{"id":558,"date":"2015-03-25T09:00:51","date_gmt":"2015-03-25T09:00:51","guid":{"rendered":"https:\/\/magoosh.com\/act\/?p=558"},"modified":"2019-08-27T20:55:03","modified_gmt":"2019-08-28T03:55:03","slug":"math-formulas-on-the-act","status":"publish","type":"post","link":"https:\/\/magoosh.com\/act\/math-formulas-on-the-act\/","title":{"rendered":"32 ACT Math Formulas – What to Absolutely Study [PDF]"},"content":{"rendered":"

\"ACT<\/p>\n

Unlike the SAT, the ACT does not provide you with a list of basic math formulas to rely upon at the beginning of the ACT math test<\/a>. This means you will need to be able to recall math formulas on the ACT. Below you will find lists of \u201cMust Know\u201d ACT math formulas, \u201cGood to Know\u201d formulas, and \u201cBonus\u201d formulas to commit to memory for the ACT! Learn them all, then check out our list of ACT math topics<\/a> to begin applying them!<\/p>\n

Must-Know ACT Math Formulas<\/h2>\n

Though the ACT tests different concepts on each exam, there are popular topics (like ratios<\/a>!) that come up again and again. This list contains the best ACT math<\/a> formulas to know. For more practice, try these ACT math practice questions<\/a>, then check out Magoosh ACT prep<\/a>.<\/p>\n

Average<\/h3>\n
    \n
  1. S<\/em>\/T<\/em> (Average = Sum\/Number of things)<\/li>\n<\/ol>\n

    Lines<\/h3>\n
      \n
    1. \n
        \n
      1. Slope intercept form:<\/strong><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

        y<\/em> = mx<\/em> + b<\/em> (where m<\/em> is the slope and b<\/em> is the y-intercept)<\/p>\n

          \n
        1. \n
            \n
          1. Slope:<\/strong><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

            \"Slope<\/p>\n

            Triangles<\/h3>\n
              \n
            1. \n
                \n
              1. Area of a triangle:<\/strong><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                1\/2bh<\/em> (1\/2 base \u00d7 height)<\/p>\n

                  \n
                1. Pythagorean Theorem:<\/strong>
                  \na<\/em>2<\/sup> + b<\/em>2<\/sup> = c<\/em>2<\/sup><\/li>\n<\/ol>\n

                  Quadrilaterals<\/h3>\n
                    \n
                  1. \n
                      \n
                    1. Perimeter of a rectangle:<\/strong><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                      2l<\/em> + 2w<\/em> (where l<\/em> is the length and w<\/em> is the width)<\/p>\n

                        \n
                      1. \n
                          \n
                        1. Area of a rectangle:<\/strong><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                          lw<\/em> (length \u00d7 width)<\/p>\n

                            \n
                          1. \n
                              \n
                            1. Volume of a box:<\/strong><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                              lwh<\/em> (length \u00d7 width \u00d7 height)<\/p>\n

                                \n
                              1. \n
                                  \n
                                1. Surface area of a rectangular solid:<\/strong><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                  2lw<\/em> + 2wh<\/em> + 2lh<\/em><\/p>\n

                                    \n
                                  1. \n
                                      \n
                                    1. Diagonal in a rectangular solid:<\/strong><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                      Apply the Pythagorean theorem twice or l2<\/sup><\/em> + w2<\/sup><\/em> + h2<\/sup><\/em> = d2<\/sup><\/em><\/p>\n

                                      Circles and Spheres<\/h3>\n
                                        \n
                                      1. \n
                                          \n
                                        1. Area of a circle:<\/strong><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                          \u03c0r2<\/sup><\/em><\/p>\n

                                            \n
                                          1. \n
                                              \n
                                            1. Circumference of a circle:<\/strong><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                              2\u03c0r<\/em><\/p>\n

                                                \n
                                              1. \n
                                                  \n
                                                1. Volume of a sphere:<\/strong><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                                  4 \/ 3\u03c0r3<\/sup><\/em><\/p>\n

                                                  Cylinders<\/h3>\n
                                                    \n
                                                  1. \n
                                                      \n
                                                    1. Volume of a cylinder:<\/strong><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                                      \u03c0r2<\/sup>h<\/em><\/p>\n

                                                      Trigonometry<\/h3>\n
                                                        \n
                                                      1. \n
                                                          \n
                                                        1. SOHCAHTOA:<\/strong><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                                          sin x<\/em> = opposite\/hypotenuse
                                                          \ncos x<\/em> = adjacent\/hypotenuse
                                                          \ntan x<\/em> = opposite\/adjacent<\/p>\n

                                                          \"Trig\"<\/p>\n

                                                            \n
                                                          1. You should also know your quadrants and where sine, cosine, and tangent are positive or negative:<\/li>\n<\/ol>\n

                                                            \"Trig<\/p>\n

                                                            Probability<\/h3>\n
                                                              \n
                                                            1. \n
                                                                \n
                                                              1. Probability:<\/strong><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                                                Number of desired outcomes \/ number of total outcomes<\/p>\n

                                                                  \n
                                                                1. \n
                                                                    \n
                                                                  1. Factorials (e.g. 8!):<\/strong><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

                                                                    To find the factorial of any integer, multiply it by every positive integer below it, e.g.:
                                                                    \n8 \u00d7 7 \u00d7 6 \u00d7 5 \u00d7 4 \u00d7 3 \u00d7 2 \u00d7 1<\/p>\n

                                                                    Bonus: the “Must Know” math formulas on the ACT also appear in your high school math classes. So, you’re really studying for two things at once. Nice.<\/p>\n

                                                                    Bonus bonus: Check out the video below to watch ACT expert Kristin discuss 6 of the must-know ACT math formulas in greater detail:<\/p>\n