Math

21 Day SAT Practice Test Schedule

Posted on by Kennon McCaa

The College Board was nice enough to publish 10 practice tests. These are the best resources available for succeeding on the SAT. Below I have created a 21 day schedule for completing all of the math practice tests and getting some extra help that will hopefully help you do your best on the SAT.

The SAT Starts at 8 AM, Do You?

Because the real test occurs around 8 AM in the morning, it is good to get used to using your brain in the morning. So, try to do your practice at 8 AM. If you are going to be your best in the morning, get to bed early in the evening (9:30 if you can).

This schedule is designed for summer studying when students have all day to study. Morning studying during the school year can be a bit of a challenge, but you can do the “morning” session by completing the problems at the wasted time at the end of a class or two.

Plenty of Sleep is Your Secret Weapon

Evening sessions should be done just before going to bed. Studies have shown that your brain will continue to work on the problems and integrate your learning into your brain after you have gone to sleep. Frequent rest and plenty of sleep are a very important part of the learning process. A lack of sleep has been shown to impair your cognitive ability more than drinking alcohol, so don’t do either!

Practice Makes it Easier

This might look like a ton of work, but the harder you work, the easier the test gets. While it might take a full 25 minutes to finish the Section 3 test when you start, after some solid practice the test might take as little as 10 minutes. It gets easier the more often you practice. Never miss a day! When you take a day off, your brain loses momentum.

Success Through Repetition

The biggest challenge of SAT prep is getting enough practice and getting comfortable with the format of the questions. This study plan tries to combat that by having students re-do the same test they have completed previously. It might seem insane, but after searching for years for an effective way to make the test seem as familiar as an old friend I have started seeing significant improvements for students that are using this strategy. I have spent years studying this test and its content is extremely repetitive (it has to be to allow for valid comparisons of students), but the test writers are masterful at changing the phrasing of the questions. By re-doing tests it helps students become more and more comfortable at focusing more on the math and less on the confusing wording. PLEASE don’t skip the “Re-do” practice, it can be extremely effective and it takes far less time to re-do a test you have done before.

Save a Tree – Printing Tips

Most people know that many printers allow for printing on both sides, choosing this simple option can cut your paper usage in 1/2. What many people do not know is that you can print multiple pages per side. This option can additionally reduce your paper usage by 1/2 again. As important as it is to save paper, it is also very important to use paper. Do NOT do these practice tests by reading them off of a screen, print them out, and write all over them. Become an expert at circling facts, underling the most important word, and crossing off incorrect answers by writing all over the practice tests.

Be Organized – Keep Your Practice Tests

The final day before the test you will want to review all of the problems you missed while practicing. In order to learn from those past mistakes you must write the test number at the top of each test packet and keep your completed practice tests.

Practice Makes Perfect! - Carter's completed official SAT practice tests that helped him get his perfect 800 on the SAT math test in 9th grade.
Practice Makes Perfect – Carter’s Practice Tests from his Perfect 800

