ACT math
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Created by:
Artbon Plus on September 23, 2010
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74 terms
Terms | Definitions |
|---|---|
 quadratic formula | [-b ± √(b² - 4ac)] / (2a) |
| slope formula | (y₂- y₁) / (x₂- x₁) |
| integers | ..., -3, -2, -1, 0, 1, 2, 3, ... |
| rationals | fractions (anything expessable as a ratio of integers) |
| reals | integers, rationals, plus special #s (like √2 or pi) |
| order of opperations | PEMDAS (Parentheses / Exponents / Multiply / Divide / Add / Subtract) |
| Arithmetic Sequences | t₁, t₁+ d, t₁+2d, ... |
| Geometric Sequences | t₁, t₁· r, t₁· r², ... |
| Factors | ex. factors of 52 are 2, 4, 13, and 26 |
| Multiples | ex. multiples of 20 are 40, 60, 80, 100, ... |
| percentages | part = (percent / 100) x whole |
| average | average = sum of terms / number of terms |
| average speed | average speed = total distance / total time |
| sum | sum = average x (number of terms) |
| mode | mode = value in the list that appears most often |
| median | median = middle value in the list |
| fundamental counting principle | if an event can happen in N ways, and another, independent event can happen in M ways, then both events together can happen in N x M ways. |
| probability | probability = number of desired outcomes / number of total outcomes |
| adding exponents | x^a · x^b = x^(a+b) |
| subtracting exponents | x^a / x^b = x^(a-b) |
| negative exponents | 1 / x^b = x^(-b) |
| multiplying exponents | (x^a)^b = x^(a·b) |
| x^0 | 1 |
| roots | √(xy) = √x · √y |
| FOIL | (x+a)(x+b) = x^2 + (b+a)x + ab |
| difference of squares | a^2 -b^2 = (a+b)(a-b) |
| a^2 + 2ab + b^2 | (a+b)^2 |
| a^2 - 2ab + b^2 | (a-b)(a-b) |
| distance formula | √[(x₂- x₁)^2 + (y₂- y₁)^2)] |
| mid-point formula | [(x₁+ x₂)/2 , (y₁+ y₂)/2] |
| intersecting lines | opposite angles are equal (each pair of angles along the same line add to 180 degrees) |
| area of triangle | area = (1/2)bh |
| angles of triangle | add up to 180 degrees |
| length of triangle sides | length of 1 side is always less than the sum of the other 2 |
| equilateral | three equal sides, all angles = 60 degrees |
| isosceles | 2 equal sides, 2 equal angles |
| similar | same shape, corresponding angles are equal, corresponding sides are in proportion |
| circle area | pi · r^2 |
| circle circumference | 2 · pi · r |
| full circle | = 360 degrees |
| length of arc | (n degree / 360 degrees) · 2 · pi · r |
| area of sector | (n degree / 360 degrees) · pi · r^2 |
| rectangle area | area = lw |
| parallelogram area | area = lh |
| rectangular solid volume | volume = lwh |
| right cylinder volume | volume = pi · r^2 · h |
| prime factors | 2, 3, 5, 7, 11, ... |
| Greatest Common Factor | ex. GCF of 200 and 60 is 20 |
| Least Common Multiple | ex. LCM of 200 and 60 is 600 |
| equation of circle | with midpoint (h,k) ... (x - h)^2 + (y - k)^2 = r^2 |
| logarithms | y = log(little b)x asks b^y = x |
| complex numbers | i^0 = 1; i^1 = i; i^2 = -1; i^3 = -i; i^4 = 1; i^5 = i; i^6 = -1; i^7 = -i |
| sin of an angle | opp / hyp |
| cos of an angle | adj / hyp |
| tan of an angle | opp / adj |
| special sin cos relationship | sin^2(angle) + cos^2(angle) = 1 |
| degree to radian | degree# · (pi / 180 degrees) |
| radian to degree | radian# · (180 degrees / pi) |
| trapezoid area | area = [(base1 + base2) / 2] · h |
| Direct Variation | y=kx |
| Inverse Variation | y=k/x |
| Slope intercept form | y=mx+b |
| Point-Slope form | y - y₁= m(x - x₁) |
| standard form | Ax + By=C, where A, B, and C are not decimals or fractions, where A and B are not both zero, and where A is not a negative |
| Dividing by a negative number in an inequality | You must flip the sign |
| Graphing < or > on a coordinate plane | dotted line |
| Graphing ≥ or ≤ on a coordinate plane | solid line |
| Graphing ≥ or > on a coordinate plane | shade upwards or to the right |
| Graphing ≤ or < on a coordinate plane | shade downwards or to the left |
| circle perimeter | 2 pi r |
| Chord | The distance from one point on the circle to another point on the circle. |
| Sector | The part of a circle that looks like a piece of pie. A sector is bounded by 2 radii and an arc of the circle. |
| arc | Part of a circle connecting two points on the circle. |
| Central Angle | An angle whose vertex is the center of the circle |
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