The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
Algebra 1 MAFS.912.A-‐CED.1.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions. MFAS Task “Follow Me” Bay Side High School created a new Twitter account. On the first day they had two followers. Suppose they triple the number of followers each day. Write an equation that relates the number of followers to the number of days that have passed since the account was created. Use your equation to find the number of followers on the tenth day. Show your work and explain what any variables you use represent. Correct Answer: y = 2(3)x-‐1 or any equivalent equation, where x is the number of days and y is the total number of followers. MAFS.912.A-‐CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. MFAS Task “Trees in Trouble” A forester has determined that the number of fir trees in a forest is decreasing by 3% per year. In 2010, there were 13,000 fir trees in the forest. Write an equation that represents the number of fir trees, N, in terms of t, the number of years since 2010. Correct Answer: N = 13000(1-‐0.03)t or any equivalent equation
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.A-‐CED.1.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Micah starts his own business of making skateboards. He needs $521 to purchase the equipment he will need to cut, build, sand, paint, and assemble the skateboards. He uses his garage to build the skateboards so he has no rental costs. It will cost approximately $53.60 per skateboard for materials and parts, which he can purchase through a wholesale company. Micah charges $94.99 for each skateboard. A. Write an equation to represent the cost of the skateboard business. Be sure to define your variables. B. Write an equation to represent the income of the skateboard business. Be sure to define your variables. C. Micah has a goal of earning between $500 and $1000 in his first month. Write an inequality that will
represent the possible number of skateboards Micah will have to sell to reach his goal. D. What is the minimum and maximum number of skateboards that Micah needs to sell to meet his goal of
earning between $500 and $1000? Minimum:________________ Maximum:________________ Correct Answers:
A. C = the cost, x = the number of skateboards; C = 521 + 53.60x B. I = the income, x = the number of skateboards; I = 94.99x C. 500 < 94.99x – (521 + 53.60x) < 1000 or any equivalent inequality or inequalities D. Minimum: 25 skateboards; 37 skateboards
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.A-‐REI.2.4a Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from this form. MFAS Tasks – Complete the Square 1 and 2 - modified A. Complete the square to create an equivalent equation in the form y = (x – h)2 + k
y = x2 + 18x + 45 B. Stephanie completes the square to create an equivalent equation in the form y = a(x – p)2 + q
y = 4x2 + 24x ‒ 13
What are the values of a, p and q? Correct Answers:
A. y = (x – 9)2 – 36 B. y = 4(x + 3)2 – 49 or y = 4(x – (-‐3))2 – 49
MAFS.912.A-‐REI.3.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
The solution to the system !!
€
Ax + By =6Cx + Dy = −10 is (-4, 2).
A. Complete the box so the second system will have the same solution as the first.
!!
€
Ax + By =6(A + C)x + ________ y = −4
B. What property can be used to explain why the solution to Ax+By =62Cx+2Dy =−20 is the same as the
solution to the systemAx+By =6Cx+Dy =−10 ?
Correct Answers:
A. (B + C) B. Multiplicative property of equality
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.F-‐BF.2.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. The graphs of f(x) and g(x) are shown.
What is the value of k for which g(x) = f(x + k)? Correct Answer: k = -‐5
f(x) g(x)
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.F-‐IF.1.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-‐1) for n ≥ 1. A contractor must pay a penalty if work on a project is not completed on time. The penalty on the first day is $300. The penalty increases to $500 on the second day, to $700 on the third day, and so on until the penalty reaches $2500. A. Write a recursive formula, P(n), that represents the penalty the contractor pays.
P(1) = 300
P(n) = _________________ B. What is the domain of P(n)? Correct Answers:
A. 200 + P(n-‐1) or P(n-‐1) + 200 B. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12
MAFS.912.F-‐IF.2.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Under certain conditions the equation, D = 15.129v2 , where D is the aerodynamic drag, in pounds, and v is velocity, in miles per hour, mph. Jarrod is driving his semi-truck at a time when these conditions are true. His velocity ranged from 42 mph and 74 mph.
• What is the average rate of change? • What are the units for the rate of change?
Correct Answers:
• 1754.964 • !"#$%&!!!"#
!"#$%
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.F-‐IF.3.7a, b, c, and e. Graph functions expressed symbolically and show key features of the graph by hand in simple cases and using technology for more complicated cases. For the function f(x) = – x2 – 6x - 5
• Plot the maximum of the function • Plot the y-intercept(s) of the function
Correct Answers: The maximum is at (-‐3, 4) and the y-‐intercepts are at (-‐5, 0) and (-‐1, 0) MAFS.912.F-‐IF.3.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. A function f(x) = 4x2 – 16x + 15 is given. Select all the statements that are true for this function.
