Algebra I Midterm Review 2013 Chapter 1 Variable vs. constant Evaluate an expression Simplify an expression Expression vs. equation Translate English words of mathematical expressions or equations Solution of an equation Solve an equation Equivalent expressions Commutative property of addition/multiplication Associative property of addition/multiplication Distributive property of multiplication over addition/multiplication Factor an expression Factors of a number or expression Factorization The number system Real, rational, irrational, integer, whole, natural, or counting numbers Prime numbers Composite numbers Addition, subtraction, multiplication, and division of fractions Identity property of addition and multiplication Inequality symbols- be able to graph on number line Absolute value – notation, definition, evaluate Be able to add, subtract, multiply, and divide signed numbers Like terms Opposite or additive inverse Property of opposites or inverse property of addition Definition of subtraction a – b = a + (-b) for all read numbers a and b Multiplicative property of zero a 1 a , for all real numbers a and b where b b b Reciprocal or multiplicative inverse Property of reciprocals or inverse property of multiplication 2 0 0 Division involving zero: , , 0 2 0 Exponential notation: power, base, and exponent Convert factored notation to exponential notation and vice versa Order of operations Grouping symbols Exponents Multiplication and division, left to right Addition and subtraction, left to right Opposite of a sum is the sum of the opposites: -(a+b) = -a + -b Definition of division: a/b 0. Chapter 2 Equivalent equations Addition and multiplication properties of equality Coefficient Combine like terms Solve linear equations in one variable Be able to clear fractions and decimals from an equation Be able to recognize equations with no solution and infinitely many solutions Formula Evaluate a formula Solve a formula for a different variable Convert decimals to fractions to percents Definition of percent Solve problems involving percents Problem solving by defining a variable, writing an equation and solving Graphing inequalities in one variable on a number line Solving inequalities in one variable Addition and multiplication properties of inequalities Work problems with inequalities Chapter 3 Interpreting graphs Cartesian coordinate plane Ordered pairs (x, y) – coordinates of a point Plot or graph a point on CCP Identify the four quadrants on the CCP Definition of linear equation in two variables – number of solutions is infinite and for a line when graphed on CCP Graph a line using any two ordered pairs that are solutions x intercept y intercept Graph a line using intercepts x = # is a vertical line and y = # is a horizontal line Real life applications that involve linear equations in two variables Rate vs. slope Slope of a line (rise / run or change in y / change in x) Slope of a vertical line is undefined since change in x = 0 Slope of a horizontal line is 0 since change in y = 0 Slope intercept form: y = mx + b Slope = m y-intercept = (0, b) A C Standard form: Ax + By = C; Solve for y: y = x B B A Slope = B C y-intercept: (0, ) B Point Slope form: y - y 1 = m (x - x 1 ) Slope = m Point (x 1 , y 1 ) Chapter 7 Systems of equations Number of solutions to a system – one, none, or infinite The system is consistent if it has at least one solution The system is inconsistent if it has no solution The system is dependent if it has two different lines The system is independent if the lines coincide (or are the same line) General Topics Know properties and definitions Be comfortable with mathematical vocabulary and symbols Be comfortable with adding, subtracting, multiplying, and dividing fractions. Be able to add, subtract, multiply, and divide signed numbers Be able to simplify and evaluate expressions using order of operations Be able to identify numbers as real, rational, irrational, integer, whole, and natural Be able to solve linear equations in one variable Be able to recognize and solve linear equation with one solution, with no solutions, and with infinite number of solutions Be able to solve and graph linear inequalities in one variable Be able to solve work problems involving percents Be able to use and transform formulas Be able to plot points on CCP Be able to find x-intercept and y-intercept of an equation Be able to graph lines, using any two solutions and using intercepts Be able to solve any work problem introduced this semester, by defining a variable, writing a linear equation or inequality in one variable, and solving Be able to solve a real life application by writing and graphing a linear equation in two variables and using this line to predict an outcome Be able to find the slope of a given line, a line passing through two ordered pairs, and of a given equation Be able to find slope and y-intercept of equations Be able to graph equations using slope and y-intercept Be able to find the equation of a line using a point and the slope or two points Be able to tell how many solutions a system has by looking at the slope and y-intercept of the two lines. Be able to tell if the system is consistent or inconsistent Be able to tell if the system is dependent or independent Be able to graph the system to find the solution (the point of intersection) Be able to solve systems by using substitution, linear combination (elimination), or Cramer’s Rule