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SAT Math Section and Strategy

16 min readβ€’november 2, 2020

harrison-burnside

Harrison Burnside


SATΒ πŸŽ“

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SAT Sections 3+4: Math

πŸ” What are the SAT Sections?

In the SAT, you will have 4-5 sections on the test (depending on whether you choose to take the essay section or not)! The sections are:
  1. Reading
  2. Grammar/English
  3. Math (No-Calculator)
  4. Math (Calculator Allowed)
  5. Writing/Essay (⚠️ OPTIONAL ⚠️)
As you can see, math is a pretty important topic on the SAT, since it makes up about 50% of the sections on your test. In this study guide, you will learn about logistics, strategies, content, and some overall tips to ace your Math No-Calculator AND Calculator sections.

⏲️ Logistics of the Math Sections

On both math sections, the first page will be a formula sheet with all of this information, mainly to help you in the Additional Topics Domain, but more on that later πŸ‘€ Try to memorize all these formulas because it can save you a lot of time on test day (because of flipping back and forth between pages πŸ“–), but be aware that you will have the reference sheet for the test:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-XAORmDsXZBjj.png?alt=media&token=59ca5329-8d05-435d-b5b0-588d8b39b85a

Image Courtesy of the College Board’s SAT Overview PDF

Section 3 - Math No-Calc

  • 25 Minutes
  • 20 Questions
    • 15 Multiple Choice Questions (MCQs)
    • 5 Grid-Ins (GIs)

Section 4 - Math with Calc

  • 55 Minutes
  • 38 Questions
    • 30 Multiple Choice Questions (MCQs)
    • 8 Grid-Ins (GIs)

🌍 Global Strategy Toolbox

What is a Global Strategy? That phrase means that the strategy can be applied on any standardized test πŸ‘ These global strategies can also help you get through the other 2 sections of the SAT faster, βŒ› so let's take a look at some of these:

🧐 Elimination

This one is simple and you've probably used it on many multiple-choice tests throughout your academic career without even realizing it! If your options are A, B, C, or D, and you know for sure it can’t be A or C, then you can eliminate those two.
Guess either B or D, and you have a 50% chance of getting that question correct! That is DOUBLE ****your chances of getting the question correct by randomly guessing, but more on that later πŸ‘

β­• Mark It

On the exam, you might get a question that you are simply stumped on ☹️ It happens to all of us. But the clock ⏳ is still ticking. If you really just don’t know, make your best guess, circle the question so you can come back if you have time, and then move on. It’s better to miss that one hard question than to not have time for the 10 easy ones that you could get right at the end of the exam.

πŸ›‘ Letter of the Day

If you do have to randomly guess on a question on your exam, IT WILL BE OKAY!! There is 1 strategy to help your score when you do have to randomly guess, and it is to pick 1 Letter of the Day (LOTD). Pick A, B, C, or D before you start your test, and mark that one answer for ALL of the questions that you have to randomly guess on. You will increase your probability of getting each individual question correct ❗

✍️ Rephrase

Sometimes you understand the concept, just not the question. Take the question out of fancy SAT language and convert it into phrasing you understand. Also, try to brainstorm everything that you know and write it down in concise statements next to the question. This can help you to understand what the question is asking you to do and can be very helpful for word problems!

🧰 SAT Math Strategy Toolbox

πŸ”š The End

To use The End, all you have to do is finish reading the question before you start working it.
This strategy makes you slow down to make sure that you are actually solving the question that you are supposed to be answering. It might seem like common sense, but using this one tip can actually help you increase your score and stop making simple mistakes 😒
WOW 🀯 This might not seem revolutionary, but everyone has made this mistake before by rushing and starting to solve the problem before you even get to the "?". Look at the example below for ideas on how this strategy might help.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-IvDLAtJLwWpj.png?alt=media&token=07a34050-7155-4690-81d3-8c0f56a6edd9

Courtesy of SAT Practice Test 9 - Section 3 - NO CALCULATOR

Why did you get it wrong? You got the correct answer for $x$! You didn't use πŸ”š The End! So let's go back to the question, and try using the strategy.
The question asked you for the answer to $2x+1$, not just $x$ 😭 If you read the question before you started working the problem, you would have seen that the correct answer would be 2 and not $x=0.5$.
Make sure to use πŸ”š The End so that you don't miss any more easy level questions because of reading errors!

