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93 Cards in this Set
- Front
- Back
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really a reading a test IMPORTANT |
READ CAREFULLY, TWICE!!!-- -write down things don't do in head -read and copy carefully |
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calculator- |
-can't think -it can do basics, plus square root -liability, be able to do fractions, not calc[
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geography of the math section |
sections contain 20 questions 2-35 minutes/section=1.75 minutes 1st7-8 are quant comparison, the remainder mixed |
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MULTIPLE CHOICe |
Multiple choice, multiple answerUse POEHave to get every selection right to get creditStill use poe |
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Quantitative Comparison |
Compare and choose ELEIMATE IF YOU CAN -ONLY NUMBERS CANT BE DONLY IF, ONLY -------- ONLY IF, ONLY NUMBERS and no variables |
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Quantitative Comparison STEPS TO CALCUALTE |
Do only as much work as you need!!! 1. ONLY NUMBERS- THEN DELETE D 2. IF ADDITTION TAKE AWAY TO COMPARE 3. COMPARE |
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SRATEGIES: KNOW THESE use on every question, make them a habit 1. Take the easy GRE first |
1.Take the easy GRE firstall count equal can mark and come backgetting question right better than getting to all!! |
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2. SRATEGIES: KNOW THESEuse on every question, make them a habit 2. BEND, DON’T PUSH |
-once you see a problem wrongly, impossible to change - IF u solve and answer not one of choices, this is what has happened -Recognize when your offtrack --More than 3 minutes, Hand not moving, Don’t know what to do next, Answer not a choiceLot of time calculating |
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how do you know your off track? |
--More than 3 minutes --Hand not moving --Don’t know what to do next --Answer not a choice --Lot of time calculating |
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what to do if you are off track? |
--BEND, DON’T PUSH, MOVER ON AND COME BACK --Walk away and comeback!!! mental strength to move away don't get stubborn!!!!!!! |
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3. STRATEGIES: KNOW THESE use on every question, make them a habit 3 POE: BALLPARK AND TRAP ANSWERS: |
-Read answers before solving -BALL PARKING Out of the ballpark, doesn’t make any sense, super obvious -Trap Answers Appear right at first glanceDon’t be tempted, if it seems to easy, it probably is |
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-Digits |
Numbers that make up other number10 digits, 0-9 -number to the left of decimal =ones or UNIT DIGIT xy in (xy.00) |
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Numbers |
-Made up of a digit (0-9) or a collection of digits- -Include negatives, fractions, decimals and square roots any number on the number line |
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Integers |
Integers are descrete -No fractional or decimal parts Ex: -1,0,1,2, -Integers are the set of whole numbers and their opposites. |
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what is Zero |
Zero is an integer - zero is neither positive nor negative, and has no sign. -KNOW!!!! IS AN INTEGER, NOT +/- ZEO IS EVEN CANT DEVIDE BY 0 |
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zero even odd? |
EVEN -Zero is an even number. In other words, its parity—the quality of an integer being even or odd—is even. The simplest way to prove that zero is even is to check that it fits the definition of "even": it is an integer multiple of 2, specifically 0 × 2. |
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1. Properties of numbers and integers |
-Numbers can be positive or negative - zero is neither +- -only integers can be defined as being odd or even, not fractions decimals..etc - EVEN=divisible by 2 WITH remainder 0 -ODD=not divisible by 2 with remainder 1 -----------Ex: 5/2=2, remainder 1 |
