# The ACT Math Shortlist

The Math section of the ACT covers a wide range of topics, from basic arithmetic and pre-algebra to logarithms, imaginary numbers, and advanced Algebra II. Preparing for such an exam can seem like an overwhelming task, and it is easy to feel paralyzed by the sheer quantity of material covered in so many years of math courses. Fortunately, not all math topics are created equal, and the test tends to favor certain topics over others. Contained here is a shortlist of topics to start with for those of you who don’t quite know where to start!

### Linear Equations

Linear functions are of paramount importance in mathematics and thus appear frequently on the ACT. The test will require you to find slopes of lines, given the coordinates of two points (remember: “rise ÷ run”), and to use these slopes to find the equations of the lines. Once you have the slope, you should use slope-intercept form if a y-intercept is provided, and point-slope form if the coordinates of a point on the line are provided.

### Systems of Linear Equations

Linear functions also appear frequently on the ACT in systems of linear equations. These types of problems usually contain two equations with two variables each – often x and y, but not always – and have no exponents. The most common way to solve these equations is through the substitution method. Keep in mind that there are precisely three possible outcomes: one solution for each variable (i.e. the two lines intersect at exactly one point), zero solutions for each variable (i.e. the two lines are parallel), and infinite solutions for each variable (i.e. the two equations are actually one and the same line).

Next come quadratic equations, which graph to parabolas. The first step to solving quadratics is to get everything on one side of the equation and zero on the other. Only once this has been done can the equation be solved! The three primary methods of solving are then:

1. Factoring the expression and setting each factor equal to zero

2. Graphing the function on your calculator and using the ZERO function under the CALC menu

3. Plugging in the constants of the function (a, b, and c) into the quadratic formula.

### Triangles

Triangles appear on the ACT in a wide variety of contexts, but there are a number of basic things you must always keep in mind. All triangles contain angles that sum up to 180°, and the area of any triangle equals base x height ÷ two. For right triangles, in particular, the Pythagorean Theorem can be used to solve for the length of a third side if given the lengths of the other two. Right-triangle trigonometry will make an appearance as well, so at some point, you will likely be asked to set up (and possibly solve) a trigonometric equation using SOH-CAH-TOA.

### Area, Perimeter, and Volume

In addition to the area of a triangle, you should also have memorized the equations for the areas of a circle, rectangle, and trapezoid. For circles, you should also know how to calculate the perimeter, known as the circumference, of the circle. 3-D solids appear less frequently than 2-D shapes, but you should also be prepared to calculate the volumes of a rectangular prism and cylinder.

This is by no means an exhaustive list of topics on the ACT Math, but it should serve as a starting point for any student preparing for the exam. If you can master these topics, you should be able to answer a majority of the first 30-40 questions of the test, and you’ll be off to a great start. Good luck!