πŸ”Œ The Plug

This strategy has 2 applications for you, as it is one of the most versatile strategies for the math section. Make sure to keep this one handy πŸŽ‰ Let's differentiate between the 2 applications by calling them The OG Plug and The Plug 5.0 πŸ‘
To use The OG Plug, all you have to do is pick some easy numbers to work with and plug them in for your variables in the question, then check that against the answers!
This strategy can help you solve almost any problem on this section involving variables, and especially problems with more than 1 use of a variable! Let's look at a practice problem together to look at this strategy in action 🦸:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-6BormLzmun27.png?alt=media&token=ba816663-ced1-4119-bbc4-055a435bbe06

Image Courtesy of SAT Practice Test 1 - Section 3 - NO CALCULATOR

If you try to solve this problem with your algebra 2 βž— knowledge, it can get really complicated with fractions and double variables 😳
  1. However, πŸ”ŒThe OG Plug can make this problem super simple for most people! Since the problem says that $x > 3$, then we just need to pick a value for X greater than 3 to plug in.
  2. So, let's pick 4 for x!
  3. When we use πŸ”ŒThe OG Plug with $x=4$, then we get: 42/13
  4. After substituting for $x=4$ in all of the answer choice, we can learn that the correct answer is
    1. Now all we have to do is plug in our number for x in all of the answer choices and see what matches the problem πŸ‘
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-3moKzyojRXbl.PNG?alt=media&token=54f2c795-cd98-4f1f-a96c-b47e6aacf63b
Answer B solves for 42/13 which is equal to our solution to the original problem ☺️
If you used algebra and added the fractions with the FOIL method and too many other steps, then you should reach the same conclusion!
To use The Plug 5.0, all you have to do is plug the numbers from the answers into the question and see which yields the right result!
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-fznagGDYhk9k.png?alt=media&token=c62fa28a-2a83-457c-abc2-a4ae1ee2fd14

Image Courtesy of SAT Practice Test 1 - Section 3 - NO CALCULATOR

If you try solving this system with elimination or substitution, you will end up with some really big numbers, or it will take a long time with lots of algebra! But using πŸ”ŒThe Plug 5.0, the answers can tell us which one is correct 🎊 !!
We just need to plug in the ordered pairs for X and Y for each answer choice and check which pair solves both equations! Let's start with letter B in the second equation πŸ‘ now we get that:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-dmY9NiZva5xG.PNG?alt=media&token=52cb9528-3e8f-4ac3-a538-83e45db88af1
That equation is true! Since we picked an awesome ✨ answer choice to start with, let's just double-check the first equation before marking the correct answer
When we plug in (3,-8) to the first equation, we get that:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-2dO4Vm0Vme9j.PNG?alt=media&token=fd6ba564-2912-4699-956e-74ea5eccb4fa
which is also true πŸŽ‰!! That means that Answer Choice B is correct 😎 Let's mark that and move on without using any algebra.

⬇️ Break it Down

This strategy helps you break up complex questions on the SAT Math section. Break it Down πŸ’” can help you answer questions that have too many variables or have tons of fractions by solving parts of an equation to put them back together 🎊
To use Break it Down, pick steps to break up different parts of the equation, solve them independently, then put all the pieces back together!
This strategy can help you solve almost any problem in this section involving:
  • Multiple variables
  • Fractions
  • Percentages
  • Ratios
Let's look at a practice problem together to look at this strategy in action 🦸:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-YvLBDKP7WhEx.png?alt=media&token=6159bb93-0827-4f21-ab02-fa44f9d0cd0e

Image Courtesy of SAT Practice Test 1 - Section 4 - CALCULATOR

When you read this question, it might be nice to use the Rephrase Global Strategy 🌍 that we discussed earlier, but you can solve it just as easily with ⬇️ Break it Down. So, the first thing that we need to do is define the variables πŸ”€ and the percentages.
We know 🧠 that:
  • p = new price
  • there was a 20% discount on p
  • there was an 8% sales tax applied
Those 3 pieces of knowledge (plus defining variable o = original price) are how we are going to ⬇️ Break it Down 😎.
  1. Our first step is that 20% off means that we will be subtracting from the original price.
    1. We now know that p=0.8* o!
    2. We also know that there is a sales tax of 8% so that would be adding to price. So, we know that p = 1.08 * 0.8 * o!
  2. Now all we need to do is take the equation and put it in terms of p.
    1. So if we divide both sides by (1.08 * 0.8),
    2. Then we get that D*p/(0.8*1.08) is the correct answer
πŸ™‹ Time to mark that and move on 😎

