Math tips and vocab Flashcards
1
Q
קודקוד של מצולע
A
vertex of square or rectangle
2
Q
Quadrilateral
A
מצולע
3
Q
מרובע חסום במעגל
A
Square ABCD is inscribed in circle O
4
Q
מהירות בבעיית תנועה
A
Rate
5
Q
1 pound
A
16 Ounces
6
Q
Equilateral Triangle
A
משולש שווה צלעות
7
Q
גובה של משולש
A
Altitude
8
Q
Tangent
A
משיק
9
Q
Consecutive positive even integers
A
2,4,6,8,10
10
Q
1/8
A
- 5%
0. 125
11
Q
1/6
A
- 6%
0. 165
12
Q
1/3
A
33%
0.33
13
Q
3/8
A
- 5%
0. 375
14
Q
2/5
A
40%
15
Q
5/8
A
- 5%
0. 625
16
Q
2/3
A
- 6%
0. 6
17
Q
3/4
A
75%
0.75
18
Q
4/5
A
80%
0.8
19
Q
5/6
A
- 3%
0. 83
20
Q
7/8
A
- 5%
0. 875
21
Q
משולש שווה שוקיים
A
Isoscles Triangle
22
Q
משולש ישר זווית
A
Right triangle
23
Q
3:4:5 Triangle
A
6:8:10
24
Q
5:12:13
A
10:24:26
25
45•:45•:90•
1:1:_\2
26
30:60:90
1 :/ 3: 2
27
מטבע הוגן
מאוזן
Fair coin
28
Diameter
קוטר
29
קו ישר שמחבר שתי נקודות שנמצאות על היקף מעגל. הקוטר הוא הארוך מבין קוים אלה.
Chord AB connects points A B on the circumference.
30
Quantitative comparison tip
Make sure to simplify expressions all the way using the enequal sign.
31
Semicircle
חצי מעגל
32
Prime number facto tip
Always decompose numbers all the way down
33
Prime numbers
1 is not a prime number
34
Geometry tip
You can't assume size according to diagram- unless it says so.
35
Data graph tip
If you misread the title of what the graph reads, you could get the question wrong. Read the titles carefully and linearly
36
Remainder tip
0 is a multiple of 7... or any other integer. So 3 is an integer- where if it is divided by 7 it leaves a remainder of 3.
37
LCM - Least common multiple
המספר הכי קטן שמתחלק בשני המספרים. 30 הינו הכפולה הקטנה ביותר של 6 ועשר.
38
GCD- Greatest common divisor.
| GCF- Greatest common factor.
The largest integer that is a factor of two numbers.
| המספר השלם הגדול ביותר שהוא גורם משותף של שני מספרים אחרים.
39
Rational number
Any number that can be expressed as a fraction
40
13 X 13
169
41
14 X 14
196
42
15 X 15
225
43
16 X 16
256
44
17 X 17
289
45
18 X 18
324
46
19 X 19
361
47
20 X 20
400
48
21 X 21
441
49
Stats tip for order of data
If they give you a set of data, make sure to organize it consecutively so that you can find the Md and the range...
50
Vertical Angles
זוויות קודקודיות
51
A line that bisects an angle
חוצה זווית לשתי זוויות שוות
52
Midpoint
נקודת האמצע על קו
53
Transversal
a line that intersects a pair of parallel lines- forming eight angles
54
Exterior Angle
זווית חיצונית למשולש
55
3 : 4 : 5 Triangle angles
a= 36.86 b = 53.13 c = 90
56
5 : 12 : 13 Triangle angles
a =
57
8 : 15 : 17 Right triangle
Remember length
58
7 : 24 : 25
Remember length
59
Sqrt (20)=Sqrt (4 X 5)
Sqrt (4) X Squrt (5)
60
Triangle Inequality
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
a < b+c
61
Triangle Inequality
The difference of the lengths of any two sides of a triangle is less than the length of the third side
A> |b - c|
62
Pentagon
five side Polygon
63
Hexagon
6 sides
64
Octagon
8 sides
65
Decagon
10 sides
66
The sum of the measures of the n angles in a polygon with n sides is
(n - 2) x 180
67
In any polygon, the sum of the exterior angles, taking one at each vertex
360
68
Regular polygon
מצולע משוכלל
69
In any regular polygon, the measure of each interior angle is
(n-2) x 180/ n
70
In any regular polygon, the measure of each exterior angle is
360/n
71
Parallelogram
מקבילית
72
Trepezoid
One pair of sides- parallel , and the other is not
73
Parallelogram area
A=bh
74
Trepezoid area
A=0.5 (b1+b2)h
75
Alternative square area formula
A=0.5d^2
Where d the length of the diagonal
76
Rectangle fact
For a given perimeter- the rectangle with the largest area; and smallest perimeter is a square
77
Arc
Two points on a circle and all points between them.
