Algebra 2 Module 1 Assessments - Carnegie Learning
Algebra 2 Module 1 Assessments Student Edition G8 FM SE.indd 1 6/3/21 9:34 PM
EXTENDING LINEAR RELATIONSHIPS End of Topic Assessment Name 1. Date A vendor at a craft show sold items for 4.50, 6.00, and 7.50. Altogether, the vendor sold 87 items for a total of 489. The vendor sold 5 more items for 6.00 than for 7.50. Which system of equations could you use to determine how many of each item were sold? a. x y z 489 z y 5 4.5x 6y 7.5z 87 b. x y z 489 y z 5 4.5x 6y 7.5z 87 c. x y z 87 y z 5 4.5x 6y 7.5z 489 d. x y z 87 z y 5 Carnegie Learning, Inc. 4.5x 6y 7.5z 489 EXTENDING LINEAR RELATIONSHIPS: Standardized Test 1
EXTENDING LINEAR RELATIONSHIPS 2. What is the solution to the system of equations? 2 1 1 x 3 1 3 2 y 2 [ 3 1 0 ][z] [ 6] 7 , 1, 2 a. (– ) 3 3 b. (1, –9, –14) 4 c. ( 5 , 1, ) 3 3. Consider the following system of linear inequalities. Which are the vertices of the solution region? 2x y 4 2 y 2x 4 y a. (–3, 2), (0, –4), and (3, 2) b. (–3, 2), (–2, 0), and (–1, –2) 3 d. (4, 3, –2) c. (0, 2), (0, –4), and (3, 2) Carnegie Learning, Inc. d. (1, 2), (2, 0), and (3, 2) 2 M ODULE 1: EXPLORING PATTERNS IN LINEAR AND QUADRATIC RELATIONSHIPS
EXTENDING LINEAR RELATIONSHIPS 4. A regional train passes by a certain train station halfway along its trip each day. The graph models the train traveling at a constant speed. Which equation best represents the graph? y 400 Distance from Start (miles) 300 200 100 4 3 2 1 0 1 2 3 4 x 100 200 300 400 Time (hours) a. f (x) 100x b. f (x) x 100 Carnegie Learning, Inc. c. f (x) 100 x d. f (x) x 100 EXTENDING LINEAR RELATIONSHIPS: Standardized Test 3
EXTENDING LINEAR RELATIONSHIPS 5. What is the solution to the system of equations? x y z 18 z 2y 5x 2y 6z 85 a. x 9, y 4, z 8 b. x 3, y 5, z 10 c. x 9, y 3, z 6 d. x 12, y 2, z 4 Axel and Carl both volunteer at a science museum. The manager needs one helper at a time for at most 18 hours this month. Axel wants to work at least 6 hours. The manager wants Carl to work no more than twice as many hours as Axel. Let a represents the number of hours that Axel works. Let c represent the number of hours Carl works. Which system of inequalities represents the constraints of this problem situation? a. a c 18 b. a c 18 a 6 a 6 c 2a c 2a c. a c 18 d. a c 18 a 6 a 6 c 2a c 2a 4 M ODULE 1: EXPLORING PATTERNS IN LINEAR AND QUADRATIC RELATIONSHIPS Carnegie Learning, Inc. 6.