21 Day Schedule

  • Day 1 (Morning): Do Section 3 Test #1 (no calculator).
  • Day 1 (Afternoon): 90 Minute SAT Strategies tutoring session.
  • Day 2 (Morning): Do SAT extra practice assigned by tutor.
  • Day 3 (Morning): Do SAT extra practice assigned by tutor.
  • Day 3 (Afternoon): Get some more tutoring!
  • Day 4 (Morning): Do SAT extra practice assigned by tutor.
  • Day 5 (Morning): Do Section 3 Test #9.
  • Day 6 (Morning): Do Section 3 Test #10.
  • Day 6 (Afternoon): Get some more tutoring!
  • Day 6 (Evening): Re-do Section 3 Test #1 (Yes, do it again!).
  • Day 7 (Morning): Do Section 3 Test #2.
  • Day 7 (Evening): Do Section 4 Test #9, questions 1-20 (calculator).
  • Day 8 (Morning): Do Section 4 Test #9, questions 21-38.
  • Day 8 (Afternoon): Get some tutoring on Section 4!
  • Day 8 (Evening): Re-do Section 3 Test #1 (Yes, do it AGAIN!).
  • Day 8 (Evening): Re-do Section 3 Test #9 (again).
  • Day 9 (Morning): Do SAT Section 4 extra practice assigned by tutor.
  • Day 9 (Evening): Do Section 4 Test #10, questions 1-20.
  • Day 10 (Morning): Do Section 4 Test #10, questions 21-38.
  • Day 10 (Evening): Do Section 4 Test #1, questions 1-20.
  • Day 11 (Morning): Do Section 4 Test #1, questions 21-38.
  • Day 11 (Afternoon): Get more tutoring on Section 4!
  • Day 11 (Evening): Re-do Section 4 Test #9 (again), all questions.
  • Day 12 (Morning): Do SAT Section 4 extra practice assigned by tutor.
  • Day 12 (Evening): Do Section 4 Test #2, questions 1-20.
  • Day 13 (Morning): Do Section 4 Test #2, questions 21-38.
  • Day 13 (Evening): Do Section 3 Test #4. (We’re skipping test #3)
  • Day 14 (Morning): Do Section 3 Test #5.
  • Day 14 (Afternoon): Get some tutoring!
  • Day 15 (Morning): Do Section 3 Test #6.
  • Day 15 (Afternoon): Re-do Section 4 Test #9 (Again!), all questions.
  • Day 15 (Evening): Do Section 4 Test #3, all questions.
  • Day 16 (Morning): Re-do Section 4 Test #10, all questions.
  • Day 16 (Afternoon): Do Section 4 Test #3, questions 21-38.
  • Day 16 (Evening): Do Section 3 Test #7.
  • Day 17 (Morning): Do Section 4 Test #4, all questions.
  • Day 17 (Evening): Re-do Section 3 Test #1 (Yes, do it again!).
  • Day 18 (Morning): Do Section 4 Test #5, all questions.
  • Day 18 (Afternoon): Get some tutoring!
  • Day 18 (Evening): Re-do Section 3 Test #9 (again).
  • Day 19 (Morning): Do Section 4 Test #6, all questions.
  • Day 19 (Evening): Re-do Section 3 Test #10 (again).
  • Day 20 (Morning): Do Section 4 Test #7, all questions.
  • Day 20 (Evening): Re-do Section 4 Test #9 (Again!), all questions.
  • Day 21 (Morning): Do Section 3 Test #8 and Section 4 Test #8.
  • Day 21 (Afternoon): Get some tutoring!
  • Day 21 (Evening): Review all the problems you missed while practicing.
  • Day 21 (Evening): Get plenty of sleep!
  • SAT Test Day! Good luck!

The Best AP Calculus Resources

Posted on by Kennon McCaa

Succeeding in AP Calculus takes work! If you are going to put in the work, make sure you are working smarter, not harder. Here are the best resources that I have found to help you be efficient and get great practice quickly. Of course, if you need tutoring in Osprey or via FaceTime/Computer, just schedule a tutoring session and we will be happy to help.

Studying for a AP Calculus Chapter Test

The files listed below are great for studying for a chapter test. They have all of the released problems from 1969 through 2012 categorized by topic. The saint who did this work will forever have my appreciation. First, open the “Table of Contents” file and look for the topic(s) that are on your chapter test. This will tell you what page numbers will contain relevant questions. Then, use the “Pages” file(s) to find the actual questions. For example, suppose your chapter test is on “Area Between Curves”, the Table of Contents says that ” Area Between Curves” can be found on pages 242-245, so open the “Pages 208-313” file and scroll to page 242 (page numbers are handwritten at the bottom of each page). Note that next to each question the year is written in pen, so the first “Area Between Curves” question is question #1 from the 1993 BC exam. Using the question number and year, then you can look up the correct answer.

For the 2020 exams, when school campuses were closed due to the Coronavirus, AP had a great series of “Live Lessons” on YouTube. They are available here: AB and BC. AP also released a series of practice problems coordinated with these live lessons. The practice problems are organized by topic and are available here: AB and BC. Because the 2020 test had only free response (FRQ) questions, there are not any multiple choice (MC) questions in this set of practice problems. Furthermore, because the 2020 test was open note and taken at home, it was designed specifically to minimize cheating and the problem style is highly concentrated on abstract functions and data in tables and graphs. As a result, these questions are not completely representative of what would normally appear on a chapter or final test, but they are still a great repository of AP style questions.

