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 |