קשת
78
Central angle
Vertex is at the center of the circle
79
Inscribed in
חסום ב
80
Rectangular solid
Box
תיבה מלבנית
81
Faces
פאות
82
Edges
Sides of rectangle
83
1 yard
36 inches
84
1 yard
3 feet
85
1 foot
12 inches
86
Inequalities tip
Don't forget to switch the direction of the unequal sign when dividing and multiplying by a negative number.
When being asked for an abstract problem- make sure they are not playing with direction switching
87
Fractions and Decimals tip
0.012 does not equal 0.1212 unless they say the word approximately
88
Word problem
Always write down and circle the variable you are trying to identify
89
Rate and distance tip
Average Rate (speed)= the total distance traveled divided by the total time spent traveling.
Not necessarily X+Y/2....
Average Speed = Total Distance/ Total Time .
90
Rate and distance tip
Don't forget that when you are asked about time, and the q mentions slower- that means more seconds. And faster means less seconds...
Thus 5 seconds faster- means 5 seconds less....
91
Quartile tip
This is a GRE method- not the one learned in Israel.
A quartile is defined as the median of half of a set of data.
data.
For the first half, {2, 5, 7, 11, 16, 24}, the median is (7 + 11)/ 2 = 9 = Q1.
The first quartile (or Q1) of a set of data is the median of the lower half of the data. For the first half, {2, 5, 7, 11, 16, 24}, the median is (7 + 11)/ 2 = 9 = Q1.
92
Normal distribution
| +1 sd
+1 SD= 34%
93
Normal distribution
| +2 SD
+2 SD= 48%
94
Linear transformation on distribution
multiplying all numbers by a number will change the standard deviation
Sy= |a|*Sx
95
Markup
Markup is the difference between the cost of a good or service and its selling price.
A markup is added to the total cost incurred by the producer in order to produce a profit.
96
% tip
When working with %, always remember to relate the percent change to the original quantity.
That is- as the question what is the original quantity at a given time?
And then - what kind of percentage change would it need to be multiplied with in order to arrive at quantity 2.
97
Semantics regarding word problems
Notice the difference between "at least" and "greater than".
98
Factoring tip
When finding the factors of two given numbers you need to look for all possible combinations
99
Tenths digit
ספרת העשיריות אשר מימין לנקודה
100
Tens digit
ספרת העשרות אשר משמאל לנקודה וגם משמאל לספרת האחדות
101
Polygon angle tip
Do not assume that a picture of a regular polygon is indeed in fact a regular polygon- they might be trying to trick you...
102
Hypotenuse
יתר
103
Triangle third side law
you can use both parts of the rule a+b>c and c>a-b.... to create a range
104
quadratic equation
משוואה ריבועית
| aX^2+bX+c=0
105
x^a=x^b
a=b ; unless x=1
106
a^2-b^2
(a+b)(a-b)
107
quadratic equation
משוואה ריבועית
108
x^a=x^b
a=b
109
(X^a)(X^b)
X^a+b
110
X^a/X^b
X^a-b= 1/X^b-a
111
X^0
0; 0^0 is non-defined
112
(X^a)(Y^a)
(XY)^a
113
(X^a)^b
X^ab
114
The quadratic formula
-b+-sqrt(b^2-4ac)/2a=x
115
Solution set for inequality
defined as the set of all real numbers that can satisfy the inequality - apparent by solving the inequality.
116
Simple interest
Based only on the initial deposit- called the principal
117
Principal (of interest)
the amount on which interest is computed- for a given period of time
118
Interest
earned on an investment over a specific time period
119
Simple interest
Based only on the initial deposit- serves as the amount on which interest is computed
120
V=P(1+rt/100)
The Value V at the end of t years equals the amount invested (P) x (1+rt/100). for a given interest of r %.
121
Compound interest
in the case of compound- interest is added to the principal at regular time intervals. Each addition of interest is termed - compounded.
In an annual interest compounding.
V=p(1+r/100)^t
122
Compound interest n times per year
V=P(1+r/100n)^nt
123
(C G) Coordinate Geometry Symmetry
P 4 is the reflection P 1 about the X-axis= P 2 and P 1 are symmetric about the x-axis
P 2 is the same for the Y axis.