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2. Properties of numbers and integers |
ODD/EVEN TO 10 -----------EVEN= -4,2,0,2,4,6,8,10 -----------ODD = -1,1,2,5,7,9,111=ODD, 0=EVENZERO—KNOW!!!!IS AN INTEGER, NOT +/-ZEO IS EVENCANT DEVIDE BY 0 |
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even odd in reference to what number set |
Since odd and even numbers are defined only in reference to the set of integers --all negative numbers can also be either odd or even. - |
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3. Properties of numbers and integers - keep in mind know |
Frations= not integers= not odd or even -Any integer is even if its units digit is even - Any integer is odd if its units digit is odd |
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odd even rules -always hold true -know by memory 3 + rules, 3 * rules |
-Even +even=even -Odd+odd= odd -Even+odd=odd -Even*even=even -Odd*odd=odd -Even*odd=even |
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odd even rules - easy to memorize |
3 + rules, 3 * rules same =same same+same=same same*same=same different: DIFFERENT +DIFFERENT= ODD DIFFERENT *DIFFEREN= EVEN |
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ODD EVEN MULTIPLICATION |
IF ONE EVEN IS MULTIPLIED THEN = EVEN ALL ODD BEING MULTIPLIED= ODD --- HAS TO BE ALL ODD |
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BSOLUTE VLAUE DEFFINITION |
DISTANCE FORM ZERO: SOLVE EQUATION TWICE, SOLVING FOR A + ANSWER AND - ANSWER |
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FACTORS |
A factor is an integer that will divide evenly into the integer in question Ex: 1,2,3,4,6,12 are factors of 12 -Start with 1 and work your way up |
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Multiples |
-The multiple of an integer are all the integers that the original integer is a factor -Ex multiples of 8 are all the integers which 8 is a factor 8,16,40,24 -infinite multiples -o is a multiple |
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Prime Numbers |
An integer that has only 2 factors ----1 and its self ex: 37 is prime |
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Prime number facts: |
-0 is not prime -2 IS THE ONLY EVEN PRIME -BECAUSE YOU CAN DIVIDE 2 INTO EVEN NUMBERS ---PRIME NUMBERS ARE ONLY POSITIVE |
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is zero prime? |
0 is not prime |
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can primes be positive? |
PRIME NUMBERS ARE ONLY POSITIVE |
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Divisibility Rules KNOW ALL 4. |
1. Integer is divisible by 2 if its units digit is divisible by 2 ----------------598,447,896 is div by 2 2. divisible by 3 if sum of digits is divisible by 3 ------------------2,145= sum=12 which is divis by 3 3. divisible by 4 if last two digits FORM a number that is divis by 4 -----------------712, 12 so divis by 4 4. divis by 5 if units digit is a 5 or 0 use calculator for everything else!! |
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what integers have divisibility rules |
2, 3, 4, 5 calc for 6, 7, 8, 9, 10 |
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remainders |
--5/2=2 remainder 1 --remainder< divisor or it can go in again --5/6 = remainder 5, because 6 goes in 0 times |
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5 RULES OF EXPONENTS |
1. a^2=a*a 2. (a^2)*(a^3)=a^(2+3)=a^5 3. (a^2)^3=a^2*3=a^6 4. (a^2/a^3)=a^(2-3)=a^-1=1/a 5. (15^12)-(15^11)=15^11(15-1)=15^11(14) - no fast rule for addition/ subtraction use factoring -------example factor:2^2+2^6=2^2(1+2^2) |
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COMPARE THESE EXPONENTS 27^4 and 9^6 |
To compare put in same base!!!!!! ---1. Break down into common powers ---both have 3 in common ----27^4= (3*3*3)* (3*3*3)* (3*3*3)* (3*3*3)= (3*3*3)^4=(3^3)^4=3^12 ----9^6=(3*3)* (3*3)* (3*3)* (3*3)* (3*3)* (3*3)= (3*3)^6=(3^2)^6=3^12 |
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Square Roots |
--a^.5*b^.5=(ab)^.5 -you can multiply square roots -Can divide square roots by making numerator and denominator both their own square roots ---Cant add or subtract square roots, unless the roots are the same ---2^.5+2^.5=2(2)^.5 -ball park by finding intigers square roots +- of the number your looking for |
