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ACT Formulas
Math Formulas 8/18/26
| Question | Answer |
|---|---|
| What do sequences start with? | a constant of c |
| arithmetic sequence | an=a1+c(n-1) |
| geometric sequence | an=a1(c)n-1 |
| log.a.b=c is | a^c =b |
| distance= | speed x time |
| variation | quantity = rate x time |
| fog (x) | f(g(x)). This is different from fg(x), which is f(x)xg(x) |
| pie radians = | 180 degrees |
| slope-intercept formula | y=mx+b |
| m=slope= | (y1-y2) / (x1 - x2) |
| b=y-intercept= | (0,b) |
| distance formula | √ [(y1-y2)^2 + (x1-x2)^2] |
| midpoint formula | m = [(x1+x2) /2, (y1+y2) /2] |
| FOIL (first, outer, inner, last | (a+b)(c+d) = ac + ad + bc + bd |
| quadratic formula | X = -b _+ √ b^2 -4ac /2a |
| discriminant | b^2 -4ac |
| if... discriminant >0, =0, <0 | >0 - 2 real solutions =0 - 1 real solution <0 - no real solutions |
| percent = | part/whole x 100% |
| a% of b = | a/100 x b =a x b /100 |
| percent change= | change/original |
| average (mean)= | sum of terms/number of terms |
| median | middle number |
| mode | most common number |
| range | biggest - smallest |
| probability | number of desired terms / total number of terms |
| P(event happens) + P(event doesn't happen) = | P(A and B) = P(A) x P(B) |
| supplementary angles add up to | 180 degrees |
| complementary angles add up to | 90 degrees |
| vertical angles are | congruent |
| angles of a triangle add up to | 180 degrees |
| area of a triangle | 1/2 base x height |
| Pythagorean theorem | a^2 + b^2 = c^2 |
| 45:45:90 triangle ratio | x:x:x√2 |
| 30:60:90 triangle ratio | x:x√3:2x |
| trapezoid area | average of bases x height = (b1 + b2) /2xh |
| perimiter | sum of sides |
| sum of angles in n-sided figure | (n-2) x 180 degrees |
| area of rectangle | length x width |
| area of parallelogram | base x height |
| circle arc length | central angle /360 degrees x circumference |
| circle sector area | central angle /360 degrees x area |
| area of a circle | pie r^2 |
| circumference of circle | 2pie r |
| vertex form for a parabola | y=a(x-h)^2 +k |
| circle equation | (x-h)^2 + (y-k)^2 = r^2 |
| center of circle radius | (h,k) r |
| axis of symmetry | x = h |
| surface area of rectangular prism | 2(length x width + length x height + width x height) |
| volume of rectangular prism | V = lwh |
| volume of right cylinder | V = pie r^2 h |
| sin | opposite/hypotenuse |
| cos | adjacent/hypotenuse |
| tan | opposite/adjacent |
| sin^2(x) + cos^2(x) = | 1 |
| sin(x)= | cos(90 -x) |
| cos(x)= | sin(90 -x) |
Created by:
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