Barron's SAT 2 Math Terms and Formulae Flashcards
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| 2376616087 | Domain | Input numbers, the x-values of a function | 0 | |
| 2376616532 | Range | Output numbers, the y-values of a function | 1 | |
| 2376618025 | Function | A process that changes a set of input numbers into a set of output numbers. One input number will always produce the same output number. | 2 | |
| 2376621319 | Relation | The association between two variables. Does not have to be a function since a function is a special type of relation. | 3 | |
| 2376624644 | (f + g)(x) | f(x) + g(x) | 4 | |
| 2376625687 | (f - g)(x) | f(x) - g(x) | 5 | |
| 2376627266 | (f * g)(x) | f(x) * g(x) | 6 | |
| 2376631664 | (f / g)(x) | f(x) / g(x), g(x) ≠ 0 | 7 | |
| 2376635534 | (f * g)(x) (Composition of Functions) | f(g(x)) | 8 | |
| 2376636484 | (g * f)(x) (Composition of Functions) | g(f(x)) | 9 | |
| 2376641173 | Inverse | Denoted by a ⁻¹. Relation that has the property where (f⁻¹ * f)(x) = (f * f⁻¹)(x) = x. If inverse of a function is not a function, you can make it one by limiting the domain. Reflection of original function over line x=y. | 10 | |
| 2376655119 | Even (function) | If f(-x)=f(x) for all domain. Outputs are equal for opposite inputs. | 11 | |
| 2376660573 | Odd (function) | If f(-x)=-f(x) for all domain. Outputs are opposite for opposite inputs. | 12 | |
| 2376930226 | Linear Function | mx + b graph of a line | 13 | |
| 2376933327 | Slope of a line | (y₂ - y₁)/(x₂ - x₁) | 14 | |
| 2376934592 | Y-intercept | b (value of y when x is zero) | 15 | |
| 2376936737 | point-slope form | y - y₁ = m(x - x₁) | 16 | |
| 2376939573 | General Equation or Standard Form | Ax + By = C | 17 | |
| 2376942018 | Slope (Standard Form) | -A/B | 18 | |
| 2376942569 | y-intercept (Standard Form) | C/B | 19 | |
| 2376944497 | Distance Formula | √(x₂ - x₁)² + (y₂ - y₁)² | 20 | |
| 2376946457 | Midpoint | ((x₁ + x₂)/2, (y₁ + y₂)/2) | 21 | |
| 2376985471 | Quadratic | Polynomial where the largest exponent is 2. Standard is ax²+bx+c. | 22 | |
| 2376988721 | X-coordinate of the vertex of parabola (Quadratic) | h= -b/2a | 23 | |
| 2376991271 | Y-coordinate of the vertex of parabola (Quadratic) | k = (4ac-b²)/4a | 24 | |
| 2377128955 | Multiplicity | Number of times a particular value appears as the root of a polynomial. | 25 | |
| 2377140309 | Fundamental Theory of Algebra | The sum of the multiplicities is the number of roots in a polynomial They are both equal to the degree of the polynomial. | 26 | |
| 2377161021 | a³ + b³ | (a + b) (a² - ab + b²) | 27 | |
| 2377162510 | a³ - b³ | (a - b) (a² + ab + b²) | 28 | |
| 2377200181 | Rational Roots | p/q p is factor of the constant at the end. q is factor of the constant in front of the x value with the largest integer. | 29 | |
| 2380440585 | Law of Sines | sin A/a = sin B/b = sin C/c | 30 | |
| 2380441314 | Law of Cosines | a² = b² + c² - 2 b c cos A b² = a² + c² - 2 a c cos B c² = a² + b² - 2 a b cos C | 31 | |
| 2380506280 | Area of a Triangle with Sine | area = 1/2 ab sin C area = 1/2 bc sin A area = 1/2 ca sin B | 32 | |
| 2380570569 | sin θ | y/r | 33 | |
| 2380570570 | cos θ | x/r | 34 | |
| 2380570571 | tan θ | y/x | 35 | |
| 2380570572 | cot θ | x/y | 36 | |
| 2380570573 | sec θ | r/x | 37 | |
| 2380570815 | csc θ | r/y | 38 | |
| 2381512188 | sin² θ + cos² θ | 1 | 39 | |
| 2381513387 | 1 + tan² θ | sec² θ | 40 | |
| 2381515466 | cot² θ + 1 | csc² θ | 41 | |
| 2381518548 | length of arc s | rθ | 42 | |
| 2381519045 | area of circle sector | (1/2)r² θ | 43 | |
| 2381572184 | trig function | y = A * trig(Bx + C) + D | 44 | |
| 2381588588 | Amplitude | Vertical dilation, value is |A| | 45 | |
| 2381589511 | Phase Shift | -C/B, the horizontal translation | 46 | |
| 2381590368 | Period | Horizontal dilation, Period of the parent function divided by B | 47 | |
| 2381594251 | Vertical Translation | D | 48 | |
| 2381598996 | csc x (Reciprocal) | 1/(sin x) | 49 | |
| 2381599266 | sec x (Reciprocal) | 1/(cos x) | 50 | |
| 2381599267 | cot x (Reciprocal) | 1/(tan x) | 51 | |
| 2381599589 | sin x (Cofunction) | cos (π/2 -x) | 52 | |
| 2381600410 | cos x (Cofunction) | sin (π/2 -x) | 53 | |
| 2381600411 | sec x (Cofunction) | csc (π/2 -x) | 54 | |
| 2381602481 | csc x (Cofunction) | sec (π/2 -x) | 55 | |
