- Oct 1, 2019
How to Use a Math Medic Answer Key
Updated: Aug 7
Answer key might be the wrong term here. Sure, the Math Medic answer keys do provide the correct answers to the questions for a lesson, but they have been carefully designed to do much more than this. They are meant to be the official guide to teaching the lesson, providing specific instructions for what to do and say to make a successful learning experience for your students.
Before we look at the details of the answer key, let's make sure we understand the instructional model first.
Experience First, Formalize Later (EFFL)
A typical Math Medic lesson always has the same four parts: Activity, Debrief Activity, QuickNotes, and Check Your Understanding. Here are the cliff notes:
Activity: Students are in groups of 2 - 4 working collaboratively through the questions in the Activity. The teacher is checking in with groups and using questions, prompts, and cues to get students to refine their communication and understanding. As groups finish the activity, the teacher asks students to go to the whiteboard to write up their answers to the questions.
Debrief Activity: In the whole group setting, the teacher leads a discussion about the student responses to the questions in the activity, often asking students to explain their thinking and reasoning about their answers. The teacher then formalizes the learning by highlighting key concepts and introducing new vocabulary, notation, and formulas in the margins.
QuickNotes: The teacher provides a few key summary statements from the activity in the QuickNotes box - making connections to the learning targets for the lesson.
Check Your Understanding: Students are then asked to apply their learning from the lesson to a new context in the Check Your Understanding (CYU) problem. This can be done individually or in small groups. The CYU is very flexible in its use, as it can be used as an exit ticket, a homework problem, or a quick review the next day.
How Do I See EFFL in the Answer Key?
You will see EFFL in the answer key like this:
Activity (blue), Debrief Activity (red), QuickNotes (red), Check Your Understanding (blue)
Anything written in blue is something we expect our students to produce. This might not be quite what we expect by the end of the lesson, but provides us with a starting point when we move to formalization.
Anything written in red is an idea added by the teacher - the formalization of the learning that happened during the Activity. Students are expected to add these "notes" to their Activity using a red pen or marker.
What Do Students Write Down For Notes?
By the end of the lesson, students will have written down everything you see on the Math Medic Answer Keys. The most important transition is when students finish the Activity and we move to Debrief Activity.
"Students, now is the time for you to put down your pencils and get out your your red Paper Mate flair pens"
We give each student a Paper Mate flair pen at the beginning of the school year and tell them they must cherish and protect it with their life. They all think we should be sponsored by Paper Mate (anyone have any leads on this?)
The lessons you see on Math Medic are all of the notes we use with our students. We do not have some secret collection of guided notes.
Do Students Have Access to Answer Keys?
Yes! Any student can create a free Math Medic account to get access to the answer keys. We often send students to the website when they are absent from a lesson or when we don't quite finish the lesson in class. We are comfortable with students having access to these answer keys because we do not think Math Medic lessons should be used as a summative assessment or be used for a grade (unless it's for completion). Our lessons are meant to be the first steps in the formative process of learning new concepts.
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2.1 Linear Functions
m = 4 − 3 0 − 2 = 1 − 2 = − 1 2 m = 4 − 3 0 − 2 = 1 − 2 = − 1 2 ; decreasing because m < 0. m < 0.
m = 1 , 868 − 1 , 442 2 , 012 − 2 , 009 = 426 3 = 142 people per year m = 1 , 868 − 1 , 442 2 , 012 − 2 , 009 = 426 3 = 142 people per year
y − 2 = − 2 ( x + 2 ) y − 2 = − 2 ( x + 2 ) ; y = − 2 x − 2 y = − 2 x − 2
y − 0 = − 3 ( x − 0 ) y − 0 = − 3 ( x − 0 ) ; y = − 3 x y = − 3 x
y = − 7 x + 3 y = − 7 x + 3
H ( x ) = 0.5 x + 12.5 H ( x ) = 0.5 x + 12.5
2.2 Graphs of Linear Functions
Possible answers include ( − 3 , 7 ) , ( − 3 , 7 ) , ( − 6 , 9 ) , ( − 6 , 9 ) , or ( − 9 , 11 ) . ( − 9 , 11 ) .