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KNOW THESE SQUARE ROOTS 1, 2, 3 |
-- 1^.5=1 -- 2^.5=1.4 --- 3^.5=1.7 |
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Algebra rules |
-Don’t assume you need to solve |
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RULE FOR INEQUALITIES |
-MULTIPLY/DIVIDE BY A NEGATIVE: ------SIWTCH THE INEQUALITY SIGN To add inequality equations: ---- multiply by -1 to get the sign facing same direction |
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KNOW THESE QUADRADIC BY MEMORY [X^2-Y^2] [(X+Y)^2] [(X-Y)^2] |
X^2-Y^2=(X+Y)*(X-Y) (X+Y)^2=X^2+2XY+Y^2 (X-Y)^2=X^2-2XY+Y^2 |
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Plugging in 1. |
If answers in terms of VARIABLES, plug in number for VARIABLES and find the answer in the answers 1. RECOGNIZE THE OPPORTUNITY!! ----- PLUG IN WHEN THE ANSWERS HAVE A VARIABLE, DO IT IMMEDIATELY |
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Plugging in steps: |
1.PLUG and INSOLVE FOR TARGET 2. CHECK ALL ANSWERS CHOICES 3.DON’T USE 0,1 and DON’T USE NUMBER ALREADY IN THE PROBLEM 4. DON’T PLUG IN THE SAME NUMBERS FOR MULTIPLE VARIABLES 5. DON’T USE CONVERSION NUMBER, EX: 60 FOR MINUTE/HR PROBLEMS |
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PLUGGING IN THE ANSWER QUESTION: (PITA) |
-When answers are all numbers plug into the problem to see if it works -Setup problem and plug in anwers ------Always start with middle numbers, saves time fiuring which way you need to go !!! |
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Plugging in on comp quant questions |
1. Plug in when there is variables, plug in more than once 2. Picking a or b means a or b is ALWAYS BIGGER 3STEPS: 1. Recognize the opportunity, when you see variables plug 2. Set up scratch paperv 3.plug in and eliminatego through FROZEN:::: FRACTIONS, REPEATS,ONE,ZERO,EXTREMEPLUG IN AT LEAST TWICE!!!! |
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plugging in: practical on quant comp |
1.PLUG IN NORMAL NUMBERS AND ELIMINATE 2 CHOICES 2.PLUG IN WEIRD NUMBERS (FRACTIONS O, 1,NEGATIVES) to TRY TO DISPROVE ***IF dIFFERENT NUMBERS GIVE YOU DIFFERENT ANSWRRS ITS D |
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FRACTIONS: |
1.Only reduce across multiplications signs 2. When Multiplying do top and bottom 3. Dividing =multiply the first by the second's recipicle ex:2/3 / 4/5=2/3*5/4=10/12=5/6 4. when comaring more than 2 fractions use bow tie to compare 2 of them, --------if right check next one to see if the relationship is rightbow tie work to compare because |
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Converting mixed numbers into fractions |
--2(2/3)=8/3 -Multiply denominator by the whole number this becomes new numerator, all over old denomitar |
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Comparing decimals |
--Line up the decimal points --ON QUANT COMP QUANTITY MEANS THE NUMBER VALUE REGARDLESS OF DECIMAL OR PERCENTAGE EX: 20%>15.00 |
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NUMBER VALUE |
REGARDLESS OF DECIMAL OR PERCENTAGE EX: 20%>15.00 |
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Ratios and proportion ----know |
Ratio of 1:2, means there are three part EACH PART IS 1/3 -add up the ratio and divide by the total number proportioned, and an multiply the quotient Through the ratio -proportion is an equivalent relationship - proportion problems have three values and ask for a 4th ---24 coins ratio 2:1 pennies to nickels, how many of each -----24/3=8….8*2=16…..8*1=8 nickeles = 24 total |
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Averages |
Immefiatly set up the blank formula!!!! sum numbers/number of #s=avg -UP/DOWN rule ex: Average of 3 numbers= 90 -If fourth number >90 average up If fourth number <90 average down |
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Median, |
MEDIAN=middle --MIDDLE NUMBER IN A LIST OF NUMBER HIGHEST TO LOWEST --ABOVE/BELOW THE MEDIAN HAVE = number of values --Odd amount in list= middle number - Even amount, average of the middle two |
