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How to Solve Geometry Problems on the PSAT/NMSQT

This is math, not art, but you should pretend you’re Rembrandt when you hit a geometry question on the PSAT/NMSQT. Why? Because geometry concerns shapes and lines, and if you can see them, you can understand them better. Follow these steps:

  • Examine the diagram, if the question has one. The little drawings on the exam are a good starting place. Look at the information they provide and notice every number and variable (45°, 2 feet, x, and so forth).

    The drawings on the PSAT/NMSQT are as accurate as possible, but they can deceive you. Something may look like a right angle, for instance, but not actually be one. Check the question; it may state that ABD is a right angle or include a little square drawn in the angle.

    But don’t assume anything! Rely on the information given and your knowledge of math, not on an estimate.

    Some diagrams are labeled not drawn to scale. If you see that phrase, be extra careful. The drawings don’t give you an idea of relative length or size.

  • If no diagram appears, sketch one in the test booklet. Don’t take time for museum-ready quality. Just be sure that you have everything in the right place.

  • Read the information supplied by the question, calculate if necessary, and add everything you can to the diagram. If the question tells you that one angle is twice as large as another and the smaller angle is labeled 30°, label the bigger angle 60°.

  • Search for basic shapes hidden inside more complicated diagrams. You may see a triangle with one side extended like a flagpole, for example. So? It’s still a triangle! Everything you know about triangles still applies.

    Plus, the “flagpole” may supply extra information, such as the measurement of an angle outside the triangle. Because straight lines always equal 180°, you can sometimes figure out the angle inside the triangle by looking at the angle outside the triangle.

  • Reread the question and identify what the test-makers want to know. Are you looking for the length of side b or trying to find out what number can’t possibly represent the length of side b? If you answer the wrong question, your math skills won’t matter.

    As you read the question, underline key words that indicate what you have to figure out. In the preceding bullet, for example, you might underline “can’t” and “length of side b.” The underlining focuses your attention on your goal.

  • Use the formula box only as a reminder. Because they have kind hearts and aren’t actually trying to torture you, the question-writers provide a little box of information at the beginning of each math section. The box tells you the number of degrees in a circle, straight line, and triangle. It also supplies formulas for area and volume, the Pythagorean Theorem, and the measurements of special right triangles.

  • If you’re nervous, peek at the box to check on these basics. However, you may be pressed for time, and turning back to find formulas can eat up precious seconds. Your goal is to know this information before you receive the test booklet.

Mathematicians love specialized terms almost as much as grammarians do. The good news is that you don’t need to know many terms to solve PSAT/NMSQT geometry problems. A few basic words will get you through. So even though your math teacher throws around words such as scalene triangle, you don’t have to memorize the fact that a scalene triangle has three unequal sides.

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