AP® Environmental Science Math Review Practice Problems

These are practice problems to prepare for the math on the
AP® Environmental Science Exam.

For basic math information and formulas, read “What students need to know about the math for the AP Environmental Science Exam”
Read “Last minute tips and hints for the APES Exam” for advice taking the exam.

If you are stuck on some problems, watch math help videos. They are:

  1. https://youtu.be/_zVClg1mtig
  2. https://youtu.be/_I7JBAQ7qSM
  3. https://youtu.be/o6J8f3_FawE
  4. https://youtu.be/CDYUzVdoIpk
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Tips and hints for the AP® Environmental Science exam

These are tidbits of important information and some common student errors that many students make on the AP Environmental Science exam.

Make sure you are studying your notes, textbook and/or a review book. Some favorite review books are: A Cartoon Guide to the Environment and ASAP and
Five Steps to a Five. But many others are good as well (Barrons, and ones by textbook publishers).

Know how to answer FRQ prompt using these terms.
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FRQ tips for the AP®Environmental Science Exam

These are some basic guidelines for writing FRQs. For help with math, read “What students need to know about the math for the AP Environmental Science Exam”

Basic FRQ information for the APES exam

  1. Always write in complete sentences.
  2. Don’t write more than the question asks for.
    1. If the FRQ asks for two examples, only the first two examples that you write are graded.
    2. If you write more, the graders will read them to check for contradictions, but you will not earn points. Contradictions will take away points.
  3. Introductory sentences or re-stating the question is not necessary. No points removed, but it can take precious time.
  4. Label each section: a. b. ci…….
  5. For a document question (#1), you DO NOT need to quote the document. Read it to get ideas, but pull specific information or examples out of your brain.
  6. Write an economic term ($ or jobs) for an economic question
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AP® Environmental Science math for students for the 2019 exam.

This is the basic information you need about APES math on the AP® Exam.

Read this post for some practice problems.

  • No Calculators. Big bummer, I know, but its the way it is.  You may have heard that this is changing for 2020….it is, but for this year, NO calculators.
  • Pre-Algebraic Word Problems. Many students struggle with setting up the problem. The actual math is not that hard, but setting it up is challenging for many. Practice this with problems your teacher assigns you or with review books.
  • Usually 8-10 Multiple Choice Questions. There are 100 multiple choice questions and 8-10 are usually math related.  The Rule of 70 is a favorite for 1 or 2 of the problems. You DO NOT need to show work for MC questions.
  • One FRQ is Half Math. You have four FRQs in 90 minutes. Question #2 will have math quesitons for half the FRQ. Over the years, the math has gotten easier on the FRQ, but this has not increased the national pass rate. To practice, go to the College Board’s website and print out some FRQ #2s from previous years. Then, go to this playlist on Youtube to help solve the problems.
Continue reading “AP® Environmental Science math for students for the 2019 exam.”

What Do Students Think is Best for AP Exam Review?

I survey my students every year after the AP Exam, because I want to improve my practice and adjust for needs the following year. For review ideas, read this post. Remember, every school, teacher and students are different. What my students need or do not need is unique to them. As a professional, you will do trial and error and your own surveys to find out the best way to prep your own students for the exam. To see a copy of my survey click on this google doc.

I have a lot of students take my course and the exam (140+) and these numbers give me good insight. Overall, my students do well on the exam and have a good amount of self-reflection afterwards. Here are the major points from the past two years of survey data:

Review Materials that Students Think are Very Helpful

  • Students reported sticky notes were the best in preparing them for the AP®  Exam (75+% average in the past two years said they were very helpful).
  • Released exams and diagnostics were also highly rated (75+% average also said they were very helpful).
  • Mastering Environmental Science coaching extra credit assignments were very helpful (70+% average). This is the online program that comes with the Withgott book. It has tutorials called “coaching” assignments. I make several “coaching” assignments as extra credit due the night before the AP®  Exam. Students drag and drop and sort content, watch videos with questions and graph analysis practice.
  • Binders were very helpful to about half my students.
  • Remind texts were very helpful to over half my students. (I do my own texts the weekend before the exam with helpful hints texted every 2 hours or so).
  • Bozeman videos were very helpful to about half my students. I give links and guidance for Bozeman videos in relation to my textbook on their 6 Week Study Plan.

Please note: There are a lot of other review ideas and materials out there that are great. These are just the ones I pick for my students.

2018 results
2018 results

Review Material not as Helpful

  • Review book that the school owns. My school has a copy of a review/test prep book for each student to check out. It is from the textbook publisher. It has not been highly rated by my students. Perhaps this is because they cannot write in it. I will have to ask this year.
  • Google folder with lots of review items–vocab lists, study cards, etc. Anything I think is helpful is uploaded into this folder, but less than 20% thought it was very helpful. (Sorry, I cannot share my review folder, because some items in it are copyrighted).
  • Other review books that the student purchased. Now, this may be skewed, because not every student bought a book.

