Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

GRE Quantitative Reasoning Prep, Exams of Advanced Education

University of WitwatersrandAdvanced Education

GRE Quantitative Reasoning Prep

Typology: Exams

2024/2025

Available from 11/17/2024

alex-david-34
alex-david-34 🇿🇦

4.5

(4)

5.6K documents

1 / 22

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
GRE Quantitative Reasoning Prep
EVEN + EVEN = - EVEN
EVEN - EVEN = - EVEN
EVEN + ODD = - ODD
EVEN - ODD = - ODD
ODD + ODD = - EVEN
ODD - ODD = - EVEN
ODD × ODD = - ODD
EVEN × ODD = - EVEN
EVEN × EVEN = - EVEN
LEAST COMMON MULTIPLE - THE LEAST POSITIVE INTEGER THAT IS A MULTIPLE OF
BOTH A AND B. FOR EXAMPLE, THE LEAST COMMON MULTIPLE OF 30 AND 75 IS 150.
THIS IS BECAUSE THE POSITIVE MULTIPLES OF 30 ARE 30, 60, 90, 120, 150, 180,
210, 240, 270, 300, ETC., AND THE POSITIVE MULTIPLES OF 75 ARE 75, 150,
225, 300, 375, 450, ETC. THUS, THE COMMON POSITIVE MULTIPLES OF 30 AND 75
ARE 150, 300, 450, ETC., AND THE LEAST OF THESE IS 150.
GREATEST COMMON DIVISOR (OR GREATEST COMMON FACTOR) - THE GREATEST
POSITIVE INTEGER THAT IS A DIVISOR OF BOTH A AND B. FOR EXAMPLE, THE GREATEST
COMMON DIVISOR OF 30 AND 75 IS 15. THIS IS BECAUSE THE POSITIVE DIVISORS OF
30 ARE 1, 2, 3, 5, 6, 10, 15, AND 30, AND THE POSITIVE DIVISORS OF 75 ARE 1, 3,
pf3
pf4
pf5
pf8
pf9
pfa
pfd
pfe
pff
pf12
pf13
pf14
pf15
pf16

Partial preview of the text

Download GRE Quantitative Reasoning Prep and more Exams Advanced Education in PDF only on Docsity!

GRE Quantitative Reasoning Prep

EVEN + EVEN = - EVEN

EVEN - EVEN = - EVEN

EVEN + ODD = - ODD

EVEN - ODD = - ODD

ODD + ODD = - EVEN

ODD - ODD = - EVEN

ODD × ODD = - ODD

EVEN × ODD = - EVEN

EVEN × EVEN = - EVEN

LEAST COMMON MULTIPLE - THE LEAST POSITIVE INTEGER THAT IS A MULTIPLE OF

BOTH A AND B. FOR EXAMPLE, THE LEAST COMMON MULTIPLE OF 30 AND 75 IS 150.

THIS IS BECAUSE THE POSITIVE MULTIPLES OF 30 ARE 30, 60, 90, 120, 150, 180,

210, 240, 270, 300, ETC., AND THE POSITIVE MULTIPLES OF 75 ARE 75, 150,

225, 300, 375, 450, ETC. THUS, THE COMMON POSITIVE MULTIPLES OF 30 AND 75

ARE 150, 300, 450, ETC., AND THE LEAST OF THESE IS 150.

GREATEST COMMON DIVISOR (OR GREATEST COMMON FACTOR) - THE GREATEST

POSITIVE INTEGER THAT IS A DIVISOR OF BOTH A AND B. FOR EXAMPLE, THE GREATEST

COMMON DIVISOR OF 30 AND 75 IS 15. THIS IS BECAUSE THE POSITIVE DIVISORS OF

30 ARE 1, 2, 3, 5, 6, 10, 15, AND 30, AND THE POSITIVE DIVISORS OF 75 ARE 1, 3,

5, 15, 25, AND 75. THUS, THE COMMON POSITIVE DIVISORS OF 30 AND 75 ARE 1,

3, 5, AND 15, AND THE GREATEST OF THESE IS 15.

