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ACT formulas 2
different formulas used on the ACT off of EriktheRed tutoring
| Question | Answer |
|---|---|
| volume for a right cylinder | pi x r^2 x h |
| area of a trapezoid | (base_1 + base_2/2) x h base 1 is on the bottom, base 2 is on the top, the height is the dotted line with the right angle |
| Area for a rhombus if l=w | lh |
| formula for the length of an arc | (n^0/360^0) x 2 x pi x r |
| formula for the area of a sector of a circle | (n^0/360^0) x pi x r^2 |
| definition of similar triangles | they have the same shape. The corresponding angles are equal, and the corresponding sides are in proportion. For example, the 3–4–5 triangle and the 6–8–10 triangle |
| the length of on side of a triangle is ALWAYS | less that the sum and more than the difference of the lengths of the other two sides |
| for a special right triangle with 1 90 degree angle and 2 45 degree angles | the hyp is x√2 and the legs are both x |
| parallel lines | have equal slopes |
| perpendicular lines | have negative reciprocal slopes : m_1 x m_2=-1 |
| cosecant (csc) | opposite of cosine; c/b or hypotenuse/adjacent |
| cotangent (cot) | opposite of tangent; b/a or adjacent/opposite |
| secant (sec) | opposite of sine; c/a or hypotenuse/opposie |
| how do you average evenly spaced numbers | average the smallest and the largest. the average of all the integers between 13 and 77 is the same as the average of 13 and 77 |
| how many degrees are on the outside of of a triangle? | 360 |
| rectangle | a four sided figure with four right angles |
| parallelogram | has two pairs of parallel sides |
| square | a rectangle with 4 equal sides |
| trapezoid | a quadrilateral with one pair of parallel sides and one pair of non parallel sides |
| how do you find the percent of increase or decrease? | add or subtract the percent number to 100 percent and multiply it by the original number |
| to find the original whole before a percent | set up an equation: think of 15%increase over x as 1.15x; |
| how do you find the combined percent increase and decrease? | take the percents off or on to 100% |
| how to find part-to-part and whole-to-whole ratios | put each number in the original ratio over the sum of numbers |
| average rate | you combine the total distance and divide it by the total time |
| how do you find the sum from the average | sum= average x number of terms |
| how do you find equations that are in terms of the other variables | it means to isolate the one variable on one side of the equation |
| how to solve for absolute values | take the equation and make two: one side equals to the positive answer and the other equals to a negative answer |
| when do you use a solid circle or an empty circle in graphing inequalities | you use a solid circle if the point is included and an empty circle if the point is not included |
| equation for a circle in a graph with r as radius and centered at (h,k) | (x-h)^2 + (y-k)^2=r^2 |
| the form of an equation that makes a parabola | y= ax^2 + bx + c |
| in a 5-12-13 triangle | the sides are all in 5-12-13 ratios: if one side is 39 and another side is 36, then the final leg is 15 |
| the sum of the measures of the interior angles of a polygon is | (n-2)x180; n=number of sides |
| how to find one angle of a regular polygon | divide the sum of the angles by the number of angles(which is the same as the number of sides |
| to find the interior angle of a polygon | ((n-2)x180)/n |
| formula for the surface area of a rectangular solid | 2lw + 2wh + 2lh |
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