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# Praxis II Math 0014

### Critical Thinking

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
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)
Division Quotient Remainder Separated Distribute Per Out of Percent Ratio of Divisor Dividend
Divisor How hany times to divide
Dividend The number being divided.
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!
Created by: 100000591047163