Studying for the AP Calculus Final Exam

The best way to study for the final exam or a mid-year mid-term is to do AP calculus questions in no particular order. The old sample exams are a great way to do this. The following items are great resources for studying for a final or mid-term.

AP Calculus Multiple Choice Questions 1969 – 1998

This is a great collection of older multiple choice problems for the AP Calculus AB or BC practice exams. Many of these questions (unaltered) appear in prep books and many of these questions seem to appear in later released tests as well. Although this is a great collection, it does not have the benefit of being quickly searched and sorted the way the spreadsheet does. Luckily, someone took the time to categorize the questions in this document. It isn’t very flashy, but it gets the job done! Of course, if you only have questions and no answers that is not help, so here is a document that includes all of the answers and solutions. It is a large file, so you might want to download one of these smaller files instead: AB and BC Answer Key (without solutions) or the BC Answer Key and Solutions.

Additional AP Calculus Practice Exams with Answers

Just looking for some AP Calculus practice problems in a random order? Here are several practice exams or sets of sample questions that have been released by the College Board in recent years:

Categorized AP Calculus Multiple Choice Questions

The categorized list of multiple choice AP Calculus problems from 1998 – 2012 for both AB and BC Calculus is by far the most organized resource that I have found. This spreadsheet is amazing because it lists 400 multiple choice questions by learning outcome, test date, question number and most importantly of all, links to every question with the answer and solution. These questions are all questions that have been released by the College Board, so you won’t find questions for every year because the College Board does not release questions every year, but the 400 questions in this spreadsheet will keep you pretty busy! Here are a few recommendations on how to best use this spreadsheet:

  • Sort the spreadsheet by “Learning Outcome” that will help all of the questions on the same topic listed together and will put them in the approximate order that you will study them throughout the year. The spreadsheet is currently sorted by “Learning Outcome.”
  • As needed, filter the spreadsheet by “Key Idea”. Even though the spreadsheet is sorted by “Learning Outcome”, sometimes a question includes multiple “Key Ideas” (and “Learning Outcomes”), so filtering can help find additional questions. Here is a picture showing how you might do that so you only see questions on “concavity”:
Filtering AP Calculus Multiple-Choice Questions By Key Idea
  • Once you have the questions organized, click on the link to the PDF file that includes question. This PDF also includes the solution at the bottom of the page, so you can quickly check your answer and perhaps learn additional techniques for solving the question.
  • If you get the question correct and it was easy for you, great, just close the PDF. However, if you struggled at all, you can click the Download icon and save the difficult questions onto your computer so that you can then re-do every challenging question over and over again until they become easy. Once a question becomes easy, move the PDF to your “Not Hard Anymore” folder. This will also allow you to have a nice set of difficult questions to review as you prepare for the final AP exam. You might create a folder structure that looks like this:
Organizing AP Calculus Multiple-Choice Questions
  • Add a column or two to the spreadsheet so you can make your own notes about each question. Perhaps you want to rate each question by difficulty or categorize them by what chapter you were studying.

Categorized AP Calculus Free Response Questions (FRQs)

Just like the invaluable categorized spreadsheet of multiple choice questions mentioned above, this spreadsheet is just as incredible, but it contains the AP Calculus Free Response Questions (FRQs) from 1998 to 2017. These questions are released by the College Board each year, so there are nearly 1,000 questions here!

Calculus Free Response Justifications

Answers to the AP Calculus FRQs are supposed to be short and sweet. Less is more when it comes to these answers. This is a comprehensive guideline for the best way to justify your answers. Memorize the wording in these answers and use them exactly as stated and whoever grades your test will love you.

Register for the October 5, 2020 SAT ASAP!

Posted on by Kennon McCaa

The October SAT is one of the three tests per year where you can select the “Question and Answer Service” (QAS). For an additional $18 you get to see a complete copy of the actual test as well as your answers. This can be really helpful for reviewing and eliminating mistakes. Got questions about the SAT? Our SAT FAQ page is packed with valuable information.

Make sure to select this option during the registration process:

Spend the extra $18 and get a full copy of the test!