EXTENDING LINEAR RELATIONSHIPS 7. What is the solution to the system of inequalities? x 12 2y y 6 3x a. –20 b. –10 20 20 10 10 0 10 20 –10 0 –10 –10 –20 –20 c. Carnegie Learning, Inc. –20 –20 10 20 10 20 d. –10 20 20 10 10 0 10 20 –20 –10 0 –10 –10 –20 –20 EXTENDING LINEAR RELATIONSHIPS: Standardized Test 5
EXTENDING LINEAR RELATIONSHIPS 8. Given f ( x ) x . Describe the transformations performed on the graph of f(x) to get g ( x) 3f (x) 4 . a. The graph of f(x) is translated to the left 4 units and dilated by a factor of 1 . 3 b. The graph of f(x) is translated up 4 units and dilated by a factor of 3. c. The graph of f(x) is translated to the right 4 units and dilated by a factor of 3. d. The graph of f(x) is translated up 4 units and dilated by a factor of 1 . Carnegie Learning, Inc. 3 6 M ODULE 1: EXPLORING PATTERNS IN LINEAR AND QUADRATIC RELATIONSHIPS
EXTENDING LINEAR RELATIONSHIPS 9. A regional train passes by a certain train station halfway along its trip each day. The graph models the train traveling at a constant speed. Which point(s) on the graph represents the time(s) when the train is passing directly beside the train station? y 400 Distance from Start (miles) 300 200 100 4 3 2 1 0 1 2 3 4 x 10. Which is the equation for the graph below? y 8 7 6 5 4 3 2 1 1 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 x 100 200 300 400 a. y x 3 2 Time (hours) b. y x 3 2 a. ( 3, 300) and (3, 300) b. ( 2, 200) and (2, 200) c. y x 3 2 d. y x 3 2 Carnegie Learning, Inc. c. ( 1, 100) and (1, 100) d. (0, 0) EXTENDING LINEAR RELATIONSHIPS: Standardized Test 7
EXTENDING LINEAR RELATIONSHIPS 11. Given f ( x) x . Which is the graph of the function g ( x) 1 f( x 1) ? 2 a. b. y 8 6 4 y 8 8 6 6 4 4 2 2 0 2 2 4 6 8 x 8 6 4 0 2 2 2 4 4 6 6 8 8 c. 2 4 6 8 x 2 4 6 8 x d. 8 6 4 8 8 6 6 4 4 2 2 0 2 2 4 6 8 x 8 6 4 0 2 2 2 4 4 6 6 8 8 8 M ODULE 1: EXPLORING PATTERNS IN LINEAR AND QUADRATIC RELATIONSHIPS Carnegie Learning, Inc. y y
EXTENDING LINEAR RELATIONSHIPS 12. Given f ( x) x . Which is the graph of the function g ( x) f (x) 3 ? a. b. y 8 6 4 y 8 8 6 6 4 4 2 2 0 2 2 4 6 8 x 8 6 4 0 2 2 2 4 4 6 6 8 8 c. 2 4 6 8 x 2 4 6 8 x d. y 8 6 4 y 8 8 6 6 4 4 2 2 0 2 2 4 6 8 x 8 6 4 0 2 Carnegie Learning, Inc. 2 2 4 4 6 6 8 8 EXTENDING LINEAR RELATIONSHIPS: Standardized Test 9
EXTENDING LINEAR RELATIONSHIPS 13. Which values for p are solutions to the inequality 8 3p 2 ? 14. Which of the following is the solution for 3a 3 12 ? 10 a. p 2 or p a. 5 a 3 10 b. p 2 and p b. 3 a 5 10 c. p 2 or p c. 5 a 3 10 d. p 2 and p d. 3 a 5 3 3 3 Carnegie Learning, Inc. 3 10 M ODULE 1: EXPLORING PATTERNS IN LINEAR AND QUADRATIC RELATIONSHIPS
EXTENDING LINEAR RELATIONSHIPS 15. The graph of g ( x) is shown. y 8 6 4 2 0 10 40 30 20 10 20 30 40 x 2 4 6 8 Which statement is true? a. The domain is all real numbers. b. The domain is x 0 . Carnegie Learning, Inc. c. The range is f (x) –2 . d. The range is 30 f (x) 30 . 16. Which of the following is the solution for 2 4x 4 ? 3 1 a. x 2 2 3 1 b. x 2 2 1 c. 3 x 2 2 1 d. 3 x 2 2 EXTENDING LINEAR RELATIONSHIPS: Standardized Test 11
EXPLORING AND ANALYZING PATTERNS Mid-Topic Assessment Name 1. Date Analyze the pattern shown. Which describes the pattern? a. linear b. quadratic c. exponential d. none of the above 2. Carnegie Learning, Inc. A student models the way some bacteria reproduce by cutting a sheet of paper in half, and then cutting each part in half, and then cutting those parts in half, and so on. What function could the student use as another model for the number of bacteria? a. f( x) 2 x b. f (x) 2x 2 c. f (x) x 2 d. f( x) x 3 2 EXPLORING AND ANALYZING PATTERNS: Standardized Test 1
EXPLORING AND ANALYZING PATTERNS 3. Analyze the pattern shown. Design 1 Design 2 Design 3 Design 4 Which algebraic expression represents the pattern? a. 2n 2 b. 2 n 2 2 c. 3n 1 d. 3 n 2 1 The diagram below shows the first four of a series of designs that an artist draws on artwork. Design 1 Design 2 Design 3 Design 4 The artist wants to use a design with a maximum of 15 shaded circles. Which design number should the artist use? a. Design 5 b. Design 6 c. Design 7 d. Design 8 2 M ODULE 1: EXPLORING PATTERNS IN LINEAR AND QUADRATIC RELATIONSHIPS Carnegie Learning, Inc. 4.