P 3 is the same for the origin.
124
(C G) Coordinate geometry distance between two points
Use the pythagorian theorem
Construct a right triangle. Sometimes you can invent a point that is not even there to construct a right triangle.
Find the hypothenus- Yeter.
125
(C G) Slope equation
Y2-Y1/X2-X1 Called rise over run
126
(C G) Horizontal line coordinate geometry
y=b; While m=0
127
(C G) Line equation
Y=mX+b
128
(C G) Parallel lines
Have the same slopes- i.e. the slopes are equal.
129
(C G) Perpendicular lines
Slopes are negative reciprocals of each other.
130
(C G) Perpendicular of Y= 2X+5
Y= - 1/2X +b
131
(C G) Intercept of X
Y=0
132
(C G) Solution to a system of two linear equations of the form Y=mX+B
It is the point where the two lines intersect on the graph
133
(C G) Solution to a system of two linear inequalities of the form: y=mx+b
Each point that satisfies an inequality is either on the line-or below/above it...
Therefore the graph might consist of the line and all of the area below it/above it.
Thus the solution of the system consists of all of the points that lie in the shaded region that is common to the two line boundaries.
134
(C G) Y=X Symmetry
For any point (a,b), a point with interchanged coordinates (b,a) is a reflection of (a,b) about the line y=x;
In other words- (a,b) and (b,a) are symmetric about the line Y=X -- this is true for any graph and for any point- about this special line.
135
(C G) Interchanged Y and X
Interchanging Y and X in the equation of any line yields another graph that is the reflection of the original graph about the line y=x
136
(C G) Parabola
Y = ax^2 + bx + c;
a, b, c are constants.
a =/o.
137
(C G) X intercept of parabola
When- ax^2 + bx + c=0
138
(C G) Vertex of parabola
Point of min or max. Determined by the value of a -+
139
(C G) Parabola symmetry
Every parabola is symmetric with itself about the vertical line that passes through its vertex.
The two x-intercepts are equidistant from this line of symmetry.
140
(C G) Parabola y coordinate
When x equals 0
141
(C G) A graph of a circle
(x-a)^2+(y-b)^2 = r^2
Center of the circle is at point a,b -- and the radius is r.
142
(C G) h(x)= |x|
A piecewise-defined function:
| h (x) = { x, x >=0 ; -X , X< =0}
143
(C G) Shifting :The graph of h(x)+c
The graph of h(x) shifted upward by c units.
144
(C G) h(x) - C
The graph of h(x) shifted downward by c units.
145
(C G) the graph of h(x+c)
The graph of h(x) shifted to the left by c units
146
(C G) The graph of h(x-c)
The graph of h (x) shifted to the right by c units.
147
f(x)=2|x-1|
The graph of |X| shifted to the right by one unit and then stretched vertically away from the x axis by a factor of 2
148
ch(x)
The graph of h(X) stretched vertically by a factor of c if c>1
149
ch(x)
The graph of h(x) shrunk vertically by a factor of c if 0<1
150
Congruent line segments
Line segments that have equal lengths
151
Line segment
A part of a line that contains all points between two end points on the line- including the end points.
152
Opposite angles = vertical angles
זוויות קודקודיות
153
congruent angles
Angles that have equal measures
154
Acute angle
has less than 90 degrees.
| זווית חדה.
155
Obtuse angle
זווית קהה
156
Polygon
A closed figure formed by 3 or more line segments
157
Side of polygon
פאות המצולע
158
Vertices
קודקודי המצולע
End points of polygons where a side is joined by two other sides.
159
Dividing polygons into triangles
Polygon with n sides can be divided into n-2 triangles
A pentagon can be divided into 3 triangles
160
Sum of measures of the interior angles of a polygon
(n-2)(180)
161
Legs of a right triangle
ניצבים
162
congruent triangles
משולשים זהים
Have 3 identical sides.
or
Have 2 identical sides and identical included angle.
or
2 Identical angles and congruent included angle.
163
Similar Triangles
have congruent angles.
| And similar sides in terms of ratios.
164
Triangle ABC and DEF are similar
AB/DE=BC/EF=AC/DF
165
Sector of a cirle
Is a region bounded by an arc of the circle and two radii.
166
Point of tangency
נקודת ההשקה
167
Radios drawn to the tangent point
Forms a 90 degree angle with the tangent.
168
A polygon is inscribed in a circle
A circle is circumscribed about the polygon
169
Inscribed right triangle
Has one side as the diameter of the circle.
| The hypothenus.
170
A polygon is circumscribed about a circle.