The vertex of f(x) is (-4, 15).
f(x) is decreasing on the interval 𝑥 < 2
f(x) is negative on the interval 1.5 < 𝑥 < 2.5
f(x) has two negative roots
The minimum of f(x) is -1.
Correct Answers: f(x) is decreasing on the interval 𝑥 < 2; f(x) is negative on the interval 1.5<x<2.5
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.F-‐LE.1.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-‐output pairs (including reading these from a table). Alicia is conducting research on bacteria in a laboratory. She records the number of bacteria cells every 18 minutes.
Time (minutes)
Number of cells of bacteria
0 64 18 96 36 144
Determine the function, B(t), that expresses the exponential growth of the number of cells of this bacterium as a function of time t in minutes. Correct Answer: B(t) = 64(1.5)t/18 or B(t) = 64(1.51/18)t MAFS.912.N-‐RN.1.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. An expression is shown.
634 • x5 Write an equivalent expression with no radical symbols. Correct Answer: 6¾(x)5/2 MAFS.912.S-‐ID.1.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). MFAS Task “Winning Seasons” Every year the Metro Stars baseball team plays 100 games. During the past decade, their number of wins each year was 41, 56, 52, 71, 66, 62, 42, 37, 52, and 58. Construct a histogram that represents the data. There are a variety of correct answers depending on the values chosen for the scale.
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.S-‐ID.2.5 Summarize categorical data for two categories in two-‐way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. MFAS Task “Marginal and Joint Frequency” modified Julie surveyed 143 students at her high school concerning their eating preferences.
What percentage, to the nearest tenth of a percent, of the male students surveyed were not vegetarians? Correct Answer: 85.9
Vegetarian Not a Vegetarian Total
Male 12 Female 33 Total 37 143
Eating Preferences
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.S-‐ID.2.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. MFAS Task “Residuals” A researcher collected data on two variables, A and B, from five subjects as shown in the table. The researcher calculated the equation of a line of fit as b = 18.0 – 1.34a.
1. Use the linear model to calculate a predicted value and the residual for each subject. Record each value in the table above.
2. Create a residual plot by graphing the residuals below. The horizontal axis is the a-axis.
2. What does your residual plot indicate about the fit of the equation? Correct Answers (see MFAS task for graph): 1. Predicted Values 15.32 12.64 11.3 7.28 4.6
Residuals 0.68 -0.64 -0.3 -0.28 0.4 2. When explaining what the residual plot indicates about the fit of the equation, the student says the
linear model is a pretty good fit since there is scatter of residuals about the horizontal axis. The student may indicate that the data set is small so it is difficult to be certain.
Subject A B C D E
a = value of variable A 2 4 5 8 10
b = value of variable B 16 12 11 7 5
Predicted Values
Residuals
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
Geometry MAFS.912.G-‐C.1.2 Identify and describe relationships among inscribed angles, radii, and chords. MFAS Task “Circles with Angles” modified Use circle A below to answer the following questions. Assume points B, C, and D lie on the circle, segments 𝐵𝐸 and 𝐷𝐸 are tangent to circle A at points B and D, respectively, and the measure of 𝐵𝐷 is 134°.
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.G-‐C.1.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. MFAS Task “Circumscribed Circle Construction” Use a compass and straightedge to construct a circle circumscribed about the triangle.
