Ms. Powell's Math

CRCT REVIEW

Click Below for "Things to Remeber" for each Unit

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Unit 7 - Systems

Unit Concepts:

Given a problem in context, write an appropriate system of linear equations or inequalities.
Solve systems of equations graphically and algebraically, using technology as appropriate.
Graph the solution set of a system of linear inequalities in two variables.
Interpret solutions in problem contexts.

Word Wall Defined:

Coefficients: a numerical factor in a term of an algebraic expression.

Intersecting Lines: lines that have one point in common or all points in common.

Linear Combination Method: a technique for solving a system of equations that involves combining two equations in order to eliminate one of the variables and solving for the remaining variable. Adding, subtracting, or multiplying a system of equations to help solve the system.

Substitution Method: a technique for solving a system of equations that involves replacing one variable with an equivalent expression and solving for the remaining variable.

System of Linear Equations: two or more equations that together define a relationship between variables usually in a problem situation. A system of equations can have no solution, one solution, or many solutions.

System of Inequalities: two or more inequalities that together define a relationship between variables usually in a problem situation. A system of inequalities can have no solution or multiple solutions

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Unit 6 - Traversing Congruency

Concepts for the Unit:

· Parallel lines have the same slope and perpendicular lines have opposite, reciprocal slopes.

· When two lines intersect, vertical angles are congruent and adjacent angles are supplementary.

· When parallel lines are cut by a transversal, corresponding, alternate interior and alternate exterior angles and congruent.

· The length of segments formed by two non-parallel transversals cutting parallel line is proportional to the distances of the parallel lines from the intersection of the transversal.

· Parallel lines can be constructed using the properties of parallel lines cut by a transversal.

Download Unit 6 Word Wall

Word Wall Defined:

Adjacent angles- angles in the same plane that have a common vertex and a common side, but no common interior points.
Alternate exterior angles- pairs of angles formed when a third line (transversal) crosses 2 lines. These angles are on opposite sides of the transversal and are outside the 2 lines.
Alternate interior angles- pairs of angles formed when a third line (transversal) crosses 2 lines. These angles are on opposite sides of the transversal and are inside the 2 lines.
Coincidental- two equivalent linear equations overlap when graphed.
Complimentary angles- Two angles whose sum is 90 degrees.
Congruent- having the same size, shape and measure. Two figures are congruent if all of their corresponding measures are equal.
Equiangular- The property of a polygon whose angles are all congruent.
Equilateral- the property of a polygon whose sides are all congruent.
Intersecting lines- Two lines in a plane that cross each other. Unless two lines are coincidental, parallel or skew, they will intersect at one point.
Linear pair- adjacent, supplementary angles. Excluding their common side, a linear pair forms a straight line.

Opposite Reciprocals- reciprocals are 2 numbers that have a product of 1; opposites are positive and negative
Parallel lines- two lines that lie in the same plane and do not intersect.
Perpendicular lines- two lines that intersect at a right angle.
Reflection line- a line that is the perpendicular bisector of the segment with endpoints at a pre-image point and the image of that point after reflection.
Regular polygon- a polygon that is both equilateral and equiangular.
Same-side exterior angles (Consecutive interior)- pairs of angles formed when a transversal crosses 2 lines. These angles are on the same side of the transversal and outside the 2 lines. The angles are supplementary.
Same-side interior angles- pairs of angles formed when a transversal crosses 2 lines. These angles are on the same side of the transversal and inside the 2 lines. The angles are supplementary.
Skew lines- two lines that do not lie in the same plane (cannot be parallel or intersect).
Supplementary angles- two angles whose sum is 180 degrees.
Transversal- a line that crosses two or more lines.
Vertical angles- two nonadjacent angles formed by interesting lines or segments.

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Unit 5 - Slippery Slope

Concepts for the Unit:

· Interpret slope as rate of change.

· Determine the meaning of slope and y-intercept in a given situation.

· Graph equations in the form of y = mx + b and Ax+By=C.

· Graph the solution set of a linear inequality, identifying whether the solution set is an open or closed half plane.

· Determine the equation of a line given a graph, numerical information that defines the line or a context involving a linear relationship.

· Solve problems involving linear relationships by gathering the data, graphing the data as a scatter plot, determining line of best fit, writing its equation, and interpreting the solution of the equation in the context of the original problem.

Download Unit 5 Word Wall

Word Wall Defined:

Constant Function: horizontal line (y=#)

Line of best fit: the line that best represents the trend established by the points in a particular scatter plot.

Linear Inequality: an inequality in two variables for which the graph of the solutions form a half-plane on one side of a line and may or may not include the line itself.

Rate of change (slope): a ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable.

Slope: the steepness of a line represented by the variable m, which may be calculated by finding the ratio of the difference between the y values of two points in the line to the difference between the corresponding x values of those two points.

Slope-intercept form: one way to write an equation of a line; uses the form y= mx+b, where m is the slope and b is the y-intercept.

Standard Form: a linear equation in the form Ax + By = C, where A, B, and C are constants.

Y-intercept: the y coordinate of a point where a graph crosses the y-axis. The y-intercept is represented by the variable b.

Undefined Slope: vertical line (x=#)

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Unit 4 - Functional Relationships

Main Topics for Unit 4:

Download Unit 4 Word Wall

Download Unit 4 Vocabulary Defined

1. Set Theory

Check Out This Helpful Resource on Set Theory

2. Functions and Relations -

Functions Versus Relations

Review Sessions - Wednesday, December 15th

Unit 4 Test - Thursday December, 16th.

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Unit 3 - Equal or Not

This is the first unit of the Algebra Strand. The following concepts will be included within this unit:
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Part 2
1. Solving inequalities with one variable
2. Graphing the solutions to one variable inequalities
3. Solving inequalities with absolute value
4. Graphing the solutions to inequalities with absolute value.

How to Solve Inequalities

How to Solve Inequalities with Absolute Value

Important Dates (Part 2):