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

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