Getting the score you want on the Math SAT section takes a lot of time and effort. However, many students aimlessly take practice tests upon practice tests without really forming a strategy to get the biggest gains per hour from their study time.

If you want to get a high math score, you need to start with a winning strategy. My first suggestion is to be methodical about it. Go and get a notebook and some sticky tabs or a binder with dividers. Students might also like to make a digital version if they don't want to print off problems. The following notebook setup is how I suggest all of my students start off.

Notebook suggestion:

Formula sheet section

Examples problem section

Missed problems

Avoidable

Comprehension

Conceptual

Time

The first section I suggest students make is a formula sheet section. I have a running list of formulae that I give to my students when we work together. However, to get students started off, I find that this video contains many of the ones they will need:

Here are a few more great resources to review:

The formula for circles, quadratic(vertex form and factored)

Remainder theorem

__p__

Exponent rules: __https://www.rapidtables.com/math/number/exponent.html__

(ignore the calculus ones)

Memorizing a few different forms of certain equations can make questions, that previously took much more than the allotted time, almost instantly solvable. For instance, I have noticed that most students do not know the vertex form of quadratic equations. However, questions about the maximum height of a projectile or the total time it was in the air can be much more easily extracted from the vertex equation than can be from standard form. Oftentimes, one of the answer choices is in this form. This "gives away" the answer without any more math being required from the student.

I then like students to keep a running list of example problems. They can number the formulae in their sheet and write the number of the formula on the problem. This gives them a way to review how to use each formula. Writing out the meaning of each term in their formulae on their sheet also helps accomplish this.

Finally, we have the missed problems section. They can subdivide it into 4 categories. "Avoidable" means they forgot to carry over a negative or they messed up addition or something similar. Keeping track of this will help them find patterns in their most common mistakes. "Comprehension" will be for problems that they couldn't even start because they didn't understand what the question was asking for. This is for problems where they find the statement confusing. "Conceptual" will be for problems where they know what they're being asked to do, but they don't know how to start. "Time" will be for problems that take longer than the allotted time for each problem. I like for students to practice timing individual questions and then mark if they run over time even if they solve them correctly.

Now for studying...

No amount of strategies can do enough to replace a lack of background knowledge.

You have not prepared completely if you are not a level 4 in all topics and are practicing at a level 4.

Take a practice section-go over the solutions.

Watch the videos if you don’t level up.

Take another practice section.

You should be level 4 in everything and then practice at level 4.

Every time you miss a question, write out the solution in a notebook, **classify the kind of mistake you made**

Write down any formula you didn’t know for the problem, describe anything you misunderstood, any strategies/calculator tricks that you could have used, and then write out the correct answer. **Go and find a similar problem to test yourself **

__Strategies:__

Now that we've gone over the bases of getting a good score, we can get started on strategies and calculator techniques that you may find useful.

**Test-taking strategies to practice on at-home tests:**

If you are completely stuck-Plug in all of the answer choices or made up reasonable numbers if you’re struggling

Plug in zero and one, (½,-½ ) to see the behavior of an equation, and make a table of values

Use guesstimation to eliminate unreasonable answer choices or to solve entire problems- keep in mind that the SAT likes using actually realistic examples from life

Utilize your calculator to its full potential in the calc section

Non-calc systems of equations-Unless they’ve solved one of the equations for one of the variables,

**elimination**is often soooooo much faster for non-calc section. Sometimes the answer is like x-y so you could solve for them together as opposed to individually

**Important topics that can help you out across multiple domains:**

**Units**-DIMENSIONAL ANALYSIS: check that the units match up on each side

**Graphs**: will carry over to reading and writing also.

Read the title/caption. What does **zero** represent on this graph? What are my **units **or how is the graph stratified? What are the axes and what is the relationship between those two variables? Increasing, decreasing, linear, exponential? What’s the intercept? What are the extrema(max, min)? Is there a value that wouldn’t physically make sense?

**Word problems:**

Start with the “gut check” if you can.

Example: graph with coffee cooling -> coffee can’t cool below the ambient temperature. There should be a horizontal asymptote around room temperature.

Look for your **slope**(the thing that is changing like meters/second or Newtons/Kg) and make sure you cancel out the correct unit!

