) (b 7) (3) (b + 7) (b 2) (2) (b 7) (b 2) (4) (b + 7) (b + 2) 9 Medication 10. The scatter plot to the right 150 shows the number of milligrams 130 of a medication in a person s 110 body for first three hours after 90 the medication is given. Which 70 equation best models the 50 relationship where h is hours after medication and m is milligrams -10 of medication in the body? (1) m = h Hours Since Medicating (2) m = h 130 (3) m = 40h (4) m = 40h Using the equation y = ax 2 + bx + c to represent a parabola on a graph, which statement is true? (1) If b is negative, the parabola opens downward. (2) If a is negative, the parabola opens upward. (3) If a is positive, the parabola opens upward. (4) If c is negative, the parabola opens downward If the function h(x) represents the number of full hours that it takes a person to assemble x sets of tires in a factory, which would be an appropriate domain for the function? (1) the set of real numbers (3) the set of integers (2) the set of negative integers (4) the set of non-negative integers Given the length of three sides of a triangle, which is a right triangle? (1) 10, 26, 24 (2) 20, 12, 18 (3) 30, 15, 26 (4) 40, 50, Milligrams of Medication in the Body 14. Which equation is represented by the accompanying graph? 1; x < 2 (1) y = { 2; x > 2 1; x 2 (2) y = { 2; x > 2 1; x < 2 (3) y = { 2; x 2 1; x 2 (4) y = { 2; x 2 14

7 ALGEBRA 1 Test A mouse population starts with 2,000 mice and grows at a rate of 5% per year. The number of mice after t years can be modeled by the equation, P(t) = 2000(1.05) t. What is the average rate of change in the number of mice between the second year and the fifth year, rounded to the nearest whole number? (1) 116 (2) 348 (3) 2205 (4) Seven less than the product of twice a number is greater than 5 more than the same number. Which integer satisfies this inequality? (1) 1 (2) 2 (3) 12 (4) A sequence is defined recursively by f(1) =16 and f(n) = f(n 1) + 2n. Find f(4). (1) 32 (2) 30 (3) 28 (4) Which statement is true about the accompanying graph? (1) It is decreasing when 1 < x < 3 and positive when x > 1. (2) It is increasing when x > 1 and negative when x < 0. (3) It is increasing when x > 1 and negative when 1 < x < 3. (4) It is decreasing when 1 < x < 3 and positive when x > 3. y = x 2 2x The two-way table below represents the travel history of the seniors in the local Travel Club. Travel Club History Gender Total Men Women Aruba Jamaica Canada Spain Total What is the approximate marginal relative frequency of the number of men and women that have traveled to Canada? (1) 16% (2) 23% (3) 39% (4) 42% What is the equation of the line with a slope of 1 that passes through the point (6, 6)? 2 (1) y = 1 2 x 3 (2) y = 1 2 x 3 (3) y = 1 x + 3 (4) y = 2x y x

8 4 ALGEBRA 1 Test Alex makes ceramic bowls to sell at a monthly craft fair in a nearby city. Every month, she spends $50 on materials for the bowls from a local art store. At the fair, she sells each completed bowl for a total of $25 including tax. Which equation expresses Alex s profit as a function of the number of bowls that she sells in one month? (1) p(x) = 50x + 25 (3) p(x) = 25x (2) p(x) = 15x + 25 (4) p(x) = 25x Which expression is equivalent to x 4 y 4? (1) (x 2 y 2 )(x 2 + y 2 ) (3) (2x 2 ) 2 (2y 2 ) 2 (2) (x 2 y 2 )(x 2 y 2 ) (4) (x 2 y 2 ) (x 2 y 2 ) A bottle rocket that was made in science class had a trajectory path that followed the quadratic equation y = x 2 + 4x + 6. What is the turning point of the rocket s path? (1) (1, 5) (2) (2, 10) (3) ( 2, 10) (4) (1, 5) What is the solution to this system of linear equations: y x = 4 and y + 2x = 1? (1) ( 1, 3) (2) (0, 4) (3) (1, 1) (4) ( 3, 3) 24 Part II Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in the space provided. [16] 25. Find the average rate of change of the function shown to the right that represents the amount of money in a savings account in Lender s Bank? Week Balance 1 $128 2 $142 3 $156 4 $170 5 $ Factor completely, the expression: 2x 3 2x 2 12x

9 x ALGEBRA 1 Test Find one point that lies in [The use of the grid is optional.] the solution set of the following y system of inequalities: y 1 2 x + 6 y > 3x 1 5 Justify your answer 28. Solve for x: 2x 2 + 4x 16 = The product of 16 and 4 less than a number is 208. Find the number. 30. MaryJo decided to solve the equation 3x 2 = x 6 by entering each of the expressions into her graphing calculator. To solve the equation as a system, she entered y 1 = 3x 2 and y 2 = x 6. When she used the calculator to find the intersection, she found x = 1 and y = 5. Show the work to check to see if MaryJo found the correct solution for x to the linear equation.

10 6 ALGEBRA 1 Test Find f( 2) for the function: f(x) ={ 3x2 1, x < 1 x + 2, x Identify the turning point of the function f(x) = x 2 2x + 8 by writing its equation in vertex form. Show your work. Part III Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [16] 33. Graph 2x + y < 7 and state one point in the solution set. y x

11 x ALGEBRA 1 Test Jonathan has been on a diet since January So far, he has been losing weight at a steady rate. Based on monthly weigh-ins, his weight, w, can be modeled by the function w = 3m where m is the number of months after January a) How much did Jonathan weigh at the start of the diet? b) How much weight has Jonathan been losing each month? c) How many months did it take Jonathan to lose 45 pounds? 35. Yolanda owns 4 rabbits. She expects the number of rabbits to double every year. a) After how many years will she have 64 rabbits? b) Write an equation to model this situation. [The use of the grid is optional.] y

12 8 ALGEBRA 1 Test Create a box plot for the ages of people listed below: 40, 25, 20, 15, 40, 40, 45, 60, 7, 10, 52, 34, 38 Part IV Answer one question in this part. The correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in the spaces provided. [6] 37. Graph the system of equations: y = x 2 + 3x 1 State the solution to the system. 2y 1 = x y x

13 ALGEBRA 1 Test 2 Part I Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. For each question, write on the space provided the numeral preceding the word or expression that best completes the statement or answers the question What are the zeros of the function, f(x) = x 2 2x 15? (1) {3, 5} (2) { 3, 5} (3) { 5, 3} (4) { 5, 3} 1 2. What is the difference when 2x 3 + x 5 is subtracted from 6x 3 x 2 + 4x + 8? (1) 4x 3 x 2 + 3x + 13 (3) 8x 3 x 2 + 5x + 3 (2) 4x 3 x 2 3x 13 (4) 8x 3 + 3x Which system of equations would have the same solution as the system: x + y = 5 3x + 2y = 10 (1) 3x + 2y = 5 (3) 3x 3y = 5 x + y = 10 3x + 2y = 10 (2) 3x 3y = 15 (4) 2x + 2y = 5 3x + 2y = 10 3x + 2y = Which situation could be modeled with an exponential function? (1) the amount of money in a savings account where $150 is deducted every month (2) the amount of money in Suzy s piggy bank which she adds $10 to each week (3) the amount of money in a certificate of deposit that gets 4% interest each year (4) the amount of money in Jaclyn s wallet which increases and decreases by a different amount each week 4 5. Which function models the relationship shown in the table? (1) f(x) = 100 (3) f(x) = 50(2) x x (2) f(x) = x (4) f(x) = x x f(x) In the dot plot below, what is the value of the median? x x x xx x x x x xx x x x x (1) 25 (2) 55 (3) 58 (4) 60 6