Class-time Review that was Helpful

I do not spend class time on content review. Instead, my students take released exams (which cannot go home as homework according to the agreement you acknowledge with your AP audit). Most students thought these were valuable to do in class:

  • FRQ strategies lesson-I pass out 4 FRQs from a recent year and I have students write all over the four with hints and strategies and have them decide how they want to tackle in 90 minutes.This is the video I record for my online section of APES. https://youtu.be/ZuPGKKFklc4
  • Mathematics review–most said the review was helpful to spend time on.
  • Experimental design practice— I give students practice problems from released APES exams and also AP Biology exams (since they have more released questions) along with the experimental design FRQ from 2012.
  • Geography review
Results from 2018. A 5 was very helpful and 1 was not helpful

* AP® is a trademark registered and/or owned by the College Board which was not involved in the production of, and does not endorse this site.

Airborne Particulates Lab Using LED Tap Lights

I recently experimented using LED tap lights as an alternate to using stereoscopes in the Airborne Particulate Lab. You can read about the lab on this post. This is a great lab for kids to practice experimental design.

I purchased LED tap lights from Amazon but they can also be found at home improvement stores.

They work with a little finesse. Here is what the kids need to use:

Students need to focus on the vaseline above the grid. If they focus on the graph paper, they won’t see any particulates. They need to hold the hand lens about 3-4 centimeters above the petri dish. That way it focuses on the particulates.

This method does work, but it takes a little more practice from the kids to see the particulates.

Air Pollution Chalk Drawings

Acid rain chalk drawing

One way to help students memorize the 3 atmospheric processes they need to know for the AP® Exam is to have them draw. Research indicates that sketching or drawing information helps students learn. From my own experience, drawing with chalk helps my students memorize better than drawing on paper. Its a fun activity in groups and the kids truly learn. The 3 processes are:

  1. Tropospheric Ozone Formation (ground-level ozone in smog)
  2. Stratospheric Ozone Depletion (the ozone hole)
  3. Acid Deposition (Acid Rain)

Supplies for Chalk Drawing

I use chalk, because it is the most economical (and eco-friendly) choice. The best chalk is from IKEA–seriously. A few boxes will last the entire year or more. Since I teach 170 students in APES, this is the best option for me.

Neon Expo Markers are another good option. You can write a mini-grant or a request on Donors Choose to fund them.

You can write on lab tables if you have the standard science black finish. If not, you can draw with chalk outside.

Instructions for Chalk Drawing

My students follow the instructions on this document. I do not have them look up information and make their own drawing, because I do not want them looking up and copying diagrams on the internet. I want them to draw out the processes with the details and specifics that have been asked on released AP® Exams. They will learn when they use their brains to make pictures.

We do the 3 drawings on separate days so that students keep the details separate in their brains. Each processes takes about 20 minutes to do and my students work in groups of 4.

I check the drawings when they are fineshed and then they erase with water and paper towels. It is an activity that truly helps students learn the complicated processes needed for the AP exam.

* AP® is a trademark registered and/or owned by the College Board which was not involved in the production of, and does not endorse this site.

February = AP® Exam Pacing Check

In February, I like to plan the rest of the year up to the AP® Exam. Pacing is crucial and while kids may complain about going too fast through content, they will complain even more if you don’t make it through everything by the AP Exam. Here’s some advice for pacing.

  • Count the chapters/topics left to cover and assign a number of weeks/days for each. Some topics need more time so check the AP® Environmental Science outline on the College Board website. Don’t forget about holidays, spring break, the prom and state testing.
  • Set days for exams and sticky to it! You will have to cut, cut, cut favorite activities, videos and labs. I have reworked plans multiple times until I’m happy with the items I have left in the time I have.
  • Do not skip anything. Sometimes a minor topic is an entire FRQ. See the 2015 #4 FRQ for an example. Many teachers skipped the chapter on cities that year due to snow days or running out of time and lamented the decision.
  • Post your pacing plan for students. Explain it to them and talk about strategy. Keeps the complaining down when you have strict deadlines and when you pick up the pace and cover chapters faster.
  • Assign content for homework. Explain to kids that NO AP® teacher has time to spoon feed everything AND also make sure students have developed AP Science Practices (which are a big part of the multiple choice section of the exam). Homework might be video notes or assigned textbook reading with reading guides or quizzes.
  • Encourage your students. I say “this semester we are going to pick up the pace, because you have the foundations down of ecology, soil, etc. We can go through the chapters faster now. I do this every year and my students always rise to the task.
  • Give sufficient time for review: I review science skills and do practice exams in class. I allow 2 weeks for this and then give the final exam a couple of days before the AP® exam. Kids review content on their own via a “6 week study guide”.