If each side of the polygon is tangent to the circle.
| Equivalently- the circle is inscribed inside a polygon.
171
Two or more circles with the same center
are called concentric circles.
172
Rectangular solid
תיבה
12 Edges.
8 vertices.
173
Face of rectangular solid
פאות התיבה
174
Edge of rectangular solid
Line segment that is the intersection of two faces.
175
Vertex of rectangular solid
The point at which edges intersect.
176
Volume of rectangular solid
V=l*w*h
177
Surface area of rectangular solid
A=2(lw+lh+wh)
178
Circular cylinder
Galil
It has an axis which is the line that connects the centers of the two bases.
179
Right circular cylinder
The axis is perpendicular to the bases.
| The length of the axis is the height of the cylinder.
180
Volume of right rectangular cylinder
V= πr^2h
181
Surface are of right rectangular cylinder
A=2(πr^2)+ 2πrh
182
When working with a parrallelogram
Don't assume that the diagonal creates a 90 degree angle with anything.
183
Similar triangles
Remember to use similarity of sides as ratio equations- instead of taking longer routes such as the `pythagorean theorem.
184
Similarity of triangles
Applies to the sides. But not necessarily to the area.
To compare the areas of two similar triangles, you need to breakdown the area equation of both triangles, and see how they compare.
185
Parameter of triangle
Knowing only the parameter of a triangle is not enough to determine it's minimal area. The maximal area can be determined using the equilateral, but the minimal area can be closed to 0 when the triangle is stretched all the way....
186
Tip
Remember to divide by 2 when calculating triangle area
187
Triangle tip
If you know that the sides of a triangle are for example 8, 15, 17... than you know it's a right triangle without even knowing the angles. This is because of the ratios triangles have with their angles.
188
Measures of central tendency
מדדי מרכז
189
Measures of position
מדדי מיקום
190
Measures of dispersion
מדדי פיזור
191
Percentiles
There are 99 percentile numbers that divide the data into 100 roughly equal groups.
192
Quartiles
(From L to Q1), (from Q1 to Md (Q2)), (from Md to Q3), (from Q3 to G).
193
Quartiles 2
Q2=Md; Divides the data into two equal parts.
Q1 divides the lower part into to equal parts (The Md).
Q3 is the median of the greater group.
194
Range
Difference between G and L. The greatest and the lowest respectively.
195
Outliers
GRE uses the term outliers in the context of range of distribution.
196
Interquartile range
Not affected by outliers.
Q3-Q1.
Measures the spread of the middle half of the data.
197
Box-plot
Also called Box-and-whisker plot.
A plotting on the number line of: L, Q1, Q2, Q3, and G.
They show where the 4 quartile groups lie
The box can be used to identify each of two middle quartile groups of data, and "whiskers" extend from them to the extreme values.
They are useful for comparing two sets of data side by side.
198
Standard Deviation
GRE algorithm:
1. Calculate the mean of n values.
2. Find the difference between the mean and each of the n values.
3. Squaring each of these differences.
4. Finding the average of the n squared differences.
5. Taking the non-negative squared root of the average squared differences.
199
Sample standard deviation
Dividing the sum of the squared differences by (n-1) instead of n.
טעות התקן.
Different than-
population standard deviation.
Which is סטיית תקן
200
Distances in SDs
Or standardization
A given point could have a distance from the mean by:
x-x'/sd....
Also creates the process of standardizing the data.
For each point it creates a measure of position relative to the rest of the data regardless of the variable and measuring units of that variable.
201
Most of the data
In any group of data, most of the data are within about 3 SDs above or below the mean.
After standardizing the mean becomes 0 and a number line extending from -3 Z and +3Z
202
Counting methods
Counting objects in probability theory
203
Set
| קבוצה
A collection of members or elements that have the same property.
Finite sets and infinite sets.
204
Empty set
קבוצה ריקה
205
Subset
{2,8} is a subset of {0,2,4,6,8}.
| 0/ is a subset of every set.
206
A list
A set in which the members are ordered
207
Element repetition in a list
repetition of elements in a list- does not add more elements in the set.
208
The number of elements |S|
S={1,2,3,4,5} ; |S| = 5 ; |0/| = 0
209
The intersection of S and T
The set of all elements that are in both S and T and is denoted by S ח T
210
The union of S and T
S U T
211
Disjoint sets
or mutually exclusive sets
S and T have no mutual elements
S ח T = 0/
212
|AUB|
|A|+|B| - |A ח B|
213
Multiplication principle
Choice 1: K ; Choice 2: M : K x M different possibilities
214
Permutations
Each order of n objects is called a permutation
215
N Factorial
!N עצרת
| 0!=1
216
n!/(n-k)!
