Algebra 1 Honors EOC Review #3 Non-Calculator Portion

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1 Algebra 1 Honors EOC Review #3 Non-Calculator Portion 1. Select any the expressions that are equivalent to [A] 15 [B] [C] 3 [D] Which expression is equivalent to : x y z? [A] x yz [B] z x [C] x yz [D] x z [E] x yz For problem 3, simplify the expression and rewrite any rational exponents in their radical form with positive exponents and indexes x y z Rewrite the expression where b, m and n are positive integers as a single radical expression in the form n m b. For problems 5 7 state whether the result will be rational, irrational, or depends on what two numbers are used. 5. The sum, difference, product or quotient of TWO rational numbers. 6. The sum, difference, product or quotient of TWO irrational numbers. 7. The sum, difference, product or quotient of a rational number and an irrational number.

2 8. Max collected data on the height of each of his 0 classmates. The boxplot shown represents his data. Use the boxplot to answer the following questions : a) What is the median height of Max s classmates? b) What the is the range of the heights? c) What is the interquartile range of the heights? d) Use the boxplot below to complete the dot plot below. 9. Which statistic cannot be determined from a box plot representing the scores on a math test in Mrs. DeRidder's algebra class? [A] the lowest score [B] the median score [C] the highest score [D] the mode

3 10. What does the correlation coefficient tell us? [A] Measure of the exponential association between two variables [B] Measure of the causation of one variable on the other [C] Measure of the linear association between two variables [D] Measure of the distance between a datum and the value predicted by a model For problems determine whether the statement is TRUE or FALSE. 11. A value of r near zero indicates there is a weak linear relationship between x and y 1. A value of r = 0.5 indicates a weaker linear relationship between x and y than a value of r = A value of r = 1 indicates that there is a cause-and-effect relationship between x and y. 14. The scatterplot below represents the forearm lengths and foot lengths of 10 people. Based on a linear model of the data, which is the best prediction for the length of a person s foot if his/her forearm length is 1 centimeters?

4 15. Eduardo notices he gets no mosquito bites when he wears a certain kind of sunscreen. He forms two possible conclusions. I. The sunscreen causes mosquitoes to stay away from him. II. There is a correlation between wearing sunscreen and getting no mosquito bites, but one does not cause the other. Which observation would provide the best evidence to support conclusion II? [A] Eduardo s friend gets mosquito bites when he goes out without sunscreen. [B] Eduardo s friend wears the same sunscreen and also gets no mosquito bites. [C] Eduardo gets no mosquito bites when he goes out at the same time of day without sunscreen. [D] Eduardo tries a new kind of sunscreen and goes out at a different time of day and gets mosquito bites. 16. Bella recorded data and used her graphing calculator to find the equation for the line of best fit. She then used the correlation coefficient to determine the strength of the linear fit. Which correlation coefficient represents the strongest linear relationship? [A] 0.91 [B] 0.3 [C] [D] 0.8 [E] 0.9 For problem 17, fill in the blanks with the appropriate words. 17. In order for a function to be a polynomial function all of the must be integers. 18. Which of the following functions below represents a POLYNOMIAL function. Select all that apply. [A] [C] [E] 4 3 f ( x) = x + 4 x 5 x 3x [B] 4 3 h( x) = x 6 x + 7 x x [D] k( x) = x 6 x + x 4 [F] x 3 g( x) = x + 4 x 5 x 3x 5 3 j( x) = x 4 x x 5 4 m( x) = x x 6x

5 19. Which of the following could be a function? [A] The height of a student in your school related to the shoe size of that student. [B] The hair length of a student in your school related to the height of that student. [C] The color of hair of a student in your school related to the age of that student. [D] The student ID number of a student in your school related to the full name of that student. 0. The domain of the function f x = 3x is restricted to the negative integers. Which values are elements of the range? [A] 1 [B] 3 [C] 0 [D] 7 [E] 9 [F] 1 [G] 1 1. The number of miles a car can be driven depends on the number of gallons of gas in its tank. The function m = 5g models a situation in which a car gets 5 miles per gallon. If the gas tank holds 0 gallons of gas, which inequality represents its range? [A] 0 g 0 [B] 0 m 500 [C] m 500 [D] g 0. Why is the given relation not a function?

