2024 Ap physics 1 released frq

3 Questions. Directions: Answer all three questions. The suggested time is about 15 minutes for answering each of the questions, which are worth 15 points each. The parts within a question may not have equal weight. Show all your work in this booklet in the spaces provided after each part.. Spectrum guide live tv

2020 Exam SAMPLE Question 1 (Adapted from: AP ® Physics 1 Course and Exam Description FRQ 1) Allotted time: 25 minutes (+ 5 minutes to submit) A small sphere of mass . M. is suspended by a string of length . L. The sphere is made to move in a horizontal circle of radius . R. at a constant speed, as shown above. The center of the circle is ...**Updated on 1/31/24 to include the 2022-23 FRQ exams!**If you are looking for past AP Biology free-response questions (FRQs) that are organized by topic, then you have come to the right place. In this post, we have linked every freely available past FRQ there is from College Board and organized it into the following major topics of AP Biology.1.38 10 J K. 23. k. B Electron charge magnitude, e 1.60 10 C 19. 1 electron volt, 1 eV 1.60 10 J 19 Speed of light, c 3.00 10 m s 8 Universal gravitational constant, G 6.67 10 m k 11 3 2<g s. Acceleration due to gravity at Earth’s surface, g. 9.8 m s 1 unified atomic mass unit, 1 u 1.66 10 kg 931 MeV 27. c2. Planck’s constant, h 6.63 10 J s ...Mike Anderson and Ovie Faruq offloaded their collection of 72 NFTs for $9.25 million this week, according to OpenSea data. Jump to Two former Barclays junk bond traders reportedly ...General Notes About 2019 AP Physics Scoring Guidelines. The solutions contain the most common method of solving the free-response questions and the allocation of points for this solution. Some also contain a common alternate solution. Other methods of solution also receive appropriate credit for correct work. https://secure-media.collegeboard ...Boneworks has gained significant attention in the gaming community since its release. With its highly realistic physics and immersive gameplay, many gamers are eager to get their h...May 11, 2020 ... The pendulum is released from rest at an angle of 60 degrees and collides with a ball of mass 0.22 kg initially at rest at the edge of a ...General Notes About 2017 AP Physics Scoring Guidelines. The solutions contain the most common method of solving the free-response questions and the allocation of points for this solution. Some also contain a common alternate solution. Other methods of solution also receive appropriate credit for correct work. The correct answer is e. The wheelchair carries a total mass of 100kg up to a height of 10m, with 300J of Work being done by the wheelchair each second. The time for the total Work does is calculated as follows: Work. P = time Work mgh. time = = Power P (100kg)(10m /s2)(10m) 10000. time = = = 33s 300J /s 300. AP Physics C: Mechanics 2001 Free-Response Questions. The materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any other use must be sought from the Advanced Placement Program. Teachers may reproduce them, in whole or in part, in limited quantities, for face-to ...If you're looking for help in AP Physics 1, check out a new course I've put together here I'm going to put together my own solutions for the 2021 AP Physics 1, AP Physics 2, AP Physics C, AP Calculus AB, AP Calculus BC, and AP Statistics Free Response questions here, after the questions are released. I'll be putting up YouTube videos explaining my solutions, but I'll link the actual pdf files ...on this page. PHYSICS C: MECHANICS. SECTION II. Time—45 minutes. 3 Questions. Directions: Answer all three questions. The suggested time is about 15 minutes for answering each of the questions, which are worth 15 points each. The parts within a question may not have equal weight.Rock X. is released from rest at the top of a cliff that is on Earth. A short time later, Rock Y. is released from rest from the same location as Rock X. Both rocks fall for several …Learn everything you need to know about the free-response section of the AP Physics 1 exam, including the format, examples, and tips. See how to answer experimental design, qualitative/quantitative translation, and short answer questions.Practice Online AP Physics 1: Unit 6: Simple Harmonic Motion - Exam Style questions with Answer- FRQ prepared by AP Physics Teachers. Skip to content. IBDP, MYP, AP, iGCSE, A-Level HOME; IB DP Menu Toggle. Physics; Biology; ... Release the pin, and measure the maximum distance (h) ...4. (10 points) A drinking fountain projects water at an initial angle of 50° above the horizontal, and the water reaches a maximum height of 0.150 m above the point of