Write down or think about the form of the answer (often obvious from the question or a “vertical scan” where you look to see how each answer choice varies) that they want where applicable and then fill it in: y=mx+b for example

Keywords: less than (no more than, shouldn't exceed), greater than(at least), equal to, per or for or for every (indicates division), “less” or “reduces by”, “increases” or “additional”. It’s a good idea to underline keywords.

Pay attention to words like “one less”, “after the first one”, or “initial fee”. When you are finding an equation to describe a situation with a fee “after the first one” then you need to multiply the additional fee by n-1

Pay attention to “reduced by” or “increased by”.** Multiplying by a whole number or dividing by a fraction or decimal will increase a number. Dividing by a whole number or multiplying by a decimal or fraction will decrease a number. **

Example: something increases by 25%. -> 100%x +25%x = 125% x =1.25 x

Something decreases by 25% -> 100%x - 25%x =75%x = .75x

__“Should I be getting a smaller number or a bigger number?”__

Get rid of the fractions before doing algebra if you aren’t comfortable with them. Just make sure to multiply through each term! 3(x+1)=3x+3

1/4y + 3(x+1)= 1/5y

5*4(1/4y) + 5*4*3(x+1)= 5*4(1/5y)

Complex fractions- flip the bottom and multiply it

1/2/3/4= ½ * 4/3

**Most common “avoidable” mistakes:**

You didn’t thoroughly read the whole problem

Example: this question wants the x, not the y value

your answer isn’t in the correct format:

Example: this question wants the answer in vertex form. A is mathematically correct, but incorrect for this question.

Simple math errors where you could have made the problem easier with guestimation:

This also works great for lines: estimate the slope and the intercept. Is it negative, or positive?

For word problems, you should make sure that your answer is realistic:

**Avoiding careless mistakes summary:**

Read all of the questions and answer choices

Make sure you answered with the number they were asking for. Common examples: they ask for x+y instead of both numbers individually

For self-generated answers, you should

**not have a negative number**or anything that exceeds 4 characters (might need to round or turn into a decimal Ex: (22/53))Make sure you rounded properly to the digit they want

Plug in your answer if applicable to check it.

Check your units

Reality gut check

**How to get through the exam: **

Make a key for yourself as follows-

Put a checkmark next to easy problems you’re confident in. Come back and double check with a double check mark if time. You can double check your solution by plugging it in or graphing if possible then move on.

Side note, consider starting with the student-produced response questions and doing the ones you find easy because you can’t guess on them if you're running out of time

For problems, you aren’t confident with, solve them, circle them, and make them your next priority to check after you have finished.

For problems you find really difficult or are blanking on, put a star next to them. Don’t spend to much time on them before moving on to a problem you can get. Come back to them at the end and at least make an educated guess if you are running out of time.

Leave 3 to 4 minutes to carefully fill in all of the bubbles on your answer sheet

__Calculator tips:__

I strongly recommend that you either borrow a graphing calculator or buy one if you don’t have one. Start practicing with it now so that you are comfortable with it on test day. If you don’t have a TI-84 then there are lots of youtube videos about how to work with your specific calculator!

The frac key math -> frac -use parentheses: (2/5)-(27/15)

Programs: ticalc.org

Polynomial root finder

Equation solver (solves system of equations) like algdos

Slope intercept form equation creator from two points

Distance formula

Arithmetic Series

Finite Geometric Series

Infinite Geometric Series

Area of a Sector

And many more! Just make sure that you aren’t wasting time pulling out a program on simple problems

Use graphing: you can graph linear equations, parabolas, inequalities, absolute values, circles

2nd calc to get intersections, max, min, zeros, table, zoom fit/trig

You can backsolve trig problems and remind yourself of the common numbers you need. You can also just use it to simplify answers to see if they match with your answer/quickly plug in answer choices or made up numbers when you are stuck

There are worksheets where you can fill in the blanks for unit circle and common trig values

__TLDR:__

-Classify mistakes: avoidable, didn’t understand the problem(how the question was asked), conceptual, time

- Write down essential formulas and practice with them

- Read the whole problem before solving

- Read all the answer choices

- Pay attention to the specific answer format of the question

- Slope-can tell you a lot without having to solve anything

- Consider real-life situations

- units on left should be same as units on right of equation

- Plug in __#s__ if stuck

- Use your calculator-intersection, y intercept, quadratic formula and much, much more

- DOUBLE CHECK especially easy ones

-answer everything, try to narrow it down to two possibilities

- Less frequent bubbling/bubble at the end

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