Arkansas

$Arkansas flag$

Skills available for Arkansas high school math standards

Standards are in black and IXL math skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practice that skill.

Show alignments for:

Arkansas Curriculum Framework: Advanced Topics and Modeling in Mathematics Arkansas Curriculum Framework: Advanced Topics and Modeling in Mathematics
Arkansas Curriculum Framework: Algebra I Arkansas Curriculum Framework: Algebra I
Arkansas Curriculum Framework: Algebra I Part A Arkansas Curriculum Framework: Algebra I Part A
Arkansas Curriculum Framework: Algebra I Part B Arkansas Curriculum Framework: Algebra I Part B
Arkansas Curriculum Framework: Algebra II/Advanced Algebra Arkansas Curriculum Framework: Algebra II/Advanced Algebra
Arkansas Curriculum Framework: Algebra III Arkansas Curriculum Framework: Algebra III
Arkansas Curriculum Framework: Bridge to Algebra II Arkansas Curriculum Framework: Bridge to Algebra II
Arkansas Curriculum Framework: Calculus Arkansas Curriculum Framework: Calculus
Arkansas Curriculum Framework: Computer Science and Mathematics Arkansas Curriculum Framework: Computer Science and Mathematics
Arkansas Curriculum Framework: Geometry Arkansas Curriculum Framework: Geometry
Arkansas Curriculum Framework: Geometry A Arkansas Curriculum Framework: Geometry A
Arkansas Curriculum Framework: Geometry B Arkansas Curriculum Framework: Geometry B
Arkansas Curriculum Framework: Mathematical Applications and Algorithms Arkansas Curriculum Framework: Mathematical Applications and Algorithms
Arkansas Curriculum Framework: Precalculus Arkansas Curriculum Framework: Precalculus
Arkansas Curriculum Framework: Statistics Arkansas Curriculum Framework: Statistics

Actions

Print standards

F Functions

F.1.ATMM Students will analyze and interpret functions using different representations in terms of an authentic contextual application
- F.1.ATMM.1 Interpret key features of graphs and tables in terms of two quantities for functions beyond the level of quadratic that model a relationship between the quantities.
- F.1.ATMM.2 Graph functions expressed symbolically and show key features of the graph using technology.
- F.1.ATMM.3 Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
  - Graph an absolute value function (A2-D.13)
- F.1.ATMM.4 Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior.
  - Graph a quadratic function (PC-C.3)
  - Match polynomials and graphs (PC-D.11)
- F.1.ATMM.5 Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available and showing end behavior.
  - Rational functions: asymptotes and excluded values (PC-E.1)
- F.1.ATMM.6 Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
- F.1.ATMM.7 Interpret the parameters of functions beyond the level of linear and quadratic in terms of a context.
F.2.ATMM Students will construct and compare various types of functions and build models to represent and solve problems
- F.2.ATMM.1 Model equations in two or more variables to represent relationships between quantities for functions beyond the level of linear and quadratic.
- F.2.ATMM.2 Represent constraints or inequalities using systems of equations and/or inequalities; interpret solutions as viable or non-viable options in a modeling context for functions beyond the level of linear and quadratic.
- F.2.ATMM.3 Compose functions (e.g., If T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time).
  - Composition of linear functions: find a value (A2-P.4)
  - Composition of functions (PC-A.11)
- F.2.ATMM.4 Write arithmetic and geometric sequences both recursively and with an explicit formula; use the sequences to model situations and translate between the two forms.
- F.2.ATMM.5 Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
  - Inverses of trigonometric functions (PC-M.9)
- F.2.ATMM.6 Use inverse functions to solve trigonometric equations that arise in modeling context; evaluate the solutions using technology and interpret them in terms of the context.
  - Solve trigonometric equations I (A2-Z.14)
  - Solve trigonometric equations II (A2-Z.15)

