PSAT: Expert Guides and Resources

Your math tool kit for the PSAT/NMSQT — techniques that allow you to cut through problems like a hot knife through butter — contains some tricks that are especially useful for algebra and function questions. Read on: Be sure you know what the symbols mean. Algebra often deals with equations (the equal sign is a dead giveaway), but you may also see these little signs: Don’t forget your calculator when you’re solving algebra and function problems.

You’ll find lots of triangles on the PSAT/NMSQT, especially right triangles. The Greeks weren’t the only mathematicians in the ancient world, but they managed to place their “brand” on geometry, a word which, by the way, comes from the Greek words for “earth measure.” Specifically, a mathematician named Pythagoras wrote the Pythagorean Theorem: a2 + b2 = c2 You can use this formula to find the sides of any right triangle, in which a and b are defined as the two legs of the triangle and c is the hypotenuse, a fancy word for the side opposite the 90̊ angle.

You will likely get some rate, time, and distance problems on the PSAT/NMSQT. Don’t you hate questions in which one guy is driving east at 40 miles an hour and a friend is moving west doing 65? You’re supposed to figure out where they meet and ignore the fact that in real life they can just call each other and explain where they are.

Math meets fortunetelling in sequences (numbers arranged in a fixed order). The PSAT/NMSQT lords provide a set of numbers (each number is called a term) and ask you to identify another term in the sequence. They may want the next term or a term many steps along. Sequences show up in two varieties on the PSAT/NMSQT: arithmetic (when the terms occur because of adding or subtracting) and geometric (when you multiply or divide to move from one term to another).

The PSAT/NMSQT loves triangles, so you need to develop a little affection for them also. Fortunately, triangles are easy to love. Here are the facts about triangles: The angles inside a triangle add up to 180°. If you know two angles, you can figure out the third. Note: This fact appears in the information box on the exam.

You will encounter polygons on the PSAT/NMSQT. A polygon is a closed, two-dimensional figure with sides made of lines. In other words, a triangle, a square, a rectangle, and any other closed shape you can create by drawing lines is a polygon. Polygons are named according to the number of sides they have: A triangle has three sides (the prefix tri means “three”), a quadrilateral has four, a pentagon has five, and so on.

Circles are everywhere, especially on the PSAT/NMSQT. It’s no accident that English contains so many references to circles: circle of friends, water circling the drain, coming full circle, and so forth. When you hit a circle question on the PSAT/NMSQT, remember these facts: The radius is a straight line from the center of the circle to its edge.

Many of the algebra and function questions you’re up against on the PSAT/NMSQT contain exponents, raised numbers or letters. The number or letter not raised is called the base. When mathematicians talk about exponents, they call them powers, as in “six to the eighth power.” The second power is referred to as a square, and the third power is a cube.

Not every algebra problem on the PSAT/NMSQT is an equation. You may need to find out what happens to one quantity when it varies directly or inversely in relation to another quantity. No sweat. You already know how to solve these problems. Direct variation questions are just ratios in disguise. To solve a problem in which two quantities (say, a and b) vary directly, remember that the ratio of a to b is a constant.