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64 Cards in this Set
- Front
- Back
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Divide 1 by 14 and round to the thousandths place.
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0.071
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What is probability?
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the study of how likely it is that a particular event will occur
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In math, if something is considered to be impossible, we say that is has a probability of ______.
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0
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In math, if something is guaranteed to be possible, we say that is has a probability of ______.
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1
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In math, if something is only somewhat likely to occur, the probability is represented as a ________.
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fraction, or as an equivalent decimal or percent
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How do you adding signed numbers? Perform the operation (-5)+(-9) = ?
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View the problem so that negative numbers is an amount owing - then perform the operation in that context. Answer: -14
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How do you subtract signed numbers? Perform the operation (-4) - (-7) = ?
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1) leave the first number, 2) change the operation to add, 3) reverse the sign of the second number, 4) perform the operation in the context of "owing/having". Answer: 3 or ("have", 3)
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When multiplying signed numbers, what must you observe?
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Multiply as normal, but observe the following rules to determine whether your answer is positive or negative: 1) pos x pos = pos, 2) pos x neg = neg, 3) neg x neg = pos
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When operating on negative signed numbers, how do you handle exponents?
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if you raise a negative number to a power which is even, the answer will be positive. If you raise a negative number to a power which is odd, the answer will be negative
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What should we do when multiplying two exponent numbers, which have the same base?
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we add the exponents
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What should we do when dividing two exponent numbers, which have the same base?
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we subtract the exponents
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A product raised to a power is equal to
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the product of each factor with that exponent applied to it
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A quotient raised to a power is equal to
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the dividend and the divisor with that exponent applied to each
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Any number to the power of 0 equals
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1
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A number with an exponent, raised to another exponent equals
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the number with the exponents multiplied
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A base raised to a negative power is equal to
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1 divided by the base to the positive of that power
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What is a binary operation?
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An operation which works with only TWO numbers
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What does it mean, if an operation is closed? Give an example.
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if you perform an operation on a given set of numbers, your answer will always be a member of that set. Integers and addition is a closed operation. Integers and division is not a closed operation.
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Is division of integers a closed operation?
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No. The result may not end up being a member of the integer set.
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What must an equation contain? What is it called otherwise?
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An __equals__ sign; an expression
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How do you combine like terms in Algebra? Provide an example. Combine like terms: 2x + 3x.
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If a term, or value uses the same variable, you can combine them, operating as indicated. 2x + 3x = 5x
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When dividing signed numbers, what must you observe?
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Divide as normal, but observe the following rules to determine whether your answer is positive or negative: 1) pos / pos = pos, 2) pos / neg = neg, 3) neg / neg = pos
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Solve for x, 2x + 6 = 3x + 2
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x = 4
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Solve for x, 5x - 7 = 3x + 9
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x = 8
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Many algebra problems ask us to find the values of consecutive integers in a pattern, such as 5, 6, 7, or 20, 30, 40. How would you solve a + b + c = 18?
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Consecutive means, one after another, increasing. In this case, it is by one. Therefore a+b+c=18 is (x)+(x+1)+(x+2)=18 which is equivalent to 3x+3=18, then we solve for x, which is 5
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The sum of three consecutive even integers is 30. What are the three integers?
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8, 10, 12
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The sum of three consecutive multiples of three is 36. What are the three integers?
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9, 12, 15
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This graph represents the inequality ...
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X > 1
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What does the empty circle & thick arrow represent?
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It represent an inequality. The empty circle means that the value can not be 1, the thick arrow indicates that it can be any number greater than 1 up to infinity.
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This graph represents the inequality ...
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x is less than or equal to 3
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What does the filled circle & thick arrow represent?
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Filled circle means 3 is included and x is any number lower than 3.
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What is the inequality?
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-4 is less than x, x is less than or equal to 3. It means that x must be between -4 and 3, but can not be -4.
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What is the difference between solving algebraic inequalities vs equations?
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Essentially the same, but you will need to ensure the final inequality is true. Some inequalities can have a nearly unlimited number of solutions.
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When solving algebraic inequalities, what must you do when multiplying or dividing by a negative number?
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flip the inequality sign
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What is a monomial?
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An algebraic expression consisting of ONE term. The term can be a lone constant, lone variable, or constant multiplied by one or more variables.
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In the monomial "4xy", what is the coefficient?
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4
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What is the coefficient of a monomial?
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The multiplicative factor of a monomial
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What is the degree of a monomial?
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the sum of the exponents (powers) of the variable terms
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What is the degree of a monomial that is just a constant?
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A monomial that is just a constant has a degree of 0.
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What is the degree of a monomial that is just a plain variable, such as x?
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A monomial that is just a plain variable, such as x, has a degree of 1
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How do you determine the degree of a monomial with several variables?
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You add the exponents of the variables.
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In a variable with no exponents, what is the default exponent value?
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1
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How can you add and subtract monomials?
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coefficient's of monomials with the exact same variables/exponents may be added or subtracted
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How would you multiply a monomial by a constant?
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multiply the constant by the coefficient of the monomial (if it does not have a coefficient, the default is 1.)
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How would you multiply a monomial by a monomial?
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multiply the coefficients, then multiply each variable (recall that when multiplying variables with exponents, we ADD the exponents.)
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How would you divide a monomial by a constant?
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just divide the coefficient by the constant
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How would you divide a monomial by a monomial?
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divide the coefficients, and then divide the variables (recall that when dividing variables with exponents, we SUBTRACT the exponents.)
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How would you raise a monomial to a power?
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Raise the coefficient to the power, and then raise each variable to the power (recall that when raising a variable to another power - you multiply the powers)
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Identify the coefficient?
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9
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What is the degree of this monomial?
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3
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Solve
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Monomial addition
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Solve
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Monomial multiply by constant
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Solve
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Monomial multiplication (recall that when multiplying variables with exponents, we ADD the exponents.)
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Solve
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Monomial division by constant
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Solve
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divide a monomial by a monomial (recall that when dividing variables with exponents, we SUBTRACT the exponents.)
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Solve
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raise a monomial to a power (recall that when raising a variable to another power - you multiply the powers)
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What is a binomial?
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polynomial with two __unlike__ terms (i.e. 3x - 4)
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What is a trinomial?
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polynomial with __three unlike__ terms
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What is a polynomial?
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sum and/or difference of one or more monomials. "Poly" just means "many"
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What is the difference between the degree of a monomial and polynomial?
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monomial is a single term, the degree is a sum of all the powers. polynomials are multiple monomials, the degree is the highest power out of all the terms
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Simplify
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Combine like terms & watch the signs!
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Simplify
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Change to one large equation, combine like terms & watch the signs!
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When subtracting polynomials, what must you think about first?
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distribute the minus sign over every term in the second polynomial. Therefore, multiplying each term in the second polynomial by -1
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Simplify
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Multiply second term by -1, change to one large equation, combine like terms & watch the signs!
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