exit. Assume air resistance is negligible. (a) Calculate the speed at which the water leaves the fountain.So on block 1 I have the weight so that is m1g, I also have the tension, I'll make that two of these lines tall, so I also have the tension. Now block 2 I have the same tension or same magnitude of tension I should say, now it's also pulling upwards, so tension, and I have its weight, which is going to be larger than the tension, so its weight ...Download free-response questions from past exams along with scoring guidelines, sample responses from exam takers, and scoring distributions. If you are using assistive technology and need help accessing these PDFs in another format, contact Services for Students with Disabilities at 212-713-8333 or by email at [email protected]: Questions 1, 4, and 5 are short free-response questions that require about 13 minutes each to answer and are worth 7 points each. Questions 2 and 3 are long free-response questions that require about 25 minutes each to answer and are worth 12 points each. Show your work for each part in the space provided after that part.Ap22 frq physics 1 - ap college board. ap college board. Course. Physics 1 (Phys 111) ... AP ® Physics 1: Algebra-Based Free-Response Questions ... Frictional forces are negligible in the pulley’s axle and between the block and the surface. Block 2 is released from rest and moves downward before momentarily coming to rest.1 point. the gravitational force One earned point is deducted for drawing any extraneous vectors. One earned point is deducted for vector lengths that do not allow the system to accelerate in the proper direction. (b) 3 points. For writing an equation for Newton’s second law for block 1. m 1 a = T - m 1 g.Example response for part (c) (ii) If the block is much more massive, then it will barely move when the disk collides and. 1 point. (c) Total for part (b) For stating or mathematically representing that if the disk is much more massive, then the block will have little effect on the motion of disk 1. OR. For stating. Questions 2 and 3 are long free-response questions that require about 25 minutes each to answer and are worth 12 points each. Show your work for each part in the space provided after that part. In the three circuits shown above, the batteries are all identical, and the lightbulbs are all identical. General Notes About 2019 AP Physics Scoring Guidelines. 1. The solutions contain the most common method of solving the free-response questions and the allocation of points for this solution. Some also contain a common alternate solution. Other methods of solution also receive appropriate credit for correct work. 2. Study with Quizlet and memorize flashcards containing terms like State the basic physics principles, laws, or equations that students could use to graphically determine the relationship between the release height of block XX and the speed at which the two-block system travels after the blocks collide and stick together., Derive an equation that relates the initial release height HXHX of block ... Download free-response questions from past exams along with scoring guidelines, sample responses from exam takers, and scoring distributions. If you are using assistive technology and need help accessing these PDFs in another format, contact Services for Students with Disabilities at 212-713-8333 or by email at [email protected]. The ... Find out how the College Board evaluates the free-response questions for the AP Physics 1 exam based on the 2019 administration. See the solutions, points, and explanations for each question and learning objective.Question 5: 2015 AP Physics 1 free response. Science > ... The mass m2 of block 2 is greater than the mass m1 of block 1. The blocks are released from rest. So let's ...the exams, and what is expected for each, see “The Free-Response Sections Student Presentation” in the . AP Physics; Physics C: Mechanics, Physics C: Electricity and Magnetism Course Description . or “Terms Defined” in the . AP Physics 1: Algebra-Based Course and Exam Description . and the . AP Physics 2: Algebra-Based Course and Exam ...AP Physics 1 Unit 8 Energy AP Classroom. 8 terms. sop1313. Preview. AP Exam. 50 terms. TaylorColeman1263. Preview. Unit 7 chem test . 42 terms. Blair_Rollen9. Preview. MND part 1 test. 8 terms. ... Block A of mass 2.0 kg is released from rest at the top of a 3.6 m long plane inclined at an angle of 30º, as shown in the figure above. Questions 2 and 3 are long free-response questions that require about 25 minutes each to answer and are worth 12 points each. Show your work for each part in the space provided after that part. (7 points, suggested time 13 minutes) Identical blocks 1 and 2 are placed on a horizontal surface at points A and E, respectively, as shown. 