πŸ‘‰πŸ‘ˆ Close Enough

This strategy is a huge time-saver when you are taking your SAT Math. Close Enough can help you eliminate answers and easily see the correct one πŸ‘
To use Close Enough, try to use common sense to see which answers are way too big or small, then find a realistic answer. Look at the answers before solving!
This strategy can help you solve almost any problem in this section involving difficult 😀 concepts, and is especially useful for multi-step problems. Let's look at a practice problem together:
To use Close Enough, try to use common sense to see which answers are way too big or small, then find a realistic answer. Look at the answers before solving!
This strategy can help you solve almost any problem in this section involving difficult 😀 concepts, and is especially useful for multi-step problems. Let's look at a practice problem together:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-OXnLFDxFwuyu.png?alt=media&token=1fd73374-ca12-4ca2-b98e-3ebc479d3fb7

Image Courtesy of PSAT Practice Test 2 - Section 4 - CALCULATOR

When you start this problem the BIGGEST TIP πŸ’‘(besides πŸ‘‰πŸ‘ˆ Close Enough) is to 🎨 Sketch it Out! Whenever you have a problem that involves an equation with an ordered pair (or a graph without one given), you should 🎨 Sketch it Out! on a hand-drawn graph!
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-YBtFNgV2P35Y.png?alt=media&token=076b09a9-3f8f-447f-9cd9-f79e9fe2c09a

🎨 Sketch it Out : Self-Created; This graph shows you that you drawing don't have to be perfect to get the idea!

To use πŸ‘‰πŸ‘ˆ Close Enough, we just need to analyze πŸ‘€ our sketch and find the direction of the slope. The line has a positive βž• slope, meaning that the line will increase in Y and X, or decrease in Y and X. With that knowledge, we know that our Y-intercept will be higher than the current Y value of our point.
We can immediately Eliminate 🧐 A and B, since those points too low. Since the slope is 5/1, that means that the slope has a larger "rise" (in Y) than "run" (in X)! That means that our Y-intercept will be D. 11, since it is the highest value possible πŸ‘ Now we get to mark that and move on!

πŸ“² Calculate

This is less of a strategy and more of an overall tip for the SAT Math Calculator (Section 4) πŸ’‘
While you are allowed to use your calculator for all of section 4, one of the biggest issues is knowing when to use your calculator and when not to! While when to use a calculator is slightly a personal decision, we have a general rule of thumb πŸ‘ for recognizing when it's needed:
To choose when to Calculate, you need to read the problem and decide whether there is a calculator function to solve the whole question. Also, you can Calculate to do simple arithmetic always to avoid simple mistakes!
There is no practice problem to review this strategy πŸ˜₯ so just use this strategy when you need it. When you see $1463 \times 17$ on your SAT, you probably need a calculator, but some people might not πŸ€” so learn your own strengths πŸ’ͺ and weaknesses before your SAT!

πŸ–‡οΈ Links + Content Review

Since the SAT covers 3️⃣ whole years of High School Math (Algebra 1, 2, and Geometry/Trig), we would need 10 of these study guides to review all of the required content πŸ˜‚ However, we can link to some AWESOME 🀩 videos and study guides to help you review all of the math that you need to review to ace the SAT:
**Khan Academyβ€”**Reviews all of the content through videos and practice questions and breaks material down into the 4 categories that we just discussed above. Khan Academy also partners with the College Board so that you can sync your current PSAT and SAT scores to help pinpoint your strong πŸ’ͺ and weak 🐢 areas. Here is a preview of one of their lessons:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-MWha4mT8hUdO.png?alt=media&token=fe2bc154-3f60-40a2-8555-2324ff00d8be

Image Courtesy of Khan Academy Heart of Algebra

Ivy Global Math Reviewβ€”This is a 40 page PDF that describes all of the content on the SAT Math sections. This PDF is awesome because it's succinct and sectioned into different content areas than the SAT Domains, so you get another perspective πŸ€” on the content. The PDF does not cover everything that Khan Academy does, but this does make it easy to work practice βž— problems and annotate the content sections. Here is a preview of the PDF :
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-zAE8o3WkNy6w.png?alt=media&token=d3ffca1b-4f1e-40ea-8e21-75936b196b83

