Test Booklet Subject: MA, Grade: HS Louisiana EoC 2013 Algebra I /Geometry Student name: Author: Common Core District: Common Core Released Tests Printed: Friday November 08, 2013
1 Teresa is simplifying an expression. step 1: 4x 2 step 2:? step 3: 2x What should Teresa add at step 2 to best complete the process? A (2x) 2 B 2 2x 2 C x 4x D (2 + 2) (x + x) 2 Use the equation to answer the question. 2x 2 + 8x 7 = 7 Natasha is completing the square to rewrite the equation. Which equation could be her result? A (x + 2) 2 = 7 B (x + 2) 2 = 9 C (x + 2) 2 = 11 D (x + 2) 2 = 15 3 A construction company spends w weeks extending an existing road. The existing road is 5 miles long. Each week the company completes 0.2 miles of the extension. Which equation models the total length ( L ) of the road over time? A L = 0.2w + 5 B L = 0.2w 5 C w = 0.2L + 5 D w = 0.2L 5 Page 1
4 Ellen organizes concerts for a band. She knows that if she charges $50 per ticket, about 400 people will buy tickets. For every $1 she lowers the ticket price, an additional 15 people will buy tickets. Ellen wrote this expression to show the total income from tickets, where x is the number of dollars the ticket price has been reduced. Which expression is equivalent to Ellen s? A 14x + 450 B 15x + 20, 000 C 15x 2 400x + 20, 000 D 15x 2 + 350x + 20, 000 5 Use the table to answer the question. (50 x) (400 + 15x) Gulf Water Temperature, Gulfport (data collected on the fifteenth of the month) A scientist measures the water temperature in the Gulf at Gulfport on the fifteenth of each month. Her data is shown in the table. What is the average rate of change between March 15 and June 15? A 2.6 F per month B 3.9 F per month C 5.2 F per month D 7.8 F per month Page 2
6 A cliff diver s height above the water, in meters, is modeled by the function h (d) = d 2 + 2d + 24, where d represents how far the diver is from the cliff. How far from the cliff will the diver be when she reaches the water? A 0 meters B 4 meters C 6 meters D 24 meters Page 3
7 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) 8 Kianna is writing an equation to model the growth rate of a vine treated with fertilizer. Which quantity is the most appropriate for modeling the growth rate? A centimeters per day B centimeters per hour C feet per hour D feet per day Page 4
9 Use the table to answer the question. T-shirt Price Statistics for Two Stores Which conclusion about T-shirt prices at Cool Clothes and Ben s Shirts is best supported by the data? A Some high-priced T-shirts at Cool Clothes make the mean higher than the median. B The fact that the mean and median are very similar at Ben s Shirts shows that all of the shirts cost under $15. C Comparing the mean prices shows that most shirts are cheaper at Ben s Shirts than at Cool Clothes. D Comparing the interquartile ranges shows that T-shirts at Cool Clothes are about twice as expensive as T-shirts at Ben s Shirts. 10 Deany collects data for a market research company on the number of dollars men and women spend on video games per year as a function of their age. She then models the data using linear functions. The correlation coefficient for the function for men is 0.30. The correlation coefficient for the function for women is 0.15. Which statement correctly describes the meaning of the correlation coefficients? A Men spend approximately twice as much as women on video games. B The function for men represents the amount they spend on video games better than the function for women. C Men spend the most on video games at age 30, and women spend the most on video games at age 15. D Men increase the amount they spend on video games by 30% each year, and women increase the amount they spend by 15%. Page 5
11 The height, in meters, of a rock as it falls at a given time (x), in seconds, can be found using the expression 5x 2 + h 0, where h 0 is the starting height where the rock falls. Part A: A rock falls from a starting height of 80 meters. Write a function, f (x), that models the height of the rock as it falls. Make sure to use proper function notation. Page 6
Part B: Using the function from part A, what is the value of f (3)? Part C: Ahmed states that the domain for this function in the given context is x 4. Explain why Ahmed is incorrect, and provide a correct domain. Page 7
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12 Melanie wants to construct the perpendicular bisector of line segment AB using a compass and straightedge. A B C D Page 9
13 Use the figure to answer the question. Missy is proving the theorem that states that opposite sides of a parallelogram are congruent. Given: Quadrilateral ABCD is a parallelogram. Prove: AB = CD and BC = DA Missy s incomplete proof is shown. Which statement and reason should Missy insert into the chart as step 3 to complete the proof? A BD = BD ; reflexive property B AB = CD and BC = DA ; reflexive property C ABD = CDB and ADB = CBD ; When parallel lines are cut by a transversal, alternate interior angles are congruent. D BAC = DCA and BCA = DAC ; When parallel lines are cut by a transversal, alternate interior angles are congruent. Page 10