2. Possibly qualified. 27.1%. 1. No recommendation. 29.6%. Source: College Board. Each test is curved so scores vary from year to year, but as we see above, in May 2022 around 50% of test takers earned scores of 1 or 2. You’ll want to …Find out how the College Board evaluates the free-response questions for the AP Physics 1 exam based on the 2019 administration. See the solutions, points, and explanations for each question and learning objective.Practice Online AP Physics 1: 5.4 Conservation of Linear Momentum - Exam Style questions with Answer- FRQ prepared by AP Physics Teachers. Skip to content. IBDP, MYP, AP, iGCSE, A-Level HOME; IB DP ... In system A, kinetic energy is not conserved. When the blocks are released, Block A speeds up away from Block B. Kinetic energy …Mike Anderson and Ovie Faruq offloaded their collection of 72 NFTs for $9.25 million this week, according to OpenSea data. Jump to Two former Barclays junk bond traders reportedly ...5 Questions. Directions: Questions 1, 4, and 5 are short free-response questions that require about 13 minutes each to answer and are worth 7 points each. Questions 2 and 3 are long free-response questions that require about 25 minutes each to answer and are worth 12 points each. Show your work for each part in the space provided after that part.Clearly describe how you will analyze the data you have collected for each part of the experiment (ramp and horizontal surface). 1. The correct answer is d. The rock is accelerating constantly at 10 m/s2, so its displacement can be calculated using simple kinematics: Δy = vit +. at2. Δy = 0 +. (−10m /s2)(7s)2.2. Continue your response to QUESTION 1 on this page. (b) Consider isothermal process C. Compare the magnitude and sign of the work W done on the gas in process C to the magnitude and sign of the work in the portion of the cycle in part (a). Support your answer using features of the graph.Sample Questions. The course description from the College Board includes 12 AP Physics 1 multiple choice practice questions along with sample free response questions. Khan …AP Physics C: Mechanics Exam Regularly Scheduled Exam Date: Monday afternoon, May 14, 2018 Late-Testing Exam Date: Wednesday afternoon, May 23, 2018 ... the release statement on page 51 of the . AP Coordinator’s Manual. During the administration of Section II, students may have no more than two calculators onThe AP Physics 1 exam is three hours long and consists of two sections: a multiple-choice section and a free-response section. AP Physics 1 Section. Timing. Number of Questions. Multiple Choice. 90 minutes. 45 single-select: discrete questions and questions in sets with one correct answer.Questions 2 and 3 are long free-response questions that require about 25 minutes each to answer and are worth 12 points each. Show your work for each part in the space provided after that part. (7 points, suggested time 13 minutes) Identical blocks 1 and 2 are placed on a horizontal surface at points A and E, respectively, as shown.AP. Physics C: Electricity and Magnetism 2022 Free-Response Questions. Continue your response to. QUESTION 3. on this page. (e) Later, the same rectangular loop with lightbulb is rotated such that a short side of the loop is 1.0 cm above and parallel to the long current-carrying wire, as shown.This question is about work and energy, not simple harmonic motion. The spring won't "go on forever" because it transfers all of its potential energy, Usp, to the block's Kinetic Energy. After it lets go of the block, the spring doesn't have any energy left, so it just stops at equilibrium. You are probably thinking of a spring with no block ...AP® Physics 1: Algebra-Based 2022 Scoring Guidelines. Question 5: Short Answer. 7 points. For obtaining a period from the graph of 1.25 seconds. For substituting the values of period and mass into a valid equation for the spring constant. Example Response. T 1.25 s.AP Exam Info and Equation Sheet for Physics 1. AP Physics 1 Released Free Response - by year, includes scoring guidelines. Mr. M's favorite internet Links for physics. Lab Information and Homework Requirements. Listed below are the various units of study and related documents and links. Measurement Review - Units, Uncertainty, Graphical Analysis.If you're looking for help in AP Physics 1, check out a new course I've put together here I'm going to put together my own solutions for the 2021 AP Physics 1, AP Physics 2, AP Physics C, AP Calculus AB, AP Calculus BC, and AP Statistics Free Response questions here, after the questions are released. I'll be putting up YouTube