PRIME NUMBER - AN INTEGER GREATER THAN 1 THAT HAS ONLY TWO POSITIVE

DIVISORS: 1 AND ITSELF

FIRST TEN PRIME NUMBERS - 2, 3, 5, 7, 11, 13, 17, 19, 23, AND 29

PRIME FACTORIZATION - EVERY INTEGER GREATER THAN 1 EITHER IS A PRIME NUMBER

OR CAN BE UNIQUELY EXPRESSED AS A PRODUCT OF FACTORS THAT ARE PRIME

NUMBERS, OR PRIME DIVISORS

COMPOSITE NUMBER - AN INTEGER GREATER THAN 1 THAT IS NOT A PRIME NUMBER

THE FIRST TEN COMPOSITE NUMBERS - 4, 6, 8, 9, 10, 12, 14, 15, 16, AND 18

ADD TWO FRACTIONS WITH THE SAME DENOMINATOR - ADD THE NUMERATORS AND

KEEP THE SAME DENOMINATOR. FOR EXAMPLE, - 8 / 11 + 5 / 11 = -8 + 5 / 11 = -

ADD TWO FRACTIONS WITH DIFFERENT DENOMINATORS - TO ADD TWO FRACTIONS

WITH DIFFERENT DENOMINATORS, FIRST FIND A COMMON DENOMINATOR, WHICH IS

A COMMON MULTIPLE OF THE TWO DENOMINATORS. THEN CONVERT BOTH

FRACTIONS TO EQUIVALENT FRACTIONS WITH THE SAME DENOMINATOR. FINALLY,

ADD THE NUMERATORS AND KEEP THE COMMON DENOMINATOR. SO: 1/3 + -2/5 =

TO MULTIPLY TWO FRACTIONS - MULTIPLY THE TWO NUMERATORS AND MULTIPLY

THE TWO DENOMINATORS. SO: (10/7) (-1/3) = (10)(-1) / (7)(3) = -10/

TO DIVIDE ONE FRACTION BY ANOTHER - FIRST INVERT THE SECOND FRACTION—THAT

IS, FIND ITS RECIPROCAL—THEN MULTIPLY THE FIRST FRACTION BY THE INVERTED

FRACTION. SO (3/10)/(7/13) = (3/10)(13/7) = 39/

PROPORTION - A PROPORTION IS AN EQUATION RELATING TWO RATIOS; FOR

EXAMPLE, 9 / `2 = 3 / 4. TO SOLVE A PROBLEM INVOLVING RATIOS, YOU CAN OFTEN

WRITE A PROPORTION AND SOLVE IT BY CROSS MULTIPLICATION

PERCENTAGE - PART / WHOLE (100) = %

PERCENT CHANGE - IF A QUANTITY INCREASES FROM 600 TO 750, THEN THE

PERCENT INCREASE IS FOUND BY DIVIDING THE AMOUNT OF INCREASE, 150, BY THE

BASE, 600, WHICH IS THE INITIAL NUMBER GIVEN

PERCENT CHANGE FORMULA - DIFFERENCE / ORIGINAL (100) = % INCREASE

CUMULATIVE PERCENT CHANGE - MUST CALCULATE EACH SUCCESSIVE PERCENT

CHANGE BY USING THE RESULT OF THE PREVIOUS CHANGE AS THE NEW ORIGINAL

ORDER OF OPERATIONS - BEDMAS (BRACKETS, EXPONENTS, DIVISION /

MULTIPLICATION, ADDITION / SUBTRACTION)

X^1 = - X

X^0 = - 1

X^-1 = - 1/X

X^M X^N = - XM+N

X^M/X^N = - X^M-N (ALSO = 1 / X^M-N)

(X^M)^N = - X^MN

(XY)^N = - X^N Y^N

(X/Y)^N = - X^N/Y^N

X^-N = - 1/X^N

(X^A)(Y^A) = - XY^A

IDENTITY - A STATEMENT OF EQUALITY BETWEEN TWO ALGEBRAIC EXPRESSIONS THAT

IS TRUE FOR ALL POSSIBLE VALUES OF THE VARIABLES INVOLVED

(A + B)^2 = - A^2 + 2AB + B^

(A - B)^3 - A^3 - 3A^2B + 3AB^2 - B^

A^2 - B^2 = - (A + B) (A - B)