EXPLORING AND ANALYZING PATTERNS 5. A quilter sews large squares made of small gray and white squares, as shown. The design depends on the size of the large square. The diagram shows the sequence of designs. Design 1 Design 2 Design 3 Design 4 The quilter wants to make large squares that each have a total of 64 small squares. How many white small squares are needed for each large square the quilter makes? a. 32 b. 36 c. 44 d. 50 6. The diagram shows patterns painted on tiles. The design used depends on the size of a tile. Design 1 Design 2 Design 3 Design 4 Carnegie Learning, Inc. Let n represent the design number. Which expression represents the number of blocks in the design? a. n 2 2n 1 b. ( n 2) (n 2) 5 c. 3 n 2 1 d. n( n 3) 1 EXPLORING AND ANALYZING PATTERNS: Standardized Test 3
EXPLORING AND ANALYZING PATTERNS Which table of values describes a function f ( x) that is linear? b. a. x f (x) x f (x) 3 6 3 7 2 1 2 4 1 2 1 2 0 3 0 2 1 2 1 5 2 1 2 8 3 6 3 11 c. 8. d. x f (x) x f (x) 3 9 3 2 2 5 2 0 1 4 1 2 0 3 0 4 1 7 1 6 2 11 2 8 3 15 3 10 The number of leaves that fall from a tree 9. in Fall triples each day. What function could be used to model the number of leaves that have fallen on a given day? a. f( x) 3 x b. f (x) 3x 3 c. f (x) x 3 d. f( x) x 3 3 A lab technician has 4 bacteria in a petri dish. The number of bacteria doubles every hour. What function could be used to model the number of bacteria at any given hour? a. f( x) 4( 2 x ) b. f( x) 4x 2 c. f (x) x 2 4 d. f( x) 4( x 2 ) 4 M ODULE 1: EXPLORING PATTERNS IN LINEAR AND QUADRATIC RELATIONSHIPS Carnegie Learning, Inc. 7.
