Gizmos for Arkansas - Mathematics: Pre-Calculus (Academic Standards adopted 2023)

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

PC.VM: : Vectors & Matrices

1.1: : Vector Quantities

1.1.1: : Students recognize, model, and write vector quantities.

PC.VM.1: : Recognize that vector quantities have both magnitude and direction and can be represented by directed line segments.

PC.VM.2: : Write vector quantities using appropriate symbols indicating magnitude and direction.

1.2: : Vector Operations

1.2.1: : Students perform operations involving vectors.

PC.VM.3: : Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

PC.VM.4: : Solve problems involving velocity and other quantities that can be represented by vectors.

PC.VM.5: : Add and subtract vectors graphically and algebraically.

1.3: : Matrix Operations

1.3.1: : Students represent and perform operations with matrices.

PC.VM.9: : Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

PC.VM.10: : Work with 2 x 2 matrices as transformations of the plane; interpret the absolute value of the determinant in terms of area.

PC.TR: : Trigonometry

2.1: : Radians

2.1.1: : Students understand, explain, and describe radian measure.

PC.TR.1: : Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

PC.TR.2: : Convert between radian and degree measure.

PC.TR.3: : Explain how the unit circle can be used to model sine, cosine, tangent, secant, cosecant, and cotangent for all real numbers.

2.2: : Unit Circle

2.2.1: : Students use the unit circle to express and find exact values for trigonometric functions.

PC.TR.4: : Construct special right triangles on the unit circle to find the exact values of sine, cosine, tangent for pi/3, pi/4, pi/6, and pi/2.

PC.TR.5: : 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 exact values for x, where x is one of these values: pi/3, pi/4, pi/6, and pi/2.

2.3: : Identities, Formulas, & Laws

2.3.1: : Students develop and apply identities, formulas, and laws using trigonometry.

PC.TR.6: : Develop the Pythagorean identity, sin²(theta) + cos²(theta) = 1.

PC.TR.7: : Apply the Pythagorean identity to find the remaining trigonometric functions when given sin(theta), cos(theata), or tan(theta) and the quadrant of the angle.

PC.TR.8: : Develop addition, subtraction, double, and half-angle formulas for sine, cosine, and tangent and use them to solve problems, including verifying other identities.

2.4: : Solve & Graph

2.4.1: : Students explore, solve, and sketch the graphs of periodic trigonometric functions.

PC.TR.12: : Explain whether a trigonometric function is even or odd and recognize the periodicity of the graph using the unit circle.

PC.TR.13: : Graph trigonometric and inverse trigonometric functions and show period, midline, and amplitude.

PC.TR.14: : Select a trigonometric function that models real-world contexts.

PC.CS: : Conic Sections

3.1: : Derive Equations

3.1.1: : Students derive equations for conic sections.

PC.CS.1: : Derive the general form of the equation of a circle using the Distance Formula or Pythagorean Theorem.

PC.CS.2: : Derive the equation of a parabola given a focus and directrix.

PC.CS.3: : Derive the equations of ellipses and hyperbolas given the foci using the Distance Formula.

3.2: : Explore Equations

3.2.1: : Students identify, analyze, and sketch the graphs of the conic sections and relate their equations and graphs.

PC.CS.5: : Generate an equivalent form of an equation for a conic section by completing the square to identify key characteristics.

PC.CS.6: : Identify, graph, write, and analyze equations of each type of conic section using properties and technology when appropriate.

PC.FN: : Functions

4.1: : Solve Problems

4.1.1: : Students derive and apply functions.

PC.FN.1: : Understand that sequences are functions, sometimes defined recursively, whose domains are a subset of the integers.

PC.FN.3: : Apply the Binomial Theorem for the expansion of (a + b)^n in powers of a and b for a positive integer n, where a and b are any number.

PC.FN.4: : Build functions to model real-world contexts using algebraic operations on functions and composition, with and without appropriate technology.

4.2: : Explore Graphing

4.2.1: : Students graph and interpret functions.

PC.FN.5: : Graph power and polynomial functions, identify zeros (when suitable factorizations are available), and show end behavior.

PC.FN.6: : Graph rational functions, identify zeros, holes and asymptotes (when suitable factorizations are available), and show end behavior.

PC.FN.7: : Graph exponential and logarithmic functions; show intercepts and end behavior.

Correlation last revised: 10/8/2025

Arkansas - Mathematics: Pre-Calculus

Academic Standards | Adopted: 2023

PC.VM: : Vectors & Matrices

PC.TR: : Trigonometry

PC.CS: : Conic Sections

PC.FN: : Functions