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SAT stuff
| Question | Answer |
|---|---|
| What is the mean? | its the same thing as the average |
| median | put the numbers in order, pick the middle: if there are two middle numbers, then find the average of these two numbers |
| mode | the number that appears most often |
| How to know if sm is a quadratic function given a table of x and y values | 1. Find the first differences (subtract the y values) 2. Find the second differences and if the 2nd difference is constant (the same number over and over) it is a quadratic → on a graph they make a U or upside down U shape |
| quadratic function formula | y = a(x-h)^2 + k vertex= (h, k) -PARABOLA |
| natural numbers | numbers you can count w/ (excludes zero) |
| whole numbers | natural numbers + zero |
| Integers | whole numbers + negatives |
| Rational numbers | numbers that can be written as a/b (repeating decimals count) |
| irrational numbers | cannot be written as a fraction, decimals that go on forever without repeating |
| factoring out a common binomial | 57x(x+b) + a (x + b)=0, factor out x+b → (x+b)(57x+a)=0 |
| formula of a circle | (x - h)² + (y - k)² = r² (h,k): The coordinates of the circle's center. (r): The radius (distance from the center to any point on the edge). |
| completing the square | X^2 + 6x +3 = 9 → X^2 + 6x + __ + 3 - 9 = 0 _____ = (6/2)^2 = 9 X^2 + 6x + 9 + 3 - 9 (x+3)^2 - 6 6 = (x+3)^2 +or- rad6 = x+3 |
| when to put the plus or minus symbol in front of your answer | x^2 = A x = + or - radA |
| Given two points, how to find the y-intercept | find the slope and then use point-slope form OR you can use y-intercept form by plugging the m and one point into the equation y = mx +b |
| compound interest. | A = P (1 + r/n)^nt → A = final amount, P = principle amount, r = annual interest rate (decimal) n = number of times compounded per year, t = yrs -you earn interest on the original money and on the interest you've already earned |
| Continuous compounding | A = Pe^rt -instead of interest being added yearly monthly, or daily, it's constantly added every instant -growth happens continuously |
| Simple interest | I = Prt → interest earned, → Total amount = A = P + I -you earn interest only on the original amount, you increase by the same amount each time |
| Percent growth | A = P (1 + r)^t |
| Percent Decay | P(1-r)^t |
| Exponential models | y = a(b)^x → a = starting value, b>1: growth, 0 < b< 1: decay x = time or number of periods (how many times the growth or decay happens) |
| Present value | PV = FV/[(1+r)^n] -present value = amount of $ needed today to end w/ a certain amount in the future -FV = future value r = interest rate per period n= # of periods -anything that changes by the same percent or same multiplier each period |
| Distance formula | rad[(x-x)^2+(y-y)^2] |
| midpoint | [ (x + x)/2, (y+y)/2] |
| quadratic formula | x = -b +or- rad(b^2 - 4ac) all divided by 2a |
| Vertex formula | b/2a |
| Vieta’s formula | if you have a quadratic equation in standard form (ax^2 + bx +c = 0), then the sum of the solutions is -b/a and the product of the solutions is c/a |
| When given two expressions that equal each other, sometimes you move everything to one side and set equal to zero, and sometimes you simply each side individually. | Move to one side→ solving for x or y, Simplify separately → two expressions are equivalent and ask for a constant like r, a, or k |
| -given an absolute value equation | |a+x| = c and |a+x| = -c |
| Discriminant > 0 | two solutions |
| Discriminant < 0 | no real solutions |
| Discriminant = 0 | one solution |
| FOIL | first, outside, inside, last (a+b)(c+d) → a * c, a*d, b*c, b*d |
| If an equation is linear... | -both the x and y variable an exponent of 1 and that x and y are not multiplied together -it can be written as a line on a graph |
| given a function, f(x) and y are the same thing, so when asked to find when f(x) is 0 | find where the graph intersects the x-axis (AKA when y = 0) -also, these points are the roots, zeros, or solutions |