X^30 - X^29 = - X(X^29) - X^

LINEAR EQUATION - A LINEAR EQUATION IS AN EQUATION INVOLVING ONE OR MORE

VARIABLES IN WHICH EACH TERM IN THE EQUATION IS EITHER A CONSTANT TERM OR A

VARIABLE MULTIPLIED BY A COEFFICIENT. NONE OF THE VARIABLES ARE MULTIPLIED

TOGETHER OR RAISED TO A POWER GREATER THAN 1

QUADRATIC EQUATION - AN EQUATION THAT CAN BE WRITTEN IN THE FORM AX^2 +

BX + C = 0, WHERE A,B,AND C ARE REAL NUMBERS AND A ≠ 0

QUADRATIC FORMULA - X = -B ± √(B² - 4AC)/2A

USE THIS TO DETERMINE THE VALUE OF VARIABLES IN QUADRATIC EQUATIONS.

QUADRATIC EQUATIONS HAVE AT MOST TWO REAL SOLUTIONS

FOIL - MULTIPLY THE FIRST, OUTER, INNER, AND LAST TERMS OF A PAIR OF

BINOMIALS

INEQUALITY - < > ≤ ≥

SLOPE (M) - RISE/RUN, Y2-Y1/X2-X 1

EQUATION OF A LINE - Y = MX + B

B IS THE Y-INTERCEPT, Y IS THE POINT ON THE Y AXIS, X IS THE POINT ON THE X AXIS.

GRAPH OF AN EQUATION - EQUATIONS IN TWO VARIABLES CAN BE REPRESENTED AS

GRAPHS IN THE COORDINATE PLANE. IN THE XY-PLANE, THE GRAPH OF AN EQUATION

IN THE VARIABLES X AND Y IS THE SET OF ALL POINTS WHOSE ORDERED PAIRS (, XY

SATISFY THE EQUATION.

GRAPHING LINEAR INEQUALITIES - GRAPHS OF LINEAR EQUATIONS CAN BE USED TO

ILLUSTRATE SOLUTIONS OF SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES. SOLVE

EACH EQUATION FOR Y IN TERMS OF X, THEN GRAPH EACH. THE SOLUTION OF THE

SYSTEM OF EQUATIONS IS THE POINT AT WHICH THE TWO GRAPHS INTERSECT.

GRAPH OF A QUADRATIC EQUATION - THE GRAPH OF A QUADRATIC EQUATION OF THE

FORM Y = AX^2 + BX + C, WHERE A, B, AND C ARE CONSTANTS AND A ≠ 0 IS A

PARABOLA

PARABOLA - THE GRAPH OF A QUADRATIC EQUATION OF THE FORM Y = AX^2 + BX +

C, WHERE A, B, AND C ARE CONSTANTS AND A ≠ 0 IS A PARABOLA THE X-INTERCEPTS

OF THE PARABOLA ARE THE SOLUTIONS OF THE EQUATION AX^2 + BX + C = 0. IF A IS

POSITIVE, THE PARABOLA OPENS UPWARD AND THE VERTEX IS ITS LOWEST POINT. IF A

IS NEGATIVE, THE PARABOLA OPENS DOWNWARD AND THE VERTEX IS THE HIGHEST

POINT. EVERY PARABOLA IS SYMMETRIC WITH ITSELF ABOUT THE VERTICAL LINE THAT

PASSES THROUGH ITS VERTEX. IN PARTICULAR, THE TWO X-INTERCEPTS ARE

EQUIDISTANT FROM THIS LINE OF SYMMETRY.