videos explaining my …Smart 2. Calculators are not allowed for any other AP Exams, including Computer Science A and Computer Science Principles, unless a student has an approved accommodation for use of a four-function calculator. *Graphing calculators with the expected built-in capabilities for AP Calculus are indicated with an asterisk.Practice Online AP Physics 1: Unit 6: Simple Harmonic Motion - Exam Style questions with Answer- FRQ prepared by AP Physics Teachers. Skip to content. IBDP, MYP, AP, iGCSE, A-Level HOME; IB DP Menu Toggle. Physics; Biology; ... Release the pin, and measure the maximum distance (h) ...With the torque from object 1 removed, the net torque and angular acceleration switch direction (becoming clockwise) to the torque from object 2. The angular velocity does not change direction immediately and is still counterclockwise. AP® Physics 1 2021 Scoring Guidelines. (c) For a linear graph between 0 and t. C. AP Physics 1 Practice Exams. AP Physics 1 Practice Exams Free Response Notes Videos Study Guides. There are plenty of great AP Physics 1 practice exams to choose from. These online tests include hundreds of free practice questions along with detailed explanations. Start your test prep right now! Do you know how to become a Physical Trainer? Find out how to become a Physical Trainer in this article from HowStuffWorks. Advertisement The US Department of Labor declared person...2022-2023- Unit 2 - Dynamics - FRQ. AP Physics 1 Page 7 of 70. Part A. Select a point value to view scoring criteria, solutions, and/or examples and to score the response. Scoring notes: · or are not acceptable labels for the force of gravity · A maximum of two points can be earned if there are any extraneous forces. 0 1 2 3Download free-response questions from past exams along with scoring guidelines, sample responses from exam takers, and scoring distributions. If you are using assistive technology and need help accessing these PDFs in another format, contact Services for Students with Disabilities at 212-713-8333 or by email at [email protected]. The ...attached to the end of a string. Block 1 is released. 2019 AP. PHYSICS C: MECHANICS FREE-RESPONSE QUESTIONS. from rest with the string horizontal, as shown above. At the bottom of its swing, block 1 collides with block 2 of. mass. M. , which is initially at rest at the edge of a table of height 2.AP Menu Toggle. AP Physics 1; AP Physics 2; AP Physics C EM; AP Physics C Mechanics; AP Biology; AP Chemistry; AP Calculus AB; AP Calculus BC; A Level Menu Toggle. A Level Math (9709) A level Bio (9700) iGCSE Menu Toggle. iGCSE Physics (0625) iGCSE Biology (0610) SAT Menu Toggle. SAT New Math; SAT English; KS 1-4 Menu Toggle. Year 2; Year 3 ...Download free-response questions from past exams along with scoring guidelines, sample responses from exam takers, and scoring distributions. If you are using assistive technology and need help accessing these PDFs in another format, contact Services for Students with Disabilities at 212-713-8333 or by email at [email protected] Video. My solutions to Free Response Question #1 from the 2019 AP Physics 1 Exam. Also included are my reflections on how to get more points on the exam. Content Times: 0:13 Reading part (a) 1:19 Solving part (a) 3:46 We made a mistake. 4:31 Fixing our mistake. 6:09 Grading notes.Catapults use levers, counterweights and the principles of projectile motion to launch their payloads. The throwing arm of the catapult acts as a lever and has a bucket on the end ...Show Video with Solutions, Q2. AP Physics 2020 Exam SAMPLE Question 1. (Adapted from: AP Physics 1 Course and Exam Description FRQ 1) Allotted time: 25 minutes (+ 5 minutes to submit) A small sphere of mass M is suspended by a string of length L. The sphere is made to move in a horizontal circle of radius R at a constant speed, as shown …Do we owe the emergence of language and self-reflection to the ancient and sustained consumption of psilocybin mushrooms? Advertisement Psychedelic research has experienced a renai... Example Response. The gravitational force is greater for objects that are closer together, and Moon B is closer to the planet than Moon A, so the gravitational force from the planet is greater for Moon B than for Moon A. Total for part (b) 3 points. 