6 [A] The graph extends forever to both the left and the right. [B] The y values between 1 and are each paired with multiple x values. [C] The x values between 1 and 3 are each paired with multiple y values. [D] The graph does not pass through the origin 3. A graph of average resting heart rates is shown below. The average resting heart rate for adults is 7 beats per minute, but doctors consider resting rates from beats per minute within normal range. Which statement about average resting heart rates is not supported by the graph? [A] A 10-year-old has the same average resting heart rate as a 0-year-old. [B] A 0-year-old has the same average resting heart rate as a 30-year-old. [C] A 40-year-old may have the same average resting heart rate for ten years. [D] The average resting heart rate for teenagers steadily decreases.

7 For problems 4 5, find the solutions to the equation. 4. 3x(7x 6) = (3x + 1)(x 5) ( 7x + 9) = 0 6. Which factorization can be used to reveal the zeros of the function f n = 1 n 11 n + 15? [A] f n = n1 n [B] f n = 4 n + 33 n + 5 [C] f n = 4 n + 33 n + 5 [D] f n = 4 n n Which equation is represented in the graph below? [A] y = x + x 6 [B] y = x x + 6 [C] y = x x 6 [D] y = x + x The graph of a quadratic function f(x) intersects the x axis at 3 and 5. What is a possible equation for f (x)?

8 9. Based on the graph below, which expression is a possible factorization of p(x)? [A] x + 3 x x 4 [B] x + 3 x 5 x x 4 [C] x 3 x + x + 4 [D] x 3 x + 5 x + x Which of the following functions have the same y intercept as the function below? Select all that apply. ƒ x = x 7 x + 1 [A] ƒ x = x 3x 4 [B] x x ƒ = + 8 [C] ƒ x = x 7 x + 6 [D] x x ƒ = If the line x = 3 is the axis of symmetry of a parabola, which coordinates below could be x intercepts of the parabola? [A] ( 1, 0) and (7, 0) [B] ( 1, 0) and (5, 0) [C] ( 3, 0) and (3, 0) [D] ( 8, 0) and (, 0)

9 3. A flying disc is thrown up in the air. The graph below shows its height after t seconds. Which of these statements is true? [A] The disc reaches its minimum height of 5 feet at 0 seconds. [B] The disc reaches its maximum height of 5 feet at 0 seconds. [C] The disc reaches its minimum height of 0 feet at 5 seconds. [D] The disc reaches its maximum height of 0 feet at 5 seconds. 33. In the equation y = x, the minimum value occurs when x is 34. If f x = x 8 x + 9, which statement regarding the vertex form of (x) is true? [A] In vertex form, f x = x + 1 and therefore has a minimum value of 1. [B] In vertex form, f x = x + 1and therefore has a minimum value of. [C] In vertex form, f x = x and therefore has a minimum value of 4.5. [D] In vertex form, f x = x and therefore has a minimum value of.

10 35. What number should be added to both sides of the equation to complete the square in x + 8 x = 17? 36. Jermaine is studying a quadratic function: he finds the function has only one root(zero) at 3.Which statements below must be true about the graph of Jermaine's function? Select all that apply. [A] The parabola must open down. [B] The vertex of his parabola must be ( 3, 0). [C] The x intercept of his parabola must be ( 3, 0). [D] The axis of symmetry of his parabola must be x = Given the equation : f ( x) = x + 8 x + 9, answer parts a d. a) What is the vertex? b) What is the y-intercept? c) What is the equation of the d) What is the maximum value axis of symmetry? of the equation? 38. Sue removes the plug from a trough to drain the water inside. The volume, in gallons, in the trough after it has been unplugged can be modeled by V t = 4 t 3 t + 63, where t is time, in minutes and V(t) is the amount of water at some time t. Which property below will give Sue the amount of time it takes the trough to drain. [A] minimum [B] maximum [C] y-intercept [D] x-intercept

11 39. Last year, a computer store sold 00 laptops at the price of $1,000 per laptop. The store manager is planning for the upcoming year. She creates the graph shown below of the projected revenue from the sales of laptop computers for next year depending on the price increase per laptop. What does the vertex of the parabola represent in terms of the context? [A] The minimum revenue from laptops will be $1,000 when the price per laptop is not increased. [B]The minimum revenue from laptops will be $00,000 when the price per laptop is not increased. [C] The maximum revenue of $5,000 occurs when the laptops are priced at $50. [D] The maximum revenue of $5,000 occurs when the laptops are priced at $1, A cannonball is shot from the top of an ocean cliff as shown. The height (in meters) of the cannonball above the water is given by h t = 5 t + 15 t + 8, where t is the number of seconds after the shot. From what height was the cannonball shot.