GRAPH OF A CIRCLE - (X - A)^2 + (Y - B)^2 = R^2 (CENTRE IS AT POINT A, B AND

RADIUS OF R)

GRAPHING A FUNCTION IN THE XY-PLANE - TO GRAPH A FUNCTION IN THE XY-PLANE,

YOU REPRESENT EACH INPUT X AND ITS CORRESPONDING OUTPUT (F)X AS A POINT (X,

Y) WHERE Y = F(X). IN OTHER WORDS, YOU USE THE X-AXIS FOR THE INPUT AND THE

Y-AXIS FOR THE OUTPUT.

WEIGHTED AVERAGE - EXAMPLE: 2 (X) + 1 (Y) / 2 + 1 = A (WHERE 2 AND 1

REPRESENT THE RATIO OF EACH ENTITY)

OPPOSITE/VERTICAL ANGLES - CREATED WHEN TWO LINES INTERSECT AT A POINT.

OPPOSITE ANGLES HAVE EQUAL MEASURES, AND ANGLES THAT HAVE EQUAL

MEASURES ARE CALLED CONGRUENT ANGLES. HENCE, OPPOSITE ANGLES ARE

CONGRUENT. THE SUM OF THE MEASURES OF THE FOUR ANGLES IS 360.

SUM OF THE MEASURES OF THE INTERIOR ANGLES OF A TRIANGLE - 180 DEGREES

SUM OF THE MEASURES OF THE INTERIOR ANGLES OF AN N-SIDED POLYGON - (N - 2)

(180 DEGREES)

EQUILATERAL TRIANGLE - A TRIANGLE WITH THREE CONGRUENT SIDES IS CALLED AN

EQUILATERAL TRIANGLE. THE MEASURES OF THE THREE INTERIOR ANGLES OF SUCH A

TRIANGLE ARE ALSO EQUAL, AND EACH MEASURE IS 60 DEGREES.

ISOSCELES TRIANGLE - A TRIANGLE WITH AT LEAST TWO CONGRUENT SIDES IS CALLED

AN ISOSCELES TRIANGLE. IF A TRIANGLE HAS TWO CONGRUENT SIDES, THEN THE

ANGLES OPPOSITE THE TWO SIDES ARE CONGRUENT. THE CONVERSE IS ALSO TRUE.

RIGHT TRIANGLE - A TRIANGLE WITH AN INTERIOR RIGHT ANGLE IS CALLED A RIGHT

TRIANGLE. THE SIDE OPPOSITE THE RIGHT ANGLE IS CALLED THE HYPOTENUSE; THE

OTHER TWO SIDES ARE CALLED LEGS.

PYTHAGOREAN THEOREM - A^2 + B^2 = C^

AREA OF A TRIANGLE - A=½BH OR BH/

THE CIRCLE TO THE TWO ENDPOINTS OF THE ARC. AN ENTIRE CIRCLE IS CONSIDERED

TO BE AN ARC WITH MEASURE 360 DEGREES

LENGTH OF AN ARC - AN ARC IS A PIECE OF THE CIRCUMFERENCE. IF N IS THE DEGREE

MEASURE OF THE ARC'S CENTRAL ANGLE, THEN THE FORMULA IS: LENGTH OF AN ARC

= 1 (N/360) (2ΠR)

CENTRAL ANGLE - A CENTRAL ANGLE OF A CIRCLE IS AN ANGLE WITH ITS VERTEX AT

THE CENTER OF THE CIRCLE.

AREA OF A CIRCLE - A=∏R²

SECTOR - A SECTOR OF A CIRCLE IS A REGION BOUNDED BY AN ARC OF THE CIRCLE

AND TWO RADII

AREA OF A SECTOR - A = ∏R² (C/360), WHERE C = THE CENTRAL ANGLE)

RECTANGULAR SOLID - A RECTANGULAR SOLID HAS SIX RECTANGULAR SURFACES

CALLED FACES, AS SHOWN IN THE FIGURE BELOW. ADJACENT FACES ARE

PERPENDICULAR TO EACH OTHER. EACH LINE SEGMENT THAT IS THE INTERSECTION OF

TWO FACES IS CALLED AN EDGE, AND EACH POINT AT WHICH THE EDGES INTERSECT IS

CALLED A VERTEX. THERE ARE 12 EDGES AND 8 VERTICES. THE DIMENSIONS OF A

RECTANGULAR SOLID ARE THE LENGTH L, THE WIDTH W, AND THE HEIGHT H.

