Integrated Math 1 Final Review

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1 Chapter 1 1. Identify the independent and dependent quantities for the following scenario: Integrated Math 1 Final Review Chapter 2 4. What is the solution to the equation: 5 (x + 4) 8 = x + 32 Independent Quantity: Dependent Quantity: 5. What is the solution to the following inequality: 4 (x + 1) Sketch a graph that: is a linear absolute value function, is continuous, and has an absolute maximum. Chapter 3 6. What are the x and y intercepts of the linear equation: 3 x + 2 y = Sketch a graph that is exponential is increasing across the entire domain, and is discrete x intercept: (, ) y intercept: (, ) 7. The basketball booster club runs the concession stand during a weekend tournament. They sell hamburgers for $2.50 each and hot dogs for $1.50 each. Which function shows the total amount earned from h hamburgers and d hotdogs? a. f(h, d ) = 2.5h + 1.5d b. f (h) = 2.5h c. f(h, d ) = 2.5d + 1.5h d. f (d) = d

2 8. Write the following equations in slope intercept form. 5 x + 2 y = Determine the solution to the following exponential equations: 256 = 4 x 6 4x + 6 y = 48 5 x+1 = 125 Chapter 4 9. Karim recently started a consulting business. In February, he had 15 clients. In March, he had 24 clients. In April he had 33 clients. If this pattern continues, how many clients will he have in August? Chapter Solve the following systems of equations: 2 x + y = 9 y = 5 x + 2 Chapter Rewrite the function f (x) = 2x 4 after x + 1.2y =. 6.8x.2y = 2 a horizontal translation 3 units right: a horizontal translation 7 units left: a vertical translation 8 units up: a vertical translation 1 unit down: 14. A cable company offers two cable plans. One plan costs $110 plus $5 per movie. The other plan costs $150 plus $1 per movie. How many movies must Neil rent in order for the plans to cost the same amount? 11. Which shows the function f (x) after a horizontal translation 5 units right and 2 units up? a. g (x) = f(x 5 ) + 2 b. g (x) = f (x + 5 ) + 2 c. g (x) = f(x 5) 2 d. g (x) = f (x + 5) 2

3 Chapter Write the inequality (or system of inequalities) represented by each of the following graphs: 17. A principal wants to order at least 800 math books. The company has 500 math books in their warehouse. They also have 600 math books in a storage unit. Which system of linear inequalities represents the constraints of this situation? Let x represent the number of math books shipped from the warehouse and y represent the number of math books shipped from the storage unit. a. x + y 800 b. x + y < 800 x 600 x 500 y 500 y 600 c. x + y 800 d. x + y 800 x 500 x 500 y 600 y Angelica is trying to sell t shirts for the pep rally. She wants to sell at least s t shirts. She currently has sold 27 t shirts and is selling 3 more every minute. Which inequality represents this situation, where m is the number of minutes? a. s m b. s 27 3 m c. s 27 3 m d. s m Chapter Draw a quick sketch of a dot plot with each of the following distributions: Skewed Right: Skewed Left: Symmetric: 16. Which is a solution to the system of linear inequalities? y > 3x 2 y < 2 x + 8 a. ( 1, 2) b. (3, 7) c. (4, 0) d. (2, 4) 20. Calculate the mean and standard deviation for the following data set. 7, 8, 9, 10, 10, 12, 14 a. Mean: b. Standard deviation:

4 21. Determine the following for the given data set: 2, 4, 5, 5, 6, 7, 8, 8, 10, 12, 18 Minimum: Median: Q1: Q3: IQR: Maximum: 22. For each data set, describe where the mean is in relation to the median. 25. a. What is the best measure of center for a skewed distribution? b. What is the best measure of center for a symmetric distribution? c. What is the best measure of spread for a skewed distribution? d. What is the best measure of spread for a symmetric distribution? Chapter The linear regression equation for a data set from a diving submarine is y = 1.5x 40.6, where y represents the depth of a submarine (in meters), and x represents the number of seconds that have gone by. Use the equation to predict what the depth of the submarine will be after 23 seconds What is the least squares regression equation for the points ( 3, 6), ( 2, 1), and (6, 4)? a. Describe the distribution of each data set. b. Predict which of the data sets has a higher standard deviation. Explain your reasoning. 24. The following box and whisker plot shows the number of miles away from school students live. 28. What is the correlation coefficient for the data: (3, 2), (5, 7), (10,9) 29. Determine the most accurate correlation coefficient for the following scatterplots. a. What fraction of students live between 11 and 14 miles away from school? b. What fraction of students live between 1 and 11 miles away from school? A) r = 0.7 A) r = 0.09 B) r = 0.7 B) r = 0.4 C) r = 0.07 C) r = 0.8 D) r = 0.07 D) r = 0.7

