# Pre-Calculus Standards

 A1.1 Add, subtract, multiply, and divide fractions with unlike denominators A1.2 Write large and small numbers in scientific notation and expand numbers written in scientific notation A1.3 Apply the order of operations to solve mathematical expressions A2.1 Write the equation of a line through two points, as well as lines parallel or perpendicular to a given line A2.2 Graph and solve linear equations A2.3 Solve systems of linear equations using graphing, substitution, and elimination A3.1 Define the imaginary number and simplify complex numbers A3.2 Solve quadratic equations using graphing, factoring, and the quadratic equation A3.3 Complete the square for a quadratic equation to determine the vertex of a parabola A3.4 Solve complicated quadratic equations A3.5 Factor polynomial functions A3.6 Use long division to simplify the division of polynomials A4.1 Write intervals in interval notation A4.2 Find the domain and range of various functions A4.3 Evaluate and simplify composite functions A4.4 Determine whether a function is even or odd A4.5 Find the inverse of a function, if it exists A5.1 Graph exponential functions A5.2 Rationalize the denominator of algebraic expressions A5.3 Simplify rational expressions A5.4 Find the zeroes of exponential functions A5.5 Evaluate logarithmic functions A5.6 Use the Laws of Logarithms to simplify logarithmic expressions A5.7 Solve exponential equations A6.1 Relate angles measured in degrees to radians A6.2 Define and evaluate the six simple trigonometric ratios A6.3 Graph the six simple trigonometric functions A6.4 Define and evaluate the inverse trigonometric functions A6.5 Solve trigonometric equations A6.6 Use the Laws of Sines and Cosines to solve application problems A7.1 Use the trigonometric addition formulas to simplify algebraic expressions A7.2 Use the trigonometric double and half angle identities to simplify algebraic expressions A7.3 Use various trigonometric identities to simplify algebraic expressions A8.1 Define the equation of a parabola given a focus and a directrix A8.2 Define the equations of the conic sections ellipse, hyperbola, and circle A8.3 Relate the graphs to the equations of the conic sections S1.1 Differentiate between natural and sampling variability S1.2 Identify IVPPSS for given situations S1.3 Differentiate among types of variables S2.1 Identify the parts of an EDA S2.2 Use various graphical tools to describe the shape of a distribution S2.3 Describe the center of a distribution using a variety of descriptors S2.4 Describe the dispersion of the data using range, IQR, variance, and standard deviation S2.5 Identify probable outliers in a sample S2.6 Identify correct situations to use mean vs. median and IQR vs. standard deviation S2.7 Compute the variance and standard deviation for a sample S2.8 Construct and interpret a boxplot for a sample S2.9 Construct and interpret a frequency table S3.1 Identify and describe the properties of a normal distribution S3.2 Standardize a variable into a test statistic using the mean and standard deviation S3.3 Find the area under a standard normal distribution between given values S3.4 Find the value of a measurement from a test statistic, mean, and standard deviation S4.1 Define and identify the important parts of experimental design S4.2 Define and identify the three basic principles of experimental design S4.3 Identify and differentiate among voluntary response, convenience, probability-based, and simple random sampling techniques S4.4 Use a random number table to conduct a simple random sample S5.1 Define a sampling distribution and compare it to a sample distribution S5.2 Define standard error and compare it to standard deviation S5.3 Differentiate between statistical accuracy and statistical precision S5.4 Define the central limit theorem and list its assumptions S6.1 Define confidence interval in terms of a parameter of interest and margin of error S6.2 Compute various confidence intervals using a Z test statistic S6.3 Interpret various confidence intervals using the Z test statistic S7.1 List the general steps to completing a statistical hypothesis test S7.2 Compare and contrast a null hypothesis with an alternative hypothesis S7.3 Relate alpha and beta to Type I and Type II errors S7.4 Define statistical power, relate it to beta, and identify ways to increase it in a hypothesis test S8.1 Identify the characteristics of a 1-sample Z test and apply it to solve a problem S8.2 Identify the characteristics of a t-distribution and differentiate it from a z-distribution S8.3 Identify the characteristics of a 1-sample t-test and apply it to solve a problem S8.4 Identify the characteristics of a 1-sample comparison of proportions test and apply it to solve a problem S9.1 Classify the association of bivariate data and graph using a scatterplot S9.2 Calculate the correlation coefficient of a set of bivariate data S9.3 Calculate the equation for the line of best fit for bivariate data S9.4 Define residual and calculate residuals for set of data S9.5 Calculate the coefficient of determination for a set of data S9.6 Identify the assumptions needed to calculate a least-squares linear regression (line of best fit) S10.1 Identify the characteristics of a 2-sample t-test and apply it to solve a problem S10.2 Identify the characteristics of a matched-pairs t-test and apply it to solve a problem S10.3 Identify the characteristics of a 2-sample comparison of proportions test and apply it to solve a problem S10.4 Identify the characteristics of a chi-squared test and apply it to solve a problem S11.1 Identify the characteristics of a 1-way ANOVA and apply it to solve a problem S11.2 Differentiate among the types of dependency that must be avoided to use an ANOVA S12.1 Define probability and calculate simple probability S12.2 Draw tree diagrams to solve counting problems S12.3 Use the counting rule to solve elementary probability problems S12.4 Calculate the number of possible permutations of a set of numbers S12.5 Calculate the number of possible combinations of a set of numbers S12.6 Calculate the mathematical expectation of an event S12.7 Calculate the odds in favor of an event occurring S13.1 Define mutually exclusive and identify events that are mutually exclusive S13.2 Use the addition rule of probability to solve problems S13.3 Define conditional probability and use it to solve problems S13.4 Use the multiplication rule of probability in coordination with conditional probability to solve problems S13.5 Use Bayes’ Formula to compute the probability of multiple interrelated events S14.1 Define discrete random variable and contrast it with a continuous random variable S14.2 Identify binomial variables and use the binomial distribution formula to determine probability S14.3 Calculate the mean of a random variable for a given probability distribution S14.4 Calculate the variance of a random variable for a given probability distribution S14.5 Calculate the mean of the binomial distribution S14.6 Calculate the variance and/or standard deviation of the binomial distribution S14.7 Use the Poisson probability distribution to calculate the probability for a situation S14.8 Use the Hypergeometric probability distribution to calculate the probability for a situation P1 Create a statistical model to predict future events (NCAA Tournament Model) P2 Effectively communicate through a reflection paper lessons learned through the development of the statistical model P3 Compare and contrast the community of Boyceville with the community represented in the movie Stand and Deliver. SS1 Use technology to calculate the standard deviation of a sample SS2 Use technology to calculate the summary statistics for a sample SS3 Use technology to calculate the correlation coefficient of a set of bivariate data SS4 Use technology to calculate the equation for the line of best fit for bivariate data SS5 Use technology to calculate the coefficient of determination for a set of data