14 10 ALGEBRA 1 Test 2 7. Dale is trying to find the height of a triangular wall. He already knows the area and the base measurement of the wall. Which is the equation of the area of a triangle, written in terms of the height? (1) h = 2 A (2) h = 2Ab (3) h b 8. Which graph displays a square root function? = b (4) h = 1 ba 7 2 A 2 (1) (2) (3) (4) 8 9. If the function f(x) represents the number of words that Janet can type in x minutes, what is the possible domain for the function? (1) The set of integers (3) The set of non-negative integers (2) The set of real numbers (4) The set of irrational numbers What is the dimension of the hypotenuse of the accompanying right triangle? (1) 12 units (2) 18 units (3) 10 units (4) 16 units y (1, 9) (9, 3) x The two-way table below represents the plans for seniors at Grant High School following graduation. Post-Education Plans Gender Total Boys Girls 2 year college year college military career undecided Total What is the conditional joint relative frequency of the number of girls planning to attend a 4 year college? (1) 11% (2) 14% (3) 20% (4) 25% 11

15 ALGEBRA 1 Test Which best describes a causal relationship? (1) one variable takes place at the same time as another (2) one variable is causing change in another (3) one variable has a relationship with another (4) one variable increases the possibility of another occurring Which is the equation of a line with a slope of 2 that passes through the point ( 2, 0)? (1) y + 2x = 4 (2) y 2x = 4 (3) y + 2 = 2x (4) y 4x = To the nearest tenth, what is the length of the hypotenuse of a right triangle if one side measures 4.5 meters and the other side measures 9 meters? (1) 10.1 meters (3) meters (2) 20.3 meters (4) meters Which rule describes the relationship between x and y in the accompanying table? (1) y = 3x (3) y = x 3 (2) y = x 3 (4) y = x + 3 x y Which function described below is quadratic? (1) y = 2x (2) x y (3) x y (4) Which statement below is true about linear functions? (1) Linear functions grow by equal factors over equal intervals. (2) Linear functions grow by equal differences over equal intervals. (3) Linear functions grow by equal differences over unequal intervals. (4) Linear functions grow by unequal factors over equal intervals Labor at the car repair shop can be represented by the function: Total charge for repairs { 150, 0 < h (h 1), h > 1 If h represents the number of hours worked, what is the charge for a 3 hour car repair? (1) $150 (2) $230 (3) $310 (4) $ y x

16 12 ALGEBRA 1 Test If g(x) = x 2 + 3x, what is the value of g( 3). (1) 0 (2) 3 (3) 18 (4) The height of a ball above the ground in feet is defined by the function h(t) = 16t t + 3 where t is the number of seconds after the ball is thrown. What is the value of h(t), two seconds after the ball is thrown? (1) 80 feet (2) 99 feet (3) 103 feet (4) 200 feet Which function below will result in a downward vertical shift of the graph of the parent function: y = x 2? (1) y = 1 2 x2 (2) y = 2x 2 (3) y = x (4) y = x Which set of data of temperatures has the largest dispersion as measured by its interquartile range? (1) 15, 17, 19, 21, 21, 22, 28 (3) 10, 19, 22, 23, 23, 29, 44 (2) 21, 23, 36, 37, 44, 48, 50 (4) 42, 47, 49, 50, 52, 59, Which equation illustrates how the expression 1.15 t can be rewritten to approximate the equivalent monthly interest rate if the annual rate is 15%? 12t (1) r = t. 12 (2) r = ( 115) 144 t. (3) r = ( 115. ) 12 (4) r 24. Which point is in the solution set to the system of inequalities: y > 2x 1 and y 1 2 x + 5? t = ( ) (1) ( 3, 10) (2) (8, 2) (3) ( 2, 1) (4) (4, 1) 24 Part II Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [16] 25. Transform the equation x 3y = 15 to express it in slope-intercept form.

17 ALGEBRA 1 Test Describe the range of a square root function Factor completely: 6x 2 4x Sales in the printing business have doubled for James in each of the last three months. During the last month, he made a profit of $520. If the pattern continues, what will be his three month total profit at the end of the next three months? 29. Find the sum of 3b 12 b + 2 and b + 2 and simplify if possible. 30. Find the area of the rectangle with a length of (x 2 2) and a width of (2x 2 x + 2).

18 14 ALGEBRA 1 Test Given h(x) = 2x 2 x + 2, find h( 2). 32. Rows of chairs are set out for a wedding. There are 6 chairs in the first row, 14 chairs in the second row, and 22 chairs in the third row. The rows continue in the same patterns for a total of 7 rows. How many chairs are set out for the wedding guests? Part III Answer all 4 questions in this part. The correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [16] 33. Jennifer and Kim enjoy making bracelets. At the beginning of this year Jennifer had already made twenty five bracelets. She continues to make eight bracelets every month. Kim just started making bracelets recently, so she had only made eleven at the beginning of the year. Kim is able to work more quickly, so she makes ten more bracelets every month. a) Write an inequality to model the situation comparing Jennifer and Kim. b) During what month(s) this year will Kim have made more bracelets than Jennifer?

19 x x ALGEBRA 1 Test Create a scatter plot to demonstrate the relationship between the snow storms this year and the average amount of salt used on the roads in town. a) Sketch a line or curve of best fit. y 15 b) Determine a function to define it. Snow storm Salt (pounds) Sketch the graph of the given data on the accompanying coordinate plane. a) Choose and state an appropriate scale so that all of the points can be plotted. b) Write a function rule for the data. y x f(x)

20 x 16 ALGEBRA 1 Test The data chart to the right represents the local Baseball Team shoe order. a) Write the linear regression equation for the line of best fit for the data in the chart. Round the numbers to the nearest hundredth. b) State the correlation coefficient to the nearest hundredth. c) Determine if the correlation is good and explain why or why not. Part IV Answer one question in this part. The correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [6] 37. Jonathan makes a weekly allowance of $25. He also makes $9.50 an hour at his job. Because of his age, Jonathan can work no more than 20 hours a week. a) Write a function for the amount of money he makes each week based on the amount of hours, h, he works. Baseball Team Shoe Order Height in Inches Shoe Size y b) What is the domain of the function for this situation? c) Sketch the graph of the function over the domain you chose.