| 2381602805 | tan x (Cofunction) | cot (π/2 -x) | 56 | |
| 2381603676 | cot x (Cofunction) | tan (π/2 -x) | 57 | |
| 2381605414 | sin 2x | 2(sin x)(cos x) | 58 | |
| 2381605684 | cos 2x | cos²x - sin²x 2 cos²x -1 1 - 2 sin²x | 59 | |
| 2408735601 | Natural Logaritm | The inverse of eⁿ or ln x. | 60 | |
| 2412743507 | Translation | Only moves the graph around the coordinate plane. Using addition | 61 | |
| 2412746340 | Stretching/Shrinking | Changing the scale can change the shape of the graph. Accomplished by multiplication and division. | 62 | |
| 2412748542 | Reflection | Keeps shape and size of graph but changes its orientation. Accomplished by negation. | 63 | |
| 2412754022 | Vertical Transformation | Occur when adding, multiplying, or negating happens after the function is applied (to the y). | 64 | |
| 2412756508 | Horizontal Transformation | Occur when adding, multiplying, or negating happens before the function is applied (to the x). | 65 | |
| 2413008169 | Order of transformation | Reflect, change scale, then translate. | 66 | |
| 2413056110 | Parabola | x-orientation: (y - k)² = 4p(x - h) y-orientation: (x - h)² = 4p(y - k) | 67 | |
| 2413086445 | Focus: Parabola | Point that all points on parabola are equidistant to x-orientation: (h + p, k) y-orientation: (h, k + p) | 68 | |
| 2413087322 | Directrix: Parabola | Line that all points on parabola are equidistant to x-orientation: x = h - p y-orientation: x = k - p | 69 | |
| 2413091079 | Vertex | Center of the parabola x-orientation: (h, k) y-orientation: (h, k) | 70 | |
| 2413128086 | Ellipse | x-orientation: (x - h)²/a² + (y - k)²/b² = 1 where a²>b² y-orientation: (x - h)²/b² + (y - k)²/a² = 1 where a²>b² | 71 | |
| 2413178806 | Center: Ellipse | (h, k) | 72 | |
| 2413200874 | Major Axis: Ellipse | x-orientation: Points are (h - a, k) and (h + a, k) 2a units long y-orientation: Points are (h , k - a) and (h , k + a) 2a units long | 73 | |
| 2413204261 | Minor Axis: Ellipse | x-orientation: Points are (h , k - b) and (h , k + b) 2b units long y-orientation: Points are (h - b, k) and (h + b, k) 2b units long | 74 | |
| 2413207866 | Foci (focus): Ellipse | Distance of c = √a² - b² from the center x-orientation: (h - c, k) and (h + c, k) y-orientation: (h, k - c) and (h, k + c) | 75 | |
| 2413226764 | Hyperbola | x-orientation: (x - h)²/a² - (y - k)²/b² = 1 y-orientation: (y - k)²/a² - (x - h)²/b² = 1 | 76 | |
| 2413234998 | Center: Hyperbola | (h, k) | 77 | |
| 2413234999 | Transverse Axis: Hyperbola | Axis is line connecting these two points, horizontal x-orientation: (h - a, k) and (h + a, k) 2a units long y-orientation: (h , k - a) and (h , k + a) 2a units long | 78 | |
| 2413235000 | Foci: Hyperbola | Distance of c = √a² - b² from the center x-orientation: (h - c, k) and (h + c, k) y-orientation: (h, k - c) and (h, k + c) | 79 | |
| 2413291038 | Conjugate Axis: Hyperbola | Axis is line connecting these two points, horizontal x-orientation: Points are (h , k - b) and (h , k + b) 2b units long y-orientation: Points are (h - b, k) and (h + b, k) 2b units long | 80 | |
| 2413291039 | Asymptotes: Hyperbola | x-orientation: y - k = ±(b / a)(x - h) y-orientation: y - k = ±(a / b)(x - h) | 81 | |
| 2413349871 | Eccentricity | A measure of the degree or elongation of an ellipse or hyperbola. (c / a) Ellipse: The closer c is to a, the more circular the ellipse. Hyperbola: The farther c is from a, the more elongated the hyperbola. | 82 | |
| 2413444755 | Polar Coordinate | (r, θ) | 83 | |
| 2413460093 | x (polar) | r cos θ | 84 | |
| 2413465518 | y (polar) | r sin θ | 85 | |
| 2413465519 | x² + y² (polar) | r² | 86 | |
| 2474234403 | What is the modulus of an complex number? a + bi | √a² + b² | 87 | |
| 2475434087 | Determinant of a 2x2 martix | ad - bc | 88 | |
| 2475499721 | Sequence | A function with domain consisting of the natural numbers. | 89 | |
| 2475500180 | Series | Sum of terms of a sequence | 90 | |
| 2475602997 | Sum of an infinite geometric series | a₁/(1-r) | 91 | |
| 2475665920 | Resultant of Vector V (v₁,v₂) and Vector U (u₁,u₂) | (v₁ + u₁, v₂ + u₂) | 92 | |
| 2479367945 | The magnitude or norm of Vector V (v₁,v₂) | √v₁² + v₂² | 93 | |
| 2479505712 | z-score | data value = x mean of values = X standard deviation = s (x-X)/s | 94 |