Download SOL study guide 2 for MSMII students only

STUDY GUIDE FOR THE SECOND SIX WEEKS PRE-ALGEBRA TEST
SOL
6.1
INFORMATION RESPONSIBLE FOR
Solve problems using fractions (like / unlike denominators) and simplifying.
Solve problems using decimals.
6.6
Rational numbers are numbers that can be written as a ratio or a fraction.
6.23
A one-step linear equation is an equation that requires one operation to solve.
A coefficient is the number in a term (example: 3x, 3 is the coefficient).
An equation is a mathematical sentence stating that two expressions are equal.
A variable is a symbol used to represent an unknown number.
A term is a number, variable, or number/variable combination.
7.2
A rational number can be written as a ratio of two integers.
An expression has no equal sign.
Expressions are simplified by using the order of operations.
The power of a number represents repeated multiplication of the number. The base is the number that is
multiplied, the exponent tells how many times to use the number.
Any number to the 0 power is 1.
7.3
Properties (commutative, associative, distributive, identity, zero property)
Inverses are numbers that when combined with other numbers results in an answer of 1 or 0.
The ADDITIVE INVERSE PROPERTY states the sum of a number and its additive inverse always equals 0
(example: 5 + (-5) = 0).
The MULTIPLICATIVE INVERSE PROPERTY states that the product of a number and its inverse
(reciprocal) always equals 1 (ex. 4 * ¼ = 1).
Zero has no multiplicative inverse.
Division by 0 is not a possible operation.
7.4
Tips are figured on the cost of the service only.
The sale price is determined by subtracting the discount from the original price of the item.
Simple interest (I) is equal to the principal (p) times the rate of interest (r) times the number of years involved
(t) or I=prt
The total cost of a loan is the amount of the original amount + the amount of interest paid.
7.5
Rules for using integers and solving problems involving integers.
The set of integers is the set of whole numbers and their opposites.
7.12
In a coordinate plane, the horizontal number line is called the x-axis, and the vertical number line is called the
y-axis.
The coordinates of a point are represented by the ordered pair (x,y) where x is the first coordinate and y is the
second coordinate.
The first coordinate of a point is its distance along the x-axis.
The second coordinate of a point is its distance along the y-axis.
The quadrants of a coordinate plane are the four regions created by the two intersecting perpendicular number
lines. Quadrants are named in counter-clockwise order.
Quadrant I uses the ordered pair (+,+).
Quadrant II uses the ordered pair (-,+).
Quadrant III uses the ordered pair (-,-).
Quadrant IV uses the ordered pair (+,-).
7.19
In a numeric pattern determine the rule or function that is being used to generate the given numbers then use
that rule to obtain what the next number should be.
In geometric sequences determine what each number is multiplied by in order to obtain the next number in the
sequence. This multiplier is called the “common ratio.”
7.20
A verbal expression is a word phrase (six times a number plus four).
A verbal sentence is a complete word statement (one fourth of a number minus 3 is 20).
An algebraic expression is a number phrase that contains at least one variable (2x-5).
An algebraic equation is a mathematical statement that says two expressions are equal (2x+1=5).
7.21
An expression is a name for a number.
An expression that contains a variable is a variable expression.
An expression that contains only numbers is a numerical expression.
An equation is a mathematical sentence that states that two expressions are equal.
An inequality is a mathematical sentence that states that one quantity is less than (<) or greater than (>)
another quantity.
7.22
A one-step equation is defined as an equation that requires the use of one operation to solve it (x + 3 = -4).
A one-step inequality is defined as an inequality that requires the use of one operation to solve (x – 4 > 9)
The inverse operation for addition is subtraction, and the inverse operation for multiplication is division.
When both expressions of an inequality are multiplied or divided by a negative number, the inequality symbol
reverses (-3x < 15 is equivalent to x > -5).
8.1
Scientific notation is used to represent very large or very small numbers.
A number written in scientific notation is the product of a decimal greater than 1 but less than 10 times a power
of 10 (310,000 = 3.1 * 105 and 0.000031 = 3.1 * 10-5)
8.3
A percent is a special ratio in which the denominator is always 100.
A discount is a percentage of the original price.
8.4
Algebraic expressions use operations with variables.
Algebraic expressions are evaluated by replacing the variables with numbers and using the order of operations
to simplify.
Replacement values are the numbers that replace the variables in an algebraic expression.
8.5
A perfect square is a whole number whose square root is a whole number.
The square root of a number is a number when multiplied by itself equals the first number.
Any whole number other than a perfect square has a square root that lies somewhere between two consecutive
whole numbers.
The square root of a whole number that is not a perfect square is an irrational number.
8.18
The domain represents all the possible values for the independent variable.
The range represents all the values for the dependent variable.
The independent variable is the “input” value.
The dependent variable depends on what value is input. It is the result you get.
The independent variable causes a change in the dependent variable.
8.14
A relation is any set of ordered pairs. The x value is the domain; the y value is the range.
A function is a relation in which there is one and only one range for each domain.
Some relations are functions; all functions are relations.
A function can be represented by a table of values where for each domain there is only one range possible.
8.15
A two-step equation is defined as an equation that requires the use of two different operations to solve. (2x + 3 =
-4)
A two-step inequality is defined as an inequality that requires the use of two different operations to solve. (3x –
4 > 9)
In an equation, the equal sign means that the value on the left is the same as the value on the right.
To keep the equality, an operation performed on one side of an equation must be performed on the other side.
The same procedures that work for equations work for inequalities.
8.16
A linear equation is an equation with two different variables whose graph is a line.
Graphing a linear equation requires determining a table of ordered pairs by substituting a value for one variable
and solving for the other, plotting the ordered pairs on a coordinate graph, and connecting the points to form a
straight line.