As noted in my previous post about the AP® Science Exams, the AP® Exams for multiple subjects are fast approaching in May and June (there are 3 different testing windows). Today’s post is focused on the math exams, specifically Calculus and Statistics. There are also Computer Science exams, which I do list below with links to their resources, but I do not have specific calculator or testing tips for these, since I do not presume to know anything about the programming/coding aspects of these exams!. Instead, since I do know math, and I do know the technology that is allowed on the math exams, I wanted to provide some strategies for approaching the math exams and some tips on what math skills/calculator skills that would be helpful to review/prepare for as you study for the exams. I first provide some general AP® exams tips, then dive a little more into the specific calculator/math skills needed for each exam. There are two Calculus exams, but the same tips apply for both.

The first administration of the AP® exams is May 3, so now would be a good time to help students who are preparing to take any of the math exams. Make sure to look carefully at the AP® Exam Schedule, as how each test and when each test is offered is different depending on the administration date (some are paper and pencil only, some are digital). The number one piece of advice I can give anyone trying to prepare for any AP® exam is to visit the College Board AP ® site directly. The resources, links, support videos, and more that are available there are incredible and will really help answer any questions you have regarding these exams.

### Math Exams

There are 5 math exams, with Calculus having two exams and Computer Science having two exams, based on different parts/foci for those courses. Each exam listed below is linked to the AP® course-specific site so you can find out exactly what topics are covered within each exam. A great way to prepare and study for these is to go to the links and look through the course concepts & skills to ensure you have the needed background. Be sure to especially look at the exam link to that is on each course to find out more details about the exam and layout and types of questions in each section. You will find links to released test items for review/practice. The Computer Science Principles exam is a little different, since it has a performance task, where students develop a computer program of their choice, and so there is a deadline for completing this that is date and time specified.

- AP Calculus AB (3 hours, 15 min)
- AP Calculus BC (3 hours, 15 min)
- AP Computer Science A (3 hours)
- AP Computer Science Principles (2 hours for Section 1; At least 12 hours in-class to complete Section 2, Performance Task)
- AP Statistics (3 hours)

### General AP® Calculus and Statistics Exam Information and Preparation Tips

The calculus and statistics exams all have two sections, whether you are taking the paper and pencil version or the digital version. Section 1, which is multiple choice, and Section 2 which is free-response (paper and pencil version) or a mix of multiple choice & free response (digital version). No matter which form of the exam you are taking, the amount of time given for each section is the same. The digital form of the exams is different from the paper and pencil form: it is either all and/or mostly multiple choice and then (depending on the specific math exam), if there are free response questions, there are fewer of them then on the paper and pencil version, and students will not be asked to draw or graph anything, but answer the questions using the keyboard (with provided mathematics symbols as needed). Below is a PDF that compares the paper and pencil vs. digital for all AP® exams. It is also a good idea to go into each AP ® Course and The Exam link, where you will actually see a side-by-side comparison of the paper and pencil versus the digital exam question types and timing. (As an example, here is the link to AP Calculus AB The Exam).

General Calculus and Statistics Preparation Tips:

- Practice, Practice, Practice
- Explore the resources on the AP® site (this is the student site) for the specific courses you are studying for
- Use previously released test items/practice tests (all available on the site)(you do have to sign up for an account to access the test banks, which you should have an College Board student id from your teacher if you are taking an AP course and/or signed up to take the ACT or SAT exams).
- Practice under same conditions the real exam will take place – i.e. 40 minutes for each section, calculator, etc. Time yourself and practice pacing

- Watch your time – Each section of the exams has a specific time limit (anywhere from 40 minutes to 1 1/2 hours)
- Answer easier questions first and come back to those that are more time consuming
- If you are stuck on a problem, particularly multiple choice, come back to it – don’t waste time.
- Answer EVERY question if possible, even if you are not sure – there is no penalty for wrong answers. AP exams are graded only on the number of questions answered correctly, so even if you have to guess, try to answer every question
- If you guess, be smart about it – try to eliminate as many answers as possible before making your guess

