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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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