EXPLORING AND ANALYZING PATTERNS End of Topic Assessment Name 1. Date Which is a function equivalent to f( n) ( n 2) 2 n 2 4 ? 2. a. 7 a. f (n) ( n 3) (n 1) n (n 1) b. f( n) b. 25 n 2n 2 2 c. 16 9i c. f (n) ( n 1) (n 1) 3 d. f( n) 3. What is the product of ( 4 3i)( 4 3i) ? d. 16 9i n (2n 4) What are the roots of the function f( x) x 2 x 7 ? 4. What is the vertex of the graph f( x) 2 x 2 8x 3 ? a. x 3 3 i a. (0, 3) b. x 1 27i b. (1, 4) 2 3 i c. x 1 3 2 3 d. x 1 3 2 c. ( 3, 4) d. ( 2, 5) Carnegie Learning, Inc. EXPLORING AND ANALYZING PATTERNS: Standardized Test 1
EXPLORING AND ANALYZING PATTERNS 5. A fruit grower determines that the bushels, f ( x) , of apples produced depends on the pounds, x , of fertilizer used according to the function f (x) 0.012 x 2 1.03x 2.46 . Which graph is an equivalent model for this relationship? a. b. y y x x c. d. y y x 6. What are the roots of the function f(x) x2 2x – 1? a. x 2 7. What is vertex of the function f(x) 2x2 8x – 3? a. (–2, 11) b. x 1 2 c. x 2 2 d. x 1 2 b. ( 2, 11 ) c. (–2, –11) d. (2, –11) 2 MODULE 1: EXPLORING PATTERNS IN LINEAR AND QUADRATIC RELATIONSHIPS Carnegie Learning, Inc. x
EXPLORING AND ANALYZING PATTERNS 8. What are the roots of the function f(x) x2 8? a. x 2 i 2 b. x 2i 2 c. x 2i 2 d. x 2 2 9. 10. What is the quadratic equation that contains the points (–2, –2), (2, 18), and (0, 4)? What is the quadratic equation that contains the points (–2, 5), (1, –4), and (0, –3)? a. f (x) x 2 2x 3 a. f (x) x 2 5x 4 b. f (x) x 2 2x 3 b. f (x) x 2 5x 4 c. f (x) x 2 2x 3 c. f (x) x 2 5x 4 d. f (x) x 2 2x 3 d. f (x) x 2 5x 4 11. Analyze the function f (x) 3 (x 3) 2 2 . What is the vertex of the function? Carnegie Learning, Inc. a. (3, 2) b. (–3, –2) c. (3, –2) d. (–3, 2) 12. Analyze the function f( x) 4 (x 2) 2 5 . What is the axis of symmetry of the function? a. x 4 b. x 2 c. x –2 d. x 5 EXPLORING AND ANALYZING PATTERNS: Standardized Test 3
EXPLORING AND ANALYZING PATTERNS 13. What is the quadratic equation that contains the points (–3, –4), (2, 21), and (0, 5)? a. f (x) x 2 6x 5 14. What is a solution to the following system of equations? 2x y 4 x2 – 7x 10 y b. f (x) x 2 6x 5 a. (16, 0) c. f (x) x 2 6x 5 b. (3, –2) d. f (x) x 2 6x 5 c. (–3, 2) d. (0, 16) 15. What is a solution to the following system 16. Which expression is equivalent of equations? to –5i 4 – 7 – 2i 6? 2x 3y 2z 34 4x – y 3z 34 a. 3i 3 b. –7i – 3 a. (5, 4, 6) c. –7i 3 b. (3, 5, 7) d. –3i – 3 c. (–4, 9, 10) d. (5, 8, 2) 4 MODULE 1: EXPLORING PATTERNS IN LINEAR AND QUADRATIC RELATIONSHIPS Carnegie Learning, Inc. x y z 15
EXPLORING AND ANALYZING PATTERNS 17. Which expression is equivalent to (9i 3) – (– 4i – 1)? 18. Which expression has 2i(–4 3i) rewritten in simplest terms? a. 13i 4 a. –8i – 6i b. –5i – 2 b. –8i 6i c. 5i 4 c. –8i – 6i2 d. –13i – 2 d. –8i – 6 19. What are the roots of the function f(x) x2 25? a. x 5i 20. What are the roots of the function f(x) –x2 –6x – 10? a. x –3 –i b. x 2i 5 b. x 3 –i c. x i 5 c. x –3 1 d. x 5 d. x 3 1 Carnegie Learning, Inc. EXPLORING AND ANALYZING PATTERNS: Standardized Test 5