A. What did you construct to locate the center of your circumscribed circle?
B. What is the name of the point of concurrency that serves as the center of your circumscribed circle?
Correct Answers
A. Perpendicular bisectors B. Circumcenter
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.G-‐C.2.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. In circle Q, the measure of arc AB is 0.92 radians. The length of circle Q’s diameter is 7.3 centimeters. What is the area of the shaded region? Correct Answer: 1.679 MAFS.912.G-‐GMD.1.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. MFAS Task “The Great Pyramid” The Great Pyramid of Giza is an example of a square pyramid and is the last surviving structure considered a wonder of the ancient world. The builders of the pyramid used a measure called a cubit, which represents the length of the forearm from the elbow to the tip of the middle finger. One cubit is about 20 inches in length. Find the height of the Great Pyramid (in cubits) if each base edge is 440 cubits long and the volume of the pyramid is 18,069,330 cubic cubits. Correct Answer: height = 280 cubits
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.G-‐GMD.2.4 Identify the shapes of two-‐dimensional cross-‐sections of three-‐dimensional objects, and identify three-‐dimensional objects generated by rotations of two-‐dimensional objects. MFAS Task “Inside the Box” Imagine a cross-section defined by plane EBCH. Sketch the cross-section and label the dimensions Correct Answer: the rectangular cross section defined by plane EBCH and gives its dimensions as 14 in. by 20 in. MAFS.912.G-‐GPE.1.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. MFAS Task “Complete the Square for Center-‐Radius” The equation of a circle in general form is:
𝑥! + 6𝑥 + 𝑦! + 5 = 0 Find the center and radius of the circle. Show all work neatly and completely.
Center = ___________________
Radius = ________
Correct Answer:
Center = (-3, 0)
Radius = 2 MAFS.912.G-‐GPE.2.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve
14 inches
12 inches
16 inches
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). MFAS Task “Writing Equations for Perpendicular Lines”
In right trapezoid ABCD, 𝐴𝐵 ⊥ 𝐴𝐷 and 𝐴𝐷 is contained in the line 𝑦 = − !
!𝑥 + 10.
a. What is the slope of the line containing 𝐴𝐵? Briefly explain how you got your answer. b. Write an equation in slope-intercept form of the line that contains 𝐴𝐵 if B is located at (−2, 7).
Show your work to justify your answer. Correct Answer:
A. the line containing 𝑨𝑩 is 2; student could answer by relating that the product of the slope of a line and the slope of a perpendicular line is -1.
B. y = 2x + 11
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.G-‐GPE.2.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. MFAS Task Perimeter and Area of a Rectangle Find the perimeter and the area of rectangle ABCD with vertices A(-1, -1), B(2, 3), C(10, -3) and D(7, -7). Show your work. Perimeter _______________ Area _______________
Correct Answers: Perimeter 30 Area 50
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.G-‐MG.1.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). MFAS Task “Estimating Area” Suppose you want to determine the approximate area of a lake at a recreational park using the information given in the park’s brochure. The triangles on the map signify the locations of picnic sites. The distances between the sites are given on the map. Use geometric shapes to model the area of the lake. Sketch the model you choose and include its dimensions. Using your model, estimate the surface area of the lake. Show your work.
374 yar
ds
800 yards
572 yar
ds
244 yards Bridge
Correct Answer: The student models the surface of the lake with a rectangle (800 yards by 374 yards) and a right triangle (with a base of 244 yards and a height of 198 yards). The student understands that he or she can estimate the surface area of the lake by summing the area of the rectangle and the area of the triangle.
The student calculates the area of the rectangle as 299,200 square yards and the area of the triangle as 24,156 square yards. He or she estimates the surface area of the lake to be 323,356 square yards.
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.G-‐MG.1.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). MFAS Task “Mudslide” A mudslide has breached a retaining wall on a local highway. The mudslide stretches for 20 meters along the highway. The mud is 3 meters high at its highest point and covers the entire width of the road, 8 meters.
The engineers from the Department of Transportation need to estimate the mass of the mud on the highway in order to determine how many trucks are needed to haul it away. 1. Create a mathematical model of the mud on the highway and estimate its volume. Show all of your work
carefully and completely. 2. Use the density estimate of the mud, 1840 kg/m3, to determine the mass of the mud on the highway. Show
all of your work carefully and completely Correct Answers: The student models the quantity of mud with a triangular prism and determines that the volume of mud is approximately 240 m3 . The student then uses the estimated volume to determine that the mass of the mud is approximately 441,600 kg.
8 meters
3 m
eter
s
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.G-‐MG.1.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). MFAS Task “Land for the Twins” Paul and Paula own a triangular tract of land with sides that measure 600 feet, 800 feet and 1000 feet. They wish to subdivide the entirety of this land into two regions of equal areas by constructing a fence parallel to the shortest side. 1. Draw a diagram that models the problem situation. Label all given lengths and include a segment that
represents the fence to be constructed. 2. The problem is to determine the length of the fence. Formulate this problem by clearly defining one or more
variables and indicating an appropriate set of equations that when solved determine the values of the variables. Formulation of the equation(s) is sufficient; it is not necessary to solve the equation(s).