5 30. What do the following r values tell you about the data set that they describe? A) r = 0.04 Chapter Answer the following questions about the graph: B) r = For the following residual plots, determine whether or not they suggest a linear model is the best function family to describe the data. a) How many people interviewed were in 11th grade? b) How many students were in 12th grade and liked jazz? c) What kind of music did 10th graders like least? d) How many more 12th graders were interviewed than 9th graders? 34. Answer the following questions using the graph: 32. Explain in words what a scatter plot would look like if a linear model would work well to describe the data. a. What subject does class A like most? b. What subject does class B like least? c. What subject does class C like most? d. What is the overall favorite subject?

6 35. The following table shows the data based on the favorite type of picnic location. 38. Write the equation of a line that is perpendicular to the line y = 2 5 x 1 that goes through the point (2, 8). a. If a table was to be made based on the class, what would be the fraction of students who liked the amusement park given that they were in class B? 39. Write the equation of a horizontal line going through the point (8, 1). 40. Write the equation of a vertical line going through the point ( 2, 5). b. If a table was to be made based on the class, what would be the fraction of students who liked the beach given that they were in class A? c. If an overall relative frequency distribution was to be made, what would be the overall fraction of students be who were in class C and chose the water park? 41. Billy constructs a line segment AB that is 6 inches long. He then constructs the segment bisector of the segment and labels the midpoint M. What is the length of segment AM? Chapter Given the figure below: Chapter What is the distance between the two points: (5, 12) and ( 1, 6) 37. What is the midpoint of a line segment with endpoints ( 5, 1) and (6, 3) What would be the coordinates of each vertex if the shape is: a. rotated 90 degrees counter clockwise? b. rotated 180 degrees counterclockwise? c. reflected across the x axis? d. reflected across the y axis? e. translated 5 left and two up?

7 43. If a triangle has vertex coordinates (5, 2), ( 2, 3) and (1, 1), what kind of transformation would cause the coordinates to change to ( 2, 5), (3, 2) and ( 1, 1)? 44. Δ GNR was rotated 90 degrees counterclockwise about the origin to create Δ XYZ. Identify each set of congruent angles and congruent sides. 46. Which set of congruence statements shows that ΔP SC is congruent to Δ RGW by the SAS Congruence Theorem? a. b. c. d. 45. Which congruence theorem can be used to determine that each set of triangles are congruent? Chapter 14/ Determine the area and perimeter of a triangle on the coordinate plane that has vertices at: (1, 2), (1, 7) and (9, 7) Perimeter: Area:

8 Triangle ABC has vertices at A(0, 1) and B(4, 1). Given each of the following points for C, determine whether the triangle will be a. equilateral d. isosceles, obtuse b. isosceles, right e. scalene, acute c. scalene, right f. isosceles, acute C(1, 5) C(0, 3) C(4, 5) a. Determine the perimeter of the composite figure. 51. Quadrilateral DEFT has vertices D(2, 7), E( 4, 4), F(5, 6), and T(11, 3). What is the best name for quadrilateral DEFT? a. trapezoid c. parallelogram b. square d. rectangle 52. A rectangle ABCD has vertices A( 2, 2), B( 2, 7) and C(4, 7). What are the coordinates of point D? a. (2, 7) c. (4, 2) b. ( 2, 4) d. (4, 2) b. Determine the area of the composite figure. 53. Square MNRP has vertices at M(4, 0) and N(7, 0). Which could be the coordinates of R? a. (7, 4) c. (7, 3) b. (4, 7) d. (5.5, 0) 54. The following figure is translated so that the point S is at the origin. What are the new coordinates of the other vertices? 49. A regular polygon KQRFGH is graphed on the coordinate plane. One of its sides has a length of 4. What is the perimeter of the polygon? *Note: The Final is all multiple choice Many of the problems on this review are not, but they cover the same content.

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