Unit 1: Review of Algebra PI A1 Use simple arithmetic to simplify or solve problems 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 PI A2 Solve linear equations including systems of linear equations 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 PI A3.1 Define the imaginary number and simplify complex numbers A3.1 Define the imaginary number and simplify complex numbers PI A3.2 Solve quadratic equations 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 PI A3.3 Use long division to simplify the division of polynomials A3.6 Use long division to simplify the division of polynomials Unit 2: Review of Functions PI A4.1 Determine the domain and range of various functions A4.1 Write intervals in interval notation A4.2 Find the domain and range of various functions PI A4.2 Perform operations on 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 PI A5.1 Graph and simplify rational expressions 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 PI A5.2 Use logarithms to simplify and solve exponential functions A5.5 Evaluate logarithmic functions A5.6 Use the Laws of Logarithms to simplify logarithmic expressions A5.7 Solve exponential equations Unit 3: Review of Trigonometry PI A6.1 Use right angle trigonometry to define the six trigonometric ratios A6.1 Relate angles measured in degrees to radians A6.2 Define and evaluate the six simple trigonometric ratios PI A6.2 Graph trigonometric functions and solve trigonometric equations A6.3 Graph the six simple trigonometric functions A6.4 Define and evaluate the inverse trigonometric functions A6.5 Solve trigonometric equations PI A6.3 Use the law of sines and cosines to solve application problems A6.6 Use the Laws of Sines and Cosines to solve application problems PI A7 Use trigonometric formulas to simplify trigonometric expressions 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 Unit 4: Conic Sections PI 8 Express the four conic sections algebraically 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 Unit 5: Introduction to Statistics PI S1 Differentiate among natural and sampling variability and identify variables S1.1 Differentiate between natural and sampling variability S1.2 Identify IVPPSS for given situations S1.3 Differentiate among types of variables PI S2.1 Use an exploratory data analysis to summarize a data set 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 PI S2.2 Identify and use the proper components within an EDA for a certain situation 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 Unit 6: Normal Distributions PI S3 Use normal distributions to describe sets of numbers 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 PI S4 Apply the properties of experimental design to carefully control a situation 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 PI S5 Use sampling distributions to investigate experimental situations #colspan 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 Unit 7: Introduction to Hypothesis Testing PI S6 Create and interpret confidence intervals for parameters 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 PI S7 Identify and use the general steps to completing a hypothesis test and recognize possible errors 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 PI S8 Differentiate among the common types of one sample hypothesis tests 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 Unit 8: Bivariate Data and Advanced Hypothesis Testing PI S9 Investigate bivariate data and calculate a bivariate EDA 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 PI S10 Differentiate among the common types of two sample hypothesis tests 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 PI S11 Evaluate the results of an Analysis of Variance and draw statistical conclusions 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 Unit 9: Elementary Probability PI S12.1 Use elementary probability and counting to solve simple problems of chance 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 PI S12.2 Use permutations and combinations to count complex situations 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 PI S12.3 Calcualte the mathematical expectation and odds of an event S12.6 Calculate the mathematical expectation of an event S12.7 Calculate the odds in favor of an event occurring Unit 10: Advanced Probability PI S13.1 Use conditional probability to solve advanced problems of chance 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 PI 13.2 Use the multiplication rule of probability to solve advanced problems of chance 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 PI S14.1 Use the binomial distribution to solve binomial variable problems 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 PI S14.2 Calculate the mean and variance of a probability distributions 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 PI S14.3 Use other probability distributions to solve more advanced problems of chance 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