# SAT Math Strategies In order to own the SAT math section, you need some strategies. Well – we’ve got ‘em. From how many questions are on the SAT math section to tangible strategies for tackling the questions, read, bookmark, and print the post below for your next study session.

## First, A Quick Overview of the SAT Math Section

You will have 80 total minutes to complete 58 questions.

You will begin with the No Calculator portion where you will solve 20 questions in 25 minutes. Of these 20 questions, the first 15 are multiple-choice and the last 5 are student-produced responses.

Once those 25 minutes have elapsed you will be allowed to get out your calculator in order to complete the remaining 38 questions. You will have 55 minutes for this portion. Of these 38 questions, yep, you guessed it, some are not multiple-choice. The first 30 will be multiple-choice, and the remaining 8 are student-produced gridded responses.

### What are Student-Produced Responses?

There are no answer choices provided for about 20% of the questions. You have to come up with an answer and grid it as either a fraction or decimal. The good news is that there are only four digits/spaces so the answer choice must be relatively simple – no crazy complicated solutions.

### What, No Calculator? No Problem!

Something that intimidates some SAT takers is that there is a portion in which you cannot use a calculator. This is different from the ACT which allows the use of a calculator on the entire math section. Never fear however, because you will find that you rarely need your calculator for any portion of the test, even when you are allowed to use it. That’s right! If you are attempting a problem and the numbers seem too difficult to manipulate without a calculator then you need to rethink your strategy. There must be a simpler way.

For information on the topics covered on the SAT, refer to the end of this post. For now, let’s turn our attention to strategy!

## Timing Strategies

### Mark it and Skip it

As we said, you will have 25 minutes to answer the first 20 No-Calculator problems and 55 minutes to answer the 38 Calculator problems, so you do not want to spend too much time on any one problem. Don’t let a question stump you for too long before you mark it, skip it, and move on. You can also mark the questions you answered but were unsure if you answered correctly. Make sure you have a watch or can see the clock because you really need to keep track of the time.

Return to your unanswered or unsure questions when you have just a few minutes left in that portion. You cannot return to the No-Calculator portion once the Calculator portion has begun, so you need to make sure you have answered everything in the first portion in that first 25 minutes.  There is not a penalty for incorrect responses; instead, you receive credit for each question you answer correctly, so do not leave any answers blank

On most standardized tests the questions get more difficult as you progress towards the end; however, there is a caveat to the SAT – the last couple of multiple-choice questions in each portion will most likely be difficult, while the first couple of student-produced gridded responses should be easy, but it sure would be tough to guess a response to a gridded question when you don’t get to just pick A, B, C, or D like you do for the multiple-choice.

So, don’t spend too long on the last couple of multiple-choice questions in each portion because you need to get to those gridded questions! Instead, skip the time-consuming multiple-choice questions, answer the student-produced response questions (at least the first couple easier ones), then go back and take an educated guess on those tricky multiple-choice questions that were taking you too long.

If you do find you have a bit of extra time, go back to those problems you were unsure of, and check them, but don’t do them the way you did them the first time. Instead, try another strategy or plug in your answer and see if it checks out.

### Solve Quickly (but Accurately)

You need to use your reasoning to try to find the quickest way to solve each problem. While you are permitted a calculator for a portion of the math SAT, all problems can be solved without one, and frequently the fastest route does not involve using a calculator. Make sure you are familiar with the calculator you bring to the test (and that it is one which is accepted for use) and know when to use it and when you can surely work more quickly without it. In fact, every problem is written so that it can be solved without a calculator, so you may be better served by reserving your calculator for when you return to check answers.

Generally, the questions for the SAT math section get more difficult as you progress towards the end of each portion of the test (with the exception of where it changes from multiple-choice to student-produced gridded as mentioned above). This means two things. One, you would like to have more time for the more challenging problems at the end, but two, you really do want to make sure you spend enough time to get those first questions correct. You need to get those easier problems right, so move quickly, but not so fast that you make careless errors.

In addition, unlike the ACT, the SAT does give you a formula sheet. This reference sheet is generally just for geometry questions.  You probably already know this information, but it is provided just in case. You should familiarize yourself with it just so you know what is provided. If a question uses an unusual formula that you would not be expected to know, that formula will be present in the question. There are some formulas you are expected to know, and some others that sure would make the test a lot easier if you knew them. Check out our Formulas for the SAT Math Section study guide here.