( 16 , 0 ) ( 16 , 0 )
- ⓐ f ( x ) = 2 x f ( x ) = 2 x
- ⓑ g ( x ) = − 1 2 x g ( x ) = − 1 2 x
y = – 1 3 x + 6 y = – 1 3 x + 6
- ⓐ ( 0 , 5 ) ( 0 , 5 )
- ⓑ ( 5 , 0 ) ( 5 , 0 )
- ⓓ Neither parallel nor perpendicular
- ⓔ Decreasing function
- ⓕ Given the identity function, perform a vertical flip (over the t -axis) and shift up 5 units.
2.3 Modeling with Linear Functions
- ⓐ C ( x ) = 0.25 x + 25 , 000 C ( x ) = 0.25 x + 25 , 000
- ⓑ The y -intercept is ( 0 , 25 , 000 ) . ( 0 , 25 , 000 ) . If the company does not produce a single doughnut, they still incur a cost of $25,000.
21.57 miles
2.4 Fitting Linear Models to Data
54 ° F 54 ° F
150.871 billion gallons; extrapolation
2.1 Section Exercises
Terry starts at an elevation of 3000 feet and descends 70 feet per second.
3 miles per hour
d ( t ) = 100 − 10 t d ( t ) = 100 − 10 t
Increasing.
Decreasing.
– 1 3 – 1 3
f ( x ) = − 1 2 x + 7 2 f ( x ) = − 1 2 x + 7 2
y = 2 x + 3 y = 2 x + 3
y = − 1 3 x + 22 3 y = − 1 3 x + 22 3
y = 4 5 x + 4 y = 4 5 x + 4
− 5 4 − 5 4
y = 2 3 x + 1 y = 2 3 x + 1
y = − 2 x + 3 y = − 2 x + 3
y = 3 y = 3
Linear, g ( x ) = − 3 x + 5 g ( x ) = − 3 x + 5
Linear, f ( x ) = 5 x − 5 f ( x ) = 5 x − 5
Linear, g ( x ) = − 25 2 x + 6 g ( x ) = − 25 2 x + 6
Linear, f ( x ) = 10 x − 24 f ( x ) = 10 x − 24
f ( x ) = − 58 x + 17.3 f ( x ) = − 58 x + 17.3
a. a = 11 , 900 a = 11 , 900 ; b = 1000.1 b = 1000.1 b. q ( p ) = 1000 p − 100 q ( p ) = 1000 p − 100
x = − 16 3 x = − 16 3
x = a x = a
y = d c − a x − a d c − a y = d c − a x − a d c − a
$45 per training session.
The rate of change is 0.1. For every additional minute talked, the monthly charge increases by $0.1 or 10 cents. The initial value is 24. When there are no minutes talked, initially the charge is $24.
The slope is − 400. − 400. This means for every year between 1960 and 1989, the population dropped by 400 per year in the city.
2.2 Section Exercises
The slopes are equal; y -intercepts are not equal.
The point of intersection is ( a , a ) . ( a , a ) . This is because for the horizontal line, all of the y y coordinates are a a and for the vertical line, all of the x x coordinates are a . a . The point of intersection will have these two characteristics.
First, find the slope of the linear function. Then take the negative reciprocal of the slope; this is the slope of the perpendicular line. Substitute the slope of the perpendicular line and the coordinate of the given point into the equation y = m x + b y = m x + b and solve for b . b . Then write the equation of the line in the form y = m x + b y = m x + b by substituting in m m and b . b .