Essentials for class time

A lot of content is “the easy stuff” and can be read and understood by students without you.
Focus on skills and difficult content during class time such as:

Supplies needed for Airborne Particulate Experimental Design Lab.
  • Difficult content like El Nino, Water and wastewater treatment, Air pollution, stratospheric ozone depletion, GPP/NPP, biogeochemical cycles and LD-50 graphing. 
  • Math. Its better to do math during class time where you can make sure students do not copy and can get help as needed. Assign content at home in exchange. Explain this strategy to kids.
  • Labs that give a lot of “bang for the buck”. Make sure labs cover many concepts, skills and topics. Students need to collect a lot of quantitative data in charts and then analyze this data. The multiple choice section of the AP Exam will have data sets for students to answer difficult questions about. An example of a lab with a lot of data collection, analysis and math is the Kill-A-Watt Lab.
  • FRQ practice, assessments and peer grading. Self-grading and peer-grading dramatically helps students understand how to write better FRQs.
Self-grading and peer-grading with highlighters. Students highlight the exact words that give the point.

* AP® is a trademark registered and/or owned by the College Board which was not involved in the production of, and does not endorse this site.

Toxins 5E Lab

Two important topics in APES are combined for this 5E–Serial dilution Lab and LC50 Lab. The lab papers needed for this lab can be found on these google doc links.
Engage, Explore, Explain
Elaborate, Evaluate
How Toxic is Toxic
LD50 of Substances

Engage: Flint, Michigan

This Engage is a short case study about lead exposure for students. Most students have heard of Flint, Michigan and its water quality problems so this adds to previous knowledge (a key component of Engage). The video piques their interest and then we discuss our own drinking water and how this problem would not occur here, because we are a newer community that does not have lead pipes. We also discuss how older cities with lead pipes can prevent lead leaching by using an additive in the water. Click to read this article explaining more about how lead gets into drinking water.

Explore: Serial Dilution

Students in AP® Environmental Science need to understand how toxins can still be prevalent in very small amounts. The best way to do this is for students to do a serial dilution. (Note: This activity is courtesy of Dan Hyke from the APSI, I attended in 2006. I have altered it and combined with LD-50 for this 5E)

Materials needed for serial dilution

As students walk through the procedure, fill in their data charts and answer the guiding questions, they hopefully will come up with the concept on their own–toxins can still be present even in very small amounts such as parts per million (ppm), parts per billion (ppb) and parts per trillion (ppt). Materials needed are: (Click on an underlined item for a link to the product)

  • Well plate
  • Plastic Pipet
  • Beaker for tap water
  • Toothpicks
  • Dropper bottle of a dye/stain/coloring such as a Food Grade Dye like FD&C Red Dye #40 Do not use regular food coloring as it dilutes much too quickly

Students use 3-4 drops of the red dye solution in the first well.  Then they fill the other wells with 9 drops of tap water. After that, they drop one drop from the previous well and stir.

Well Tray at the end of the lab

Students are often concerned when their solution is clear by well 7. I tell them that’s normal and they are to still make the transfers. They need to move the molecules in order to understand the point of the lab.

Students creatively identify shades of red and pink and learn about ppm, ppb, and ppt on their data sheet. Some students will need help with these circles. I tell them that “their brains will hurt” today.

Sample serial dilution data
Students using an online thesaurus to get creative on shades of red

Explain: Student Sense-Making

In a good 5E, students should be able to develop the concept you want them to on their own. Developing good guiding questions is your job as the teacher to lead them to it.  For this lab, students should make a CLAIM or a STATEMENT that “Substances can be in water even if you cannot see it, smell it or taste it.

Elaborate: LC50 Lab

We use the results from the salinization Lab to do LC-50. Students bring their salinization labs back to class and we collect class data. (Students save all work in their APES binder) This time, however, we want “opposite” data–the number of seeds that DIED, instead of the number that germinated.

Students fill in the chart for their group’s data and then all students copy class data. I often make a chart on the board for groups to fill in.

From there, using a document camera or on the board, teach students how to find the LC-50 by drawing a line from 50% on the y axis to where it hits the dose-response curve and then down to the x axis. Read the concentration that kills 50% of seeds. If you need help with this, I made this video for absent kids that may help you understand how to do this lab:


This 5E does not have its own Evaluate–rather students are assessed for these skills and knowledge on their next exam.

* AP® is a trademark registered and/or owned by the College Board which was not involved in the production of, and does not endorse this site.

Trees, Forestry and Deforestation 5E

Take students outside to measure trees, discover ecosystem services of trees and forests, develop math skills, deforestation and sustainable forestry in the “I Love Trees 5E” Lab. If you are lucky enough to teach at a school next to a forested area, take the kids there. If not, trees on the school grounds, park or other area work just as well.