1: Algebra-Based 2022 Scoring Guidelines. Walkthrough of the 2022 AP Physics 1 FRQ #1 Join My Discord Study Server: https://discord.gg/8WGtt3rLink to the released FRQs:https://secure-media.collegebo...These are longer questions, so grab some paper and a pencil, or open up a blank page on your computer. After you finish, you can see how you did with Unit 4 FRQ (Energy) Answers . ⏱ The AP Physics 1 exam has 5 free-response questions, and you will be given 90 minutes to complete the FRQ section. (This means you should give yourself …In among the suspended falls and running into painted tunnels, animation sometimes uses real science. Here are 10 real physics moments in cartoons. Advertisement It might seem weir...After you finish, you can see how you did with Unit 3 FRQ ( Circular Motion & Gravitation) Answers. ⏱ The AP Physics 1 exam has 5 free-response questions, and you will be given 90 minutes to complete the FRQ section. (This means you should give yourself ~18 minutes to go through each practice FRQ.) 🤔 Need a quick refresher of the unit as a ...Boneworks has gained significant attention in the gaming community since its release. With its highly realistic physics and immersive gameplay, many gamers are eager to get their h...Learn everything you need to know about the free-response section of the AP Physics 1 exam, including the format, examples, and tips. See how to answer experimental design, qualitative/quantitative translation, and short answer questions.good frq practice ap physics kinematics frq quiz test booklet name when the toy was released, the center of the string was moving with an initial speed of at. Skip to document. ... AP1 Tipers Unbalanced Forces Set 1; AP Physics 1 released questions, course; practice test 2; 2022 G6 US - Eye Level Math olympiad; 2021 G6 US - Eye Level Math olympiad;4. (10 points) A drinking fountain projects water at an initial angle of 50° above the horizontal, and the water reaches a maximum height of 0.150 m above the point of exit. Assume air resistance is negligible. (a) Calculate the …Download free-response questions from past exams along with scoring guidelines, sample responses from exam takers, and scoring distributions. If you are using assistive technology and need help accessing these PDFs in another format, contact Services for Students with Disabilities at 212-713-8333 or by email at [email protected] Unit 2 - Dynamics - FRQ. AP Physics 1 Page 7 of 70. Part A. Select a point value to view scoring criteria, solutions, and/or examples and to score the response. Scoring notes: · or are not acceptable labels for the force of gravity · A maximum of two points can be earned if there are any extraneous forces. 0 1 2 3Crying in dreams often signifies that dreamers are experiencing tension or stress in their waking hours and are struggling to express their feelings. Crying in dreams allows for an...AP Exam Info and Equation Sheet for Physics 1. AP Physics 1 Released Free Response - by year, includes scoring guidelines. Mr. M's favorite internet Links for physics. Lab Information and Homework Requirements. Listed below are the various units of study and related documents and links. Measurement Review - Units, Uncertainty, Graphical Analysis.Correct answer: “The two blocks land the same distance from their respective tables.”. For indicating that the change in potential energy from release to launch is the same for the two cases For an indication (explicit or implicit) that the launch velocities are the same. ii. 2 points. Correct answer: “Block 1”.AP Physics C: Mechanics 2001 Free-Response Questions. The materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any other use must be sought from the Advanced Placement Program. Teachers may reproduce them, in whole or in part, in limited quantities, for face-to ...Practice Online AP Physics 1: 5.4 Conservation of Linear Momentum - Exam Style questions with Answer- FRQ prepared by AP Physics Teachers. Skip to content. IBDP, MYP, AP, iGCSE, A-Level HOME; IB DP ... In system A, kinetic energy is not conserved. When the blocks are released, Block A speeds up away from Block B. Kinetic energy …2022 AP Student Samples and Commentary - AP Physics 1 FRQ 1. AP® Physics 1: Algebra-Based. Sample Student Responses and Scoring Commentary. Inside: Free … AP Physics 1 Practice Exams. AP Physics 1 Practice Exams Free Response Notes Videos Study Guides. There are plenty of great AP Physics 1 practice exams to choose from. These online tests include hundreds of free practice questions along with detailed explanations. Start your test prep right now! A. Derive an expression for the acceleration of the system using F, m, g and µ. B. Derive an expression for the normal force between the two masses using only the term F. #5 explanation. Δy = (1/4)gt^2. explanation on next slide. An Atwood's Machine is shown at right with masses 6m and 2m attached to the string.You probably spend too much of your day sitting. Join a walking group to get more physical exercise in your routine. Walking groups also present you with the opportunity to meet ne...