neither parallel or perpendicular
perpendicular
( – 2 , 0 ) ( – 2 , 0 ) ; ( 0 , 4 ) ( 0 , 4 )
( 1 5 , 0 ) ( 1 5 , 0 ) ; ( 0 , 1 ) ( 0 , 1 )
( 8 , 0 ) ( 8 , 0 ) ; ( 0 , 28 ) ( 0 , 28 )
Line 1 : m = 8 Line 1 : m = 8 Line 2 : m = – 6 Line 2 : m = – 6 Neither Neither
Line 1 : m = – 1 2 Line 1 : m = – 1 2 Line 2 : m = 2 Line 2 : m = 2 Perpendicular Perpendicular
Line 1 : m = – 2 Line 1 : m = – 2 Line 2 : m = – 2 Line 2 : m = – 2 Parallel Parallel
g ( x ) = 3 x − 3 g ( x ) = 3 x − 3
p ( t ) = − 1 3 t + 2 p ( t ) = − 1 3 t + 2
( − 2 , 1 ) ( − 2 , 1 )
( − 17 5 , 5 3 ) ( − 17 5 , 5 3 )
- ⓐ g ( x ) = 0.75 x − 5.5 g ( x ) = 0.75 x − 5.5
- ⓒ ( 0 , − 5.5 ) ( 0 , − 5.5 )
x = − 3 x = − 3
no point of intersection
( 2 , 7 ) ( 2 , 7 )
( – 10 , –5 ) ( – 10 , –5 )
y = 100 x − 98 y = 100 x − 98
x < 1999 201 x > 1999 201 x < 1999 201 x > 1999 201
Less than 3000 texts
2.3 Section Exercises
Determine the independent variable. This is the variable upon which the output depends.
To determine the initial value, find the output when the input is equal to zero.
6 square units
20.012 square units
P ( t ) = 75 , 000 + 2,500 t P ( t ) = 75 , 000 + 2,500 t
(–30, 0) Thirty years before the start of this model, the town had no citizens. (0, 75,000) Initially, the town had a population of 75,000.
Ten years after the model began.
W ( t ) = 0. 5 t + 7 . 5 W ( t ) = 0. 5 t + 7 . 5
( − 15 , 0 ) ( − 15 , 0 ) : The x -intercept is not a plausible set of data for this model because it means the baby weighed 0 pounds 15 months prior to birth. ( 0 , 7 . 5 ) ( 0 , 7 . 5 ) : The baby weighed 7.5 pounds at birth.
At age 5.8 months.
C ( t ) = 12 , 025 − 205 t C ( t ) = 12 , 025 − 205 t
(58.7, 0) (58.7, 0) : In roughly 59 years, the number of people inflicted with the common cold would be 0. (0,12,025) (0,12,025) : Initially there were 12,025 people afflicted by the common cold.
y = − 2 t +180 y = − 2 t +180
In 2070, the company’s profit will be zero.
y = 30 t − 300 y = 30 t − 300
(10, 0) In 1990, the profit earned zero profit.
During the year 1933
- ⓐ 696 people
- ⓒ 174 people per year
- ⓓ 305 people
- ⓔ P ( t ) = 305 + 174 t P ( t ) = 305 + 174 t
- ⓕ 2,219 people
- ⓐ C ( x ) = 0.15 x + 10 C ( x ) = 0.15 x + 10
- ⓑ The flat monthly fee is $10 and there is an additional $0.15 fee for each additional minute used
- ⓐ P ( t ) = 190 t + 4360 P ( t ) = 190 t + 4360
- ⓑ 6,640 moose
- ⓐ R ( t ) = 16 − 2.1 t R ( t ) = 16 − 2.1 t
- ⓑ 5.5 billion cubic feet
- ⓒ During the year 2017
More than 133 minutes
More than $42,857.14 worth of jewelry
2.4 Section Exercises
When our model no longer applies, after some value in the domain, the model itself doesn’t hold.
We predict a value outside the domain and range of the data.
The closer the number is to 1, the less scattered the data, the closer the number is to 0, the more scattered the data.
61.966 years
Interpolation. About 60 ° F . 60 ° F .