VOLUME OF RECTANGULAR SOLID - V = LWH

SURFACE AREA OF RECTANGULAR SOLID - A = 2(LW + LH + WH) -- THE SUM OF THE

AREAS OF THE SIX FACES

LENGTH OF DIAGONAL IN RECTANGULAR PRISM - A^2+B^2+C^2 = D^2 OR

L^2+W^2+H^2 = D^2 (A IS NOT AREA, JUST A SIDE LENGTH)

CIRCULAR CYLINDER - A CIRCULAR CYLINDER CONSISTS OF TWO BASES THAT ARE

CONGRUENT CIRCLES AND A LATERAL SURFACE MADE OF ALL LINE SEGMENTS THAT

JOIN POINTS ON THE TWO CIRCLES AND THAT ARE PARALLEL TO THE LINE SEGMENT

JOINING THE CENTERS OF THE TWO CIRCLES. THE LATTER LINE SEGMENT IS CALLED

THE AXIS OF THE CYLINDER. A RIGHT CIRCULAR CYLINDER IS A CIRCULAR CYLINDER

WHOSE AXIS IS PERPENDICULAR TO ITS BASES.

VOLUME OF A RIGHT CIRCULAR CYLINDER - V = (PI)R^2H

SURFACE AREA OF A RIGHT CIRCULAR CYLINDER - A = 2(ΠR^2) + 2ΠRH

FREQUENCY/COUNT - THE FREQUENCY, OR COUNT, OF A PARTICULAR CATEGORY OR

NUMERICAL VALUE IS THE NUMBER OF TIMES THAT THE CATEGORY OR VALUE APPEARS

IN THE DATA. A FREQUENCY DISTRIBUTION IS A TABLE OR GRAPH THAT PRESENTS THE

CATEGORIES OR NUMERICAL VALUES ALONG WITH THEIR ASSOCIATED FREQUENCIES.

RELATIVE FREQUENCY - THE RELATIVE FREQUENCY OF A CATEGORY OR A NUMERICAL

VALUE IS THE ASSOCIATED FREQUENCY DIVIDED BY THE TOTAL NUMBER OF DATA.

RELATIVE FREQUENCIES MAY BE EXPRESSED IN TERMS OF PERCENTS, FRACTIONS, OR

DECIMALS. A RELATIVE FREQUENCY DISTRIBUTION IS A TABLE OR GRAPH THAT

PRESENTS THE RELATIVE FREQUENCIES OF THE CATEGORIES OR NUMERICAL VALUES

AVERAGE (ARITHMETIC MEAN) - TO CALCULATE THE AVERAGE OF N NUMBERS, TAKE

THE SUM OF THE N NUMBERS AND DIVIDE IT BY N.

WEIGHTED AVERAGE/MEAN - WHEN SEVERAL VALUES ARE REPEATED IN A LIST, IT IS

HELPFUL TO THINK OF THE MEAN OF THE NUMBERS AS A WEIGHTED MEAN OF ONLY

THOSE VALUES IN THE LIST THAT ARE DIFFERENT. THE NUMBER OF TIMES A VALUE

APPEARS IN THE LIST, OR THE FREQUENCY, IS CALLED THE WEIGHT OF THAT VALUE.

