Function shifts Vertical Shifts Vertical function shifts are highly intuitive. They occur from either a coefficient placed in front of the variable(s) in the function or because of a constant term added to the function equation. Sample Function: y = 2(x+1)2 − 5 Here the function is shifted down by 5 units, and is multiplied by a factor of 2.…
SOHCAHTOA SOHCAHTOA is a pneumonic device used to remind students of the three trigonometric functions and their equivalents on a right triangle. Problems utilizing SOHCAHTOA will often have students solve for a missing side length on a triangle, or occasionally find a formula to express a side length (where there may only be variables or a mixture…
Negatives The easiest simple mistake to make on an ACT math section is to make a sign error. Whether it’s addition, subtraction, division, or multiplication, negatives make it easy to switch a sign (or to forget to switch a sign) and lose points on a question that a student would otherwise have gotten right.It’s important…
Area/Perimeter of basic shapes On the ACT, students may be asked to calculate the areas of certain common shapes, including triangles, rectangles, and circles. The test will provide students with these formulas, but it’s good to be comfortable with using them before the test, so that questions involving these concepts are just about automatic! The…
Quadratic skills There are four crucial skills a student needs to have when it comes to quadratic equations: to factor, foil, zero parentheses, and graph parabolas. To start, it’s worth remembering what a typical quadratic equation looks like: ax2 + bx + c There are three terms: a quadratic (squared) term, a linear term, and a constant. Quadratics are often expressed…
Ratio Ratios tell the proportional quantity of one thing to another. Ratios are often expressed either with a colon – the ratio of kids to adults is 6:1 (read six to one, meaning there are six kids for each 1 adult) – or like a fraction – the ratio of kids to adults is 61. It’s…
Picking Numbers Some questions on the ACT can be made easier by plugging in real numbers in place of variables. Picking numbers can give a student a more intuitive understanding of the problem, instead of keeping things very theoretical. When choosing numbers for a problem, it can be helpful to try and identify: what is…
Solving Equations Basic Skills Distribute. Distributing involves applying a leading coefficient or sign to all of the terms within a pair of parentheses or other grouping of numbers/variables. For example, when a -5 is put in front of the binomial (x + b), it affects both of those terms, even though when it is written…
Linear Equations/Slope Key Skills Calculate Slope from Two Points If given two points on a line, a student should be able to calculate the slope of that line. The phrase often used to teach this is “rise over run”. Calculate the change in y values and divide it by the change in x values. (y2…
Exponents The main test with exponents is to know when to perform the core three math operations to exponents: Three Main Exponent Operations Exponents are added together when we those exponents share the same base number and that number is multiplied by itself x2 • x5 = x5 + 2 = 7 = x7 Exponents are subtracted together when we those exponents share the same…