Image Courtesy of Ivy Global Math Review

The Organic Chemistry Tutor's Math SAT YouTube Reviewβ€”Helps cram all of the SAT Math content into your brain in 2.5 hours. This review is best for students that are already strong in the math sections or have very little time ⏳ to review for the test. This review has math problems throughout for watchers to practice in all 8 of the mini-lessons in the video 🎦 This review is the shortest on the list and can just refresh you on the most difficult concepts on the test.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-oF3TosB2L8Vx.png?alt=media&token=5f8b60a6-8d29-44e0-af1e-6b3ffe56c4b6

Image Courtesy of YouTube

⁉️ Types of Questions

You will need to have learned all of Algebra 2 to master the content in this section!
The College Board has published a list of topics in 4️⃣ categories that you need to focus to succeed on the SAT! We can break up all of the categories with emojis πŸ˜‚ so make sure to remember them when we discuss strategies:
  • πŸ’™ Heart of Algebra: 19 questions on the SAT
    • Linear Equations
    • Systems of Equations
    • Functions + Notation
  • πŸ“‰ Problem Solving and Data Analysis: 17 questions on the SAT
    • Ratios, Percentages, + Proportions
    • Reasoning with Data
    • Using Statistics + Probability
    • Modeling Data (Using Graphs, Charts, and Tables)
  • πŸ”‘ Passport to Advanced Math: 16 questions on the SAT
    • Multiplying + Factoring Polynomials
    • Integer + Radical Exponents
    • Quadratic, Radical, Rational, Polynomial, + Absolute Value Equations
All of the topics in Passport to Advanced Math are building on the skills in Heart of Algebra.
  • πŸ“ Additional Topics in Math: 6 questions on the SAT
    • Plane + Coordinate Geometry
    • Trigonometry
    • Complex + Imaginary Numbers
You won't need to know all of the SAT Domains and be able to recognize 🧐 them on test day, but when you get your score report, you get sub-scores based on these categories. The scale is from 1-15 so you will be looking for a 1️⃣5️⃣ in all of your sub-scores 🎊

βž— Practice Problems

We have curated 11 practice problems for you to try from each of the SAT Domain Categories so that you can find your Strengths πŸ’ͺ + Weaknesses 🐢 before test day πŸŽ‰ Try to time yourself for about 12-14 minutes because that correlates to the amount of time you will have on test day.
{Note: the Problem Solving + Data Analysis Questions are from Section 4 since they are only tested on that section}
GOOD LUCK 🀞 but you won't need it πŸ™ƒ

Heart of Algebra πŸ’™ 4 Questions

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-UF4F7sGWBoOB.png?alt=media&token=1b394b9e-2e83-409d-ad81-0791a038e3cf

Courtesy of SAT Practice Test 3 - Section 3 - NO CALCULATOR

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-x6BSxgd6G2XP.png?alt=media&token=c45a381b-aec8-4e94-b037-3e3605194ac0

Courtesy of SAT Practice Test 3 - Section 3 - NO CALCULATOR

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-VYB25wjw9ZGO.png?alt=media&token=43ceb074-0ae3-4f0e-894a-f45817907ff4

Courtesy of SAT Practice Test 3 - Section 3 - NO CALCULATOR

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-oEhRtBXZVpeI.png?alt=media&token=44d68fca-6368-466a-b372-5ca74c0a493d

Courtesy of SAT Practice Test 3 - Section 3 - NO CALCULATOR

Problem Solving and Data Analysis πŸ“‰ 3 Questions

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-TkJqk97aHHXp.png?alt=media&token=0641146c-c49e-40b5-8be2-964f8617a030

Courtesy of SAT Practice Test 5 - Section 4 - CALCULATOR

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-1VrBuo2bpIjD.png?alt=media&token=34e47b51-acf4-4d7b-9458-d7b65fcc344e

Courtesy of SAT Practice Test 5 - Section 4 - CALCULATOR

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-679eo2CAgrEm.png?alt=media&token=a5c7051f-4ce0-4767-bdb7-0ef5d18ace39

Courtesy of SAT Practice Test 5 - Section 4 - CALCULATOR

Passport to Advanced Math πŸ”‘ 3 Questions

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-W4dTbbowTedw.png?alt=media&token=a6afea81-04de-4893-8783-689e401822f2

Courtesy of SAT Practice Test 6 - Section 3 - NO CALCULATOR

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-HaR2rqGx6CVs.png?alt=media&token=a3e0118f-3a25-45af-ba91-4fdeafde7ffb