MEDIAN - TO CALCULATE THE MEDIAN OF N NUMBERS, FIRST ORDER THE NUMBERS

FROM LEAST TO GREATEST. IF N IS ODD, THEN THE MEDIAN IS THE MIDDLE NUMBER

LIST - A LIST IS LIKE A FINITE SET, HAVING MEMBERS THAT CAN ALL BE LISTED, BUT

WITH TWO DIFFERENCES. IN A LIST, THE MEMBERS ARE ORDERED; THAT IS,

REARRANGING THE MEMBERS OF A LIST MAKES IT A DIFFERENT LIST. THUS, THE

TERMS "FIRST ELEMENT," "SECOND ELEMENT," ETC., MAKE SENSE IN A LIST. ALSO,

ELEMENTS CAN BE REPEATED IN A LIST AND THE REPETITIONS MATTER. FOR EXAMPLE,

THE LISTS 1, 2, 3, 2 AND 1, 2, 2, 3 ARE DIFFERENT LISTS, EACH WITH FOUR

ELEMENTS, AND THEY ARE BOTH DIFFERENT FROM THE LIST 1, 2, 3, WHICH HAS

THREE ELEMENTS

MULTIPLICATION PRINCIPLE - SUPPOSE THERE ARE TWO CHOICES TO BE MADE

SEQUENTIALLY AND THAT THE SECOND CHOICE IS INDEPENDENT OF THE FIRST CHOICE.

SUPPOSE ALSO THAT THERE ARE K DIFFERENT POSSIBILITIES FOR THE FIRST CHOICE

AND M DIFFERENT POSSIBILITIES FOR THE SECOND CHOICE. THE MULTIPLICATION

PRINCIPLE STATES THAT UNDER THOSE CONDITIONS, THERE ARE KM DIFFERENT

POSSIBILITIES FOR THE PAIR OF CHOICES.

PERMUTATION - THE NUMBER OF WAYS IN WHICH A SET OF VALUES CAN BE

ORDERED. FORMULA: N(N-1)(N-2)(N-3) ETC. SYMBOLIZED BY N!

NUMBER OF PERMUTATIONS OF N OBJECTS TAKEN K AT A TIME - N! / (N-K)!

COMBINATION - IN CONTRAST WITH PERMUTATION, THIS IS THE NUMBER OF WAYS IN

WHICH A SET OF VALUES CAN BE ORDERED BUT WITHOUT COUNTING DIFFERENT

ORDERS FOR THE SAME VALUES. FORMULA: NUMBER OF WAYS TO SELECT WITH

ORDER / NUMBER OF WAYS TO ORDER =

NUMBER OF COMBINATIONS OF N OBJECTS TAKEN K AT A TIME - N! / K!(N-K)!,

SOMETIMES NOTATED AS NCK

PROBABILITY - PROBABILITY OF EVENT OCCURRING IS DEFINED BY THE RATIO P(E) =

NUMBER OF OUTCOMES THAT SATISFY EVENT E / THE NUMBER OF POSSIBLE

OUTCOMES

PROBABILITY OF TWO OR MORE EVENTS BOTH OCCURRING - P(A AND B) = P(A) X

P(B)

PROBABILITY OF EITHER ONE OR ANOTHER EVENT OCCURRING - P(A) + P(B) -

P(AB)

PROBABILITY OF NEITHER OF MULTIPLE EVENTS OCCURRING - THE PRODUCT OF 1 -

P(A), 1 - P(B), ETC.

GROUP EQUATION - T = G1 + G2 - B + N (T IS TOTAL, GROUPS G, B IS MEMBERS

OF BOTH GROUP, N IS MEMBERS OF NEITHER)

PROBABILITY OF EVENT E AND F - E X F (IF E AND F ARE INDEPENDENT)

PROBABILITY OF EVENT E OR F - E + F (IF E AND F ARE MUTUALLY EXCLUSIVE)

PROBABILITY OF EVENT E OR F BUT NOT BOTH - E + F - P(E AND F)