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Mode, |
Mode=most --Number in a list that appears most |
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Range |
Difference between greatest and smallest number |
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Standard deviation 1. |
1.Immediately draw bell curve and fill in the percentages --1sd=34% on each side of mean=68 total --2sd=14%more on each side of mean= 28 more ---------2sd=96% of all data 3 sd = 2% more on each side so 98% of all data |
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Standard deviation %s |
2,14,34 1sd=68% 2sd=28 more, total 96% 3sd= 4% more, total 98% |
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statistics facts --know |
need mean to calculate sd, won't have to that on test!!!! - to find mean, add/ subtract sd to it to get to the score looking for, subtract form where where you are form whats left in the 2,14,34 total |
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Charts |
-Ets charts make it hard to find info you need -START WITH THE CHARTS-NOTE THE FOLLOWING INFO -INFO IN TITLES – what is each chart telling you -ASTRICKS, FOOTNOTES, PARANTHESES, SMALL PRINT- don’t miss critical info -FUNNY UNITS- in thousands, in millions, be aware of the unit changes -READ EVERYTHING BEFORE YOU START THE QUESTIONS. -Aproximate if appropriate |
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can you rely on the shapes? |
-DON’T RUST THE SHAPES , THEY TRY TO TRICK YOU |
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DEGREES, LINES, AND ANGLES |
-LINE=180 DEG -2 LINES INTERSECT, 4 ANGLES FORMED, SUM=360 -2 lines are PERPINDICULARly INTERSECT= 4 90 DEG ANGLES -3 INSIDE ANGLES IN A TRIANGLEADD UP TO =180 -4 INSIDE ANGLES OF ANY 4 SIDED SHAPE =360, REGARDLESS IF SQUARE OR MESSED UP SQUARE |
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VERTICLE ANGLES |
-ANGLES THAT ARE ACROSS FROM EACH OTHER (sideways/updown)WHEN TWO LINES INTERSECT X OPPSISTE SIDDES IN THIS, X SUM =360 |
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Parallel Lines, |
Parallel Lines, must be told -Never intersect - When Parallel Lines interst with a third line two types of angles are formed ----- Big and small -Big= any other big, -small = any other small -Sum of any big and any small=180 ------Immediately identify big or small |
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Triangles basics |
-RULE OF 180Every triangle has three interior angles that add to 180 |
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EQULATERIAL TRIANGLES |
special isoceles: - all 3lenghts the same =angles the same=60 -All three sides are the same length, Thus all three angles the same, Thus all three angles =60, 180/3=60 |
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ISOCELES Triangles |
= 2 the sides same, 2 angles the same -2 sides are equal -thus 2 angles are equal |
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Angle/ Side Relationship |
-LONGEST SIDE OPPOSITE LARGEST INTERIOR ANGLE -SHORTEST SIDE OPPOSITE SMALLEST ANGLE - -EQUAL ANGLES=OPPISTE EQUAL SIDES |
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THE THIRD SIDE RULE |
-The length of any one side of a triangle must be less than the sume of the other two sides -And greater than the difference between the other two sides X<y+z x>y-z |
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Area of a triangle |
A=1/2bh -Height = straight up -Point to base |
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Pythagorean theorem |
Only on right triangles - a^2+b^2=c^2 |
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RIGHT ISOSCELES |
SQUARE CUT IN HALF= RIGHT ISOSCELES= RATIO 2:45 DEG+1: 90SIDES =X+X+X*2^.5 |
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30:60:90 triangles |
-ARE Equilateral triangles divided in half vertically -to find are of Equilateral triangles Create a 30:60:90. -Ratio of sides---> base=x, heigth=x*(3)^.5 hypot=2x So … x: x*3^.5:2x -See an equalaterl triangle find height immediately |
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Chord |