- Free response/short answer questions
- Read through all of them first and plan out which one (s) you feel most confident about and do those first.
- Don’t skip any (you will get zero). Even if you are unsure, write down something relevant or related and make an attempt to try to get at least some partial points.
- Show all your work when doing calculations (even if you use the calculator!!) – again, part credit is always possible
- In the multi-part questions, attempt to answer each part. They are graded separately so you can get partial credit even if you don’t have all the parts correct.
- Be sure to label your answers and work in an organized way so the readers can find your work/solutions
- If you make a mistake DON’T spend time erasing – just cross through it and move on (time saver!!)
- Don’t round your partial answers -round at the end (3 decimals places)
- LABEL all your solutions with the appropriate units!! So important!!
- LABEL any graphs or diagrams, which includes titles, axes, etc.
- Pay attention to directions – look for key words that indicate what the expected outcome should include and look like. Here is a sampling of the mathematical exam ‘task verbs’:

- Be sure to know the AP policies for testing day!

### Calculator Tips for the Calculus and Statistics Exams

Handheld calculators are allowed on all 7 of the science exams, but it’s important to know the AP® calculator policy and which calculators are allowed for each test. I have included a table below (also in the calculator policy) for quick reference.

Exam | Type of Calculator (s) Allowed | P/P Section 1 (MC) | P/P Section 2 (FR) | Digital (MC & FR) |

Calculus AB | Graphing Calculator | Not Allowed for Part A, Required for Part B | Required for Part A, Not Allowed for Part B | Allowed for All Sections, but not Required for Section 1, Part A and Section II Part B |

Calculus BC | Graphing Calculator | Not Allowed for Part A, Required for Part B | Required for Part A, Not Allowed for Part B | Allowed for All Sections, but not Required for Section 1, Part A and Section II Part B |

Statistics | Graphing Calculator with Statistical Capabilities; (Can use a non-graphing Calculator IF it has the required statistics computational capabilities needed for the course) | Allowed | Allowed | Allowed |

As you can see from the chart, a graphing calculator is going to be the most useful tool for the AP® math exams. Also note, there are problems in the Calculus Exams where you will not be allowed to use a calculator at all (except if you are taking the digital form of the exams). Make sure you have an approved calculator. It’s helpful to know the unapproved features, as are the special instructions, so be sure to review those sections of the calculator policy. For example, no QWERTY keyboards, no stylus/pens allowed, but you can use a touch-screen calculator, like the fx-CG500 graphing calculator as long as you use your fingers. All the Casio graphing calculators are approved for the AP® math exams – if you don’t have one already, I would recommend the fx-9750GIII as your best option, but if you want color, then go with the fx-CG50Prizm. The support videos below have a little of each – the main difference between them is the color.

Unlike the AP® science exams, only the statistics exam provides a formula sheet and also table sheets for use during the exam. I’ve attached a PDF of the statistics Formula and Table Sheets below:

General AP Calculus Exam Calculator Tips

- Show your work! On the non-calculator portions of the calculus exams, you must be able to show mathematical steps that led to your results using mathematical notation and the set-up you used to get to your to your solution. This includes showing the equation you are solving for, or the integral you might be evaluating or the derivative of the function you might be finding. The calculator is just a tool to get to the solutions (when allowed), but showing work is important!!
- Do not leave anything blank – even on multiple choice, make a guess (after narrowing things down). There is no penalty for wrong answers on the AP.
- Watch your time! Answer those questions that you know you can do quickly first, then come back to those that will take a bit more work and thought.

Specific AP Calculus Exam Calculator Skills/Tips with Video Support As Needed

- Know your calculator and where the functionality for specific operations is and the syntax of these. I’ve attached some Quick Start PDF’s for the fx-9750GIII and fx-CG50 Prizm graphing calculators that walk through some of the more common functionality. You’ll notice that the processes are almost identical for the two calculators – the beauty of Casio and consistency for it’s models.