21 ALGEBRA 1 Test 3 Part I Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. For each question, write on the space provided the numeral preceding the word or expression that best completes the statement or answers the question Which expression is equivalent to (x 2 + 3x 4)(x 5)? (1) x 3 + 8x 2 19x + 20 (3) x 3 2x 2 11x + 20 (2) x 3 2x 2 19x + 20 (4) x 3 8x 2 11x What are the zeros of (x 2)(x 2 9)? (1) { 3, 2, 3} (2) { 3, 3} (3) { 3, 0, 3} (4) {0, 3} 2 3. The formula for converting degrees Celsius to Fahrenheit is F = 9 C Which expression is correctly written to convert 5 Fahrenheit temperatures into degrees Celsius? (1) C = 9 5F 160 F + 32 (3) C = 5 9 (2) C = 5 F 160 (4) C = 32F What are the restrictions of the domain of the function F(x) = 2 x 9? (1) x 3 (2) x ± 3 (3) x 9 (4) x What is the value of f(2) when f(x) = { 3x2 + x 1, x 1 2x, x < 1 (1) 4 (2) 7 (3) 11 (4) What are the possible values for x in the equation 4x 2 = 64? (1) x = 0 (2) x = 4 (3) x = 4, 4 (4) x = 0, 4, Samuel s Car Service will charge a flat travel fee of $4.75 for anyone making a trip. They charge an additional set rate of $1.50 per mile that is traveled. What is an equation that represents the charges? (1) y = 1.5x (3) y = 1.5x (2) y = 4.75x (4) y = 4.75x The accompanying frequency table indicates the grades on the math midterm in Ms. Dennis class. In which interval does the median of the data lie? (1) (3) (2) (4) Frequency Table Interval Tally Frequency IIII I IIII IIII IIII II IIII 4 8

22 18 ALGEBRA 1 Test 3 9. What is the interquartile range of the data set below? Growth in feet of oak trees: 68, 80, 73, 90, 120, 94, 76, 112, 101, 94, 72 (1) 22 (2) 28 (3) 52 (4) A rocket is launched from the ground. The function h(t) = 4.9t t models the height of a rocket launched from the ground t seconds after it is launched. If all other factors remain the same, which of the following function models the height of a rocket above the ground after t seconds if it is launched from a platform 100 feet in the air? (1) h(t) = 4.9t t (3) h(t) = 4.9t t (2) h(t) = 4.9t t 100 (4) h(t) = 4.9t (t + 100) What is the sum of 2x 2 5x + 3 and 4x 2 + 4x 6 (1) 6x 2 x 3 (3) 2x 2 + 9x 3 (2) 6x 2 x 3 (4) 6x 2 + 9x Which situation describes a correlation that is not a causal relationship? (1) Car color and number of car accidents (2) Hours spent studying and test score (3) Amount of exercise each week and the time it takes to run a mile (4) Distance to reach a destination and the amount of gasoline used Which function has the largest maximum? (1) y = x 2 + 2x 1 (3) y = 2x 2 3x + 4 y (2) x y (4) Which are the side lengths of a right triangle? (1) 10, 15, 20 (2) 11, 16, 22 (3) 12, 18, 26 (4) 20, 21, Veronica earned $150 at work this past week in her paycheck. She wants to buy some necklaces which cost $6 each. She writes a function to model the amount of money she will have left from her paycheck after purchasing a certain number of necklaces. She writes the function, f(x) = 150 6x. Determine what x and f(x) stand for in the function. (1) x = weeks; f(x) = dollars left (3) x = necklaces; f(x) = dollars left (2) x = dollars left; f(x) = weeks (4) x = dollars left; f(x) = necklaces Maxwell and Jessica went to the candy store. Maxwell bought one chocolate covered cookie and two lollipops for $2.50. Jessica bought one chocolate covered cookie and four lollipops for $3.00. How much does one lollipop cost? (1) $0.25 (2) $0.40 (3) $.50 (4) $ x

23 ALGEBRA 1 Test If x = a 2, which situation would always double the value of x? b (1) Doubling the value of a. (3) Doubling the value of b. (2) Halving the value of a. (4) Halving the value of b Jessica is planning to build a square playing field. She wants to see how long the sides of the field will need to be for different areas. Her results are summarized in the following table. All values are rounded to the nearest hundredth when necessary. Area (square feet) Side Length (feet) What is the average rate of change in the side length as the area increases from 100 square feet to 900 square feet? (1).025 (2) 20 (3) 40 (4) The selling prices for a group of cars were recorded when the cars were new and for an additional five years. The results are summarized in the tables below. Which car s price dropped at a constant percent rate each year? (1) Year Cost (2) Year Cost (3) Year Cost (4) 0 25, , , , , , , , , , , , , , , , Five friends decided to do an Math Study experiment to see how studying impacted their test scores. Each student 80 studied for a different amount of time and recorded his or her test score on a math unit test. The results are shown in 30 the scatter plot to the right. Based on their data, which function best models 0 the relationship between studying and test score on the math unit test? (1) f(x) = 7x + 60 (3) f(x) =60x + 14 Year Cost 0 25, , , , , , Hours Spent Studying (x) (2) f(x) =14x + 60 (4) f(x) = 1 x Which is the correct solution set for 4x 2 + 4x 3 = 0? (1) {2, 3} (2) { 1 2, 3} (3) {1, 2} (4) { 1 2, 3 2 } In the expression 5x 3 4x 2 + 2x + 3, what is the coefficient of the quadratic term? (1) 5 (2) 4 (3) 3 (4) 4 22 Test Score f(x)

24 20 ALGEBRA 1 Test The table below displays data collected from the census. What is the linear correlation coefficient between years of education past 8 th grade and average yearly salary in the United States to the nearest hundredth? Years of education past 8 th grade Average Yearly Salary 2 years (10th grade) 23,088 4 years (High School Graduate) 32,552 6 years (Associates Degree) 39,884 8 years (Bachelors Degree) 53,976 9 years (Masters Degree) 66, years (Doctorate) 80,600 (1).96 (2).97 (3).98 (4) Which function below correctly illustrates the absolute value function? (1) a = { a, if a 0 a, if a 0 a, if a > 0 (3) a = { a, if a < 0 (2) a = { a, if a 0 a, if a 0 a, if a < 0 (4) a = { a, if a < 0 24 Part II Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in the space provided. [16] 25. Find the 5 th term sequence defined as: a(n) = (n + 3) n Solve: = x 2 x 3

25 ALGEBRA 1 Test Simplify: (x 2 + 4)(2x 2 + x 1) Find the y-intercept(s), if any for the equation: y = x Tim makes wooden salad bowls to sell at a monthly craft fair near his home town. Each month he spends $45 on specialty wood and other materials from his local lumber store. At the craft fair, Tim sells each completed salad bowl set for a total of $22, including tax. Express Tim s profit as a function of the number of units that he sells. 30. The Rockford s have a square play area that is built around a center sandbox that is in the shape of a circle. The sides of the play area are tangent to the circle. They want to determine the amount of grass seed to buy for the spring. If the diameter of the circular sandbox is represented by d use function notation to write a function to represent the play area only.