-A line that connects two points on the circumference of a circle -Diameter is the longest cord -Radius not a cord because it doesn’t connect to points on the circumferen |
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Circumference/ Arc/ centeral angles |
C=(2pI)r or pi*D arc= slice of the circumference centeral angle= starts from the center and goes to two points on the circumference -360 degrees in a circle, so a 60 deg centeral angle = 60/360=1/6 of the circumference of the circle |
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Area of the circle |
A=Pi*r^2 TO FIND RADIUS: Find the square root of number being multiplied by pi in area formula |
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quadrants in graph |
No where (x,y).... (-,-),(-,+), (+,+),(+,-) are located quickly |
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Diagonals in three dimensions, square or rectangle |
-Find diagonal across base - Use that combined with the height to find the diagonal |
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Surface Area, square or rectangle |
6 sides, a rectangle can have up to 3 different areas for the sides. H, B, L |
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PLUGGING IN ON GEOMETRY PROBLEMS |
-PLUG IN IF VARIABLES IN ANSWER CHOICES -MUST FOLLOW GEOMETRIC LAWS -NO DRAWING, IT MEANS DRAW YOUR SELF -DRAW MORE THAN ONCE AND ELIMINATING ANSWERS BASED ON THE DRAWING IS LIKE PLUGGING IN |
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PROBABILITY |
-Prob= number of possible outcomes that satisfy the condition/total number of outcomes |
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-2 most important laws of probability |
1.-probability of A AND B HAPPENING= P(A)*P(B) PROB OF A OR B= P(A)+ P(B) |
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PROB GETTING HEADS TWICE WHY? |
=1/2*1/2=1/4 |
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PROB OF ONE EVENT OR ANOTHER |
ADD PROBABILITIES: EX:: DECK OF CARDS PROB YOU SELECT 1 CARD AT RANDOM, PROB YOU GET 7 OR 4? --7=4/52=1/13, PROB OF 4=4/52=1/13, SO ADD THEM UP =2/13 |
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PROB EQUATIONS |
-LIST OUT!!!!! -PROB EVENT HAPPENING + PROB EVENT NOT HAPPENIG =1' ----- PROBS HAVE TO ADD UP 100% --EX: PROB OF WINNING =.25, PROB OF LOSSING =.75 (1-.25) |
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FACTORIALS |
EX: FACTORIAL 6!=6*5*4*3*2*1=720 -SYMBOL =! -0!=1 -WRITE IT OUT AND CANCEL!!!! |
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Permutations |
-Permutation=arrangement of things in a particular order order matters EX: How many different ways can you arrange 5 books in a shelf=5*4*3*2*1 or 120 OR 5! -5 options FOR first book, 4 options FOR second book…. |
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Permutation 5 people running a race, winner gets gold, 2nd place gets silver, 3rd gets bronze. How many orders of of gold, silver, and bronze winners can there be with 5 racers? |
5*4*3=60 ORDER MATTERS |
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SOLVING permutations, -when order matter, ex ROWS, LINE ETC |
-Figure out how many slot you have -Write down the number of options for each slot -Multiply them |
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Combination: the order is irrelevant |
Ex: 5 flavours of ice cream, asked to bring home three? How mny combinations of three flavours can you take from 5 options? = 5*4*3/(3*2*1)=10 |
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To solve A combination |
1.Figure how many slots you have 2.Fill them as you would a permutation(n*n-1*n-2)Divide by the factorial of the number of slots |
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CONDITIONS IN PROB QUESTIONS |
CONSIDER FINDING NUMBER OF POSSIBILITIES WITHOUT CONDITION AND WITH CONDITION AND ADDING THEM |
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FUNCTION ARE MASKED WITH FUNKY SYMBOLS *@# |
JUST FOLLOW DIRECTIONS |
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GROUP PROBLEM FORMULA |
T= group(A)+group(B)-in both(AB)+Neither T=A+B-AB+N, then solve |
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hdh |
dd |
