Functions & Algebra | Data Analysis & Probability

The High School Assessments student's knowledge of Core Learning Goals at the indicator level. Some indicators have assessment limits which indicate more specifically what will be assessed. Assessment items and other instructional resources at the indicator level can be viewed in the CLG Toolkit.

## Goal 1 Functions and Algebra

The student will demonstrate the ability to investigate, interpret, and communicate solutions to mathematical and real-world problems using patterns, functions, and algebra.

Expectation

1.1 The student will analyze a wide variety of patterns and functional relationships using the language of mathematics and appropriate technology.

#### Indicators

1.1.1 The student will recognize, describe, and/or extend patterns and functional relationships that are expressed numerically, algebraically, and/or geometrically.

###### Assessment limits:
• The given pattern must represent a relationship of the form y = mx + b (linear), y = x2 + c (simple quadratic), y = x3 + c (simple cubic), simple arithmetic progression, or simple geometric progression with all exponents being positive.
• The student will not be asked to draw three-dimensional figures.
• Algebraic description of patterns is in indicator 1.1.2

1.1.2 The student will represent patterns and/or functional relationships in a table, as a graph, and/or by mathematical expression.

###### Assessment limits:
• The given pattern must represent a relationship of the form mx + b (linear), x2 (simple quadratic), simple arithmetic progression, or simple geometric progression with all exponents being positive.

1.1.3 The student will apply addition, subtraction, multiplication, and/or division of algebraic expressions to mathematical and real-world problems.

###### Assessment limits:
• The algebraic expression is a polynomial in one variable.
• The polynomial is not simplified.

1.1.4 The student will describe the graph of a non-linear function and discuss its appearance in terms of the basic concepts of maxima and minima, zeros (roots), rate of change, domain and range, and continuity.

###### Assessment limits:
• A coordinate graph will be given with easily read coordinates.
• “Zeros” refers to the x-intercepts of a graph, “roots” refers to the solution of an equation in the form p(x) = 0.
• Problems will not involve a real-world context.
Expectation

1.2 The student will model and interpret real-world situations using the language of mathematics and appropriate technology.

#### Indicators

1.2.1 The student will determine the equation for a line, solve linear equations, and/or describe the solutions using numbers, symbols, and/or graphs.

###### Assessment limits:
• Functions are to have no more than two variables with rational coefficients.
• Linear equations will be given in the form: Ax + By = C, Ax + By + C = 0, or y = mx + b.
• Vertical lines are included.
• The majority of these items should be in real-world context.

1.2.2 The student will solve linear inequalities and describe the solutions using numbers, symbols, and/or graphs.

###### Assessment limits:
• Inequalities will have no more than two variables with rational coefficients.
• Acceptable forms of the problem or solution are the following:
Ax + By < C, Ax + By < C, Ax + By > C, Ax + By > C, Ax + By + C < 0, Ax + By + C < 0, Ax + By + C > 0, Ax + By + C > 0, y < mx + b, y < mx + b, y > mx + b, y > mx + b, y < b, y < b, y > b, y > b, x < b, x < b, x > b, x > b, a < x < b, a < x < b, a < x < b, a < x < b, a < x + c < b, a < x + c < b, a < x + c < b, a < x + c < b.
• The majority of these items should be in real-world context.
• Systems of linear inequalities will not be included.
• Compound inequalities will be included.
• Disjoint inequalities will not be included.
• Absolute value inequalities will not be included.

1.2.3 The student will solve and describe using numbers, symbols, and/or graphs if and where two straight lines intersect.

###### Assessment limits:
• Functions will be of the form: Ax + By = C, Ax + By + C = 0, or y = mx + b.
• All coefficients will be rational.
• Vertical lines will be included.
• Systems of linear functions will include coincident, parallel, or intersecting lines.
• The majority of these items should be in real-world context.

1.2.4 The student will describe how the graphical model of a non-linear function represents a given problem and will estimate the solution.

###### Assessment limits:
• The problem is to be in a real-world context.
• The function will be represented by a graph.
• The equation of the function may be given.
• The features of the graph may include maxima/minima, zeros (roots), rate of change over a given interval (increasing/decreasing), continuity, or domain and range.
• “Zeros” refers to the x-intercepts of a graph, “roots” refers to the solution of an equation in the form p(x) = 0.
• Functions may include step, absolute value, or piece-wise functions.

1.2.5 The student will apply formulas and/or use matrices (arrays of numbers) to solve real-world problems.

###### Assessment limits:
• Formulas will be provided in the problem or on the reference sheet.
• Formulas may express linear or non-linear relationships.
• The students will be expected to solve for first degree variables only.
• Matrices will represent data in tables.
• Matrix addition, subtraction, and/or scalar multiplication may be necessary.
• Inverse and determinants of matrices will not be required.
Date: 8/2004