Gizmos for Alabama - Mathematics: Precalculus (Course of Study adopted 2016)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

N: : Number and Quantity

N-CN: : The Complex Number System

1.1.1: : Represent complex numbers and their operations on the complex plane.

N-CN.1: : Students will: Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

N-CN.2: : Students will: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

N-CN.3: : Students will: Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

N-VM: : Vector and Matrix Quantities

1.5.1: : Represent and model with vector quantities.

N-VM.5: : Students will: Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).

N-VM.6: : Students will: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

N-VM.7: : Students will: Solve problems involving velocity and other quantities that can be represented by vectors.

1.5.2: : Perform operations on vectors.

N-VM.8: : Students will: Add and subtract vectors.

N-VM.8.a: : Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

N-VM.8.b: : Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

N-VM.8.c: : Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

N-VM.9: : Students will: Multiply a vector by a scalar.

N-VM.9.a: : Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as ??(???, ?? subscript ??) = (?????, ???? subscript ??).

N-VM.9.b: : Compute the magnitude of a scalar multiple ???? using ||????|| = |??|??. Compute the direction of ???? knowing that when |??|?? ? 0, the direction of ???? is either along ?? (for ?? > 0) or against ?? (for ??

1.5.3: : Perform operations on matrices and use matrices in applications.

N-VM.11: : Students will: Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

A: : Algebra

A-APR: : Arithmetic with Polynomials and Rational Expressions

2.2.1: : Use polynomial identities to solve problems.

A-APR.13: : Students will: Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined, for example, by Pascal’s Triangle.

A-REI: : Reasoning with Equations and Inequalities

2.3.1: : Solve systems of equations.

A-REI.14: : Students will: Represent a system of linear equations as a single matrix equation in a vector variable.

A-CS: : Conic Sections

2.4.1: : Understand the graphs and equations of conic sections.

A-CS.15: : Students will: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from second-degree equations.

A-CS.15.a: : Formulate equations of conic sections from their determining characteristics.

F: : Functions

F-IF: : Interpreting Functions

3.1.1: : Interpret functions that arise in applications in terms of the context.

F-IF.16: : Students will: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

F-IF.17: : Students will: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

3.1.2: : Analyze functions using different representations.

F-IF.18: : Students will: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F-IF.18.a: : Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

F-IF.18.b: : Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

F-IF.18.c: : Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

F-IF.18.d: : Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

F-BF: : Building Functions

3.2.1: : Build a function that models a relationship between two quantities.

F-BF.19: : Students will: Compose functions.

3.2.2: : Build new functions from existing functions.

F-BF.20: : Students will: Determine the inverse of a function and a relation.

F-BF.21: : Students will: Verify by composition that one function is the inverse of another.

F-BF.22: : Students will: Read values of an inverse function from a graph or a table, given that the function has an inverse.

F-BF.23: : Students will: Produce an invertible function from a non-invertible function by restricting the domain.

F-BF.24: : Students will: Understand the inverse relationship between exponents and logarithms, and use this relationship to solve problems involving logarithms and exponents.

F-BF.25: : Students will: Compare effects of parameter changes on graphs of transcendental functions.

F-TF: : Trigonometric Functions

3.3.1: : Recognize attributes of trigonometric functions and solve problems involving trigonometry.

F-TF.26: : Students will: Determine the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses.

F-TF.27: : Students will: Use the sum, difference, and half-angle identities to find the exact value of a trigonometric function.

F-TF.28: : Students will: Utilize parametric equations by graphing and by converting to rectangular form.

F-TF.28.b: : Solve applied problems that include sequences with recurrence relations.

3.3.2: : Extend the domain of trigonometric functions using the unit circle.

F-TF.29: : Students will: Use special triangles to determine geometrically the values of sine, cosine, and tangent for pi/3, pi/4, and pi/6, and use the unit circle to express the values of sine, cosine, and tangent for pi – x, pi + x, and 2pi – x in terms of their values for x, where x is any real number.

F-TF.30: : Students will: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

3.3.4: : Prove and apply trigonometric identities.

F-TF.33: : Students will: Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1, and use it to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the angle.

F-TF.34: : Students will: Prove the addition and subtraction formulas for sine, cosine, and tangent, and use them to solve problems.

G: : Geometry

G-GPE: : Expressing Geometric Properties with Equations

4.2.1: : Translate between the geometric description and the equation for a conic section.

G-GPE.36: : Students will: Derive the equation of a parabola given a focus and directrix.

G-GPE.37: : Students will: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

4.2.2: : Explain volume formulas and use them to solve problems.

G-GPE.38: : Students will: Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.

S: : Statistics and Probability

S-ID: : Interpreting Categorical and Quantitative Data

5.1.1: : Summarize, represent, and interpret data on a single count or measurement variable.

S-ID.39: : Students will: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

S-ID.40: : Students will: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

S-ID.41: : Students will: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

5.1.2: : Interpret linear models.

S-ID.42: : Students will: Compute (using technology) and interpret the correlation coefficient of a linear fit.

S-ID.43: : Students will: Distinguish between correlation and causation.

S-IC: : Making Inferences and Justifying Conclusions

5.2.1: : Understand and evaluate random processes underlying statistical experiments.

S-IC.44: : Students will: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

S-IC.45: : Students will: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.

5.2.2: : Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

S-IC.46: : Students will: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

S-IC.47: : Students will: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

S-IC.48: : Students will: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

S-IC.49: : Students will: Evaluate reports based on data.

S-MD: : Using Probability to Make Decisions

5.3.1: : Calculate expected values and use them to solve problems.

S-MD.50: : Students will: Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.

S-MD.51: : Students will: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

S-MD.52: : Students will: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.

S-MD.53: : Students will: Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.

5.3.2: : Use probability to evaluate outcomes of decisions.

S-MD.54: : Students will: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

S-MD.54.a: : Find the expected payoff for a game of chance.

S-MD.54.b: : Evaluate and compare strategies on the basis of expected values.

Correlation last revised: 9/16/2020

Alabama - Mathematics: Precalculus

Course of Study | Adopted: 2016

N: : Number and Quantity

A: : Algebra

F: : Functions

G: : Geometry

S: : Statistics and Probability