CONTINUOUS PROBABILITY DISTRIBUTION - RELATIVE FREQUENCY DISTRIBUTIONS ARE

OFTEN APPROXIMATED USING A SMOOTH CURVE—A DISTRIBUTION CURVE OR

DENSITY CURVE—FOR THE TOPS OF THE BARS IN THE HISTOGRAM. THE REGION

BELOW SUCH A CURVE REPRESENTS A DISTRIBUTION, CALLED A CONTINUOUS

PROBABILITY DISTRIBUTION. THERE ARE MANY DIFFERENT CONTINUOUS PROBABILITY

DISTRIBUTIONS, BUT THE MOST IMPORTANT ONE IS THE NORMAL DISTRIBUTION,

WHICH HAS A BELL-SHAPED CURVE

LENGTH OF A DIAGONAL IN A PARALLELOGRAM - P^2 + Q^2 = 2((A^2) + (B^2)),

WHERE P AND Q ARE THE DIAGONALS AND A AND B ARE SIDES. YOU MAY NEED TO

CONSTRUCT A RIGHT TRIANGLE BY CONNECTING A TOP CORNER WITH THE BASELINE

AND THEN FINDING ITS HYPOTENUSE (WHICH WILL SERVE AS THE LENGTH OF THE

ANGLED SIDE).

IF XY > 0, THEN - X > 0 AND Y > 0 OR X < 0 AND Y < 0

IF XY < 0, THEN - X > 0 AND Y < 0 OR X < 0 AND Y > 0

IF A VEHICLE TRAVELS A CERTAIN DISTANCE AT A MPH AND TRAVELS THE SAME

DISTANCE AT B MPH, THE AVERAGE RATE IS - 2AB / A + B (ONLY WORKS WHEN THE

DISTANCE IS THE SAME AT BOTH SPEEDS!)

COMMON RIGHT TRIANGLE LENGTH RATIOS - 1: 1 :√

MEASUREMENT OF ANGLE X ORIGINATING ON THE EDGE OF A CIRCLE - 1/2 THE ARC IT

CUTS (BETWEEN THE POINTS OF THE TWO LINES EXTENDING FROM IT ACROSS THE

CIRCLE)

UNITS DIGIT OF 3^X - WILL ALWAYS END IN 3, 9, 7, 1, IN THAT SEQUENCE

(A + B) (A - B) - A² - B²

  • (A - B) - (B - A)

Y X 10^X - MOVE DECIMAL POINT X DIGITS TO THE LEFT/RIGHT

A² X B² - (AB)²

CENTRAL ANGLE OF SECTOR - ARC/

SOLVE THE PERCENTAGE OF CIRCUMFERENCE COVERED BY AN ARC IN TERMS OF THE

CENTRAL ANGLE - X/360 = % OF CIRCUMFERENCE

MEASURE OF ANY INSCRIBED ANGLE (WITHIN A CIRCLE) WHOSE TRIANGLE BASE IS A

DIAMETER - 90 DEGREES

INSCRIBED ANGLE Y IN TERMS OF ARC - Y = ARC/

ADDING FRACTIONS WITH DIFFERENT DENOMINATORS - CROSS MULTIPLY (BOTTOM

TO TOP, TOP TO BOTTOM), TAKING THOSE VALUES AS YOUR NEW NUMERATOR, AND

THEN ALSO MULTIPLY THE DENOMINATORS AND USE THAT AS YOUR NEW

DENOMINATOR

  • (- Y < - X) - Y > X (NOTE THE REVERSAL OF THE INEQUALITY

(A + B) (C + D) - AC + AD + BC + BD

X¹ - X

X⁰ - 1

(AB)ⁿ - AⁿBⁿ

A³/A² - A³−²

MULTIPLYING DECIMALS - WORK AS IF THEY WERE WHOLE INTEGERS. THEN, COUNT

THE NUMBER OF DIGITS TO THE RIGHT OF THE DECIMAL PLACE IN EACH FACTOR,

COMBINE THEM, AND PLACE THE POINT THAT MANY DIGITS TO THE LEFT OF YOUR

NEW PRODUCT

DISTANCE FORMULA - SPEED X TIME = DISTANCE

WORK FORMULA - RATE X TIME = WORK/OUTPUT

SURFACE AREA OF A HEMISPHERE - S = 2ΠR² (WITHOUT BASE); S = 3ΠR² (WITH

BASE)

AREA OF AN EQUILATERAL TRIANGLE - √3S² / 4

AREA OF A HEXAGON - A = (3√3 / 2)T (WHERE T IS THE SIDE LENGTH)

DIAGONAL OF A SQUARE - D = S√2 (WHERE S EQUALS THE LENGTH OF A SIDE)