12 41. A cliff diver s height above the water, in meters, is modeled by the function h d = d + d + 4, whered represents how far the diver is from the cliff. How far from the cliff will the diver be when she reaches the water? 4. In the equations listed a, b, c, and d are real numbers. Which of the equations could have solutions that are non-real? Select all that apply. [A] ax = b [B] ax + bx = 0 [C] [D] ax + bcx + d = 0 [E] a bx + c = d ax + bx + c = Is the equation A = t a model of exponential growth or exponential decay, and what is the rate (percent) of change per time period? 44. Rachel and Marc were given the information shown below about the bacteria growing in a Petri dish in their biology class. Rachel wants to model this information with a linear function. Marc wants to use an exponential function. Which model is the better choice? Explain why you chose this model. 45. Which scenario represents exponential growth? [A] A water tank is filled at a rate of gallons/minute. [B] A vine grows 6 inches every week. [C] A species of fly doubles its population every month during the summer. [D] A car increases its distance from a garage as it travels at a constant speed of 5 miles per hour.

13 46. What is the equation of the function represented by this table of values? [A] y = 5x + 3 [B] y = 1x + 3 [C] y = 3 5 x [D] y = 5 3 x 47. Michael has $5 in his savings account. Option 1 will add $100 to his account each week. Option will double the amount in his account at the end of each week. Write a function in terms of x to model each option of saving. Michael wants to have at least $700 in his account at the end of 7 weeks to buy a mountain bike. Determine which option(s) will enable him to reach his goal. Justify your answer. 48. A formula is expressed as D = a( + kt). Express k in terms of D, a and t. 49. Tim was asked to solve the equation : kx = my mx for x. Use the following to answer questions The ages of three friends are consecutively one year apart. Together, their ages total 48 years. Which equation can be used to find the age of each friend (where a represents the age of the youngest friend)? [A] 3a = 48 [B] a(a + 1)( a + ) = 48 [C] a + (a 1) + (a ) = 48 [D] a + (a + 1) + (a + ) = What are the ages of the friends?

14 5. When the function f x = x is multiplied by the value a, where a > 1, the graph of the new function, g x = ax. [A] opens upward and is wider [C] opens downward and is wider [B] opens upward and is narrower [D] opens downward and is narrower 53. The graph of the function f(x) and the transformed graph f(x) + k are shown below. What is the value of k?

15 54. Use the graph to answer the question Which equation relates f(x) with g(x)?. [A] g(x) =f(x)+5 [B] g(x) = f(x) 5 [C] g(x) = f(x + 5) [D] g(x) =f(x 5) 55. How is the graph of g x = x. related to the graph of f x x =. [A] The graph of is reflected across the y-axis and translated UP units. [B] The graph of is reflected across the x-axis and translated UP units. [C] The graph of is reflected across the y-axis and translated DOWN units. [D] The graph of is reflected across the x-axis and translated DOWN units. [E] The graph of is reflected across the x-axis and translated RIGHT units.

16 56. Given the function f x = x, the graph below is a translation of f(x). Write a function g(x) that represents the graph Giv en : f ( x) = x 7 x + 6 x 5, find f(3) f(4). 58. Select all the expressions that are equivalent to [A] 3 x 4 9 x y? y [B] 3 x y [C] 9 x y [D] 9 x y [E] 3 x + y3 x y 59. Which expression is equivalent to [A] x 9 x + 0? 4 x x [B] x + 5 x x + [C] x 5 x + 4 [D] x 5 x x +

17 60. If the first Now = 5, what formula can be used to find the terms of this pattern? 5, 10,0, 40,80 [A] Next = Now 15 [B] = Now [C] Next = Now [D] Next = 4 Now The Smith Family Reunion and the Jones Family Reunion both include a visit to a family friendly amusement park in Florida. The Smith family pays $ for passes for 10 adults and 18 children. The Jones family pays $ for passes for 11adults and 19 children. Which system of equations below can be used to solve for the price of the adult and child admissions? [A] 88 = C; 951 = 10A + 18C [B] 88 = 18A + 10C; 951 = 11A + 19C [C] 88 = 10A + 18C; 951 = 11A + 19C [D] 88 = 10A + 18C; 951 = 19A + 11C 6. Match the system of inequalities with the appropriate graph. [1] y + 3 x 14 x 4 [] x 6 10 y + 6 x > 30 [3] y < 7 x y 3 x + 1 [4] 6 y < 16 x y > x + 6

18 [A] [B] [C] [D]