Courtesy of SAT Practice Test 6 - Section 3 - NO CALCULATOR

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-PZrSzDkoOGao.png?alt=media&token=f6fdf135-9811-4263-ab15-84b90cabe932

Courtesy of SAT Practice Test 6 - Section 3 - NO CALCULATOR

Additional Topics in Math πŸ“ 1 Question

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-ITFQoW2yZNch.png?alt=media&token=ee240a83-fb1d-441d-b2ba-7f069c2a86a7

Courtesy of SAT Practice Test 6 - Section 3 - NO CALCULATOR

βœ… Solutions + Strategy Applications

Make sure to check your work πŸ‘¨β€πŸ’Ό and see where you struggled πŸ˜– so you can improve next time! There are solutions for every questions and the possible strategies that could be used πŸ”₯ The explanations for all of the questions are on this website so check those out if you don't understand πŸ˜• where the answer came from!
There were more medium and hard questions than easy questions on the practice problems, so don't feel bad about missing a few πŸ™Œ

Heart of Algebra πŸ’™ 4 Questions

  1. C; The best strategy to use here would be to pick small numbers to use for πŸ”Œ The OG Plug for X + Y and see which expression matches your original solution.
  2. D; For this question, make sure to 🎨 Sketch it Out on a graph and see how the slope goes through points besides the origin a.k.a (0, 0).
  3. D; For this question, using ⬇️ Break it Down is good to rewrite/check the equation to see which of each I, II, and III are true.
  4. 370; For this question, you should try to ✍️ Rephrase the question from English β€”> Math and solve your system.

Problem Solving and Data Analysis πŸ“‰ 3 Questions

  1. A; This problem doesn't have a major strategy since it is just plugging in numbers and dividing from the data table 😭
  2. C; This problem, again, doesn't have a major strategy since it is just multiplying numbers from the problem 😭
  3. C; This problem involves using ✍️ Rephrase to translate the question from English β€”> Math and solve for your mean.

Passport to Advanced Math πŸ”‘ 3 Questions

  1. C; This problem doesn't have a major strategy since it is just solving the radicals & subtracting 😭
  2. D; The best strategy to use here would be to pick small numbers to use for πŸ”Œ The OG Plug for X and see which expression matches your original solution.
  3. D; There are 2 main ways to solve this problem:
  1. Using an algebraic formula and recognizing that (a+b)^2=(a^2+2ab+b^2)
  2. OR using πŸ”Œ The OG Plug for A + B and see which expression matches your original solution.

Additional Topics in Math πŸ“ 1 Question

  1. 30; This problem can use 🎨 Sketch it Out and drawing 2 triangles to try to see which sides are parallel and equal to find the ratio since these triangles are similar.

πŸ’­ SAT Math In Review

Here is a final review of everything in this guide in a simple bullet-point format: πŸ˜‚
  • SAT Math is 2 of your 4 sections on the Test (+ the Essay, but that's optional)
  • The No-Calc (Section 3) is shorter than the Calc (Section 4) portion
    • You will get the same formula sheet βœ–οΈ on both sections, but we recommend memorizing it
    • Both sections have a combination of MCQs and GIs
  • There are 4 major strategies for ALL Sections of the SAT on test day:
    • Elimination: Mark out answers that you know are incorrect then pick from the remaining
    • Mark It: Don't spend too long on one question; Mark it and move on with your LOTD
    • Letter of the Day: Pick one letter before the test and mark it for all of the guess questions
    • Rephrase: Sometimes you get the concept but not the question, so put it in new words
  • There are 5 major strategies to use on the math section on test day:
    • The End: Make sure to answer what the question is asking
    • The Plug: Substitute real numbers for the variables and check against the answer choices
    • Break It Down: Piece together the problem from solvable pieces instead of all at once
    • Close Enough: Eliminate answers that are wayy too big or small; Find the medium
    • Calculate: Only use your calculator when you need it for complex equations with big numbers
  • While strategy is awesome to help improve your score, practice is what makes progress permanent!
  • Content knowledge is also important for the math sections so make sure to learn all of Algebra 2, if possible, before taking your SAT!
    • Make sure to use one of the content reviews to see what you know and what you forget πŸ€”
  • The SAT is broken up into 4 "Domains" of content so know what fits into the bigger categories to see what to do to improve your score the most
  • Again: PRACTICE, PRACTICE, PRACTICE!
    • Try using our hand-picked practice problems from released SATs (1, 3, 5, 6) in the 4 domains

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