Circle equations The default equation of a circle looks like this: (x−h)2 + (y−k)2 = r2 where r is the radius of the circle, and the x and y binomials indicate where the center of the circle is. Circle questions on the ACT math section will normally provide either a graph or an equation. Whichever one is provided must be used…

c = product of roots, b = sum of roots, a = scaling When factoring an exponential equation (ax2+bx+c into (x-d)(x-e)), the signs and magnitudesof b and c can provide a lot of information that is useful for factoring. Example Equation: x2 + 3x − 10 C C should always be the starting place any time a student factors. It gives direct and specific information…

Volume of a prism Simple Shapes The volume of a simple 3d object is equal to the area of the base object multiplied by the height of the object Complex Shapes The shapes above all have right vertices, meaning that their heights are consistently perpendicular. Not all 3D shapes have perpendicular vertices, which means that…

Permutation Permutation is similar to the counting principles discussed earlier. However, permutation questions involve options which are mutually exclusive. Here is a sample ACT question involving Permutation: Unlike with the security lock question covered above, once a plant is used in one display spot, it cannot be used in a different display spot. So instead…

Vectors Vectors are a way of expressing magnitude (size) and direction. The magnitude of a vector will often be described using variables, most commonly the variables i and j. The direction of the vector will be indicated by an arrowhead at the end of the vector line. Vector Skills Adding To add together any two…

Ellipses Ellipses are a rare but important shape to know about for the ACT math section. Here are the main properties of an ellipse that students will be expected to know: Key Skills for Ellipses What is an Ellipse? An ellipse is an oval shape. It is similar to a circle, but where one of its…

Scientific notation Scientific Notation is a way to express very large or very small numbers by the number’s most significant digits combined with an exponential expression of base 10. This notation usually includes a whole number with one or two decimals after it: 2.38. This will then be followed by an exponential expression of:  × 10a , where…

Least Common Multiple (LCM) The Least Common Multiple refers to the smallest possible number that is evenly divisible by a given pair or set of numbers. For example, the least common multiple of the numbers 2 and 3 is 6. The easiest trick for finding the least common multiple of any series of numbers is to find the…

Imaginary (Complex) numbers Imaginary numbers refer to irrational numbers that cannot exist in the real word, but which do exist in math. The most common imaginary number to see on the ACT is the imaginary number i, or the square root of -1. When in Doubt, Try to Square It The best piece of advice for problems…

Logarithms A logarithm is the inverse of taking something to an exponential power. When something is expressed as log5125, in a sense it’s asking what exponent would 5 need to be taken to to get 125. This is why log5125 = 3.That’s why the first core skill of logarithms is to be able to rewrite logs in exponential form.…