As you’ve probably already read, in order to thrive on the SAT No Calculator Math section—and to finish all 60 questions on the ACT Math section in time—nothing beats just understanding how numbers work.

And to help you with that knowledge, the first step is learning how NOT to re-create the mathematical wheel…in other words, just memorizing a certain amount of simple arithmetic, so you don’t have to take out your scratch work (or your calculator, if you’re taking the ACT), and fritter away valuable time evaluating something you should (and can!) already just KNOW.

To help you, I broke these math facts down by topic. What you should do is use them to either make flashcards, rewrite them by hand on a page, or use technology (like Quizlet) to quiz yourself until these feel comfortable.

### 1) Multiplication tables up to 12

I’m going to take a leap of faith and assume you know your addition and subtraction facts. Please don’t disappoint me!

Also, I don’t mention division separately, because division and multiplication are inverses of each other. If you know your times tables, you also know how to divide!

### 2) Perfect Squares up to 25

Squaring numbers comes up in tons of topics, from calculating distance formula, to executing Pythagorean theorem, FOIL-ing binomials, or doing the law of cosines. Make it easy on yourself and just memorize these.

0

^{2}= 01

^{2}= 12

^{2}= 43

^{2}= 94

^{2}= 165

^{2}= 256

^{2}= 367

^{2}= 498

^{2}= 649

^{2}= 8110

^{2}= 10011

^{2}= 12112

^{2}= 14413

^{2}= 16914

^{2}= 19615

^{2}= 22516

^{2}= 25617

^{2}= 28918

^{2}= 32419

^{2}= 36120

^{2}= 40021

^{2}= 44122

^{2}= 48423

^{2}= 52924

^{2}= 57625

^{2}= 625

### 3) Perfect Cubes up to 6

0

^{3}= 01

^{3}= 12

^{3}= 83

^{3}= 274

^{3}= 645

^{3}= 1256

^{3}= 216, and10

^{3}= 1,000 for good measure.

### 4) Powers of 2 up to 10

2

^{0}= 12

^{1}= 22

^{2}= 42

^{3}= 82

^{4}= 162

^{5}= 32(Memory tip: 3+2 = 5, so 32 = 2^{5})2

^{6}= 642

^{7}= 128(Memory tip: 28 is a multiple of 7, so 2^{7}= 128)2

^{8}= 2562

^{9}= 5122

^{10}= 1,024(Memory tip: 2^{10}= 1024)

When you’re memorizing, it’s helpful if you find what I call an “anchor point”—a fact that you just remember, and can base the rest off of. For powers of 2, it’s not necessary for me to know cold that 2^{9} = 512. Instead, 2^{10}
= 1,024 is one of my anchor points. So if I’m trying to find 2^{9}, I know it’s the power of 2 that comes before 1,024…hence, referring to my memory of the pattern, it’s 512.

### 5) Pythagorean Triples

A Pythagorean triple is a set of 3 integers that make Pythagoras’s theorem true. (For those of you who forgot Pythagoras’s theorem, it’s A^{2} + B^{2} = C^{2}.) So instead of getting a nasty radical for one of the numbers, they’re all pretty. There are a few groups of numbers that you should just memorize, so you don’t have to actually do the Pythagorean math each time you see a right triangle (or a distance formula question). Here are my favorites:

3 – 4 – 5

**(And its multiples! Like 6 – 8 – 10, 15 – 20 – 25, and 30 – 40 – 50, etc.)**

5 – 12 – 13

**(This one sometimes comes as 10 – 24 – 26, which is the original doubled.)**

8 – 15 – 17

7 – 24 – 25

### 6) Fraction to Decimal to Percent Conversions

This is perhaps my favorite thing in the world. The ability to understand that each number can be written in three different ways can make your life SO much easier. You now have flexibility when solving problems, because you can use whichever form is going to make the problem easier for you. In addition, you can now recognize the correct answer choice, even if you got a decimal as your answer, and the answer choices are all written as fractions.

1/11 --> 0.0909… --> 9.09…%

For 11ths, take the numerator and multiply by 9. Use two digits. Repeat!1/10 --> 0.1 --> 10%

1/9 --> 0.111… --> 11.1…%

For 9ths, take the numerator and repeat!1/8 --> 0.125 --> 12.5%

1/6 --> 0.1666… --> 16.66…%

2/11 --> 0.1818… --> 18.18…%

2/10 = 1/5 --> 0.2 --> 20%

2/9 --> 0.222… --> 22.2…%

2/8 = 1/4 --> 0.25 --> 25%

3/11 --> 0.2727… --> 27.27…%

3/10 --> 0.3 --> 30%

3/9 = 2/6 = 1/3 --> 0.333… --> 33.3…%

4/11 --> 0.3636… --> 36.36…%

3/8 --> 0.375 --> 37.5%

4/10 = 2/5 --> 0.4 --> 40%

4/9 --> 0.444… --> 44.4…%

5/11 --> 0.4545… --> 45.45…%

5/10 = 4/8 = 3/6 = 1/2 --> 0.5 --> 50%

6/11 --> 0.5454… --> 54.54…%

5/9 --> 0.555… --> 55.5…%

6/10 = 3/5 --> 0.6 --> 60%

5/8 --> 0.625 --> 62.5%

7/11 --> 0.6363… --> 63.63…%

6/9 = 4/6 = 2/3 --> 0.666… --> 66.6…%

7/10 --> 0.7 --> 70%

8/11 --> 0.7272… --> 72.72…%

6/8 = 3/4 --> 0.75 --> 75%

7/9 --> 0.777… --> 77.7…%

8/10 = 4/5 --> 0.8 --> 80%

9/11 --> 0.8181… --> 81.81…%

5/6 --> 0.8333… --> 83.33…%

7/8 --> 0.875 --> 87.5%

8/9 --> 0.888… --> 88.8…%

9/10 --> 0.9 --> 90%

10/11 --> 0.9090… --> 90.90…%

As an extra hint, when you’re calculating by hand, fractions tend to be easier to work with. When you’re using a calculator, decimals tend to be easier.

### Okay, breathe.

**Phew.** That’s a whole bunch of data to dump on you all at once. But when you break it down and study it in chunks, it becomes manageable…plus, when you’ve got this stuff down cold, test math (and other kinds, too) gets SO much easier. In all my years of teaching the tests, I’ve never seen these things fail to show up over and over again—this foundational material will never go out of style. Knowing it will save you stress, work, and time on your math sections, and that means a higher score with less angst. Definitely worth putting in a little work at the outset! So make those flashcards, okay?