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# Praxis II Math 0014

### Critical Thinking

Question | Answer |
---|---|

Inductive Reasoning | Developing generalizations based on observation of a limited number of related events or experiences Based on observation |

Deductive Reasoning | Arriving at specific conclusions based on general principals, observations, or experiences. Based on previous experience or truth. |

Problem Solving | The ability to apply and adapt a variety of mathematical strategies to solve problems. |

Relative magnitude | Size relationship b/t numbers; is the number smaller, larger, close or the same? |

Natural numbers ( Counting Numbers) | 1,2,3,4,5,6,7.... |

Whole Numbers | All the Counting numbers and 0 ex: 0,1,2,3,4,5,6,7.... |

Integers | All the natural and whole numbers including the negatives of those numbers ex: -7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7.... |

Rational Numbers | All integers are rational numbers, also fractional numbers or fractions, any integer over any integer ex: 1/2, 1/4, 4/1, 7/8... |

Prime Number | An integer other than 0 and 1 that has only 2 factors; itself and 1; a number that is divisible only by itself ex: 3,5,7,11,13,17... |

Even numbers | An integer divisible by 2: 2n. |

Odd Numbers | An integer that is not divisible by 2: 2n - 1. |

Complex Numbers | The numbers with "I" in them: 6 - 2i. |

Addition | Carrying (regrouping) Sum More than In addition to Exceeds Increased by Altogether Sum And Extra Combined Total of Count up |

Subtraction | Borrowing (regrouping) Less than/ fewer than Decreased by Diminished Take away Difference Deduct |

Subtrahend | Number subtracted from another |

Minuend | Number to be subtracted from |

Difference | Answer |

Multiplication | Multiplicant Mutiplier Product Times Twice Of Multiplied by Increased by |

Multiplicant | Number to be multiplied. (Top number) |

Multiplier | Number being multiplied by. (Bottom number) |

Product | Answer |

Division | Quotient Remainder Separated Distribute Per Out of Percent Ratio of Divisor Dividend |

Divisor | How hany times to divide |

Dividend | The number being divided. |

Quotient | Answer |

Arithmetic Sequence | Add the same value each time; add 3 each time ex: 1,4,7,10,13,16,19 |

Geometric Sequence | Multiply the same value each time; multiply by 2 each time ex: 2,4,8,16,32,63,128 |

Fibonacci numbers | The next number is found by adding the two numbers before it. Ex: 0,1,1,2,3,5,8,13,21,34... |

Equivalence | Being equal in value or amount |

1/5 | A.). 2/10 B.). 1/2 C.) 4/16 D.). 5/7 |

Equivalent Fractions | Found by multiplying the numerator and denominator by the same number |

Equivalent Decimal | Found by dividing the numerator by the denominator of the equivalent decimals |

Equivalent percents | Found by moving the decimal point over to the right to create a whole number of the Equivalent Decimal given ex: 0.25 = 25% |

Factor | Prime or composite number that is multiplied to get a product. The breakdown of a larger number. |

Factoring | The process of taking a number apart and expressing it as the product of its factors. |

2 | A factor of all even numbers |

10 | A factor of all numbers ending in 0 |

5 | A factor of all numbers ending in 0 and 5 |

3 | Is a factor of that number if it is a factor of the sum of it's individual digits found within the number ex: 65,331 6 +5+3+3+1=18 3 is a factor of 18 |

9 | Is a factor of that number if it is a factor of the sum of it's individual digits found within the number ex: 89,172 8+9+1+7+2= 27. 3 x 9 = 27 |

11 | Is a factor of a three digit number if ithe middle digit is the sum of the two outside digits. Ex: 682 6+2=8 |

Multiples | Found by multiplying a whole number by a whole number |

Lowest common Multiple | A number that is a multiple of 2 numbers being compared as is the lowest of all the multiples. |

Ratio | A comparison between two numbers. : / 5 dogs to 3 cats |

Proportion | 2 ratios with an equal sign b/t them; 2 ratios that are equal to one another. 5/3=10/6 or 2:3=4:6. |

The ratio of apples to oranges in a grocery store is 6/7, and there are 246 apples. How many oranges are there? | A.). 900 B.). 621 C.). 287 D.). 21 |

Percent | Per one hundred Fifty percent 50% 0.50 50/100 |

What percentage of 105 is 36.75 | Set up the cross multiplation fractions X/ 100 = 36.75/105 Cross multiply 105x = 3675 Divide by 105 to get x by itself X= 35% |

Equals | Is Are Was Were Will be Gives yields |

18 is what % of 20? | Divide the number you have by the number possible and multiply by 100 to find a percent. A.). 45 B.). 56 C.). 60 D.). 90 18/20= 0.9x 100= 90% |

A pair of shoes is on a 20% off sale rack. The sale price is $60. What is the original price. | A.). $75 B.). $62 C.). $72 D.). $74 X equals the original price X-(0.20)x=60 Add x to both sides to isolate the variable 60/0.8= 75 |

Associative Property | Numbers can be grouped or regrouped in an operation in any manner w/o changing the answer; doesn't matter the order or how the numbers are combined the answer will always be the same. Addition and multiplication are both associative |

Associative Property of addition | A + (B+C)= ( A+B) + C |

Associative Property of addition | 3 + (4+6) = (3+4) + 6 (10). (7) 3+. (10). +6 13. 13 |

Associative Property of multiplication | A x (B x C) = ( A x B) x C |

Associative Property of multiplication | 3 x ( 4 x 6 )= ( 3 x 4) x 6 (24). (12) 3x (24). X. 6 (72) (72) |

Commutative Property | Numbers in an operation can change order w/o changing the answer; doesn't matter the order of the numbers the answer will always be the same. Addition and multiplication are both commutative |