26 22 ALGEBRA 1 Test Explain the steps necessary for solving the following equation. x 2 8x 20 = The following data is the set of quiz scores from Ms. Jones algebra class: 56, 82, 78, 90, 99, 73, 85, 95, 76, 88, 100 a) Create a box plot for the data. b) Find the median grade for the class. Part III Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [16] Hours Wages 33. A teacher surveyed a small senior class to find out how many hours they worked last week and their wages. The information from each student is summarized in the table. a) Find the linear regression equation for the data in the table. Round all coefficients to the nearest hundredth b) Using your regression, how much money would someone make if he or she worked 25 hours last week? Round to the nearest cent.

27 ALGEBRA 1 Test Sketch the graph of the function: y = x + 3 y 23 x 35. Sketch the graph of the function h(x) = x 2 6x 5. Label all intercepts. Label the vertex and state if it is a maximum or minimum point. y x

28 x 24 ALGEBRA 1 Test The cost of operating Jelly s Doughnuts is $1600 per week plus $.10 to make each doughnut. a) Write a function, C(d), to model the company s weekly costs for producing d doughnuts. b) What is the total weekly cost if the company produces 4,000 doughnuts? c) Jelly s Doughnuts makes a gross profit of $.60 for each doughnut they sell. If they sold all 4000 doughnuts they made, would they make money or lose money for the week? How much? Part IV Answer one question in this part. The correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in the spaces provided. [12] 37. Sketch the graph of all of the solutions to the equation y = 1 4 (2)x where 0 x 5. y Find the average rate of change between f(2) and f(5).

29 ALGEBRA 1 June 2014 Part I Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. For each statement or question, choose the word or expression that, of those given, best completes the statement or answers the question. Record your answers in the space provided. [48] When solving the equation 4(3x 2 + 2) 9 = 8x 2 + 7, Emily wrote 4(3x 2 + 2) = 8x as her first step. Which property justifies Emily s first step? (1) addition property of equality (2) commutative property of addition (3) multiplication property of equality (4) distributive property of multiplication over addition 1 2. Officials in a town use a function, C, to analyze traffic patterns. C(n) represents the rate of traffic through an intersection where n is the number of observed vehicles in a specified time interval. What would be the most appropriate domain for the function? (1) { 2, 1, 0, 1, 2, 3, } (3) {0, 1 2, 1, 1 1 2, 2, } (2) { 2, 1, 0, 1, 2, 3} (4) {0, 1, 2, 3, } 2 3. If A = 3x 2 + 5x 6 and B = 2x 2 6x + 7, then A B equals (1) 5x 2 11x + 13 (2) 5x x 13 (3) 5x 2 x + 1 (4) 5x 2 x Given: y + x > 2 y 3x 2 Which graph shows the solution of the given set of inequalities? y y y y x x x x (1) (2) (3) (4) 4 5. Which value of x satisfies the equation 7 9 x =? (1) 8.25 (2) 8.89 (3) (4) The accompanying table shows the average Year Balance, in Dollars yearly balance in a savings account where interest is compounded annually. No money is deposited or withdrawn after the initial amount is deposited Which type of function best models the given data? (1) linear function with a negative rate of change (2) linear function with a positive rate of change (3) exponential decay function (4) exponential growth function 6

30 26 ALGEBRA 1 June A company that manufactures radios first pays a start-up cost, and then spends a certain amount of money to manufacture each radio. If the cost of manufacturing r radios is given by the function c(r) = 5.25r + 125, then the value 5.25 best represents (1) the start-up cost (2) the profit earned from the sale of one radio (3) the amount spent to manufacture each radio (4) the average number of radios manufactured 7 8. Which equation has the same solution as x 2 6x 12 = 0? (1) (x + 3) 2 = 21 (2) (x 3) 2 = 21 (3) (x + 3) 2 = 3 (4) (x 3) 2 = A ball is thrown into the air from the edge of a 48-foot-high cliff so that it eventually lands on the ground. The accompanying graph shows the height, y, of the ball from the ground after x seconds. For which interval is the ball s height always decreasing? (1) 0 x 2.5 (3) 2.5 < x < 5.5 (2) 0 < x < 5.5 (4) x 2 y x What are the roots of the equation x 2 + 4x 16 = 0? (1) 2 ± 2 5 (2) 2 ± 2 5 (3) 2 ± 4 5 (4) 2 ± What is the correlation coefficient of the linear fit of the data shown to the right, to the nearest hundredth? (1) 1.00 (3) 0.93 (2) 0.93 (4) y x Keith determines the zeros of the function f(x) to be 6 and 5. What could be Keith s function? (1) f(x) = (x + 5)(x + 6) (3) f(x) = (x 5)(x + 6) (2) f(x) = (x + 5)(x 6) (4) f(x) = (x 5)(x 6) Given: L = 2 M = 3 3 N = 16 P = 9 Which expression results in a rational number? (1) L + M (2) M + N (3) N + P (4) P + L 13

31 ALGEBRA 1 June Which system of equations has the same solution as the system below? 2x + 2y = 16 3x y = 4 (1) 2x + 2y = 16 (2) 2x + 2y = 16 (3) x + y = 16 (4) 6x + 6y = 48 6x 2y = 4 6x 2y = 8 3x y = 4 6x + 2y = The table below represents the function F. x F(x) The equation that represents this function is (1) F(x) = 3 x (2) F(x) = 3x (3) F(x) = 2 x + 1 (4) F(x) = 2x John has four more nickels than dimes in his pocket, for a total of $1.25. Which equation could be used to determine the number of dimes, x, in his pocket? (1) 0.10(x + 4) (x) = $1.25 (3) 0.10(4x) (x) = $1.25 (2) 0.05(x + 4) (x) = $1.25 (4) 0.05(4x) (x) = $ If f(x) = 1 x + 9, which statement is always true? 3 (1) f(x) < 0 (3) If x < 0, then f(x) < 0. (2) f(x) > 0 (4) If x > 0, then f(x) > The Jamison family kept a log of the distance they traveled during a trip, as represented by (10,390) (8,350) the accompanying graph. During which interval was their average (6,230) speed the greatest? (4,180) (1) the first hour to the second hour (2,110) (2) the second hour to the fourth hour (1,40) (3) the sixth hour to the eighth hour Elapsed Time (hours) (4) the eighth hour to the tenth hour Christopher looked at his quiz scores shown below for the first and second semester of his Algebra class. Distance Traveled (miles) Semester 1: 78, 91, 88, 83, 94 Semester 2: 91, 96, 80, 77, 88, 85, 92 Which statement about Christopher s performance is correct? (1) The interquartile range for semester 1 is greater than the interquartile range for semester 2. (2) The median score for semester 1 is greater than the median score for semester 2. (3) The mean score for semester 2 is greater than the mean score for semester 1. (4) The third quartile for semester 2 is greater than the third quartile for semester 1. 19