14 Rosa graphs the line y = 3x + 5. Then she dilates the line by a factor of 1 with (0, 7) as the center of 5 dilation. Which statement best describes the result of the dilation? A The result is a different line 1 the size of the original line. 5 B The result is a different line with a slope of 3. C The result is a different line with a slope of 1. 3 D The result is the same line. Page 11
15 Use the graph to answer the question. Kelly dilates triangle ABC using point P as the center of dilation and creates triangle A B C. By comparing the slopes of AC and CB and A C and C B, Kelly found that ACB and A C B are right angles. Which set of calculations could Kelly use to prove ABC is similar to A B C? A B C D Page 12
16 Hector knows two angles in triangle A are congruent to two angles in triangle B. What else does Hector need to know to prove that triangles A and B are similar? A Hector does not need to know anything else about triangles A and B. B Hector needs to know the length of any corresponding side in both triangles. C Hector needs to know all three angles in triangle A are congruent to the corresponding angles in triangle B. D Hector needs to know the length of the side between the corresponding angles on each triangle. Page 13
17 Use the figure to answer the question. Triangle STR is drawn such that segment ST is tangent to circle Q at point T, and segment SR is tangent to circle Q at point R. If given any triangle STR with these conditions, which statement must be true? A Side TR could pass through point Q. B Angle S is always smaller than angles T and R. C Triangle STR is always an isosceles triangle. D Triangle STR can never be a right triangle. 18 A circle has this equation. x 2 + y 2 + 4x 10y = 7 What are the center and radius of the circle? A center: (2, -5) radius: 6 B center: ( -2, 5) radius: 6 C center: (2, -5) radius: 36 D center: ( -2, 5) radius: 36 Page 14
19 Use the pyramid to answer the question. This right pentagonal pyramid has a height of 8 inches and a base area of 61.94 square inches. To the nearest hundredth, what is the volume of the pyramid? A 80.00 cubic inches B 165.17 cubic inches C 240.00 cubic inches D 495.52 cubic inches 20 Use the diagram to answer the question. An aviary is an enclosure for keeping birds. There are 134 birds in the aviary shown in the diagram. What is the number of birds per cubic yard for this aviary? Round your answer to the nearest hundredth. A 0.19 birds per cubic yard B 0.25 birds per cubic yard C 1.24 birds per cubic yard D 4.03 birds per cubic yard Page 15
21 Use the diagram to answer the question. Beth is going to enclose a rectangular area in back of her house. The house wall will form one of the four sides of the fenced-in area, so Beth will only need to construct three sides of fencing. Beth has 48 feet of fencing. She wants to enclose the maximum possible area. What amount of fence should Beth use for the side labeled x? A 12 feet B 16 feet C 24 feet D 32 feet Page 16
22 Use the diagram to answer the question. Leah needs to add a wheelchair ramp over her stairs. The ramp will start at the top of the stairs. Each stair makes a right angle with each riser. Part A The ramp must have a maximum slope of 1. To the nearest hundredth of a foot, what is the shortest length 12 of ramp that Leah can build and not exceed the maximum slope? Show your work or explain your answer. Length of ramp: Work/Explanation: Part B Leah decides to build a ramp that starts at the top of the stairs and ends 18 feet from the base of the bottom stair. To the nearest hundredth of a foot, what is the length of the ramp? Page 17
Part C To the nearest tenth of a degree, what is the measure of the angle created by the ground and the ramp that Leah builds in part B? Page 18
23 Use the table to answer the questions. State Information Population density for a state is represented by the number of people per square mile. Part A Which of the states listed in the table has the greatest population density and what is that density? Round your answer to the nearest tenth and make sure to include correct units. State: Population Density: Part B A certain state has a population density that is higher than Louisiana. Describe the different ways the population and land area of this state could be the same or different from Louisiana. Page 19
24 Use the graph to answer the questions. Part A Fire Hose Water Path Explain what the maximum value of this represents in this situation. Make sure to identify the maximum and include information about the x -value and y -value in your explanation. Part B What does the x-intercept of the graph represent in terms of the water spray? Use specific information about the coordinates of the x -intercept in your answer. Page 20
Part C How does the slope of the function change across the interval 0 x 20? Page 21
Geometry Reference Sheet Page 22 STOP