Student using a homemade clinometer to measure the height of a tree at school

Teacher Preparation

For this 5E, you need to make clinometers using cardboard, string/yard, a piece of metal (anything with a little weight) and a straw. You can have students make the clinometers if you would like, but I had my student lab assistant make 10 clinometers for me to save class time. They can be reused over and over. I made one clinometer for each group of 4 students.

Class set of clinometers that can be reused over and over

You also need two sewing tape-measures for each group of students and a tree map. I identified the trees ahead of time in the study area and googled their density. You could teach students how to identify trees using the iNaturalist app or a field guide if you want.

Materials for 1 group of students. One clinometer, two tape measures, and a tree map of the school grounds


An engage section of a 5E should be very short. For this 5E, I asked kids about the biggest tree they’ve ever seen. I find that personal questions where kids can share with their elbow partner and the rest of the class is very engaging. Another part of the Engage sections is review the photosynthesis equation–a good 5E builds on previous knowledge.

I show my own pictures with large trees (like Sequoias or Redwoods at the National Parks or large oak trees in town). Students like to see their teacher’s pictures.

This picture was taken 10 years ago in Sequoia National Park. My children are now older and one is in my APES class. Kids LOVE to see this.

Explore #1

Students head outside to take data in this Explore. Its helpful to demonstrate how to use the clinometer before heading outside. You or your students will choose a tree and measure the tree height using a homemade clinometer. They will also measure the tree circumference using the measuring tapes, the distance the tree to a building and the condition of the tree. After measurements, students will do math calculations using given formulas to help them determine the height, diameter, volume and mass (using the density), and the carbon sequestered by the tree.

Students hold the clinometer with the plumb line straight down and then walk forward or backwards until they can see through the straw to the top of the tree.
Students measure the circumference of the tree using measuring tapes and then use a formula to find the diameter.
Students use two measuring tapes to measure the distance from the tree to the student using the clinometer. The easiest way to do this is to “leapfrog” two tapes as shown above.

Explore #2

Students head back to class to enter their tree’s data on iTreeTools. 
Data chart for the results from iTree is below:

Total benefits for this year $
Carbon Dioxide Sequestered $
Annual CO2 equivalent of carbon kg
Storm Water runoff avoided $
Air Pollution Removed each year $
Carbon monoxide removed g
Ozone removed g
Nitrogen Dioxide removed g
Sulfur dioxide removed g
Particulate matter < 2.5 microns removed g
CO2 Stored to date $
Life CO2 equivalent of carbon kg

Explain: Student-Sense-Making

Students work through a series of questions to help them discover the scientific concept on their own. Sample questions:

  1. What are the $ benefits of your tree? _________________
  2. Review: What is the photosynthesis equation:
  3. Draw a picture of the tree and show how molecules are moving
  4. Where does the C from CO2 end up?
  5. Think about it: How does cutting down trees for lumber and paper affect atmospheric carbon?
  6. Think about it: How does cutting down trees and burning them affect atmospheric carbon?
  7. Many species of trees increase in density, as they get older. How does this affect carbon sequestration? (Hint, the mass increases also).
Sample drawing for #3 above. The idea is for students to understand that carbon creates biomass in trees and other producers.

These and other questions help students discover the scientific concept/s and make a CLAIM. This is the place for formative assessment. Walk around and check student claims. Make sure they understand what you want them to understand.

Question :: How can how trees provide ecosystem services regarding climate
change, air pollution and water pollution:
Claim :: (Complete sentence answer to the question above.—Make sure you write
about ALL THREE ecosystem services)    

Explain: New Understandings and Vocabulary

This is the place for formal science instruction. in this E, students will watch a series of 3 mini videos that describe more ecosystem services of trees and why tree-sitters do what they do. Students record more ecosystem services of trees on their lab report. Its best to do this portion as a class so that you can stop and discuss. However, it can be done at home, if needed, to save time. One video is a lovely TedTalk about trees.


In this section, students learn about deforestation and then sustainable forest solutions. Students will watch a series of 6 mini videos and fill in a T-chart with facts about deforestation and facts about sustainable forestry. Two sample videos are:

While there are some counter-arguments to sustainable forestry, students need to understand some solutions for exams. You can discuss places you agree or disagree with sustainable forestry.


The evaluate section of this 5E is unique, engaging and fairly easy to grade. Students will fill in the branches of the tree drawing with 5 ecosystem services:

Students then describe problems with deforestation next to the stump:

And methods of sustainable forestry next to this drawing:

The Evaluate section can be done individually or with a partner–with or without notes. You decide which is best for your students.

Open Access Picture credits: https://commons.wikimedia.org/wiki/File:Stubb.jpg