Directions: Questions 1, 4, and 5 are short free-response questions that require about 13 minutes each to answer and are worth 7 points each. Questions 2 and 3 are long free-response questions that require about 25 minutes each to answer and are worth 12 points each. Show your work for each part in the space provided after that part.. Depraved indifference vs reckless endangerment

Download free-response questions from past exams along with scoring guidelines, sample responses from exam takers, and scoring distributions. If you are using assistive technology and need help accessing these PDFs in another format, contact Services for Students with Disabilities at 212-713-8333 or by email at [email protected]. Next Video. My solutions to Free Response Question #1 from the 2019 AP Physics 1 Exam. Also included are my reflections on how to get more points on the exam. Content Times: 0:13 Reading part (a) 1:19 Solving part (a) 3:46 We made a mistake. 4:31 Fixing our mistake. 6:09 Grading notes.Example Response. The gravitational force is greater for objects that are closer together, and Moon B is closer to the planet than Moon A, so the gravitational force from the planet is greater for Moon B than for Moon A. Total for part (b) 3 points. 1: Algebra-Based 2022 Scoring Guidelines.Practice Online AP Physics 1: Unit 6: Simple Harmonic Motion - Exam Style questions with Answer- FRQ prepared by AP Physics Teachers. Skip to content. IBDP, MYP, AP, iGCSE, A-Level HOME; IB DP Menu Toggle. Physics; Biology; ... Release the pin, and measure the maximum distance (h) ... General Notes About 2019 AP Physics Scoring Guidelines. 1. The solutions contain the most common method of solving the free-response questions and the allocation of points for this solution. Some also contain a common alternate solution. Other methods of solution also receive appropriate credit for correct work. 2. May 11, 2020 ... The pendulum is released from rest at an angle of 60 degrees and collides with a ball of mass 0.22 kg initially at rest at the edge of a ...than “AP Physics 1: Algebra-Based” and I will help you. If you are giving the Physics 2: Algebra-Based Exam, say: Look at your exam packet and confirm that the exam title is … Solutions to Questions 1, 4, and 5 of the publicly released 2022 FRQs (all of the 13 minute questions). AP Physics C: Mechanics. AP Physics 1 Free Response Question Answers for Simple Harmonic Motion. 👋 Welcome to the AP Physics Unit 6 FRQ (Simple Harmonic Motion) Answers. Have your responses handy as you go through the rubrics to see how you did! ⏱ Remember, the AP Physics 1 exam has 5 free-response questions, and you will be given 90 minutes to …Download free-response questions from past exams along with scoring guidelines, sample responses from exam takers, and scoring distributions. If you are using assistive technology and need help accessing these PDFs in another format, contact Services for Students with Disabilities at 212-713-8333 or by email at [email protected]: P1 Q3 C Score: 2. In part (a)(i) 1 point was earned for having the same maximum value in each cycle at the bump. The graph does not have a constant slope between bumps or abrupt transitions at the bumps. In part (a)(ii) the point was earned because the average velocity indicated is consistent with the incorrect graph.AP Physics 1 Practice Tests. Real AP Past Papers with Multiple-Choice Questions. The AP Physics 1 Exam consists of two sections: a multiple-choice section and a free-response section. The multiple-choice section consists of two question types. Single-select questions are each followed by four possible responses, only one of which is correct.Questions 2 and 3 are long free-response questions that require about 25 minutes each to answer and are worth 12 points each. Show your work for each part in the space provided after that part. (7 points, suggested time 13 minutes) Identical blocks 1 and 2 are placed on a horizontal surface at points A and E, respectively, as shown.A. Derive an expression for the acceleration of the system using F, m, g and µ. B. Derive an expression for the normal force between the two masses using only the term F. #5 explanation. Δy = (1/4)gt^2. explanation on next slide. An Atwood's Machine is shown at right with masses 6m and 2m attached to the string.May 9, 2019 ... Solutions to the 2019 AP Physics 1 FRQ #1 See highlighted comments for any mistakes or corrections. ✓ Join My Discord Study Server: ...AP Physics 1 Free Response Question Answers for. Momentum. 👋 Welcome to the AP Physics Unit 5 FRQ ( Momentum) Answers. Have your responses handy as you go through the rubrics to see how you did! ⏱ Remember, the AP Physics 1 exam has 5 free-response questions, and you will be given 90 minutes to complete the FRQ section.It's no secret that untreated anxiety disorders can take a major toll on your emotional well-being. But because anxiety triggers a cascade of physical symptoms, it can also have an...Directions: Questions 1, 4, and 5 are short free-response questions that require about 13 minutes each to answer and are worth 7 points each. Questions 2 and 3 are long free-response questions that require about 25 minutes each to answer and are worth 12 points each. Show your work for each part in the space provided after that part..

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