The SAT Math No Calculator test is the shortest of all four parts of the test, in terms of both questions and time to answer. You get 25 minutes to do 20 questions. Of those 20 questions, 15 are multiple choice questions with 4 answer choices each, while 5 are grid-in questions.

The material on the SAT Math No Calculator test is broken up into four content areas:

- Heart of Algebra
- Problem Solving & Data Analysis
- Passport to Advanced Math
- Additional Topics in Mathematics

I know what you’re thinking – what do these content areas actually mean? Great question – let’s get into that now, starting with Heart of Algebra.

##### Heart of Algebra

The Heart of Algebra content area features questions on systems of equations, literal equations, inequalities, exponents, logarithms, and imaginary numbers.

Problems that ask about **systems of equations** may ask you to name variables and write equations using those variables. Often, you will also need to solve a system of equations, using either substitution or elimination.

Remember that for a system of linear equations in two variables, there are three cases:

- No solution (the two lines are parallel, with the same slope and different y-intercepts)
- One solution (the two lines intersect at one point, since they have different slopes)
- Infinitely many solutions (the two lines are equivalent, meaning they have the same slope and the same y-intercept)

You will also encounter questions on writing and solving **inequalities**. Remember that multiplying or dividing by a negative number on both sides of an inequality has the effect of reversing the inequality symbol!

Another algebra topic on the SAT Math No Calculator test involves solving **literal equations**. These equations have more than one variable, and you may need to distribute through parentheses, navigate fractions, and combine like terms to solve for a given variable. For example, given ax + by = c, you might be asked to solve for y.

Two more important algebra topics that go hand-in-hand are **exponents** and **logarithms**. Remember that logarithms are really just another way of talking about exponents, using different notation.

Take some time to review the rules of exponents, and make sure you know how to do a change of base (for example, writing 4 as 2 squared, or 8 as 2 cubed).

Another topic you will want to be familiar with is **imaginary numbers**. When working with imaginary numbers, the key is to remember that i squared is equal to -1. This is often necessary to solve these problems or to simplify your answers. Imaginary numbers also appear in the solutions for some quadratic equations (more on this later).

##### Problem Solving and Data Analysis

The Problem Solving and Data Analysis content area contains questions on ratios and proportions, percentages, rates, unit conversions, probability, statistics, and analyzing or summarizing data from tables, charts, and graphs.

Remember that a **ratio** is a way to relate two numbers. For example, if we say that the ratio of red to blue marbles is 5 to 3, this means that there are 5 red marbles for every 3 blue marbles (also written as 5:3).

On the other hand, a **proportion** compares two ratios or fractions. For example, if the ratio of red marbles to blue marbles is 5 to 3, that is equivalent to saying the ratio is 10 to 6 (since 5/3 = 10/6).

Remember that a **percentage** tells you what part of something you have. A percentage is also expressed as a fraction with a denominator of 100. For example, if 25% of drivers are under 30 years of age, that means that 25 of every 100 drivers are under 30.

Some questions may ask you to calculate a **rate**, which describes how one variable changes when another is changed. You may also be given a rate and a starting amount, and asked to calculate the ending amount, based on a change in one of the variables.

Rates come in the context of two different **units** (for example, a car travels in miles per hour, or a pump moves gallons of water per minute).

It is important to pay attention to the units on a graph, since these can help you to determine what the slope (rise over run) means.

**Probability** describes the likelihood that an event will occur. Questions on probability may ask you about a variety of scenarios.

For example, you might be asked the chance of rolling a sum of 7 on two 6-sided dice. You could also be asked to use a table to calculate the probability that a student will have a 3.0 or higher GPA.

The key is to remember that a probability comes from a fraction. The numerator is the number of desired outcomes, and the denominator is the total possible outcomes.

**Statistics** are used to describe a data set, or to compare two or more different data sets. Questions on statistics may ask you to calculate the mean, median, maximum, minimum, standard deviation, or other measures of a data set. You may also be asked to compare these measures between two different data sets.

You may also see some concept-based questions about what the mean or standard deviation tells us about a data set. You could even see questions about factors that would bias any data that was collected in a study.

Finally, you may be asked to analyze or summarize data from tables, charts, and graphs. You may need to determine what type of relationship exists between two variables, based on a graph. You may also be asked to calculate a rate or slope given information from a table.