Yes, trend appears linear because r = 0. 985 r = 0. 985 and will exceed 12,000 near midyear, 2016, 24.6 years since 1992.
y = 1 . 64 0 x + 13 . 8 00 y = 1 . 64 0 x + 13 . 8 00 , r = 0. 987 r = 0. 987
y = − 0.962 x + 26.86 , r = − 0.965 y = − 0.962 x + 26.86 , r = − 0.965
y = − 1 . 981 x + 6 0. 197 y = − 1 . 981 x + 6 0. 197 ; r = − 0. 998 r = − 0. 998
y = 0. 121 x − 38.841 , r = 0.998 y = 0. 121 x − 38.841 , r = 0.998
( −2 , −6 ) , ( 1 , −12 ) , ( 5 , −2 0 ) , ( 6 , −22 ) , ( 9 , −28 ) ( −2 , −6 ) , ( 1 , −12 ) , ( 5 , −2 0 ) , ( 6 , −22 ) , ( 9 , −28 ) ; y = −2 x −10 y = −2 x −10
( 189 . 8 , 0 ) ( 189 . 8 , 0 ) If 18,980 units are sold, the company will have a profit of zero dollars.
y = 0.00587 x + 1985 .4 1 y = 0.00587 x + 1985 .4 1
y = 2 0. 25 x − 671 . 5 y = 2 0. 25 x − 671 . 5
y = − 1 0. 75 x + 742 . 5 0 y = − 1 0. 75 x + 742 . 5 0
Review Exercises
y = − 3 x + 26 y = − 3 x + 26
y = 2 x − 2 y = 2 x − 2
Not linear.
( –9 , 0 ) ; ( 0 , –7 ) ( –9 , 0 ) ; ( 0 , –7 )
Line 1: m = − 2 ; m = − 2 ; Line 2: m = − 2 ; m = − 2 ; Parallel
y = − 0.2 x + 21 y = − 0.2 x + 21
y = − 3 00 x + 11 , 5 00 y = − 3 00 x + 11 , 5 00
a) 800 ; b) 100 students per year ; c) P ( t ) = 100 t + 1700 P ( t ) = 100 t + 1700
Extrapolation.
Midway through 2024.
y = − 1.294 x + 49.412 ; r = − 0.974 y = − 1.294 x + 49.412 ; r = − 0.974
Early in 2022
Practice Test
y = −1.5 x − 6 y = −1.5 x − 6
y = − 2 x − 1 y = − 2 x − 1
Perpendicular
( − 7 , 0 ) ( − 7 , 0 ) ; ( 0 , − 2 ) ( 0 , − 2 )
y = − 0.25 x + 12 y = − 0.25 x + 12
y = 875 x + 10 , 675 y = 875 x + 10 , 675
a) 375 ; b) dropped an average of 46.875, or about 47 people per year ; c) y = − 46.875 t + 1250 y = − 46.875 t + 1250
Early in 2018
y = 0.00455 x + 1979.5 y = 0.00455 x + 1979.5
r = 0.999 r = 0.999
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Access for free at https://openstax.org/books/precalculus/pages/1-introduction-to-functions
- Authors: Jay Abramson
- Publisher/website: OpenStax
- Book title: Precalculus
- Publication date: Oct 23, 2014
- Location: Houston, Texas
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- Section URL: https://openstax.org/books/precalculus/pages/chapter-2
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Helping math teachers bring calculus to life
Review Lessons 1.4-1.6
Unit 1 day 9 ced topic(s): 1.2 , 1.3, unit 1 da y 1 day 2 day 3 day 4 day 5 day 6 day 7 day 8 day 9 day 10 day 11 day 12 all units.
In FR Quad students solve four free response questions and compete against other teams to score points for the answers they write up on the class grid. Students will review important concepts about average and instantaneous rates of change and the rates of change of linear and quadratic functions. Get ready for a lively and fast-paced review activity that encourages student-to-student conversations and high-level collaborative work!
Activity: FR Quad
Lesson Handout
Instructions.