My son Carter is just in 9th grade, but he will be taking the October test as a diagnostic check-up and a chance for me to analyze the latest trends in the test questions.

Make sure to register ASAP because registration after Sept. 6th requires paying the “Late Registration Fee.”

You can register for the test here.

More Free Official SAT Sample Tests

Posted on by Kennon McCaa

The College Board has recently released two more free sample tests on their website. Now there are 10 free practices tests available online!

We have all of the math sections available on this page.

The topic of Standard Deviation is starting to appear on the test more and more. It does not appear often, but it was not on any of the original 8 practice tests. Because most students have not taken statistics, this is a way to help those that have as well as help many students learn something new. If you do not know what Standard Deviation is, think of it as a measure of variability in data. If a stock price changes by a tiny bit here and there then it has a small standard deviation, but if a stock price changes frequently and has wild ups and downs then it has a large standard deviation. Alternatively, you could think of standard deviation as a way of measuring how thrilling a roller coaster is; a kiddie coaster has a small standard deviation while a full size roller coaster has a large standard deviation.

As always, a student’s success is determined by their long-term understanding of math and the work they have put in during their entire education, so we recommend studying hard every day in school and then doing dedicated test prep of 10-15 minutes per day (don’t miss any days!!) over an 8-10 week span to do your best on the SAT. With 10 free practice tests, that is enough to keep you practicing for about 45 days!

Our New Storefront for 2019!

Posted on by Kennon McCaa
Transformative Tutoring in Osprey, FL

We had a wonderful 2018-2019 school year and we are excited to make a difference in the community again this year. We had so many success stories and helped transform so many students last year! We know 2019-2020 will be even more amazing for our families! We recognize that the success of our students not only changed their lives, but changed the dynamics of their families. We received many reports of improved relationships and reduced stress and we are hoping to build on that success in the years to come. If your family is having math problems, come see us and experience the transformation.

Top 10 Questions To Do Together

Posted on by Kennon McCaa

In my years of teaching and tutoring, I have helped hundreds of students. Some had small problems they needed help with while others were basically starting from scratch. At Transformative Tutoring, we believe that every parent should spend a little time doing math with their child. Sure, your child gets a grade at the end of each year and perhaps has to pass an EOC exam, but what does that all mean?

Understanding Grades and SAT or ACT Scores

The best way to understand what that letter grade or SAT/ACT score means is to spend a little time actually having your child do some math with you. You might be surprised to find out that your teenager, who got just a B in Algebra 2, Precalculus or Calculus, is still adding and subtracting by counting on their fingers. (I would estimate that over 20% of high school students that have completed Algebra 2 still count on their fingers when not allowed to use a calculator.)

Students Are Growing Up in a Cashless, Digital World

Today’s children, in fact all of us, live in a digital age. Most middle class children rarely use coins and bills the way we did when we grew up. We had to know that four quarters made a dollar, but today’s children cannot buy anything with a quarter, so they don’t really care about quarters. Today’s children might have digital currency such as gift cards, debit cards, prepaid cards or iTunes credits, but they rarely handle cash. As a result, they use math for about 45 minutes a day about 180 days a year, exclusively in math class.

Compounding the problem for this digital generation is that calculators can do all their dirty work. In fact, you don’t even have to have a calculator anymore, just ask your smartphone something like, “Hey Siri, what’s 315 divided by 3.875?” As soon as most children find these error-free paths of least resistance they (ab)use them and shut their brains off entirely to the world of math. Before you know it, math doesn’t make any sense to them and they become incapable of thinking mathematically.

Beware of the Tools for Avoiding Math Homework

When a struggling math student hits high school there is often no easy way out and their struggles worsen. Did you know that every answer to every math textbook problem is available online? Most high school kids do! Now, they can breeze through their homework using sites like Slader, which has used crowd-sourcing to categorize every problem and answer, often with full solutions so students can “show their work.” Textbook publishers have tried to stay one step ahead by creating online homework assignments where the problems insert randomized numbers so that no two students get exactly the same question. However, in the great arms race to avoid doing math homework, once again there was a counter-attack in the form of an app called PhotoMath. Simply take a picture of any math problem and it will solve it for you, no thinking required! I have even heard reports of students using this app in their classroom to cheat on tests!

