The Ultimate Guide to SAT Math

Sample Size Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample. The BIGGER the sample size, the better the chance it will give ACCURATE results. Margin of Error Confidence interval, tells you how reliable your surveys are. The higher MOE, the more inaccurate the results are. The lower MOE, the more accurate the results are. A good rule is that if the difference between two numbers or percentages is smaller than the margin of error, you cannot conclude that one is greater or smaller than the other. Linear Equation Positive Correlation - Going Up Negative Correlation- Going Down Quadratic Equations To find the x coordinate (h) of the vertex (h, x) of any parabola or quadratic function, you can use the following formula: h = -b/2a THE DISCRIMINANT: (b^2-4ac) -if positive, equation has 2 distinct real solutions, if 0 then 1 real solution, if negative there are no solutions Cubic Equation A biology class at Central High School predicted that a local population of animals will double in size every 12 years. The population at the beginning of 2014 was estimated to be 50 animals. If P represents the population n years after 2014, then which of the following equations represents the class's model of the population over time? P = 50(2)x/12. The student first recognizes that a population that doubles in size over equal time periods is increasing at an exponential rate. An exponential growth model can be written in the form y equals a open parentheses 2 close parentheses to the power of x over b end exponent where a is the population at time 0, since 2 raised to the zeroth power is 1 and b is the doubling time, since when x equals 12 comma 2 is raised to the first power, and the population will be 2 to the power of 1 cross times a equals 2 a. From the way the variables were defined, the population at time n equals 0 is 50 and the doubling time is 12. The gas mileage for Peter's car is 21 miles per gallon when the car travels at an average speed of 50 miles per hour. The car's gas tank has 17 gallons of gas at the beginning of a trip. If Peter's car travels at an average speed of 50 miles per hour, which of the following functions f models the number of gallons of gas remaining in the tank t hours after the trip begins? f(t) = 17 - 50t/21. Don't forget that the speed, distance, and time formulas.