| 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 |