##### Passport to Advanced Math

The Passport to Advanced Math content area includes questions on quadratic equations, polynomials, zeros and roots, factoring, and divisibility.

Remember that a **quadratic equation** has only one variable, and the highest power of that variable is 2. Quadratic equations can be solved by factoring or by using the **quadratic formula**. Sometimes, it will be faster to factor a quadratic than to use the quadratic formula.

Also, keep in mind that there are three cases for the solutions of a quadratic equation, based on the sign of the **discriminant** (the term under the radical in the quadratic formula).

- If the discriminant is positive, then the quadratic has two real roots
- If the discriminant is zero, then the quadratic has one real repeated root
- If the discriminant is negative, then the quadratic has two complex roots

When we graph a quadratic equation, we get a **parabola**. A parabola has symmetry about the vertical line through its vertex (the highest or lowest point on the graph).

You may also see questions about the** zeros (or roots)** of polynomials (values of a variable that make the polynomial equal to zero).

The concepts of **factors** and zeros are also closely related. If a polynomial f(x) has a factor of x – a, then f(x) has a zero at x = a, meaning f(a) = 0.

##### Additional Topics in Math

The Additional Topics in Math content area contains questions on geometry, trigonometry, and angles.

Geometry questions may ask you about the **area** of squares, rectangles, circles, and triangles, or the **volume** of boxes, pyramids, spheres, or cones. You will be given equations for these areas and volumes at the beginning of the test, but don’t be fooled! You need to be familiar with how to use these equations well before test day.

Trigonometry questions may ask you about the “big three” functions (**sine, cosine, **and** tangent**). You should know how these three functions are found from the three sides of a triangle (choose an angle, and look at the **opposite, adjacent, **and **hypotenuse** – soh cah toa!)

You may also see **similar triangles**, which have a ratio that relates the length of a side of the smaller triangle to the length of the corresponding side of the larger triangle.

It is also important to know how to use **special triangles**, such as 30-60-90 and 45-45-90 triangles. The ratios between the sides of these triangles are given on the formula sheet at the beginning of the test. However, you should be comfortable with using them long before test day.

Finally, questions on **angles** could ask about angles that are complementary (add up to 90 degrees) or supplementary (add up to 180 degrees). You may also see questions about angles that involve parallel lines (such as** alternate interior, corresponding, **and** vertical angles**).

##### Other Considerations

Here are a few other considerations for the Math No Calculator test that do not fit into any of the categories above.

First, remember that the list of concepts given here is not exhaustive – however, it is a good starting point.

The fact that there is no calculator on this part of the test means that your arithmetic has to be fast and accurate, and your graphing skills need to be sharp.

Remember that you can often eliminate fractions to make problems easier to work with. Often, this is done by cross-multiplying (as in a proportion), or multiplying both sides of an equation by a least common denominator (LCD).

For any picture you see, do not assume that it is complete! For one thing, the image may not be to scale. You may also need to add in one or more lines (for example, a radius or diameter on a circle), or extend an existing line, or bisect an angle. Making these changes can make it easy to see how to solve the problem.

When solving a problem, make sure you know what is being asked before you start. You will waste valuable time if you “over solve” (for example, solving for both x and y when you only need x.)

Take at least a couple of timed practice tests before the real thing. This will let you to work on your overall pacing, find shortcuts on longer problems, and tell you where your mistakes tend to happen under time pressure (Basic algebra? Arithmetic? Misreading problems?)

Make sure you are sharp on your vocabulary! This can help you to solve problems that seem unsolvable. For example, what does a “right isosceles triangle” imply about the ratios of the sides?

Finally, don’t be afraid to skip questions and come back to them. Don’t get frustrated – it might just be a sign that your brain needs more time to think about the solution. Another problem may remind you of the concept or equation you need to solve the one you skipped.

##### Conclusion

There is a wide variety of math concepts on the SAT Math No Calculator Test. Now that you know what to expect, you are in a much better position to begin preparing.

Your best bet is to start early and get in a little practice each day. This will help you to refresh your memory on math concepts you have already learned, and it will also give you time to learn what you may have missed.

If you need some guidance with the test prep process, the best thing to do is schedule a free consultation call with one of Testive’s Student Success Advisors!