APPLICATIONS OF QUADRATICS Mid-Topic Assessment Name 1. What is the solution set of the quadratic inequality x 2 x 30 12 ? Date 2. a. x (– , –7] or x (6, ) a. 0 b. x (– , –6] or x [7, ) b. 1 c. x (– , –7) or x (6, ) c. 2 d. x (– , –6) or x [7, ) 3. A golf ball is hit upward from a height of 0.1 feet with an initial vertical velocity of 150 feet per second. When in time t, is the golf ball above 100 feet? Round to the nearest tenth. How many possible solutions are there for a system with a linear and a quadratic equation? d. all of the above 4. A basketball is thrown upward from a height of 10 feet with an initial vertical velocity of 20 feet per second. When in time t, is the basketball higher than 15 feet? Round to the nearest tenth. Carnegie Learning, Inc. a. 0.7 t 8.7 a. 0.3 t 0.9 b. 0.7 t 8.7 b. 0.3 t 0.9 c. 0.2 t 9.2 c. 0.3 t 0.9 d. 0.2 t 9.2 d. 0.3 t 0.9 APPLICATIONS OF QUADRATICS: Standardized Test 1
APPLICATIONS OF QUADRATICS 5. A softball is hit upward from a height of 6 feet with an initial vertical velocity of 35 feet per second. When in time t, is the softball above 10 feet? Round to the nearest tenth. 6. What is the solution set of the quadratic inequality x 2 2x 21 14 ? a. x ( 5, 7) b. x ( 7, 5) a. 0.1 t 2.1 c. x [ 5, 7 ] b. 0.1 t 2.1 d. x [ 7, 5 ] c. 0.1 t 2.1 d. 0.1 t 2.1 What is the solution set of the quadratic inequality x 2 5x 35 15 ? 8. Which type of functions are never oneto-one? a. x ( , 5) or x ( 10, ) a. linear and absolute value b. x ( , 10) or x ( 5, ) b. linear and exponential c. x ( , 5 ] or x [ 10, ) c. quadratic and exponential d. x ( , 10 ] or x [ 5, ) d. quadratic and absolute value Carnegie Learning, Inc. 7. 2 M ODULE 1: EXPLORING PATTERNS IN LINEAR AND QUADRATIC RELATIONSHIPS
APPLICATIONS OF QUADRATICS 9. Which statement about the relationship between a function and its inverse is true? 10. The function h(x) is graphed. Which point will be on the graph of its inverse? y a. The point (-x, -y) is on the graph of the 8 inverse function. 6 b. The graph of the inverse function is 4 the reflection of the function across 2 the y-axis. 8 6 4 0 2 2 4 6 8 x 2 c. The graph of the inverse function is 4 the reflection of the function across 6 the line y x. 8 d. The point (x, -y) is on the graph of the inverse function. a. (–6, 2) b. (2, –6) c. (4, –3) d. (–4, 3) Carnegie Learning, Inc. APPLICATIONS OF QUADRATICS: Standardized Test 3
APPLICATIONS OF QUADRATICS End of Topic Assessment Name 1. Date The table shows the number of visitors to the Daisy Festival on certain days since May 1. Days Since May 1 Number of Visitors 0 215 3 520 6 725 9 865 12 955 15 1025 18 970 21 874 24 710 27 490 30 207 Which type of function would best model the data? a. linear b. quadratic Carnegie Learning, Inc. c. exponential d. piecewise function APPLICATIONS OF QUADRATICS: Standardized Test 1
APPLICATIONS OF QUADRATICS 2. What is the solution set of the quadratic inequality 2 x 2 2x 12 36 ? a. x (– , –4] or x [3, ) b. x (– , –3] or x [4, ) c. x [–4, 3] d. x [–3, 4] 3. Choose the correct word or phrase to complete the following sentence. A quadratic function is a one-to-one function. a. always b. sometimes c. never Carnegie Learning, Inc. d. different from 2 M ODULE 1: EXPLORING PATTERNS IN LINEAR AND QUADRATIC RELATIONSHIPS
APPLICATIONS OF QUADRATICS 4. The scatterplot represents the population of a certain animal species in the years since 2005. 5. Which statement about the relationship between a function and its inverse is NOT true? a. The domain of a function is the range of the inverse of the function. b. The range of a function is the domain of the inverse of the function. c. The graph of the inverse of a function is the reflection across the line y x of the graph of the function. Which of the following statements about the graph is true? a. The y-intercept represents the d. The inverse of a function is always a function. population of the animal species in 2005. b. The y-intercept tells how the population of the species has changed since 2005. c. The y-intercept indicates that an Carnegie Learning, Inc. exponential function would best model the data. d. The y-intercept indicates the greatest recorded population of the animal species in the years since 2005. APPLICATIONS OF QUADRATICS: Standardized Test 3