The SAT has a No Calculator Section

Eventually, the day of reckoning for all college bound students arrives, and that is the day of the SAT or ACT. These tests require students to know what they are doing and to actually understand and apply the math skills, formulas, strategies and concepts that they have, or haven’t, been using all of these years. Sadly, the arrival of that first SAT or ACT score is often the first day that a parent actually becomes aware of the magnitude of their child’s struggles with math. Now, they have a big problem on their hands, not much time to fix it and a jam packed schedule. Yes, there were B’s (many teachers require a student to be completely incompetent AND disrespectful to get a C grade these days, so a B should be considered a serious warning sign, especially if your child is well liked by their teachers) along the way that tried to serve as warning signs. Yes, there were some below average PSAT, PSAT 8/9, or EOC scores that tried to be the harbinger of the peril ahead, but these signs often were not obvious enough to raise enough concern to cause someone to take action.

Spend 5 Minutes Doing Math Together

So, today, and for the next few days, I beg you to sit down and spend a few minutes doing these problems with your child and without a calculator (20 of the 58 SAT math questions do not allow a calculator, while all 60 of the ACT math questions do allow a calculator) and see with your own eyes if your child needs help with arithmetic, Algebra 1, Geometry or Algebra 2.

SAT or ACT?

Posted on by Kennon McCaa

For the past few months, my daughter has been working with Kennon on ACT Math prep and she has already seen an improvement in her score. He does a great job with explaining all types of math problems and equations and knows how to motivate his students to achieve their goals. He is very passionate about teaching his students and watching them learn and progress. Transformative Tutoring has been a great experience!

A. C.

The SAT and ACT are radically different tests when it comes to the math section. In this post, we will attempt to outline the key differences and hopefully help you select the test that might be best for you. Before registering for one test or the other, check with your favorite school(s) to be sure they accept whichever test you plan to take.

Watch my fast-paced, funny and in-depth YouTube videos for SAT Prep!

Assess Your SAT & ACT Skills First

Invest one minute watching your child do this worksheet without a calculator. If they struggle some (more than 2 minutes, more than 1 mistake), the ACT is probably a much better choice for them. If they passed the 10 question quick quiz, have them do a an official ACT practice test and then an official SAT practice test to see which they are more comfortable with. Do the ACT test first because it does not list any formulas, whereas SAT tests do include formulas, so you should get an unbiased assessment of how many geometry formulas they still remember.

Learn more about the details of the SAT by watching this YouTube video

Side by Side Comparison

SATACT
Bright Futures – 75% Scholarship1200 (81st %)Composite: 25 (82nd %)
Bright Futures – Full Scholarship 1340 (93rd %) Composite: 29 (92nd %)
Questions22 questions each module (there are 2)60 questions
Time Allowed35 minutes per module60 minutes
Type of Questions48 multiple choice
10 short answer
(4 choices per question)		60 multiple choice (20 easy, 20 medium, and 20 advanced)
(5 choices per question)
DifficultyA couple of the questions are harder. Generally, all of the wording confuses many students, but tutoring and practice pay off.The questions are shorter and often require only one step and a simple formula.
SummaryThink deep thoughts, understand the concepts and be a good problem solver.It’s a race against time. Lots of easy questions that must be answered quickly.
FormulasMany are provided.Must be memorized.
Geometry15% or soNearly 50%
Probability2%10%
Trig.2% (1 question)7% (5 questions)
FOIL, Parabolas15% (single biggest topic)5%
Algebra50% or more20% or less
TopicsHeavy on:
Parabolas
FOIL & Factoring
General Algebra & Lines
Systems of Equations

Light on: Trig (1 question)

Far fewer topics to learn.		Heavy on: Geometry
Moderate on: Trigonometry

Lots of single questions on a wide variety of topics:
Logarithms
Matrices
Probability
Statistics
Permutations
Sequences & Series
Separate Science Score/SectionNoYes (mainly reading complicated graphs)

Win $100 and Free Tutoring

Posted on by Kennon McCaa
100 Dollar Eraser Contest

Transformative Tutoring will be at the Family Living’s Summer Camp Fair at Nathan Benderson Park on Saturday, March 30, 2019 from 10 AM until 2 PM. Register online for free admission to the Camp Fair or visit the tutoring studio for a free ticket or two.