Prep: Make copies of the four free response questions. You will need one copy of each FRQ per group, not per student. Choose two squares to be the “magic squares” (instructions below).
Create groups of 3-4 students. Give each group a different colored whiteboard marker. Project the game board provided on page 2 of the activity handout.
Teams work to complete the FRQs in whatever order they wish. Once they have an answer, they write it in the proper box on the screen using their team’s colored marker. If another group believes the answer is wrong, they can write their own answer beneath it.
Once a team has written in a particular square, they cannot write in that square again, even if they want to modify their answer.
Only one person from each group can be at the board at a time. All other group members must stay at their table.
Special points are given for completing a full FRQ, correcting someone else’s answer, answering a part (e) question, having 4 in a row, or having answered a question in a Magic Square. See point values on page 3 of the activity handout.
Once all the questions are completed or there are only 5 minutes remaining in class (whichever comes first), reveal the correct answer to each square and identify which team won the square. Emphasize to students the importance of proper justifications, especially in FRQ #2. Providing rationale for selecting a function type to model a scenario is a critical skill in AP Precalculus and we want students to practice giving these justifications early and often.
Have students calculate their totals and award a prize for the first-place team.
1.1 Multiple Representations
Practice Solutions
Corrective Assignment
Application Walkthrough
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IMAGES
COMMENTS
You will see EFFL in the answer key like this: Activity (blue), Debrief Activity (red), QuickNotes (red), Check Your Understanding (blue) Anything written in blue is something we expect our students to produce. This might not be quite what we expect by the end of the lesson, but provides us with a starting point when we move to formalization.
While lesson plans are always free with a Math Medic account, our Assessment Platform provides ready-made and editable homework, quizzes, and tests that align perfectly with our lesson plans. Our Assessment Platform allows teachers the flexibility of adapting our assessments to meet their own needs, delivering assignments digitally or on paper ...
AI Homework Help. Expert Help. Study Resources. Log in Join. Lesson 1 2 Answer Key Precalculus Math Medic b381bd9006.pdf... Pages 2. Identified Q&As 16. Solutions available. Total views 66. High School Summer Program. MATH. MATH MTH101. UltraFlagOctopus11.
A candy company uses pints of chocolate to make candy. The more chocolate they use, the more boxes of candy are produced. 11. The amount of money is Josh's savings account decreases for each semester he attends college. 12. As the number of cats Mr. Sullivan owns increases, the number of mice in his barn decreases. 13.
Find step-by-step solutions and answers to Precalculus - 9780076602186, as well as thousands of textbooks so you can move forward with confidence. ... Math. Algebra; Precalculus. 2nd Edition. Carter, Cuevas, Day, Malloy. ISBN: 9780076602186. ... Section 1-2: Analyzing Graphs of Functions and Relations. Section 1-3: Continuity, End Behavior, and ...
Helping math teachers bring calculus to life. Log In. Lesson Plans. 150 Days of AP Calculus; 150 Days of AP Precalculus; AP Calculus BC Lessons; Assessments. Review Course. Workshops. See the Medics; Request A Workshop; Blog. ... All lesson plans are under this license from the Creative Commons.
2.1 Change in arithmetic and geometric sequences Notes. Class notes 94% (16) 14. AP Pre-Cal Midterm Review Unit 1 - 2. Practice materials 100% (6) 2. Lesson 4.5 Answer Key - AP Precalculus - Calc Medic. Assignments 100% (5) 5.
SOLUTIONS. 1.1 Practice. For each function, identify what the dependent and independent variables represent. 1. is a function where is the number of books in the library and is the number of students in the school. 2. is a function where is the number of years since kindergarten and is the number of Pokemon cards.
Exercise 64. Exercise 65. Exercise 66. Exercise 67. Exercise 68. Find step-by-step solutions and answers to Precalculus - 9781938168345, as well as thousands of textbooks so you can move forward with confidence.