- If you will use a function (s) more than once, be sure to save it in the GRAPH Menu (Y1=, Y2=, etc) *
- If you need to use a number or calculated value again, store it by assigning it a number so that it can be recalled quickly
- Set the calculator to ‘radian’ mode as this is the mode for both calculus exams *
- Be able to graph a function and choose the most appropriate window, which you should be able to determine yourself if it is not given
- Know how to solve equations multiple ways – graphically (most efficient), Equation Solver (good for polynomials or systems), substitution, etc. *
- Know how to evaluate a definite integral with the proper syntax (practice this!!) on your calculator *
- Be able to find specific values for given equations, such as the derivative at a specific point (again, this comes back to knowing your calculator and the syntax)*

(*Please note – any video shown for a specific graphing calculator model would have the same steps for the other model as well).

General AP Statistics Exam Calculator Tips

- As mentioned above, the AP Statistics Exam is the only one that provides a formula and tables sheet for use on both the paper and pencil and digital forms of the exam. It’s a really good idea to be familiar with this so you are not hunting around trying to find specific formulas and/or trying to determine how to use the provided table of values. Here is the PDF to download again:

- Be familiar with any formulas that are NOT on the provided formula and table sheet.
- Formula for mean

- Formula for standard deviation when combining random variablews
- Formula for expected counts (chi-square tests)

- Always include the context in your answers and work. Be precise.
- Know the correct statistical notation and use it appropriately.
- Be familiar with the notation used on the formulas sheet (for example, U means union and an upside down U is intersection)
- Chi test, t-test, probability, etc.

- Use a calculator strategically Show your work on free response – work and writing out the formulas are going to get you more points than only a solution. Use the calculator to check your answers!!
- Don’t leave anything blank!! Guess (narrow it down as much as you can) on any multiple choice questions. There is no penalty for a wrong answer. And on free response, write down anything you know related to the question as this can earn you partial credit.

Specific AP Statistics Exam Calculator Skills/Tips with Video Support As Needed

- Be familiar with your calculator and know how to use the Stat Menu
- Know how to find one- and two-variable statistics (to find mean, standard deviation, 5-number summary, least squares regression line, r and r^2)*
- Know how to create statistical plots (histograms, Box-and Whisker, scatter plots, etc.)
- Know how to find regressions from scatter plots
- Know how to do probability calculations*
- Probability of getting exactly X successes in a binomial (BinomialPDF)
- Probability of getting at-most X successes in a binomial (BinomialCDF)
- Find the area for an interval in a normal distribution (Normalcdf)
- Find a boundary value in a normal distribution (invNorm)
- Area for an interval in a t-distribution (tcdf)
- Find a boundary value in a t-distribution (invT)

- Be familiar with what type of information provided as a clue for the type of significance test you should do*
- Do you have a table of frequencies provide? If yes, then most likely an X^2 test
- If you have only one set of samples, you are either going to do a x^2 GOF (1 variable) or a x^2 Independent test (2 variables)
- If you have 2 or more samples/groups, you are doing a x^2 homogeneity test

- Is there statistical output (say from Minitab) – do a Linear Regression t-test
- Are you given proportions? Do a proportions z-test
- For 1 sample/group, do the 1-Proportions z-test
- For 2 samples/groups, do the 2-Proportion z-test

- Are you given means? Do a means t-test
- For 1 sample/group, do a mean t-test (or a paired t-test)
- For 2 samples/groups, do a 2 mean t-test

- Do you have a table of frequencies provide? If yes, then most likely an X^2 test
- Do you have a table of frequencies provide? If yes, then most likely an X^2 test

My last words of advice – PRACTICE!! And be sure to log in to the AP Student Portal (if you are in an AP course, you should have a College Board ID) and go to the specific courses for the exams you plan to take. There is a plethora of resources available there, from video tutorials, daily AP hints/tips, released tests and practice items, and more. It’s an amazing place to help get you ready. Good luck