Correct Answers 1. The student draws a diagram such as the following
2. Let l be the length of the fence and h be the height of the triangular half of the tract. The
total area of the region is ½ (600)(800) square feet = 240,000 square feet. Therefore the area of the triangular half to be 120,000 sq.ft., so , ½hl = 120000 . Since the triangular half-‐region is similar to the original triangular region, 𝒉
𝟖𝟎𝟎= 𝒍
𝟔𝟎𝟎. So the equations ½hl =
120000 and 𝒉𝟖𝟎𝟎
= 𝒍𝟔𝟎𝟎 can be used to solve for l.
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.G-‐SRT.3.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. http://www.cpalms.org/Public/PreviewResourceAssessment/Preview/72367 modified
Suppose ∆𝐷𝐸𝐹 is a right triangle where ∠D is the right angle. Also, ∆𝑃𝑄𝑅 is a right triangle and ∠Q is the right angle. Which must be true if 𝑚∠𝐸 ≅ 𝑚∠𝑃?
cos (E) = sin (R) sin (E) = sin (P) sin (R) = cos (F) cos (F) = sin (P) cos (F) = cos (R) sin (E) = cos (P)
Correct answer:
ý cos (E) = sin (R) ý sin (E) = sin (P) sin (R) = cos (F) ý cos (F) = sin (P) ý cos (F) = cos (R) sin (E) = cos (P)
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.G-‐SRT.3.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. MFAS Task “River Width” A farmer needs to find the width of a river that flows through his pasture. He places a stake (Stake 1) on one side of the river across from a tree stump. He then places a second stake 50 yards to the right of the first (Stake 2). The angle formed by the line from Stake 1 to Stake 2 and the line from Stake 2 to the tree stump is 72º. Find the width of the river to the nearest yard. Show your work and/or explain how you got your answer.
Stake 1 Stake 2
Tree Stump
72º
Correct answer: 154 feet
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
Algebra 2 MAFS.912.A-‐APR.2.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). https://www.illustrativemathematics.org/content-‐standards/HSA/APR/B/2/tasks/592 “The Missing Coefficient” Consider the polynomial function P(x) = x4 – 3x3 + ax2 – 6x + 14, where a is an unknown real number. If (x – 2) is a factor of this polynomial, what is the value of a? Correct answer: 1.5 or 𝟑𝟐 MAFS.912.F-‐BF.2.4 Find inverse functions. a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x³ or f(x) = (x+1)/(x–1) for x ≠ 1. b. Verify by composition that one function is the inverse of another. c. Read values of an inverse function from a graph or a table, given that the function has an inverse. d. Produce an invertible function from a non-‐invertible function by restricting the domain. The height, in feet, of the water in a trough as it drains is given by where t is time in hours.
1. Find the inverse of h(t). 2. Does the domain of h(t) have to be restricted so that h-1(t) is a function? Explain your answer. 3. Explain how the graphs of h(h-1(t)) and h-1(h(t)) can be used to verify that the functions are inverses.
Correct answers: 1. h-‐1(t) = (-‐4t + 8)2 or any equivalent equation 2. No. The domain and range of h(t) is 𝒕 ≥ 𝟎 so the domain and range of h-‐1(t)
would also be 𝒕 ≥ 𝟎 . 3. To verify that the functions are inverses of each other the graph of h(h-‐1(t)) and the graph
of h-‐1(h(t)) should both be the line y = x.
h(t)=2−0.25 t
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.A-‐REI.2.4 Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from this form. Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. MAFS.912.N-‐CN.3.7 Solve quadratic equations with real coefficients that have complex solutions. MAFS.912.A-‐SSE.2.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. c. Use the properties of exponents to transform expressions for exponential functions. https://www.illustrativemathematics.org/content-‐standards/HSN/CN/C/7/tasks/1690 modified “Completing the Square” Renee reasons as follows to solve the equation x2 + x + 1 = 0. First I will rewrite this as a square plus some number
x2 + x + 1 = 0 (x + ½)2 + ¾ = 0
Now I can subtract ¾ from both sides of the equation
(x + ½)2 = - ¾ But I can’t take the square root of a negative number so I can’t solve this equation.
A. Show how Renee might have continued to find the complex solutions of x2 + x + 1 = 0. B. Apply Renee’s reasoning to find the solutions to x2 + 4x + 6 = 0.
Correct answers: A.
x+ 12( )2=− 3
4
x+ 12( )2= − 3
4
x+ 12 = − 3
4
x+ 12 =
−34
x+ 12 =
i 32
x =− 12 +
i 32
B.
x2 +4x+6=0x+2( )
2+6−4=0
x+2( )2=−2
x+2( )2= −2
x+2= i 2x =−2+ i 2
Equivalent final answers are accepted.