32 28 ALGEBRA 1 June 2014 y 20. The graph of y = f(x) is shown to the right. Which point could be used to find f(2)? B (1) A (3) C C (2) B (4) D D A x 21. A sunflower is 3 inches tall at week 0 and grows 2 inches each week. Which function(s) shown below can be used to determine the height, f(n), of the sunflower in n weeks? I. f(n) = 2n + 3 II. f(n) = 2n + 3(n 1) III. f(n) = f(n 1) + 2 where f(0) = 3 20 (1) I and II (2) II, only (3) III, only (4) I and III A cell phone company charges $60.00 a month for up to 1 gigabyte of data. The cost of additional data is $0.05 per megabyte. If d represents the number of additional megabytes used and c represents the total charges at the end of the month, which linear equation can be used to determine a user s monthly bill? (1) c = d (3) c = 60d 0.05 (2) c = 60.05d (4) c = d The formula for the volume of a cone is V = 1 3 πr2 h. The radius, r, of the cone may be expressed as (1) 3V (2) V (3) 3 V (4) 1 V π h 3 π h π h 3 π h The diagrams below represent the first three terms of a sequence. Term 1 Term 2 Term 3 Assuming the pattern continues, which formula determines a n, the number of shaded squares in the nth term? (1) a n = 4n + 12 (2) a n = 4n + 8 (3) a n = 4n + 4 (4) a n = 4n

33 ALGEBRA 1 June 2014 Part II Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [16] Draw the graph of y = x 1 on the set of axes below. y x 26. The breakdown of a sample of a chemical compound is represented by the function p(t) = 300(0.5) t, where p(t) represents the number of milligrams of the substance and t represents the time, in years. In the function p(t), explain what 0.5 and 300 represent. 27. Given 2x + ax 7 > 12, determine the largest integer value of a when x = 1.

34 x x 30 ALGEBRA 1 June The vertex of the parabola represented by f(x) = x 2 4x + 3 has coordinates (2, 1). Find the coordinates of the vertex of the parabola defined by g(x) = f(x 2). Explain how you arrived at your answer. [The use of the set of axes below is optional.] y 29. On the set of axes below, draw the graph of the equation y = 3 4 x + 3. y Is the point (3, 2) a solution to the equation? Explain your answer based on the graph drawn.

35 ALGEBRA 1 June The function f has a domain of {1, 3, 5, 7} and a range of {2, 4, 6}. Could f be represented by {(1, 2), (3, 4), (5, 6), (7, 2)}? Justify your answer Factor the expression x 4 + 6x 2 7 completely. 32. Robin collected data on the number of hours she watched television on Sunday through Thursday nights for a period of 3 weeks. The data are shown in the table below. Sun Mon Tues Wed Thurs Week Week Week Using an appropriate scale on the number line below, construct a box plot for the 15 values.

36 32 ALGEBRA 1 June 2014 Part III Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [16] 33. Write an equation that defines m(x) as a trinomial where m(x) = (3x 1)(3 x) + 4x Solve for x when m(x) = A rectangular garden measuring 12 meters by 16 meters is to have a walkway installed around it with a width of x meters, as shown in the accompanying diagram. Together, the walkway and the garden have an area of 396 square meters. x x 16 m Garden 12 m x Walkway Write an equation that can be used to find x, the width of the walkway. x Describe how your equation models the situation. Determine and state the width of the walkway, in meters.

37 ALGEBRA 1 June Caitlin has a movie rental card worth $175. After she rents the first movie, the card s value is $ After she rents the second movie, its value is $ After she rents the third movie, the card is worth $ Assuming the pattern continues, write an equation to define A(n), the amount of money on the rental card after n rentals. Caitlin rents a movie every Friday night. How many weeks in a row can she afford to rent a movie, using her rental card only? Explain how you arrived at your answer. 36. An animal shelter spends $2.35 per day to care for each cat and $5.50 per day to care for each dog. Pat noticed that the shelter spent $89.50 caring for cats and dogs on Wednesday. Write an equation to represent the possible numbers of cats and dogs that could have been at the shelter on Wednesday. Pat said that there might have been 8 cats and 14 dogs at the shelter on Wednesday. Are Pat s numbers possible? Use your equation to justify your answer. Later, Pat found a record showing that there were a total of 22 cats and dogs at the shelter on Wednesday. How many cats were at the shelter on Wednesday?

38 34 ALGEBRA 1 June 2014 Part IV Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. A correct numerical answer with no work shown will receive only 1 credit. The answer should be written in pen. [6] 37. A company is considering building a manufacturing plant. They determine the weekly production cost at site A to be A(x) = 3x 2 while the production cost at site B is B(x) = 8x + 3, where x represents the number of products, in hundreds, and A(x) and B(x) are the production costs, in hundreds of dollars. Graph the production cost functions on the accompanying set of axes and label them site A and site B y Cost (hundreds of dollars) State the positive value(s) of x for which the production costs at the two sites are equal. Explain how you determined your answer Number of Products (hundreds) x If the company plans on manufacturing 200 products per week, which site should they use? Justify your answer

39 ALGEBRA 1 August 2014 Part I Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. For each statement or question, choose the word or expression that, of those given, best completes the statement or answers the question. Record your answers in the space provided. [48] Which statement is not always true? (1) The product of two irrational numbers is irrational. (2) The product of two rational numbers is rational. (3) The sum of two rational numbers is rational. (4) The sum of a rational number and an irrational number is irrational A satellite television company charges a one-time installation fee and a monthly service charge. The total cost is modeled by the function y = x. Which statement represents the meaning of each part of the function? (1) y is the total cost, x is the number of months of service, $90 is the installation fee, and $40 is the service charge per month. (2) y is the total cost, x is the number of months of service, $40 is the installation fee, and $90 is the service charge per month. (3) x is the total cost, y is the number of months of service, $40 is the installation fee, and $90 is the service charge per month. (4) x is the total cost, y is the number of months of service, $90 is the installation fee, and $40 is the service charge per month If 4x = 0, the roots of the equation are (1) 25 and 25 (2) 25, only (3) 5 and 5 (4) 5, only 3 4. Isaiah collects data from two different companies, each with four employees. The results of the study, based on each worker s age and salary, are listed in the accompanying tables. Which statement is true about these data? (1) The median salaries in both companies are greater than $37,000. (2) The mean salary in company 1 is greater than the mean salary in company 2. (3) The salary range in company 2 is greater than the salary range in company 1. (4) The mean age of workers at company 1 is greater than the mean age of workers at company Which point is not on the graph represented by y = x 2 + 3x 6? (1) ( 6, 12) (2) ( 4, 2) (3) (2, 4) (4) (3, 6) 5

40 36 ALGEBRA 1 August A company produces x units of a product per month, where C(x) represents the total cost and R(x) represents the total revenue for the month. The functions are modeled by C(x) = 300x and R(x) = 0.5x x 100. The profit is the difference between revenue and cost where P(x) = R(x) C(x). What is the total profit, P(x), for the month? (1) P(x) = 0.5x x 150 (3) P(x) = 0.5x 2 500x (2) P(x) = 0.5x x 350 (4) P(x) = 0.5x x What is one point that lies in the solution set of the system of inequalities graphed? (1) (7, 0) (2) (3, 0) (3) (0, 7) (4) ( 3, 5) 7 8. The value of the x-intercept for the graph of 4x 5y = 40 is (1) 10 (2) 4 5 (3) 4 5 (4) Sam and Jeremy have ages that are consecutive odd integers. The product of their ages is 783. Which equation could be used to find Jeremy s age, j, if he is the younger man? (1) j = 783 (2) j 2 2 = 783 (3) j 2 + 2j = 783 (4) j 2 2j = A population that initially has 20 birds approximately doubles every 10 years. Which graph represents this population growth? (1) (2) (3) (4) Let f be a function such that f(x) = 2x 4 is defined on the domain 2 x 6. The range of this function is (1) 0 y 8 (2) 0 y < (3) 2 y 6 (4) < y < Which situation could be modeled by using a linear function? (1) a bank account balance that grows at a rate of 5% per year, compounded annually (2) a population of bacteria that doubles every 4.5 hours (3) the cost of cell phone service that charges a base amount plus 20 cents per minute (4) the concentration of medicine in a person s body that decays by a factor of one-third every hour 12

