The SAT Math with Calculator test is the fourth and final section of the SAT. Students have 55 minutes to complete 38 questions. The first 30 of which are multi choice followed by 8 grid-in questions (meaning you grid in your numerical answer). This section counts for ⅔ of the total SAT math score. The SAT Math section (both non calculator and calculator) divides questions into 4 distinct categories: Heart of Algebra, Problem Solving & Data Analysis, Passport to Advanced Math, Additional Topics in Mathematics. But before we get into the different categories and their contents, a quick note about equations on the SAT:
Unlike the ACT, students are given a list of equations at the start of both math sections. Students are sometimes misguided to think these are the only equations needed for the test, but they in fact only cover geometry! Over the next few sections, we’ll touch on a few of the other formulas you need to know.
Heart of Algebra
Heart of Algebra is the first category of SAT Math questions you will encounter. They include but are not limited to, linear equations, Inequalities, absolute value, functions, graphs
Linear Equations are, usually, the most straightforward kind of Heart of Algebra problem. Think of the classic “solve for x” questions you’ve done in school. You may also see systems of equations here that require you to use two equations in tandem to solve for both x and y.
Inequality questions require students to balance and simplify a given inequality. Remember that < means less than and ≤ means less than or equal to!
Absolute Values are denoted by the two straight lines on the sides of a variable or equation |x|. They represent a number’s distance from 0, which, for SAT purposes, boils down to: if the number is negative make it positive. However, remember that you have to simplify what’s between the absolute value signs before turning it positive!
Graphs questions require students to discern knowledge based on an x,y coordinate graph. You will often be asked about the equations of lines given in y=mx+b form, and identifying a line’s slope and intercepts.
Problem Solving & Data Analysis
Problem Solving & Data Analysis questions deal with reading and analyzing data presented in both tables and graphs as well as ratios, rates, and percentages.
Reading and analyzing data questions ask students to examine graphs and tables and identify specific data or trends within them. Students are never expected to have familiarity with the subject of the data or know specific formulas for it, instead the test is seeing whether students can come to their own conclusions based on a never before seen data set.
The second question above deals with ratio. A ratio is a way to relate two numbers. For example if you had 20 green balls and 10 yellow ones you would have a ratio 2 to 1 (2:1) green to yellow.
Rate describes the ratio between two somehow related numbers. For example the speed of your car. A car travels at a rate of 20 miles/1 hour. You might have an “interest rate” on a loan you take out from the bank where you are charged a certain amount more each month based on how much you owe.
Percentage refers to the parts of a whole if a number is converted to a fraction out of 100 and is denoted by the symbol %. These questions often deal with real world problems like a discount or at a store and, like was mentioned above, the interest rate of a loan or savings account at a bank.
Passport to Advanced Math
These questions usually fall on the harder end of the difficulty spectrum. They deal with more complicated topics usually learned in Algebra II. They include but are not limited to: quadratic equations, non-linear graphs, exponents and radicals, and functions.
Students will see Quadratic equations in one of two forms as shown below:
These can be solved with the quadratic formula, which is not required by the SAT but is helpful to know!
Non-linear graphs come in the form of exponential or logarithmic graphs as well as parabolas. Remember that parabolas are the graphed form of a quadratic equation!
Students will often have to use exponents or radicals (an example of which being a square root √) to simplify equations or complete word problems.
Functions are equations that take inputs (x) and give outputs f(x). Here’s an example questions where the functioned is defined by g(x):
Additional Topics in Math
Additional Topics in Math, in short, contains everything else. These questions primarily deal with geometry, trigonometry, and angles. Within these categories are area and volume, right triangles, special right triangles, similar triangles, and sine, cosign, and tangent.
As mentioned above, area and volume equations are given at the beginning of each SAT Math section. That does not mean students should assume they do not need to work on these problems! They are often more complicated than just plugging numbers into an equation like finding the arc length of a circle!
Most tests will have questions that will require you to find the sides and hypotenuse of right triangles, which can be easily solved with the pythagorean theorem: a2+b2=c2 where a and b are the sides of the right triangle and c is the hypotenuse!
Similar triangles are ones that are proportional to each other, meaning each length of the smaller triangle has a corresponding length on the bigger triangle!
Angle questions revolve around solving for the missing angles in a shape or set of lines. A few important rules to remember here are:
Angles on a straight line add up to 180 degrees
The angles of a triangle add up to 180 degrees
The angles of a square or rectangle add up to 360 degrees
Sine, cosine, and tangent angle relationships on right triangles are also crucial to remember!
Words to Live by (on the SAT Math Calculator section)
1. We’ve gone over the vast majority of material covered on the SAT Math with Calculator section, but this list is not all-inclusive! Collegeboard is always updating and fine tuning its tests meaning some tests have more of some kinds of problems than others. Your tutor is your best resource to knowing what to expect come test day and your work with Testive is your best resource for being ready for every type of question you may encounter!
2. Remember to use your calculator! It’s called the SAT Math Section WITH Calculator for a reason! Students are often taught in school not to rely on your calculator, but that kind of mental math is for the SAT Math WITHOUT calculator. The test is designed and timed around using a calculator to solve problems and more often than not, require one. It’s there so use it!
3. While the equations chart is handy, it’s always better to have as many equations memorized as possible. Don’t waste valuable time flipping to the front of your test booklet to find the area of a circle! It only takes little extra work to memorize the formulas needed for the SAT Math sections, and can give you the added time edge to score those crucial extra points! Besides, that list doesn’t have all the equations you’ll use anyway!
4. The list of topics is a great starting point, but the only real way to improve your score is practice! Knowing what is on the test is only the beginning! Knowing what to do on the test is what really matters! And what better way to get you started on that journey than with a free consultation call with one of Testive’s Student Success Advisors!