AREA OF A TRIANGLE - AB SIN C / 2, WHERE A AND B ARE ANY TWO SIDES AND C IS

THE ANGLE BETWEEN THEM

RELATIONSHIP BETWEEN DIAGONAL OF A HEXAGON AND SIDE - THE LONGEST

DIAGONAL IS 2 S (WHERE S IS THE LENGTH OF A SIDE)

PERIMETER OF A HEXAGON - P = 6R (WHERE R IS A GIVEN RADIUS)

FORMULA FOR DISTANCE BETWEEN TWO POINTS ON A COORDINATE GRAPH - D = √(X₂

  • X₁)² + (Y₂ - Y₁)² (NB THAT THE SQRT SIGN EXTENDS ACROSS THE ENTIRE FORMULA

COORDINATES FOR THE MIDPOINT OF THE LINE SEGMENT JOINING 2 POINTS - (X₁ + X₂

/ 2, Y₁ + Y₂ / 2) (AN AVERAGE OF THE COORDINATES OF THE ENDPOINTS)

SUBTRACTING FROM BOTH SIDES OF AN INEQUALITY - REVERSE THE CENTRAL SIGN

ADDING TO BOTH SIDES OF AN INEQUALITY - CENTRAL SIGN REMAINS THE SAME

MULTIPLYING OR DIVIDING BY A NEGATIVE NUMBER IN AN INEQUALITY - REVERSE THE

CENTRAL SIGN

MULTIPLYING OR DIVIDING BY A POSITIVE NUMBER IN AN INEQUALITY - CENTRAL SIGN

REMAINS THE SAME

TYPES AND CHARACTERISTICS OF TRIANGLES - SCALENE: NO TWO SIDES OR ANGLES

EQUAL

ISOSCELES: TWO EQUAL SIDES AND ANGLES

EQUILATERAL: ALL THREE SIDES AND ALL ANGLES EQUAL

EACH ANGLE MUST BE 60 DEGREES

RIGHT: ONE ANGLE IS A RIGHT ANGLE (90)

CONGRUENT TRIANGLES - 1. EACH SIDE OF THE FIRST TRIANGLE EQUALS THE

CORRESPONDING SIDES OF THE SECOND TRIANGLE

2. TWO SIDES OF THE FIRST TRIANGLE EQUAL THE CORRESPONDING ANGLES OF THE

SECOND TRIANGLE, AND THEIR INCLUDED ANGLES ARE EQUAL. THE INCLUDED ANGLE

IS FORMED BY THE TWO SIDES OF THE TRIANGLE

3. TWO ANGLES OF THE FIRST TRIANGLE EQUAL THE CORRESPONDING ANGLES OF THE

SECOND TRIANGLE, AND ANY PAIR OF CORRESPONDING SIDES ARE EQUAL

MEDIAN OF A TRIANGLE - A LINE DRAWN FROM A VERTEX (POINT) TO THE MIDPOINT

OF ITS OPPOSITE SIDE. THE MEDIANS OF A TRIANGLE CROSS AT A POINT THAT DIVIDES

EACH MEDIAN INTO TWO PARTS: ONE PART OF ONE THIRD THE LENGTH OF THE

MEDIAN AND THE OTHER PART OF TWO THIRDS THE LENGTH

ANGLE BISECTORS OF A TRIANGLE - LINES THAT DIVIDE EACH ANGLE OF A TRIANGLE

INTO TWO EQUAL PARTS; THEY CROSS IN THE MIDDLE OF A CIRCLE INSCRIBED IN THE

CENTER OF THE TRIANGLE

SUM OF ANY TWO SIDES OF A TRIANGLE - GREATER THAN THE LENGTH OF THE THIRD

SIDE

ANGLE INSCRIBED IN A SEMICIRCLE - MUST BE A RIGHT ANGLE

CONVERTING DIAMETER TO RADIUS - D = 2R; SO D² = 4R²

COMBINATION FORMULA - C = (N)(N - 1)(N - 2)...(N - R+1) / (R)(R - 1)(R - 2)...(1)