SAT Topics: Geometry & Trigonometry
Unlike some of the College Board's names, this one is straightforward. This category covers Geometry and Basic Trigonometry. There are basic trigonometric ratios on the SAT, but nothing more sophisticated than that. There are no inverse or reciprocal trigonometric functions, and there are no problems involving the law of sines or the law of cosines. Two of the sub-categories are a little bit larger and more elementary, and two are a little bit smaller and more advanced.
Slightly More Common and Less Advanced Topics
Area & Volume — This category contains lots of work with formulas. You don't have to memorize anything, because most of the formulas you need are given on the reference page, and if you need a more advanced formula, they will give it to you. You do need to be able to use formulas backwards, however. Given an area or a volume, you need to be able to calculate one of the sides. Given the volume and height of a prism, you might need to calculate the base area. There is also a small number of rare or unique problems in this category that might require some creative reasoning. Here are the easy, medium, and hard practice problems from the SAT Practice Problem Databank.
Line, Angles, & Triangles — Roughly half of these could be called reasoning with angles
. They give you a figure with some angles labeled, and you have to deduce one of the other angles. The important principles to remember here are the Triangle Sum Theorem (the three corners of a triangle always add up to 180°), and the rules for parallel lines (when a transversal crosses a pair of parallel lines, it forms four acute angles, all equal to each other, four obtuse angles, all equal to each other, and the acute angles are supplementary to the acute angles). The other half of the problems in this category have to do with proportions. Similar figures come up frequently. So do triangles crossed by a line parallel to one of the sides. If you can set up and solve proportions in situations like this, you'll do fine here. Here are the easy, medium, and hard practice problems from the SAT Practice Problem Databank.
Slightly Less Common and More Advanced Topics
These are a little less abundant in the College Board's practice problem databank than the first two categories above. If we assume that the proportions in the databank are similar to those on actual tests, then you're a little less likely to meet these. These two categories are also much more heavily skewed towards the hard
difficulty level.
Right Triangles & Trigonometry — There is nothing about areas or perimeters here. Those have already been covered above. This category is dominated by the Pythagorean Theorem and by basic trigonometric ratios. If you can use the Pythagorean Theorem forwards and backwards and if you remember SOH-CAH-TOA, you shouldn't have much trouble here. You never really need to know special triangles
(i.e. 45-45-90 and 30-60-90 triangles), but they come up fairly frequently, and being able to recognize when you are working with them can save you some time and hassle. If you forget the proportions among the sides, the special triangles are given on the reference page. On the SAT, you never need to worry about reciprocal or inverse trig functions. If you meet a rare problem that looks like a fancy trig problem, you can probably solve it by using complementary angles. (The sine of one angle equals the cosine of its complement and vice versa.) Here are the easy, medium, and hard practice problems from the SAT Practice Problem Databank.
Circles — Again, there is nothing about area or circumference here. Those have already been covered above. At least half of the problems in this category have to to with the equation of a circle in the coordinate plane, i.e. (x-h)2+(y-k)2=R2. If the circle is given to you in this form, you can read the coordinates of the center (h,k) and the radius (the square root of the number on the right) directly from the equation. In rare cases you might need to complete the square
to make the equation look like this. The rest of the problems in this category have to do with converting radians to degrees or vice versa, or with circular arcs. With circular arcs, you can probably solve the problem by remembering that the arc is the same fraction of the circumference that the central angle is of 360 degrees. Here are the easy, medium, and hard practice problems from the SAT Practice Problem Databank.