| A | B |
|---|
| Integers are...? | All numbers with no fractional or decimal parts; multiples of 1 |
| PEMDAS | Parentheses Exponents Multiplication Division Addition, Subtraction |
| Addition and Multiplication are... | Commutative: doesn't matter in what order operation is performed |
| Addition and Multiplication are... | Associative: can be regrouped without changing the result |
| Sum of values = | Average value x Number of values |
| A fraction with the _________ denominator with have the larger value | smaller |
| What is one way you can determine whether a fraction is larger/smaller than another? | Compare via common denominator |
| Odd + Odd = | Even |
| Even + Even = | Even |
| Odd + Even = | Odd |
| Odd x Odd = | Odd |
| Even x Even = | Even |
| Odd x Even = | Even |
| A number is divisible by 2 if... | the last digit is divisible by 2 |
| A number is divisible by 3 if... | the sum of its digits is divisible by 3 ex: 4,317 = 4+3+1+7 = 15 |
| A number is divisible by 4 if... | the last two digits are divisible by 4 |
| A number is divisible by 5 if... | the last digit is 0 or 5 |
| A number is divisible by 6 if... | it is divisible by both 2 and 3 |
| A number is divisible by 9 if.. | the sum of the digits is divisible by 9 |
| Average value = | Sum of values /Number of values |
| ((x^2))^4 | x^ (2x4) = x^8 |
| x^4 times x^7 = | x^ (4+11) = x^11 |
| x^4 divided by x^2 | x^ (4-2) = x^2 |
| The exponent of a power of 10 tells us how many _____ the number would have if written out. | zeroes |
| To make a fraction/decimal a percent... | multiply by 100% |
| Only ____ radicals can be added to or subtracted from one another | Like |
| To find the probability of two events... Ex: possibility of throwing a 5 on two dies... | multiply together the two probabilities Ex: 1/6 x 1/6 = 1/36 |
| 13 is 33 1/3% of what number? | whole = 13/ (1/3) = 39 |
| To raise a power to an exponent... | multiply the exponents |
| x^0 = | 1 |
| 10^6 | 1,000,000 (6 zeroes) |
| x^(-2) = | 1/(x^2) |
| 18 is what % of 3? | 18 = & x 3 18/3 (100%) = 600% |
| 19% = | 19/100 |
| Example: In a classroom of 30 students, the ratio of boys to students in a class is 2/5. How many are boys? | 2/5 x 30/1 = 12 |
| (6squr3) x (2squr5) = | (6 x 2) x (squr3 x squr5) = 12squr15 |
| ax + ay = a(x + y) | Common Factor |
| x^2 - y^2 = (x + y)(x + y) | Difference of Squares |
| x^2 + 2xy + y^2 = (x + y)^2 | Perfect Square Trinomial |
| (ac)x^2 + (ad + bc)x + bd = (ax + b)(cx + d) | General Trinomial |
| x = -b +- sqrt b^2 - 4ac / 2a | Quadratic Formula |
| (a + bi) + (c + di) = (a + c) + (b + d)i | Adding Operation on Complex Numbers |
| (a + bi) - (c + di) = (a - c) + (b - d)i | Subtracting Operation on Complex Numbers |
| (a + bi)(c + di) = (ac - bd) + (ad + bc)i | Multiplying Operatiion on Complex Numbers |
| a + bi / c + di = (a +bi)(c - di) / (c = di)(c - di) = (ac + bd / c^2 + d^2) + ( (ba - ad)i / c^2 + d^2 | Dividing Operation on Complex Numbers |
| (x - r) is a factor of a polynomial equation if and only if F(r) = 0 | Factor Theorem |
| if b/c is a root of an equation with the interger coefficients F(x) = a sub n x to the power of n + a sub n-1 x to the power of n-1 ...+ a sub 1 x + a sub 0 then b is a factor of a sub 0 and c is a factor of a sub n | Rational Roots Theorem |
| if a < b then a + c < b + c if a < b and c > 0 then ac < bc If a < b and c < 0 then ac > bc If b > 0 then l a l < b is eqquivalent to -b< a <b If b > 0 then l a l > 0 is equivalent to a > b or a < -b | Properties of Inequalities |