41 ALGEBRA 1 August Which graph shows a line where each value of y is three more than half of x? 37 (1) (2) (3) (4) The accompanying table shows the average diameter of a pupil in a person s eye as he or she grows older. What is the average rate of change, in millimeters per year, of a person s pupil diameter from age 20 to age 80? (1) 2.4 (3) 2.4 (2) 0.04 (4) Which expression is equivalent to x 4 12x ? (1) (x 2 6)(x 2 6) (3) (6 x 2 )(6 + x 2 ) (2) (x 2 + 6)(x 2 + 6) (4) (x 2 + 6)(x 2 6) The third term in an arithmetic sequence is 10 and the fifth term is 26. If the first term is a 1, which is an equation for the nth term of this sequence? (1) a n = 8n + 10 (3) a n = 16n + 10 (2) a n = 8n 14 (4) a n = 16n The graph of the equation y = ax 2 is shown. If a is multiplied by 1 2, the graph of the new equation is (1) wider and opens downward (2) wider and opens upward (3) narrower and opens downward (4) narrower and opens upward The zeros of the function f(x) = (x + 2) 2 25 are (1) 2 and 5 (2) 3 and 7 (3) 5 and 2 (4) 7 and 3 18

42 38 ALGEBRA 1 August During the 2010 season, football player McGee s earnings, m, were million dollars more than those of his teammate Fitzpatrick s earnings, f. The two players earned a total of 3.95 million dollars. Which system of equations could be used to determine the amount each player earned, in millions of dollars? (1) m + f = 3.95 (3) f 3.95 = m m = f m = f (2) m 3.95 = f (4) m + f = 3.95 f = m f = m What is the value of x in the equation x = ? (1) 4 (2) 6 (3) 8 (4) The accompanying table shows the number of grams of carbohydrates, x, and the number of Calories, y, of six different foods. Which equation best represents the line of best fit for this set of data? (1) y = 15x (3) y = 0.1x 0.4 (2) y = 0.07x (4) y = 14.1x A function is graphed on the set of axes to the right. Which function is related to the graph? (1) (3) (2) (4) The function h(t) = 16t represents the height, h(t), in feet, of an object from the ground at t seconds after it is dropped. A realistic domain for this function is (1) 3 t 3 (3) 0 h(t) 144 (2) 0 t 3 (4) all real numbers If f(1) = 3 and f(n) = 2f(n 1) + 1, then f(5) = (1) 5 (2) 11 (3) 21 (4) 43 24

43 ALGEBRA 1 August 2014 Part II Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [16] In the equation x x + 24 = (x + a) (x + b), b is an integer. Find algebraically all possible values of b. 26. Rhonda deposited $3000 in an account in the Merrick National Bank, earning 4.2% interest, compounded annually. She made no deposits or withdrawals. Write an equation that can be used to find B, her account balance after t years. 27. Guy and Jim work at a furniture store. Guy is paid $185 per week plus 3% of his total sales in dollars, x, which can be represented by g(x) = x. Jim is paid $275 per week plus 2.5% of his total sales in dollars, x, which can be represented by f(x) = x. Determine the value of x, in dollars, that will make their weekly pay the same. 28. Express the product of 2x 2 + 7x 10 and x + 5 in standard form.

44 40 ALGEBRA 1 August Let f be the function represented by the accompanying graph. Let g be a function such that g(x) = 1 2 x2 + 4x + 3. Determine which function has the larger maximum value. Justify your answer. 30. Solve the inequality below to determine and state the smallest possible value for x in the solution set. 3(x + 3) 5x 3

45 ALGEBRA 1 August The table below represents the residuals for a line of best fit. 41 Plot these residuals on the set of axes below. Using the plot, assess the fit of the line for these residuals and justify your answer. 32. A student was given the equation x 2 + 6x 13 = 0 to solve by completing the square. The first step that was written is shown below. x 2 + 6x = 13 The next step in the student s process was x 2 + 6x + c = 13 + c. State the value of c that creates a perfect square trinomial. Explain how the value of c is determined.

46 x 42 ALGEBRA 1 August 2014 Part III Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [16] 33. On the axes, graph f(x) = 3x. y If g(x) = f(x) 2, how is the graph of f(x) translated to form the graph of g(x)? If h(x) = f(x 4), how is the graph of f(x) translated to form the graph of h(x)? 34. The formula for the area of a trapezoid is A = 1 2 h(b 1 + b 2 ). Express b 1 in terms of A, h, and b 2. The area of a trapezoid is 60 square feet, its height is 6 ft, and one base is 12 ft. Find the number of feet in the other base.

47 ALGEBRA 1 August Let f(x) = 2x 2 and g(x) = 2x 4. On the set of axes below, draw the graphs of y = f(x) and y = g(x). y 43 x Using this graph, determine and state all values of x for which f(x) = g(x). 36. A school is building a rectangular soccer field that has an area of 6000 square yards. The soccer field must be 40 yards longer than its width. Determine algebraically the dimensions of the soccer field, in yards.

48 44 ALGEBRA 1 August 2014 Part IV Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. A correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be written in pencil. [6] 37. Edith babysits for x hours a week after school at a job that pays $4 an hour. She has accepted a job that pays $8 an hour as a library assistant working y hours a week. She will work both jobs. She is able to work no more than 15 hours a week, due to school commitments. Edith wants to earn at least $80 a week, working a combination of both jobs. Write a system of inequalities that can be used to represent the situation. Graph these inequalities on the set of axes below. Determine and state one combination of hours that will allow Edith to earn at least $80 per week while working no more than 15 hours.