V Vectors

V.3.ATMM Students will represent and model vector quantities and perform operations on vectors
- V.3.ATMM.1 Recognize vector quantities as having both magnitude and direction; represent vector quantities by directed line segments and use appropriate symbols for vector and their magnitudes (e.g., v, |v|, ||v||, v)
- V.3.ATMM.2 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
- V.3.ATMM.3 Solve problems involving velocity and other quantities that can be represented by vectors.
- V.3.ATMM.4 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 magnitudes.
- V.3.ATMM.5 Determine the magnitude and direction of the sum of two given vectors in magnitude and direction form.
  - Find the magnitude and direction of a vector sum (PC-U.9)
- V.3.ATMM.6 Understand vector subtraction; v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w pointing in the opposite direction; represent vector subtraction graphically by connecting the tips in the appropriate order and perform vector subtraction component-wise.
  - Subtract vectors (PC-U.8)
  - Add and subtract three-dimensional vectors (PC-V.3)
- V.3.ATMM.7 Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise [e.g., as c(v_x, v subscript y) = (cv_x, cv subscript y)]
  - Multiply a vector by a scalar (PC-U.10)
  - Scalar multiples of three-dimensional vectors (PC-V.4)
- V.3.ATMM.8 Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v; compute the direction of cv knowing that when the |c|v ≠ 0, the direction cv is either along v (for c > 0) or against v(c < 0).
  - Find the magnitude of a vector scalar multiple (PC-U.11)
  - Determine the direction of a vector scalar multiple (PC-U.12)

MO Matrix Operations

MO.4.ATMM Students will perform operations on matrices and use matrices in applications
- MO.4.ATMM.1 Use matrices to represent and manipulate data (e.g., to represent payoffs or incidence relationships in a network).
- MO.4.ATMM.2 Multiply matrices by scalars to produce new matrices (e.g., all the payoffs in a game are doubled).
  - Multiply a matrix by a scalar (PC-L.4)
- MO.4.ATMM.3 Add, subtract, and multiply matrices of appropriate dimensions.
- MO.4.ATMM.4 Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
  - Matrix operation rules (PC-L.2)
  - Properties of matrices (PC-L.8)
- MO.4.ATMM.5 Understand that zero and identity matrices play a role in matrix addition and multiplication similar to 0 and 1 in real numbers; the determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
- MO.4.ATMM.6 Represent a system of linear equations as a single matrix equation in a vector variable.
- MO.4.ATMM.7 Find the inverse of a matrix if it exists, and use it to solve systems of linear equations; utilize technology to find the inverse of matrices with dimensions of 3 x 3 or greater.

PS Probability and Statistics

PS.5.ATMM Students will interpret linear models, calculate expected values to solve problems, and use probability to evaluate outcomes of decisions
- PS.5.ATMM.1 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.
  - Write a discrete probability distribution (PC-Y.2)
  - Graph a discrete probability distribution (PC-Y.3)
- PS.5.ATMM.2 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
  - Expected values of random variables (PC-Y.4)
- PS.5.ATMM.3 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value (e.g., find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices; find the expected grade under various grading schemes).
  - Write the probability distribution for a game of chance (PC-Y.7)
  - Expected values for a game of chance (PC-Y.8)
- PS.5.ATMM.4 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value (e.g., find a current data distribution on the number of TV sets per household in the United States and calculate the expected number of sets per household; how many TV sets would you expect to find in 100 randomly selected households?).
- PS.5.ATMM.5 Find the expected payoff for a game of chance (e.g., find the expected winnings from a state lottery or a game at a fast-food restaurant).
  - Expected values for a game of chance (PC-Y.8)
- PS.5.ATMM.6 Evaluate and compare strategies on the basis of expected values (e.g., compare a high-deductible versus a low-deductible automobile insurance policy using various but reasonable chances of having a minor or major accident).
  - Choose the better bet (PC-Y.9)

Arkansas

Show alignments for:

Actions

F Functions

F.1.ATMM Students will analyze and interpret functions using different representations in terms of an authentic contextual application

F.1.ATMM.1 Interpret key features of graphs and tables in terms of two quantities for functions beyond the level of quadratic that model a relationship between the quantities.