The number of ways to select and order k objects out n objects
The number of permutations of n objects taken k at a time
217
Combinations
Selecting K objects without caring about orders.
Number of ways to select without order=
The number of ways to select with order
: by
The number of ways to order
218
The numbers of N objects taken K at a time
n!/k!(n-k)!
Given a set S
The formula gives:
The number of subsets of S that consist of k elements.
219
N choose 0
n!/0!n! = 1
| the only subset of S with 0 elements is the empty set.
220
Random experiment
The result is uncertain
221
Sample space
The set of all possible outcomes for a random experiment.
222
Event
A particular set of outcomes
223
Random selection
Each of the events is equally likely to to be selected (occur)
224
P(E)
The number of names in event E/The total number of possible outcomes in the experiment
225
E ח F
The event that both E and F occur
226
P(E) U P(F)
P(E) + P (F) - P (E ח F)
227
P(E) ח P (F)= 0
The events are mutually exclusive
228
Independent events
E and F are independent if the occurrence of one event doesn't affect the occurrence of the other.
In which case P (E ח F)= P(E)*P(F)
229
Non independent events
P (E ח F) =\ P (E) * P (F)
230
A random variable
For a random variable that represents a randomly chosen value from a distribution of data, the probability distribution of the random variable is the same as the relative frequency distribution of the data.
The distribution can be represented by a histogram.
231
The mean of a random variable X
The expected value
| The sum of each value of X multiplied with its probablity
232
Discrete random variables
Consist of discrete points on a number line
233
In the histogram for a random variable
the area of each bar is proportional to the probability represented by the bar.
234
Uniform distribution
One in which every outcome has the same probablity
235
In a normal distribution- about 2/3 of the data
are located within 1 SD of the mean
236
In a normal distribution almost all of the data is located
within 2 SD of the mean
237
In a normal distribution M+2SD
34%+14%
238
In a normal distribution M+3SD
34%+14%+2%
239
Data entry tip
If the question says: "give your answer to the nearest .01"
| You need to be extra careful
240
Range of definition
Sometimes they might try to trick you with the range of definition of a function. You need to make sure the function is either specifically defined (i.e= x=/1) or define it yourself... especially if there is a division line. Don't become too habituated.
241
Sum of arithmetic sequence
n(a1+an)/2
242
Arithmetic sequence term
an = a1 + (n-1)d
an = am+ (n-m)d
243
Zero
Is an integer
244
Coordinate geometry
Inequalities can be used for the area beneath or above a line. Then you can use these inequalities to check if any point satisfies the inequality to determine if it's in the aforementioned area.
245
Sets
It can be wise to solve set problems with Venn diagrams.
246
Within 2 standard deviations of the mean
All numbers from -2SD till +2SD
247
Drawn to scale
Even a coordinate geometry X and Y axes need to be proclaimed as drawn to scale.
248
Range comparison tip
Be extra sure not to forget about >= . if something needs to be larger than something else... then it can't be equal to something else
249
Geometric Progression
a(n)= r * a(n-1)
a(n) = a1 * r ^ (n-1)
250
Sum of Geometric progression
a1 * (1-r^n)/1-r
251
0.17 Billion
170 Million
252
0.17 Million
170,000
253
Before you answer a question
Read it until the end one more time, to make sure what they want of you
254
The word non-negative
Actually means positive or zero
255
When evaluating quantitative comparison
Make sure to check between numbers which are positive and larger than the classic choice of 1 & 2.
Pick 6 & 8, or even larger numbers, just to make sure if anything changes. Do the same for negative numbers.
256
When answering a multiple choice question
Look at all answer choices as sometimes there are different levels of perceived truth
257
If they tell you in a question that one of the variables =/ 0
Be prepared to divide something by that element
258
Classic combinatorics formula accounting for subgroups among which order does not matter
Total number of items!/FirstGroup! SecondGroup! ThirdG!etc
259
Overlapping sets formula
Total = G1+G2-Both+Neither
260
When you have marbles with different colours pulled out of a hat
Sometimes the order does not matter
261
Nearest whole percent
They asked me for the nearest whole percent of 0.666
And I accidentally gave 66%/
It should have been 67%
262
CG common mistake
I was looking at a point in the (-,-) quadrant of the graph. And failed to think about the fact that (c,d) are both negative- and so the larger absolute value makes a variable smaller in this case.
