Properties of Real #s Commutative Associative Distributive Identity Inverse Zero Square Root Property If , then Quadratic Equations To solve: Factor: set equation to 0; factor; set each factor to 0; check Quadratic Formula: Completing the Square Factoring Look for GCF first!! GCF: Difference Of Perfect Squares: Trinomial: Polynomials Add – combine like Subtract – add the opposite Multiply- distribute Divide – divide each term Variation Direct Variation – x & y increase/decrease together Inverse Variation – as x increases, y decreases Solving Equations Distribute to get rid of parentheses. Combine like terms on the same side of the =. Get all variables on one side and the constants on the other. Divide or multiply to solve. Inequalities Solve like an equation. Graph on a # line (open circle <,>; closed circle ) Test critical points or put in calc. State Solution with and /or. ** reverse inequality when multiplying or dividing by a negative value Real Number System Exponents Absolute Value Equations Interval Notation (1,5] Use ( ) for < or >; [ ] for Pythagorean Theorem To find a missing side of a right triangle: Where c is the hypotenuse Solve System of Equations Substitution – solve one of the equation for x or y and sub into the other. Elimination/Addition – create opposites by mult equation and add equations Degree Monomial – sum of exponents Polynomial – highest exponent
Data Quantitative – dealing with #s Qualitative- dealing with descriptions Univariate – one variable; no relationships Bivariate – two variables; relationships; causes Causal – cause/effect relationship Population Data –all members of the group Sample Data – a subset of the group Shapes of Distributions Graphs Histograms – data grouped in intervals Dot Plots – shows all data Box & Whisker – data grouped in quartiles
Correlation Coefficient: indicates the strength of the relationship where -1 = perfect negative correlation; 1 = perfect positive correlation; 0 = no correlation More Statistics Measures of Central Tendency Mean = average (calc = ) Median= middle term Mode = most frequent Measures of Dispersion/Spread Range = maximum value – minimum value Interquartile Range – Quartile 3 – Quartile 1 Standard Deviation – how much variation from the mean STAT CALC 1VAR STATS σx Also = Variance – how far the data is spread out (standard deviation)2 Outliers – values that are far away from the rest of the data; affects mean; if outliers exist, it is best to use median Regressions STAT EDIT enter into list1 and list2 STAT CALC choose the correct regression 5 Statistical Summary Minimum, Q1, median, Q3, maximum Quartiles divide the data into 4 equal parts. Percentiles divide the data into 100 equal parts. Percentile Rank = Residuals -the difference between measured data and predicted data (actual – predicted) Contingency Table – a 2-way frequency table used to organize 2 categorical variables into 1 display Frequency – using the actual counts in each cell Cell – the intersection of 2 categories Relative frequency – using the percent instead of the count in each cell Marginal Totals – the totals for each row and column in a contingency Relative marginal distribution – the percent for each row and column Conditional relative distribution – the percent you get in each row or column just that row or column as the total (instead of the actual total) Perimeter – the sum of all the sides Area Triangle = Rectangle = Square = Parallelogram = Sequences Arithmetic – adding a common difference Explicit equation: Where is the first in the sequence And d is the common difference Equation Type: Linear Ex: {3,7,11,15,…} adding 4 Geometric – multiplying by a common Explicit equation: Where is the first element in the sequence And r is the common Equation Type: Exponential Ex: {9,27,81,…} multiplying by 3 Recursive –the next term is found using the previous term; the first term must be given as part of the definition of the function Ex: