**Which of these quantitative skills are needed for students in your major? **

- Definition of absolute value and absolute value functions.
- Graph of absolute value functions.
- Solve absolute value equations.
- Solve absolute value inequalities.

- Redefine a complex problem into a sequential set of parts that can be translated into the language of programming logic.

- Design, write, test, and debug computer programs.

- Graph parabolas, hyperbolas, and ellipses.
- Find vertices and foci for hyperbolas and ellipses and vertices and directrixes for parabolas.
- Use parabolas, hyperbolas, and ellipses to model tunnels, satellite dishes, and other objects.

- Represent bivariate quantitative data using a scatter plot and describe how the variables might be related.
- Compute and interpret a correlation coefficient given bivariate numerical data.
- Distinguish between correlation and causation and between conspiracy and coincidence.
- Critique graphical displays in the media.

- Summarize categorical data by constructing frequency tables and relative frequency tables.
- Display categorical data with bar graphs.
- Exploring two categorical variables by analyzing contingency tables.
- Critique graphical displays in the media.

- Distinguish between an observational study and a statistical experiment.
- Describe the purpose of random selection in an observational study and the purpose of random assignment in a statistical experiment.
- Understand the types of conclusions that can be drawn from an observational study and from an experiment.
- Describe a method for selecting a random sample from a population.

- Incorporate fundamental data management concepts such as data structures within computer programs.

- Summarize univariate data using an appropriate graphical display.
- Describe the shape of a distribution of numerical data and identify any outliers in the data set.
- Summarize univariate data using appropriate numerical summary measures.
- Interpret differences in shape, center and spread in the context of the data sets, accounting for possible extreme data points.
- When appropriate, use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages.
- Critique graphical displays in the media.

- Calculate derivatives using product, quotient, and chain rules.
- Solve related rates problems.
- Use derivatives to find maximum and minimum values.
- Use the tangent line to approximate functions.

- Definition of exponential functions.
- Use exponential functions to model growth and decay.
- Graph of exponential functions.
- Solving exponential equations.

- Explore essentials of creating a family/personal budget.
- Understand the difference between simple and compound interest and their effects on savings and expenditures.
- Explore saving and investment accounts.
- Explore loan payments, credit card accounts and mortgages.
- Explain debt and deficit
- Explain tax systems

- Calculate integrals using the idea of an antiderivative.
- Calculate integrals using u-substitution.
- Use integrals to represent area, net change, and other quantities approximated by a sum.

- Definition of linear functions.
- Slope-intercept form and point-slope form.
- Parallel and perpendicular lines.
- Piecewise functions.
- Solve linear equations.
- Solve linear inequalities.
- Interpret slope and intercept.
- Use linear functions to model relationships.
- Fit a line to data points that are perfectly linear.

- Construct a scatterplot of bivariate numerical data.
- Calculate a correlation coefficient.
- Calculate the least squares regression line of best fit.
- Interpret the slope and y-intercept (if appropriate) of the least squares regression line in context.

- Definition of logarithmic function.
- Properties of logarithm.
- Graph of logarithm functions.
- Solving logarithm equations.
- Using logarithm to solve exponential equations.

- Translate arguments into formal language and symbols
- Recognize and apply standard techniques of logical deduction.
- Recognize and avoid common logical fallacies.

- Use function notation, understand functions as processes, and interpret statements that use function notation in terms of a context.
- Construct graphs and tables that model changing quantities and interpret key features in terms of the quantities.
- Interpret the slope and the intercept of a linear model in the context of the data.
- Graph linear and exponential functions and identify critical points.
- Compute and interpret the correlation coefficient of a linear fit.
- Distinguish between situations that can be modeled with linear functions and those modeled with exponential functions.
- Use linear and exponential functions to model contextual situations such as costs and growth of savings accounts.

- Describe characteristics of a normal distribution and calculate and interpret a z-score using the mean and standard deviation of the normal distribution.
- Calculate areas under a normal curve and interpret these areas as probabilities in context.
- Approximate population percentages using a normal distribution.

- Convert between parametric and rectangular (x, y) equations.
- Graph parametric equations.

- Convert between polar and rectangular (x, y) equations.
- Graph polar equations.

- Definition of polynomial functions.
- Characteristics of polynomial functions: degree, zeros, multiplicity, turning points.
- Long division and/or synthetic division.
- Solve polynomial equations.
- Solve polynomial inequalities.

☐ Probability – Theory and Computation

- Define sample space and events.
- Distinguish between discrete and continuous random variables.
- Explain that a probability distribution describes the long-run behavior of a random variable.
- Calculate probabilities of unions, intersections and complements of events.
- Use permutations and combinations to compute probabilities of compound events and solve problems.
- Discuss the law of large numbers vs. law of averages myth.
- Estimate probabilities empirically and interpret probabilities and long-run relative frequencies.
- Distinguish between independent events and dependent events.
- Use data in two-way tables to calculate probabilities, including conditional probabilities.
- Calculate expected value.
- Calculate standard deviation of a discrete variable

☐ Probability – Reasoning and Interpretation

- Explain probability as a measure of the likelihood that an event will occur.
- Describe events as subsets of a sample space using characteristics of the outcomes, or as unions, intersections, or complements of other events.
- Interpret probabilities of the union and intersection of independent and dependent events.
- Interpret probabilities in context.
- Interpret expected value in context.
- Interpret conditional probabilities in cases such as the false positive paradox.
- Analyze risk in health situations and understand the difference between absolute changes in risk and relative changes in risk.
- Interpret expected payoff for a game of chance.

- Definition of quadratic functions
- Graph quadratic functions: vertex, intercepts, maximum or minimum
- Solve quadratic equations: factoring, quadratic formula, graphically.
- Solve quadratic inequalities.

- Understand the use of units, thinking of numbers as adjectives.
- Study multiple ways of comparing quantities including the use of indices, e. g. the consumer price index and its relationship to the changing value of the dollar.
- Investigate ways of finding exact and approximate areas and volumes of geometric and irregular shapes.
- Estimate quantities.
- Evaluate plausibility of numerical answers.

- Display time series data using a time series plot.
- Compute and interpret average rate of change from data, graphs, or function equations.
- Estimate and interpret instantaneous rate of change from data, graphs, or function equations.

- Definition of rational functions.
- Graph of rational functions (including asymptotes).
- Solve rational equations.
- Solving rational inequalities.

- Write and use functions that call themselves to perform calculations, solve problems, or process data.

☐ Statistical Inference – Theory and Computation

- Describe characteristics of the sampling distribution of a sample mean and of a sample proportion.
- Define and apply the central limit theorem for random samples.
- Calculate a confidence interval for a population mean given a random sample.
- Calculate a confidence interval for a population proportion.
- Calculate a confidence interval for the difference in two population means or two population proportions.
- Carry out a test of hypotheses about a population mean given a random sample.
- Carry out a test of hypotheses about a population proportion.
- Carry out a test of hypotheses about the difference in two population means or two population proportions.

☐ Statistical Inference – Interpretation

- Describe statistics as a process for making inferences about population parameters based on a random sample from that population.
- Explain the concept of sample-to-sample variability and describe how this understanding relates to statistical inference.
- Explain the meaning of margin of error and interpret margin of error in context.
- Explain the meaning of a confidence interval and interpret a confidence interval in context.
- Interpret a P-value in context and use a P-value to reach a conclusion in a hypothesis testing context.
- Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
- Evaluate reports or print media articles based on statistical data.

- Solving system of equations.
- Set up systems of equations to solve problems involving mixtures, travel, and work rates, and other contexts.

- Graph trigonometric functions (sine, cosine, tangent).
- Use sine and cosine functions to model periodic phenomena.
- Solve triangles based on partial information about angles and sides, in applied settings.
- Solve trigonometric equations.

University Operator: (919) 962-2211 | © 2022 The University of North Carolina at Chapel Hill |