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