49 ALGEBRA 1 January 2015 Part I Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. For each statement or question, choose the word or expression that, of those given, best completes the statement or answers the question. Record your answers in the space provided. [48] 1. The owner of a small computer repair business has one employee, who is paid an hourly rate of $22. The owner estimates his weekly profit using the function P(x) = x. In this function, x represents the number of (1) computers repaired per week (3) customers served per week (2) hours worked per week (4) days worked per week Peyton is a sprinter who can run the 40-yard dash in 4.5 seconds. He converts his speed into miles per hour, as shown below. 40 yd 3ft 5280ft 60sec 60 min 45. sec 1yd 1mi 1min 1hr Which ratio is incorrectly written to convert his speed? (1) 3 ft (2) 5280 ft (3) 60 sec (4) 60 min 1yd 1mi 1min 1hr 2 3. Which equation has the same solutions as 2x 2 + x 3 = 0? (1) (2x 1)(x + 3) = 0 (3) (2x 3)(x + 1) = 0 (2) (2x + 1)(x 3) = 0 (4) (2x + 3)(x 1) = Krystal was given $3000 when she turned 2 years old. Her parents invested it at a 2% interest rate compounded annually. No deposits or withdrawals were made. Which expression can be used to determine how much money Krystal had in the account when she turned 18? (1) 3000( ) 16 (3) 3000( ) 18 (2) 3000(1 0.02) 16 (4) 3000(1 0.02) Which table of values represents a linear relationship? x f(x) x f(x) x f(x) x f(x) (1) (2) (3) (4) 5 6. Which domain would be the most appropriate set to use for a function that predicts the number of household online-devices in terms of the number of people in the household? (1) integers (3) irrational numbers (2) whole numbers (4) rational numbers 6

50 46 ALGEBRA 1 January The inequality 7 2 x < x 8 is equivalent to 3 (1) x > 9 (2) x > 3 (3) x < 9 (4) x < The value in dollars, v(x), of a certain car after x years is represented by the equation v(x) = 25,000(0.86) x. To the nearest dollar, how much more is the car worth after 2 years than after 3 years? (1) 2589 (2) 6510 (3) 15,901 (4) 18, Which function has the same y-intercept as the accompanying graph? (1) y = 12 6 x 4 (2) y = 6x (3) 6y + x = 18 (4) y + 3 = 6x Fred is given a rectangular piece of paper. If the length of Fred s piece of paper is represented by 2x 6 and the width is represented by 3x 5, then the paper has a total area represented by (1) 5x 11 (2) 6x 2 28x + 30 (3) 10x 22 (4) 6x 2 6x The graph of a linear equation contains the points ( 3, 11) and ( 2, 1). Which point also lies on the graph? (1) (2, 1) (2) (2, 4) (3) (2, 6) (4) (2, 9) 11 y x 12. How does the graph of f(x) = 3(x 2) compare to the graph of g(x) = x 2? (1) The graph of f(x) is wider than the graph of g(x), and its vertex is moved to the left 2 units and up 1 unit. (2) The graph of f(x) is narrower than the graph of g(x), and its vertex is moved to the right 2 units and up 1 unit. (3) The graph of f(x)) is narrower than the graph of g(x), and its vertex is moved to the left 2 units and up 1 unit. (4) The graph of f(x) is wider than the graph of g(x), and its vertex is moved to the right 2 units and up 1 unit Connor wants to attend the town carnival. The price of admission to the carnival is $4.50, and each ride costs an additional 79 cents. If he can spend at most $16.00 at the carnival, which inequality can be used to solve for r, the number of rides Connor can go on, and what is the maximum number of rides he can go on? (1) r 16.00; 3 rides (3) r 16.00; 14 rides (2) r 16.00; 4 rides (4) r 16.00; 15 rides 13

51 ALGEBRA 1 January Corinne is planning a beach vacation in July and is analyzing the daily high temperatures for her potential destination. She would like to choose a destination with a high median temperature and a small interquartile range. She constructed box plots shown in the diagram below. 47 Which destination has a median temperature above 80 degrees and the smallest interquartile range? (1) Ocean Beach (3) Serene Shores (2) Whispering Palms (4) Pelican Beach Some banks charge a fee on savings accounts that are left inactive for an extended period of time. The equation y = 5000(0.98) x represents the value, y, of one account that was left inactive for a period of x years. What is the y-intercept of this equation and what does it represent? (1) 0.98, the percent of money in the account initially (2) 0.98, the percent of money in the account after x years (3) 5000, the amount of money in the account initially (4) 5000, the amount of money in the account after x years The equation for the volume of a cylinder is V = πr 2 h. The positive value of r, in terms of h and V, is (1) r = V (2) r = Vπ h (3) r = 2Vπh (4) r = V 16 πh 2 π 17. Which equation has the same solutions as x 2 + 6x 7 = 0? (1) (x + 3) 2 = 2 (2) (x 3) 2 = 2 (3) (x 3) 2 = 16 (4) (x + 3) 2 = Two functions, y = x 3 and 3x + 3y = 27, are graphed on the same set of axes. Which statement is true about the solution to the system of equations? (1) (3, 0) is the solution to the system because it satisfies the equation y = x 3. (2) (9, 0) is the solution to the system because it satisfies the equation 3x + 3y = 27. (3) (6, 3) is the solution to the system because it satisfies both equations. (4) (3, 0), (9, 0), and (6, 3) are the solutions to the system of equations because they all satisfy at least one of the equations Miriam and Jessica are growing bacteria in a laboratory. Miriam uses the growth function f(t) = n 2t while Jessica uses the function g(t) = n 4t, where n represents the initial number of bacteria and t is the time, in hours. If Miriam starts with 16 bacteria, how many bacteria should Jessica start with to achieve the same growth over time? (1) 32 (2) 16 (3) 8 (4) 4 19

52 48 ALGEBRA 1 January If a sequence is defined recursively by f(0) = 2 and f(n + 1) = 2f(n) + 3 for n 0, then f(2) is equal to (1) 1 (2) 11 (3) 5 (4) An astronaut drops a rock off the edge of a cliff on the Moon. The distance, d(t), in meters, the rock travels after t seconds can be modeled by the function d(t) = 0.8t 2. What is the average speed, in meters per second, of the rock between 5 and 10 seconds after it was dropped? (1) 12 (2) 20 (3) 60 (4) When factored completely, the expression p 4 81 is equivalent to (1) (p 2 + 9)(p 2 9) (3) (p 2 + 9)(p + 3)(p 3) (2) (p 2 9)(p 2 9) (4) (p + 3)(p 3)(p + 3)(p 3) In 2013, the United States Postal Service charged $0.46 to mail a letter weighing up to 1 oz. and $0.20 per ounce for each additional ounce. Which function would determine the cost, in dollars, c(z), of mailing a letter weighing z ounces where z is an integer greater than 1? (1) c(z) = 0.46z (3) c(z) = 0.46(z 1) (2) c(z) = 0.20z (4) c(z) = 0.20(z 1) A polynomial function contains the factors x, x 2, and x + 5. Which graph(s) below could represent the graph of this function? (1) I, only (2) II, only (3) I and III (4) I, II, and III 24 Part II Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [16] 25. Ms. Fox asked her class Is the sum of 4.2 and 2 rational or irrational? Patrick answered that the sum would be irrational. State whether Patrick is correct or incorrect. Justify your reasoning.

53 ALGEBRA 1 January The school newspaper surveyed the student body for an article about club membership. The accompanying table shows the number of students in each grade level who belong to one or more clubs. If there are 180 students in ninth grade, what percentage of the ninth grade students belong to more than one club? A function is shown in the accompanying table. If included in the table, which ordered pair, ( 4, 1) or (1, 4), would result in a relation that is no longer a function? Explain your answer. x f(x) Subtract 5x 2 + 2x 11 from 3x 2 + 8x 7. Express the result as a trinomial. 29. Solve the equation 4x 2 12x = 7 algebraically for x.