APPLICATIONS OF QUADRATICS 6. What are the solutions to this system of equations? y 2x 1 {y x 2 4 a. (1, –3) and (3, –5) b. (1, 3) and (3, 5) c. (–1, 3) and (–3, –5) d. (1, 3) and (–3, –5) 7. The table shows the number of visitors to the Daisy Festival on certain days since May 1. Days Since May 1 Number of Visitors 0 215 3 520 6 725 9 865 12 955 15 1025 18 970 21 874 24 710 27 490 30 207 Which regression equation best models the data? b. f(x) –3.5035x2 104.58x 221.76 c. f( x) 620.58 ( 0.999 ) x d. The regression cannot be determined. 4 M ODULE 1: EXPLORING PATTERNS IN LINEAR AND QUADRATIC RELATIONSHIPS Carnegie Learning, Inc. a. f( x) 0.5212x 694.73
APPLICATIONS OF QUADRATICS 8. Your friend drops an apple from a bridge that is 120 feet above a river. The function h(t) –16t2 120 gives the height of the apple above the river after t seconds. What is the inverse of the function in terms of the problem situation? (t) (t) (t) a. h 1 (t) t 120 b. h 1 c. h 1 d. h 16 9. If f–1 x , what is the domain of f(x)? a. x 0 b. x 0 c. all real numbers d. The domain cannot be determined. t 120 16 t 120 16 1 t 120 16 10. The function f(x) –3x2 570x gives the revenue from television sales when x is the price of the television. What is the inverse of the function in terms of the problem situation? 11. What are the solutions to this system of equations? y 2x 5 {y x 2 10 a. (3, 1) and (–5, –15) b. (–3, 1) and (–5, 15) c. (–3, –1) and (5, 15) d. (3, 1) and (5, 15) 3 a. f 1 (x) 95 x 9025 3 b. f 1 (x) 95 x 9025 Carnegie Learning, Inc. 3 c. f 1 (x) 95 x 9025 3 d. f 1 (x) 95 x 9025 APPLICATIONS OF QUADRATICS: Standardized Test 5
APPLICATIONS OF QUADRATICS 12. The quadratic regression equation f(x) 1.256x2 – 3.9x 7.49 models the set of data in the scatterplot. 13. What is the directrix of the parabola given by the equation y2 12x? a. x 3 b. y 3 c. x –3 d. y –3 What is the best prediction for the value of x when f(x) 6? a. x 0.4 and x 2.75 b. x 1.5 c. x 0.1 and x 3 Carnegie Learning, Inc. d. x 25 6 M ODULE 1: EXPLORING PATTERNS IN LINEAR AND QUADRATIC RELATIONSHIPS
APPLICATIONS OF QUADRATICS 14. What is the equation of a parabola with a focus at (2, –3) and a directrix of x 5, as shown? 15. The parabola shown has a focus 5 at ( 5 , 0) and a directrix at x . 2 2 Which of the following is the form of this parabola? a. y2 –6x – 4y 12 a. y2 4x 25 b. y2 4x – 6y 12 b. y2 25x 4 c. y2 –4x – 4y 12 c. y2 – 10x 0 d. y2 –6x – 6y 12 d. y2 10x 0 16. What are the solutions to this system of equations? Carnegie Learning, Inc. y 3x 2 {y x 2 5x 2 17. What are the solutions to this system of equations? y x 2 {y x 2 2 a. (0, –2) and (2, –8) a. (0, –2) and (1, 3) b. (0, 2) and (–2, 8) b. (0, 2) and (1, 3) c. (0, –2) and (–2, –8) c. (0, –2) and (–1, –3) d. (0, 2) and (2, 8) d. (0, 2) and (–1, –3) APPLICATIONS OF QUADRATICS: Standardized Test 7
The diagram below shows the first four of a series of designs that an artist draws on artwork. Design 1 Design 2 Design 3 Design 4 The artist wants to use a design with a maximum of 15 shaded circles. Which design number should the artist use? a. Design 5 b. Design 6 c. Design 7 d. Design 8
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