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Algebra 1: Learning Targets CHAPTER 6 As the chapter moves along, place a check mark by those things that you have mastered. ___ I can define variable(s) to represent unknown(s) in a word problem. ___ I can represent a word problem with one or two equations. ___ I can solve a system of equations using Substitution. ___ I can solve a system of equations using Elimination. Review topics: 1. I can solve a system of equations using Equal Values. 2. I can use generic rectangles to multiply two polynomials. 3. I can set up a proportion to represent a situation. 4. I can solve an equation involving a proportion. 5. I can solve linear equations containing one or two variables. Algebra 1: Learning Targets At the end of Chapter 7 you will be able to: Semester 2 (12 days) As the chapter moves along, place a check mark by those things that you have mastered. ___ I understand that growth rate and slope are the same. ___ I can determine the growth rate of a line using growth triangles on the graph. ___ I can find the slope of a line without graphing using ___ I understand that horizontal lines have a slope of 0. ___ I understand that the slope of a vertical line is undefined. ___ I understand that parallel lines have the same slope. ___ I understand that perpendicular lines have slopes that are opposite reciprocals. (e.g. 2/3 -3/2) ___ I can find x- and y-intercepts of a line without graphing. ___ I can write the equation of a line given its slope and a point, without graphing. ___ I can write the equation of a line given two points, without graphing. ___ I can find the slope of a line when its equation is given in standard form. (i.e. Ax+By=C) y . x Algebra 1: Learning Targets At the end of Chapter 8 you will be able to: Semester 2 (14 days) As the chapter moves along, place a check mark by those things that you have mastered. ___ I understand that rewriting the area of a rectangle from a sum to a product is called factoring. ___ I can factor expressions having a common factor. ___ I can factor quadratic expressions using generic rectangles and diamond problems. ___ I understand that the graphs of the quadratic equations that we will study are parabolas. ___ I understand that standard form of the equation of a parabola is y = ax2 + bx + c. ___ I understand that factored form of the equation of a parabola is y = a(x – d)(x – e) where d and e are the xintercepts of the graph. ___ I can make a table from a quadratic equation. ___ I can make a quadratic equation from a table. ___ I can make a quadratic equation from its graph. ___ I can make a quadratic equation from the x-intercepts and one other point on the parabola. ___ I can find the line of symmetry of a parabola from a graph. ___ I can find the line of symmetry of a parabola from a table. ___ I can find the line of symmetry of a parabola from the equation in factored form. ___ I understand that the vertex is always on the line of symmetry. ___ If a table shows symmetry, then I can find the x-coordinate of the vertex. ___ I can locate the vertex of a parabola from its graph. ___ I can use the equation and the x-coordinate of the vertex to find its y-coordinate. ___ I understand that y = ax2 + bx + c has infinitely many solutions. ___ I understand that ax2 + bx + c = 0 has zero, one, or two solutions. ___ I understand that the solution(s) to ax2 + bx + c = 0 correspond to the x-intercepts (roots) of the parabola y = ax2 + bx + c and that there can be zero, one, or two solutions/x-intercepts. ___ I know how to solve equations like ax2 + bx + c = 0 by factoring and using the Zero Product Property. ___ I understand that some quadratic expressions can not be factored. ___ I can solve equations like ax2 + bx + c = 0 using the Quadratic Formula. ___ I understand that the Quadratic Formula must be used to solve equations containing expressions that can not be factored. Algebra 1: Learning Targets At the end of Chapter 9 you will be able to: Semester 2 (10 days) As the chapter moves along, place a check mark by those things that you have mastered. ___ I understand that < means “is less than” and > means “is greater than or equal to” ___ I understand that inequalities such as x > 4 or -3 < x < 10 have infinitely many solutions. ___ I understand that solutions to inequalities having one variable can be represented on a number line using boundary point(s) and shading. ___ I understand that the boundary point for a solution set of an inequality such as 2x + 3 < 11 is found by solving the equation 2x + 3 = 11. ___ I understand that I must test some value in the inequality, other than the boundary, to determine the direction to shade on the number line to represent the complete solution to the inequality. ___ When graphing solutions on a number line, I understand that the symbol ○ (open circle) is used to show that the boundary point is not included in the solution set. It is used with inequality symbols < and >. ___ When graphing solutions on a number line, I understand that the symbol ● (closed circle) is used to show that the boundary point is included in the solution set. It is used with inequality symbols < and >. ___ I understand that |x| is read “the absolute value of x” and tells how far x is from 0 on a number line. ___ I understand that solutions to inequalities having two variables can be represented on an (x,y) graph using boundary line and shading. ___ I understand that the boundary line for a solution set of an inequality such as 2x + 3y < 12 is the line having equation 2x + 3y = 12. ___ I understand that I must use the inequality to test some point not on the boundary line to determine which side of the boundary line to shade. ___ When graphing solutions on an (x,y) graph, I understand that the symbol - - - (dotted line) is used to show that points on the boundary line are not included in the solution set. It is used with inequality symbols < and >. ___ When graphing solutions on an (x,y) graph, I understand that the symbol ___ (solid line) is used to show that points on the boundary line are included in the solution set. It is used with inequality symbols < and >. ___ I understand that in a system of inequalities, the solutions are those points that make all of the inequalities true. ___ I can find solutions to a system of inequalities by graphing each boundary line, testing points from each region, and shading the region(s) containing points whose coordinates satisfy all of the inequalities. ___ I understand that some inequalities (or systems of inequalities) have no solution. Algebra 1: Learning Targets At the end of Chapter 10 you will be able to: Semester 2 (16 days) As the chapter moves along, place a check mark by those things that you have mastered. ___ I understand that a number divided by itself such as x equals 1 unless the denominator is 0. x ___ I can find values to exclude because they would make the denominator be 0. ___ I understand that a rational expression looks like a fraction such as x 3 . x4 ___ I can simplify a rational expression in which the numerator and denominator contain identical factors. ___ I understand that I cannot simplify a rational expression unless the numerator and denominator are in factored form. YOU CANNOT CANCEL TERMS! x2 1 IS NOT EQUAL TO x4 2 ___ I can multiply rational expressions and write the product in simplest form. ___ I can divide rational expressions and write the quotient in simplest form. ___ I can eliminate fractions in equations by multiplying both sides by a common denominator. ___ I can make equations easier to solve by multiplying or dividing both sides by a common factor. “Rewriting” ___ I can recognize when two equations are equivalent and understand that they have the same solution. ___ I can solve equations by “Undoing” the operations in reverse order. ___ I can solve equations by using the “Looking Inside” method. ___ I can solve absolute value equations like |2x – 6| = 14. ___ I can solve perfect square equations like (x – 4)2 = 25. ___ I can find both boundary points for an absolute value inequality and graph its complete solution. ___ I can rewrite a quadratic equation from standard form into perfect square form by Completing the Square. ___ I understand that xn means that there are n factors of x. ___ I can simplify products of exponential expressions. Example: (x2)(x3) = x5 ___ I can simplify quotients of exponential expressions. Example: ___ I can simplify powers of exponential expressions. Example: (x2)3 = x6 ___ I understand that x0 = 1. ___ I understand that x-n = 1 . xn x8 x3 5 x