54 x 50 ALGEBRA 1 January Graph the following function on the set of accompanying axes. x, 3 x < 1 f(x) = { 4, 1 x 8 f(x) 31. A gardener is planting two types of trees: Type A is three feet tall and grows at a rate of 15 inches per year. Type B is four feet tall and grows at a rate of 10 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height. 32. Write an exponential equation for the graph shown to the right. Explain how you determined the equation.

55 ALGEBRA 1 January 2015 Part III Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [16] Jacob and Zachary go to the movie theater and purchase refreshments for their friends. Jacob spends a total of $18.25 on two bags of popcorn and three drinks. Zachary spends a total of $27.50 for four bags of popcorn and two drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a bag of popcorn and the price of a drink, to the nearest cent. 34. The graph of an inequality is shown to the right. a) Write the inequality represented by the graph. b) On the same set of axes, graph the inequality x + 2y < 4. c) The two inequalities graphed on the set of axes form a system. Oscar thinks that the point (2, 1) is in the solution set for this system of inequalities. Determine and state whether you agree with Oscar. Explain your reasoning.

56 52 ALGEBRA 1 January A nutritionist collected information about different brands of beef hot dogs. She made a table showing the number of Calories and the amount of sodium in each hot dog. a) Write the correlation coefficient for the line of best fit. Round your answer to the nearest hundredth. b) Explain what the correlation coefficient suggests in the context of this problem. 36. a) Given the function f(x) = x 2 + 8x + 9, state whether the vertex represents a maximum or minimum point for the function. Explain your answer. b) Rewrite f(x) in vertex form by completing the square. Part IV Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. A correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be written in pencil. [6] 37. New Clarendon Park is undergoing renovations to its gardens. One garden that was originally a square is being adjusted so that one side is doubled in length, while the other side is decreased by three meters. The new rectangular garden will have an area that is 25% more than the original square garden. Write an equation that could be used to determine the length of a side of the original square garden. Explain how your equation models the situation. Determine the area, in square meters, of the new rectangular garden.

57 ALGEBRA 1 Correlation of Standards

58 54 Correlation of Standards QUESTION STANDARD TEST 1 TEST 2 TEST 3 1 A.REI.3 A.SSE.3 A.APR.1 2 F.IF.1 A.APR.1 A.REI.4 3 F.IF.2 A.REI.4 A.CED.4 4 S.ID.2 F.LE.1 A.CED.3 5 A.APR.1 F.LE.2 F.IF.2 6 A.APR.1 S.ID.2 A.REI.4 7 F.IF.7 A.CED.4 F.IF.5 8 F.LE.2 F.IF.7 S.ID.2 9 A.SSE.2 F.IF.5 S.ID.5 10 S.ID.6 8.G.B.7 F.BF.1 11 F.IF.4 S.ID.9 A.PRR.1 12 F.IF.5 S.ID.5 S.ID GB.6 A.REI.10 F.IF.9 14 F.IF.7 F.IF.6 8.G.B.6 15 F.IF.6 F.IF.7 N.Q.2 16 A.SSE.1 F.LE.3 A.CED.2 17 F.IF.3 F.LE.1 A.APR.1 18 F.IF.4 A.CED.2 F.IF.6 19 S.ID.5 F.1F.2 F.LE.1 20 A.REI.10 A.REI.4 S.ID.6 21 A.CED.2 F.BF.3 A.REI.4 22 A.SSE.2 S.ID.2 A.SSE.1 23 F.IF.4 A.SSE.3 S.ID.8 24 A.REI.11 A.REI.12 A.REI.3

59 Correlation of Standards 55 QUESTION STANDARD TEST 1 TEST 2 TEST 3 25 F.IF.6 A.SSE.3 F.IF.3 26 A.SSE.3 F.IF.7 F.BF.3 27 A.REI.12 A.SSE.3 A.REI.5 28 A.REI.4 F.IF.2 A.CED.3 29 A.CED.1 8.G.B.7 F.IF.7 30 A.REI.11 A.SSE.2 N.RN.3 31 F.IF.2 A.APR.1 F.BF.1 32 F.IF.8 F.IF.2 F.BF.1 33 A.REI.12 F.IF.3 A.REI.1 34 N.Q.1 A.CED.1 S.ID.1 35 F.IF.7 S.ID.6 S.ID.6 36 S.ID.1 F.IF.8 F.IF.7 37 A.REI.6 F.IF.7 F.IF.7

60 56 Correlation of Standards QUESTION STANDARD JUNE 2014 AUGUST 2014 JANUARY A-REI.A N-RN.B A-SSE.A 2 F-IF.B F-LE.B N-Q.A 3 A-APR.A A-REI.B A-SSE.B 4 A-REI.D S-ID.A F-BF.A 5 A-REI.B A-REI.D F-LE.A 6 F-LE.A A-APR.A F-IF.B 7 F-LE.B A-REI.D A-REI.B 8 A-REI.B F-IF.C F-IF.A 9 F-IF.B A-CED.A F-IF.C 10 A-REI.B F-LE.A A-APR.A 11 S-ID.C F-IF.A A-REI.D 12 A-SSE.B F-LE.A F-BF.B 13 N-RN.B A-CED.A A-CED.A 14 A-REI.C F-IF.B S-ID.A 15 F-LE.A A-SSE.A F-IF.B 16 A-CED.A F-LE.A A-CED.A 17 F-IF.A F-BF.B A-REI.B 18 F-IF.B F-IF.C A-REI.D 19 S.ID.A A-CED.A A-SSE.B 20 F.IF.A A-REI.B F-IF.A 21 F.IF.A S-ID.B F-IF.B 22 A.CED.A F-IF.C A.SSE.A 23 A.CED.A F-IF.B A-CED.A 24 F.LE.A F-IF.A A-APR.B

61 Correlation of Standards 57 QUESTION STANDARD JUNE 2014 AUGUST 2014 JANUARY F.IF.C A-SSE.B N-RN.B 26 F.LE.B F-BF.A S-ID.B 27 A.REI.B A-REI.C F-IF.A 28 F.BF.B A-APR.A A-APR.A 29 A.REI.D F-IF.C A-REI.B 30 F.IF.A A-REI.B F-IF.C 31 A.SSE.A S-ID.B A-CED.A 32 S.ID.A A-REI.B F-LE.A 33 A.REI.B F-BF.B A-CED.A 34 A.CED.A A-CED.A A-REI.D 35 F.BF.A A-REI.D S-ID.C 36 A.CED.A A-CED.A F-IF.C 37 A.REI.D A-CED.A A-CED.A

62

63 AVAILABLE ONLY AT THE TOPICAL REVIEW BOOK COMPANY ALGEBRA 1 MADE EASY Common Core Standards Edition Written by: MaryAnn Casey Topical Review Book Company A quick reference guide for the NEW COMMON CORE STANDARDS of ALGEBRA 1 Loaded with lots of examples ISBN # WEBSITE: topicalrbc@aol.com PRODUCING TEST REVIEW MATERIAL SINCE 1936.