There are two common misconceptions about domain. The first is the false idea that the square root of 0 is undefined. Ask students if they can think of a number that when multiplied by itself gives 0. They should conclude that 0 satisfies this condition! The second misconception comes up more frequently with rational functions and that is that ...
Find step-by-step solutions and answers to Precalculus - 9781285499949, as well as thousands of textbooks so you can move forward with confidence. ... Calculus. Math Foundations. Probability. Discrete Math. View all. Science. Biology. Chemistry. Physics. Medicine. Computer Science. Engineering. Earth Science.
Interpreting Graphs of Functions (Lesson 1.2) Learning Targets . Describe how two quantities vary with respect to each other from a graph in a contextual scenario. Determine when a function is increasing or decreasing. Interpret key points and graph behavior in context.
Introduction to Systems of Equations and Inequalities; 9.1 Systems of Linear Equations: Two Variables; 9.2 Systems of Linear Equations: Three Variables; 9.3 Systems of Nonlinear Equations and Inequalities: Two Variables; 9.4 Partial Fractions; 9.5 Matrices and Matrix Operations; 9.6 Solving Systems with Gaussian Elimination; 9.7 Solving Systems with Inverses; 9.8 Solving Systems with Cramer's Rule
Exercise 94. Exercise 95. Exercise 96. Find step-by-step solutions and answers to Precalculus - 9780321900517, as well as thousands of textbooks so you can move forward with confidence.
Support us and buy the AP Pre-Calculus workbook with all the packets in one nice spiral bound book. 1.1.A Describe how the input and output values of a function vary together by comparing function values. 1.1.B Construct a graph representing two quantities that vary with respect to each other in a contextual scenario.
The goal is for students to understand how slope at a single point can be approximated by finding the rate of change over a very short interval of time. Since Pamela's distance traveled is a strictly increasing function, we chose to use the word "speed" instead of "velocity". Students with a physics background may be comfortable with ...
Introduction to Systems of Equations and Inequalities; 9.1 Systems of Linear Equations: Two Variables; 9.2 Systems of Linear Equations: Three Variables; 9.3 Systems of Nonlinear Equations and Inequalities: Two Variables; 9.4 Partial Fractions; 9.5 Matrices and Matrix Operations; 9.6 Solving Systems with Gaussian Elimination; 9.7 Solving Systems with Inverses; 9.8 Solving Systems with Cramer's Rule
PRE- Calculus Q1 Week6 - Application of Conic Sections; PRE- Calculus Q1 Week2 - Circle; ... Lesson 4 5 Answer Key Precalculus Math Medic 40ed81ad43. Subject: Pre-Calculus. 357 Documents. Students shared 357 documents in this course. Level: Standard. Info More info. AI Quiz. AI Quiz. Download. 0 0.
Review Lessons 1.4-1.6. Overview. In FR Quad students solve four free response questions and compete against other teams to score points for the answers they write up on the class grid. Students will review important concepts about average and instantaneous rates of change and the rates of change of linear and quadratic functions.
Exercise 167. Exercise 168. At Quizlet, we're giving you the tools you need to take on any subject without having to carry around solutions manuals or printing out PDFs! Now, with expert-verified solutions from Precalculus 3rd Edition, you'll learn how to solve your toughest homework problems. Our resource for Precalculus includes answers ...
AP Pre-Cal Midterm Review Unit 1 - 2. AP Precalculus. Practice materials. 100% (6) Comments. ... Lesson 4. 5 - Graphing and Manipulating Exponential Functions QuickNotes Check Your Understanding ... Lesson 4.5 Answer Key - AP Precalculus - Calc Medic. Topic: Unit 2: Exponential and Logarithmic Functions. Subject: AP Precalculus. 572 Documents.
Download File. Application Walkthrough. 1.3 Rates of Change in Linear and Quadratic Functions. 1.11B Polynomial Long Division and Slant Asymptotes. 2.5.A Exponential Function Context and Data Modeling. 2.5.B Exponential Function Context and Data Modeling. 2.13A Exponential and Logarithmic Equations and Inequalities.