Commutative Property of addition | A + B = B + A |

Commutative Property of addition | 60 + 15 = 15. +. 60 75. =. 75 |

Commutative Property of multiplication | A X. B =. B. X. A |

Commutative Property of multiplication | 10. X. 5. =. 5. X. 10 50. =. 50 |

Distributive Property | One operation may change to another. This property is used to make equations simplier by breaking them apart. Can be used when multiplying with parenthesis. |

Distributive Property | A (B + C) =. AB. +. AC |

Distributive Property | 4 (3+2). =. 4(3). +. 4(2) 4. (5). =. 12. +. 8 20. =. 20 |

Transitive Property | If X is related to Y and Y is related to Z then X is related to Z. |

Transitive Property | 5 > 4 and 4 > 3 then 5 > 3 |

Additive Inverse | The opposite of the number, the number when added to (n) the result is 0 |

Additive Inverse | The additive inverse of 2 is: A.). 0 B.). -2 C.). 4 D.). -4 |

Multiplicative Inverse | The reciprocal, the number when multiplied by (n) the result in the product of 1. |

Powers of zero | Anything to the zero power will create an answer of 0. 1' = 0 |

Multiplicative Inverse yields one | Any number multiplied by its inverse gives an answer of one. Ex: x * 1/x = 1 |

Absoloute value | Never negative Ex: 3. =. 3 -6. =. 6 |

Negative Exponents | Any number to a negative exponent is the same as one over that number with a positive exponent. Ex: 6 -2 = 1/6 2 |

Parallell lines | Non- vertical lines in a plane with the same slope. || |

Perpendicular lines | 2 lines in a plane with the product of the slopes equaling -1. |

Pythagorean Theorem | Used to explain the lengths of a rt. triangle. The 2 legs ( a + b ) squared equal the length of the hypotenuse (c) given any two values of the 3, the 3rd value can always be found. |

Pythagorean Theorem | A2 + B2 = C2 |

Slope | Given 2 point. (x1,y1), (x2,y2): To find the slope (m) use m= y2-y1/ x2-x1. |

Edges | sides or arches of a 1- dimensional figure |

Vertices | The end points or edges of the figure which is 0 dimensional |

Angles | When 2 sides meet at a vertex measured in degrees |

2 dimensional figures | Equilateral triangle Rhombus Square Isosceles triangle Rectangle Trapezoid Right triangle Kite Chevron Scalene triangle Ellipse Circle Parallelogram Ellipse Circle Parallelogram |

Polygons | 2 dimensional figures in which: All edges are segments Every vertex is the endpoint of 2 or more edges No 2 sides cross each other |

10 | Decagon |

11 | Undecagon |

12 | Dodecagon |

Three-dimensional figures include the following | Sphere ellipsoid ovoid cone cylinder prism pyramid |

polyhedrons | are three-dimensional figures and shapes in which: all faces are plane regions every edge is the edge of two faces every vertex is the vertex of three or more faces no two faces cross each other |

4 | tetrahedron |

6 | cube |

8 | octahedron |

12 | dodecahedron |

18 | icosahedron |

transformation | changes the position of the shape upon a coordinate plane resulting in the same value and magnitude. The shape moves from one place(coordinate)to another. |

rotation (turn) | the shape is turned on 360° axis |

reflection (flip) | the shape is a mirror image |

translation (slide) | the shape moves by sliding into another area in the plane |

King Henry's Dad Mark, Larry, Gary, Drinks Chocolate Milk. | Kilo Hecto deka m l g deci centi milli |

1 foot | 12 inches |

1 yard | 36 inches 3 feet |

one-mile | 5280 feet 1760 yards |

1 pound | 16 ounces |

1 ton | 2000 pounds |

1 cup | 8 fluid ounces |

1 pint | 2 cups |

one quart | 4 cups two pints |

1 gallon | 4 quarts |

perimeter rectangle | 2l + 2w |

area of a rectangle | l x w |

perimeter of the triangle | a + b+ c s1 +s2+ s3 |

area of a triangle | 1/2 bh |

Pythagorean theory | all angles equal 180° |

perimeter of the square | 4s |

area of the square | s2 |

perimeter circle | 2(3.14)r 3.14d |

area of the circle | (3.14)r2 |

volume | measured in cubes and is the amount of cubes that is required to fill the object completely. |

cube | A3 |

rectangular prism | length times width times height |

prism | based times height |

pyramid | 1/3 base time height |

cylinder | 3.14 r2h |

cone | 1/3 3.14 r2h |

sphere | 4/3 3.14 r2 |

rate | rate= distance/time |

angles | consistent two rays that share the same endpoint (vertex). The two rays are the sides of the angle. |

acute angle | any angle that is less than 90° but greater than 0° |

obtuse angle | any angle is greater than 90° but less than 180° |

right angle | any angle measuring exactly 90° two lines that meet at a right angle are said to be perpendicular |

complementary angles | when two angles are measured the sum of their degrees is equal to 90° |

supplementary angles | when two angles are measured the sum of their degrees is equal to 180° |

favorable outcome | what someone wants to happen |

total outcome | all the things that could happen |

probability | the measure of the likelihood that an event will occur. Fractions ratios decimals percentages |

probability | to get the probability of an event count the number of times the event can acquire and divide that number by the possible number of outcome |

probability | what is the probability of rolling at three on a standard six sided die there are six possible outcomes there is only one favorable, therefore the probability of rolling up three is 1:6, 1/6, or 1 to 6 or .6 0r 16.7% |

event | this set of outcomes found with in a probability it is the occurrence ( one or more outcomes) of the probability |

combination | a selection of numbers or objects which order is not important and there is no repetition |

permutation | an arrangement of numbers or objects in which order is important and there is no repetition. If factorial is a number that is successfully multiplied down to the number one denoted by! |

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