F.1.ATMM.2 Graph functions expressed symbolically and show key features of the graph using technology.

F.1.ATMM.3 Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

F.1.ATMM.4 Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior.

F.1.ATMM.5 Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available and showing end behavior.

F.1.ATMM.6 Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

F.1.ATMM.7 Interpret the parameters of functions beyond the level of linear and quadratic in terms of a context.

F.2.ATMM Students will construct and compare various types of functions and build models to represent and solve problems

F.2.ATMM.1 Model equations in two or more variables to represent relationships between quantities for functions beyond the level of linear and quadratic.

F.2.ATMM.2 Represent constraints or inequalities using systems of equations and/or inequalities; interpret solutions as viable or non-viable options in a modeling context for functions beyond the level of linear and quadratic.

F.2.ATMM.3 Compose functions (e.g., If T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time).

F.2.ATMM.4 Write arithmetic and geometric sequences both recursively and with an explicit formula; use the sequences to model situations and translate between the two forms.

F.2.ATMM.5 Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

F.2.ATMM.6 Use inverse functions to solve trigonometric equations that arise in modeling context; evaluate the solutions using technology and interpret them in terms of the context.

V Vectors

V.3.ATMM Students will represent and model vector quantities and perform operations on vectors

V.3.ATMM.1 Recognize vector quantities as having both magnitude and direction; represent vector quantities by directed line segments and use appropriate symbols for vector and their magnitudes (e.g., v, |v|, ||v||, v)

V.3.ATMM.2 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

V.3.ATMM.3 Solve problems involving velocity and other quantities that can be represented by vectors.

V.3.ATMM.4 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 magnitudes.

V.3.ATMM.5 Determine the magnitude and direction of the sum of two given vectors in magnitude and direction form.

V.3.ATMM.7 Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise [e.g., as c(vx, v subscript y) = (cvx, cv subscript y)]

V.3.ATMM.8 Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v; compute the direction of cv knowing that when the |c|v ≠ 0, the direction cv is either along v (for c > 0) or against v(c < 0).

MO Matrix Operations

MO.4.ATMM Students will perform operations on matrices and use matrices in applications

MO.4.ATMM.1 Use matrices to represent and manipulate data (e.g., to represent payoffs or incidence relationships in a network).

MO.4.ATMM.2 Multiply matrices by scalars to produce new matrices (e.g., all the payoffs in a game are doubled).

MO.4.ATMM.3 Add, subtract, and multiply matrices of appropriate dimensions.

MO.4.ATMM.4 Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.

MO.4.ATMM.5 Understand that zero and identity matrices play a role in matrix addition and multiplication similar to 0 and 1 in real numbers; the determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

MO.4.ATMM.6 Represent a system of linear equations as a single matrix equation in a vector variable.

MO.4.ATMM.7 Find the inverse of a matrix if it exists, and use it to solve systems of linear equations; utilize technology to find the inverse of matrices with dimensions of 3 x 3 or greater.

PS Probability and Statistics

PS.5.ATMM Students will interpret linear models, calculate expected values to solve problems, and use probability to evaluate outcomes of decisions

PS.5.ATMM.1 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.

PS.5.ATMM.2 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

PS.5.ATMM.5 Find the expected payoff for a game of chance (e.g., find the expected winnings from a state lottery or a game at a fast-food restaurant).

PS.5.ATMM.6 Evaluate and compare strategies on the basis of expected values (e.g., compare a high-deductible versus a low-deductible automobile insurance policy using various but reasonable chances of having a minor or major accident).

V.3.ATMM.7 Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise [e.g., as c(v_x, v subscript y) = (cv_x, cv subscript y)]