Our summer camp schedule for 2019 is as follows:

  • June 10-14 & 17-21 – Intro to Computer Programming in C# – 9 AM – Noon – This is a two week camp.
  • June 10-14 – Middle School Math Competitions – 1 PM – 4 PM
  • August 5-9 – Preparing for Success in Calculus – 9:30 AM – 11:30 AM
  • August 5-9 – SAT Math Review 600+ – 12:30 PM – 3:00 PM
  • August 5-9 – SAT Math Review Below 600 – 4 PM – 6:30 PM

Pricing and registration for all camps will be available online soon. Please use the Contact Us page to express immediate interest. All camps have a maximum of 6 students.

Visit our booth to enter your guess at the number of erasers in our giant jar of erasers for your chance to win $100 and 2 free hours of tutoring. The person with the closest guess will be announced via an email to all participants and a Facebook post. If there are multiple entries with the closest guess then a random number will be chosen to determine the winner. Online entries are not permitted. You must visit our booth at the Camp Fair to enter.

Preparing for Success on Test Day

Posted on by Kennon McCaa

One Week Before Test Day

  • Start reviewing & reworking past mistakes as you lead up to test day. So, go back through all of your practice tests and find any questions you missed and make sure you can do them with ease. If you find any that still are awkward, then make a list of which test #, section # & question # and we can review them in the final week before you crush this test. Keep up the great work. Your extra effort in this final week can really make an enormous difference. You’ve got this! Finish strong!
  • Buy some peppermint gum. Peppermint helps with concentration.

Thursday

Friday

  • Find an old school watch if you want to bring one on Saturday. Advanced watches such as the Apple Watch are NOT permitted.
  • Pack your backpack:
    • Bring your registration confirmation information.
    • Bring your picture ID.
    • Find your calculator.
      • Make sure your calculator has lots of battery life.
      • Make sure your calculator is in degree mode. If you don’t know what that means, then it won’t matter what mode you are in.
    • Sharpen your trusty handful of #2 pencils.
    • Pack your peppermint gum.
    • Pack a snack or two.
    • Prepare your water bottle.
  • Review my full SAT study guide.
  • Do another practice test or two. I recommend section 3, test 8.
  • Pick out your favorite outfit. Do you have something you wear that makes you feel awesome, powerful, smart and/or relaxed? Wear it on test day to improve your mood.
  • Set your alarm early enough to have a quality breakfast and arrive to the testing center early. You don’t want to be nervously standing at the end of a long line.
  • Go to bed at your normal time or a little bit earlier.

Saturday

At home

Arriving at your test site

  • Arrive early.
  • Leave your phone in the car. Phones can only get you in trouble inside the testing center. They are NOT allowed during breaks.
  • Have your picture ID and registration form ready.
  • Start chewing that peppermint gum.
  • Use the restroom one last time.

During the Test

  • Do the less difficult non-multiple choice problems first. 80% are easy!! Do the hard ones later. Do these easy problems first. They’re a nice warm-up.
  • If you have to guess on a non-multiple choice problem, guess “2”.
  • Quickly decide if a question is easy (1), medium (2) or difficult (3). You probably don’t want to invest much time on difficult questions. 90-95% of the questions are 1’s and 2’s. Stick to the 1’s and 2’s and you’ll do great. Battle the 3’s and you’ll get bogged down and potentially lose confidence. You can always do the 3’s last if you have time. Spending 5 minutes on a problem 95% of people will get wrong is a terrible use of valuable time.
  • Always pick the most likely answer before going to the next question. That’s your best guess and you’ll have to use it if you run out of time.
  • Put a question mark next to answers you are not certain of. You can review these questions as you fill in all the bubbles near the end of the test.
  • Write “+” next to questions you are certain are answered correctly.
  • To save time, bubble in all of your answers for each page once you have completed the page. That is faster than going one question at a time.
  • Review my test problem solving strategies in my full SAT study guide.

After the Test

  • Go unwind. Do something fun and relaxing.
  • Drop me a quick note to let me know how it went.