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## Study Tips for the SAT Math Section

### Do a practice timed test

In order to best mimic the process that you will use when you take the actual SAT, print out a practice test and a bubble sheet, set a timer for 25 minutes for the first (no-calculator) portion, and start-problem solving. If you do not finish, go ahead and finish the remaining questions, but mark that you needed additional time. Then do the same for the calculator portion (55 minutes).

### Identify Your Weaknesses & Learn From Them

Once you’ve completed your practice test, check your answers. Of the ones you missed, you should really look for a couple of things:

One, are there patterns in your mistakes? Are you missing geometry questions, or abstract questions, or questions with lots of words? Did you struggle with the student-produced gridded questions? Did you need extra time?  What can you do to speed up your process? Identify your weaknesses.

Two, when you check your answers, try to figure out what you did wrong. Don’t just say, “Oh, I missed those eight questions.” Figure out how to do them!  Wrap your brain around the problem. See if you can figure out how to do it before you even look at the explanation. And then, try another question like it (you can always just change the numbers to write a new problem for yourself).

All of this is called “metacognition” which just means “thinking about your own thinking.”  If you do not analyze your mistakes, you can do all the practice tests in the world, but you’re just going to keep making the same mistakes.  Practice does NOT make perfect. Perfect practice makes perfect!

### Do More Problems; Attack with Strategy and Purpose

Because you need to move quickly, consider how you go about each problem.  This is not a test like you take in high school where the teacher tells you that you will not get credit if you don’t do it the way he or she wants.  Do what works for you, but keep in mind you should be jotting, and drawing, and trying out numbers, looking for patterns, writing algebraic equations, and basically spitting out your ideas on paper. What kinds of strategies might you try?

## Problem Solving Strategies for SAT Math

### Draw a Picture

Some questions are abstract and a quick sketch may help you “see” what the problem is asking.

Example:  A cube has 2 faces painted red and the remaining faces painted blue.  The total area of the red faces is 32 cm2.  What is the volume of the cube in cubic centimeters?

Draw a quick sketch of the cube and mark what you know so that you can see what the problem is asking.

Oh, each red face must have an area of 16 cm squared so each side must be 4 cm.  The Volume must be 4 x 4x 4 or 64 cm cubed.

### Plug-in Numbers

Variables got you down?  Sometimes the variables make the problem seem more difficult than it actually is. Try to substitute numbers (and pick “smart” numbers that make the problem easier) and see if you can manipulate the problem that way.

Example: When the positive integer n is divided by 9, the remainder is 7.  What is the remainder when n+3 is divided by 9?

Try a number.  Let’s see, what number could be divided by 9 and leave a remainder of 7?  Well, 16 divided by 9 is 1 and the remainder would be 7.  So what is the remainder for 16+3 divided by 9?

### Make a Table or List and Look for a Pattern

It doesn’t have to be beautiful, but it needs to be organized enough that you know what you mean and what you are looking for.

Example:  Each term in a certain arithmetic sequence is always greater than the one preceding it, and the difference between two consecutive numbers is always the same.  If the 3rd and 5th terms are 19 and 79, what is the 7th term?

Aha, the sequence is adding 30 each time!

### “Act” It Out

Obviously you can’t just stand up in the testing room and start moving things around, but you can essentially “act” out a problem by jotting things down on paper.

Example: A classroom has 8 tables that will seat up to 4 people.  If 26 students are seated at the tables and none of the tables are empty, what is the greatest possible number of tables at which 4 people are seated?

### Use Logic

Don’t make random guesses, at least make them logical.

Example:  In the xy-coordinate plane, lines s and t are perpendicular.  Line s goes through the origin and contains point (-2,-1).  Line t also contains the point  (-2,-1) and point (0,n).  What is the value of n?

If the answer choices are A) -5     B) -3 C) -2 D) 2 E) 3   then a very quick sketch shows that the answer cannot be positive.  At least use your logic here and eliminate poor answer choices.

### Don’t Make the Problem Harder Than It Is

Make sure you answer the problem that is asked. Don’t do steps that are unnecessary.

Example:  If (2x-8)(2x+8)=36, what is the value of 4×2?