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.F-‐LE.1.4 For exponential models, express as a logarithm the solution to = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology MFAS task “Snail Invasion” modified In 1966, a Miami boy smuggled three Giant African Land Snails into the country. His grandmother eventually released them into the garden, and in seven years there were approximately 18,000 of them. The snails are very destructive and had to be eradicated. According to the USDA, it took 10 years and cost $1 million to eradicate them. The function 𝑃(𝑡) = 3𝑒!.!"! for 0 ≤ 𝑡 ≤ 7 can be used to model the number of snails where t is time in years. To the nearest thousandth of a year, how long does it take for the snail population to reach 9,000? Correct answer: 6.457 years MAFS.912.F-‐TF.1.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle; convert between degrees and radians. In terms of π, how long is the arc subtended by an angle of !!
! on a circle of radius 6.7 cm?
Correct answer: 𝟔𝟕
𝟔π or 𝟏𝟏 𝟏
𝟔π
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.F-‐TF.1.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. https://illuminations.nctm.org/Lesson.aspx?id=2870
Correct answer: This is a suggested activity to help students understand the concepts in the standard. Please see the activity for further information.
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.F-‐TF.3.8 Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to calculate trigonometric ratios. Given sin 𝜃 = ! !
!! find the value of cos(θ).
Correct answer: cos 𝜃 = !"
!!
MAFS.912.G-‐GPE.1.2 Derive the equation of a parabola given a focus and directrix. Write the equation of the parabola with focus at (−1,3) and directrix at 𝑦=9. Correct answer: 𝒚 = − 𝟏
𝟏𝟐(𝒙!𝟏)𝟐!𝟑 or any equivalent equation
MAFS.912.N-‐CN.1.2 Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. What is the product of (6 – 9i)(5 + 4i)? Write your answer in the form a + bi.
Correct answer: 75 – 21i
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.S-‐CP.1.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). https://www.illustrativemathematics.org/content-‐standards/HSS/CP/A/1/tasks/1884 modified The robotics team sponsor has information for the ten students on the robotics team on notecards. The students are identified by an ID number: S1, S2, …, S10. For each student, the following information is also on the card. Gender Grade level Whether or not the student is currently enrolled in a science class Whether or not the student is currently participating on a school sports team Typical number of hours of sleep on a school night Suppose that one student on the robotics team will be selected at random to represent the team at an
upcoming competition. This can be viewed as a chance experiment. Which one of the following is the sample space for this experiment?
The following questions have not gone through the extensive review that items for Florida Standards Assessments do. If there was more than one accepted correct answer, it was noted in the answer section. They are provided for classroom teachers as a way to deepen their understanding of both the standards and the depth of knowledge that are tested on the EOCs. MFAS tasks can be found on CPALMS. http://www.cpalms.org/Public/
MAFS.912.S-‐CP.1.4 Construct and interpret two-‐way frequency tables of data when two categories are associated with each object being classified. Use the two-‐way table as a sample space to decide if events are independent and to approximate conditional probabilities. https://www.illustrativemathematics.org/content-‐standards/HSS/CP/A/1/tasks/949 modified On April 15, 1912, the Titanic struck an iceberg and rapidly sank with only 710 of her 2,204 passengers and crew surviving. Data on survival of passengers are summarized in the table below. (Data source: http://www.encyclopedia-‐titanica.org/titanic-‐statistics.html)
Survived Did not survive Total First Class passengers 201 123 324 Second Class passengers 118 166 284 Third Class passengers 181 528 709 Total passengers 500 817 1317
Calculate the following probabilities. Round your answers to three decimal places.
1. If one of the passengers is randomly selected, what is the probability that this passenger was in first class? 2. If one of the passengers is randomly selected from the first class passengers, what is the probability that
this passenger survived? Correct answer: 1. 𝟑𝟐𝟒
𝟏𝟑𝟏𝟕 2. 𝟐𝟎𝟏
𝟑𝟐𝟒
MAFS.912.S-‐ID.1.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. MFAS task “Probability of your next texting thread” modified The length of a text conversation is called a thread. Suppose the distribution of a student’s past texting threads is normal with a mean of 9 texts and a standard deviation of 3 texts. Determine the probability that a randomly selected texting thread contains at least 13 texts. Correct answer: 0.918
