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Transcript of Tips for Success Get ready for This Course Tips for Success Use the Text Get Help Preparing for...
Tips for Success Get ready for This Course Tips for Success Use the Text Get Help Preparing for Tests Manage your Time
1.1 Number Operations
Types of Numbers
Natural Numbers (N): {1,2,3,…} Whole Numbers (W): {0,1,2,…} Integers: (Z): {…-2, -1, 0, 1, 2, …} Rational Numbers (Q): {a/b a and b are integers and b ≠ 0} Irrational Numbers (I) : {Any non repeating -non terminating number} Real Number (R): {The set of all rational and irrational
numbers}
SimplifySimplify
a. 2 + 48 ÷ 6b. 5(8 - 6) + 2(4 -1)c. 3 - 4(2 - 7)d. 5 + [2 + (4 - 1) + 3(6 ÷ 2)]e. [24 - (2 8)] + 4(12 - 7)
1.1 Number Operations
1.2 Variables in Algebra
Definition of Algebraic Expression
A collection of letters (called variables) and real numbers(called constants) combined using the operations of addition, subtraction, multiplication and division is calledan algebraic expression.
• Term An expression separated by a plus or minus sign• Variable A letter that represents a number• Coefficient A number in front of a variable
Algebraic ExpressionsAlgebraic Expressions
5 + 5 + xx 6 6 yy 3 3 yy – 4 + – 4 + xx
44xx means 4 means 4 xx
andand
xyxy means means xx yy
1.2 Variables in Algebra
Evaluate if Evaluate if aa = 2, = 2, b b = 3, and = 3, and cc = 4 = 4
• 3a - 2b• 4ac - 3a• 4(a + 2c)
1.2 Variables in Algebra
1.3 Exponents and PowersExponents
If a is a real number and n is a natural number, then the nth power of a, or a raised to the nth power, written as an, is the product of n factors, each of which is a. exponent base an = a • a • a … • a
72 is read as seven to the second power or 7 squared.
43 is read as 4 to the third power or 3 cubed.
1.3 Exponents and Powers
1.3 Exponents and Powers
A formula is an equation that describes a known relationship among measured quantities.
Formula Meaning
A = lw Area of a rectangle
A = πr2 Area of a circle
V = lwh Volume of a rectangular solid
d =rt Motion equation
Order of OperationOrder of Operation
1.1. Do all operations within grouping symbols such as parentheses or brackets.
2. Evaluate any expressions with exponents.3. Multiply or divide in order from left to
right.4. Add or subtract in order from left to right.
1.4 Order of Operation
1. 24 - 12 + 3 • 52. 16 + 21 ÷ 3 - 63. 4 • (3 + 7) - 2 • 44. 3 + (2 + 3)2 - 7
1.4 Order of Operation
Evaluate the expression if Evaluate the expression if xx = 2, = 2, yy = 4, and = 4, and zz = 5 = 5
• x + 2z - 5• x3 + 3x - 2• 4 • (3x - y)2 + 5 • 4
1.4 Order of Operation
€
4. 6 +2x
y− z
An An equation is formed when an equal sign is formed when an equal sign is placed between two expressions.is placed between two expressions.
Equations that contain variables are Equations that contain variables are open open sentences.sentences.
Equations that do not contain variables are Equations that do not contain variables are closed sentences.closed sentences.
1.5 Equations and Inequalities
Check whether the numbers 3, 4, and 5 are Check whether the numbers 3, 4, and 5 are solutions of the following equations.solutions of the following equations.
1.1. 33x x - 5 = 7- 5 = 72.2. 44xx22 - 31 = 5 - 31 = 53.3. 33xx + 7 = 2 + 7 = 2xx + 12 + 12
1.5 Equations and Inequalities
1.5 Equations and InequalitiesA solution of an inequality is a value of the variable that makes the inequality a true statement.
The solution set of an inequality is the set of all solutions.
1.5 Equations and Inequalities
Order on Real-Number Line
a < b a is less than b a < b a is less than or equal to b a > b a is greater than b a > b a is greater than or equal to b a ≠b a is not equal to b
1.5 Equations and Inequalities
Determine if x = 3 is a solution of each
inequality
n 3x - 1 < 5n 2x - 3 > 5x + 2n 4x + 9 > 3(x + 4)
Addition Subtraction Multiplication Division Equals
sum difference product quotient is
plus minus times divided by gives
added to subtracted multiply into yields
more than
less than twice per same
increased decreased by of ratio
total less double
1.6 Models
Write each statement in mathematical terms
1. Twice the sum of 3 and a number is 4.
2. Three more than the square of a number is 6.
3. 15 is 5 less than three times a number.
4. The square of a number increased by 6 is -4.
1.6 Models