(2x-8)(2x+8)=36

4×2-64=36

4×2=100  Stop here!  You don’t need to solve for x.  Don’t waste your time with extra steps. Notice what the question was asking.

## Concepts You Can Expect to be Covered on the Test

Your SAT score report will include your Math section score, which ranges from 200 to 800, as well as three subscores which show how you performed in three categories: Heart of Algebra, Problem Solving and Data Analysis, and Passport to Advanced Math.

Note: Additional Topics in Math contribute to your total score, but do not get reported as a subscore.

For the Heart of Algebra questions (roughly 33% of total questions) you may need to:

• Find distance on a number line, between points on a coordinate plane, or in terms of absolute value
• Use word to symbol translation and linear equations and inequalities to solve real-world problems in context
• Manipulate and evaluate variable expressions and equations (including absolute value)
• Solve linear and quadratic inequalities and match with appropriate graphs
• Find and interpret slope and intercepts from equations, word problems and graphs (also using properties of parallel and perpendicular lines)
• Match, interpret, and analyze information from graphs in the coordinate plane
• Solve and interpret systems of linear equations and linear inequalities both in context of real-world problems and without context

For Problem Solving and Data Analysis concepts (roughly 29% of total questions) you will need to:

• Solve multi-step problems using ratios, proportions, rate, percentages, and/or conversion of units of measure
• Refer to data, charts, frequency tables, and graphs to interpret information
• Demonstrate knowledge of measures of central tendency and distribution (mean, median, mode, range), how to compute each, and how to compute for a missing data point given a measure of central tendency
• Compute probabilities of an event, its complement, and combinations (conditional and joint probability) in context
• Demonstrate knowledge of the fundamental counting principle and Venn Diagrams
• Understand the fundamentals of statistics (random sampling, distribution, standard deviation, confidence interval, and interpretation of results)
• Interpret key features and relationships between variables in graphs
• Understand differences between linear, quadratic, and exponential relationships in context (frequently as simple and compound interest or growth/decay)
• Extend patterns, both arithmetic and geometric, increasing and decreasing by common factors or ratios

Passport to Advanced Math concepts (roughly 28% of total questions) may test your ability to:

• Manipulate exponents in powers of 10, and scientific notation, and apply properties of rational exponents
• Demonstrate knowledge of the real number system – rational, irrational, and complex numbers
• Add, subtract, multiply, and divide polynomials
• Create and interpret quadratic or exponential functions in context
• Analyze, solve, and graph quadratic or other nonlinear equations and systems
• Manipulate expressions and equations with exponents, integer and rational powers, radicals, and fractions with variables in the denominator
• Interpret and evaluate functions and composite functions
• Interpret functions and their graphs
• Identify intercepts and maximum and minimum values
• Find domain and range and asymptotes
• Understand increasing and decreasing, end behavior, and transformations/translations
• Write functions that are directly or inversely proportional or exponential

Additional Topics in Math questions (roughly 10% of total questions) frequently combine multiple geometry concepts into one question in context. These concepts include your ability to:

• Calculate lengths and midpoints of line segments (overlapping segments and those in the coordinate plane)
• Compute perimeter and area of polygons and circumference and area of circles
• Use properties of parallel lines, other angle properties, and similar figures and ratios to find missing angle measures or side lengths/distances
• Use properties of isosceles and right triangles to compute unknown side lengths and angle measures (symmetry, Pythagorean theorem, etc…)
• Demonstrate knowledge of right triangles (30o, 60o, 90o; 45o, 45o, 90o) and apply trigonometric ratios (sine, cosine, tangent) to solve for missing values
• Manipulate between area, volume, and surface area
• Understand the trigonometry of the unit circle and basic trig identities to solve problems involving radians and angle measures
• Understand circle relationships such as central and inscribed angles, arc length and sector area, tangents and chords
• Create the equation of a circle in the coordinate plane by finding the center and radius
• Manipulate (add, subtract, multiply, divide, simplify) complex numbers (i=-1)

Now that you’re armed with timing and problem-solving strategies, and knowledge of the content of the test, you’re ready to train for the math marathon that is the SAT math section! You can find hundreds of practice problems with explanations that teach you the concepts you need to know in Olive Book’s SAT course. Just visit www.olive-book.com to enroll.