Graduate Record Examinations

GENERAL Zero (0)

SQUARE ROOTS

only number equal to its opposite ab=0 => a=0 or/and b=0 + + +
11 121 12 144 13 169 14 196 15 225 16 256 17 289 18 324 19 361

Signs in multiplication or division
/* + -

Consecutive integers

2 = 1.414 3 = 1.732 5 = 2.645

n, n+1, n+2… n + (n+2) = 2(n+1)

Every number has a finite set of factors (or divisors) and an infinitive set of multiples 3 isdivisor of 12 12 is divisible by 3 3 is a factor of 12 12 is multiple of 3

EXPONENTS
x-a = 1/xa xa xb = xa+b xa ya = (xy)a (xa)b = xab xa / xb = xa-b x1 = x x0 = 1
24 16

Prime numbers

2, 3, 5, 7, 11, 13, 17, 19, 23

LCM of 6 & 10 =30 GCF of 6 & 10 =2

(multiply the shared prime factors to find all common factors) * E O +E O E E E E E O O E O O O E

23 8

25 32

26 64

27128

28 256

29 512

210 1024

Even & Odd

PERCENT
x% = x/100 =((F – I )/I) *100 x y is ⎛ y − x ⎞ * 100 % greater than x ⎟ ⎜ ⎝ x ⎠ x is ⎛ y − x ⎜ ⎜ y ⎝
⎞ ⎟ * 100 % greater than y ⎟ ⎠

1) Parenthesis 2) Exponents 3) Multiplication & Division (left to right) 4) Addition & Subtraction (left to right) Recognition of multiples: 2 – last digit is even 3 – sum of digits is a multiple of 3 4 –last 2 digits are multiple of 4 5 – last digit is 5 or 0 6 – sum of digits is a multiple of 3 and last digit is even 8 – last 3 digits are multiple of 8 9 – sum of digits is a multiple of 9

PEMDAS:

if a ax: bx: cx 3) c__ a+b+c

1

María Elena Ortega H.

FRACTIONS AND DECIMALS To compare fractions: cross-multiply Basic fractions
2/3 = 0.666 3/4 = 0.75 3/8 =0.375 3/11 = 0.2727 5/8 =0.625 17/15 = 1.1333

ALGEBRA

(x – y) (x + y) = x2 – y2 (x – y) 2= x2 -2xy +y2 (x + y) 2= x2 +2xy +y2

Note: most problems involving systems of equations do not require to solve the system -> read carefully

a% of b = b% of a

ANGLES Angles

INEQUALITIES
y 2y y

Acute: 90° Straight: =180°
b° a° c° d°

a° + b° + c° + d° =180°

00 xa< a 0n (integers) xm< xn x

Vertical angleshave equal measure a° = c° & b° =d°
a° b° d° c°

WORD PROBLEMS Age problems:
Distance problems:

Years ago => subtraction Years from now => addition Rate = distance Time

if 1 angle formed by the intersection of 2 lines is a right angle => 4 angles are right angles (lines are perpendicular) a° =b° =c° =d° = 90° if a pair of parallel lines cut by a transversal that is not perpendicular toparallel lines
a° d° b° c° e° h° f° g°

Interest problems:

Note: often just asked for simple rate

Simple: Interest = Yrt Compound : Interest = Y(1+(r/cc))t*cc

Remainder problems: pick up a # that fits the given
conditions and see what happens
q a b => aq + r = b

4 angles are acute & 4 are obtuse a°= c°= e°= g° & b°= d°= f°= h° d°+ e°= 180° & c°+ f°= 180° & …

Clock problems:30° between each hour number 20 minutes => moves 10° the hour leg

Work problems:

R * T = Q (T: time, R: rate, 1: #activities) 2 working together to complete the same activity=> 1 1 completed work: ( 1 + 1 ) * T + =1
Tx Ty Tx Ty

POLYGONS Sum of interior angles: (180°)(n-2) Each interior angle: (n-2)(180°)/n Sum of exterior angles: (taking 1 at each vertex)=
Each exterior angle: (360°)/nAny polygon can be divided into triangles 360°

t

Mixture problems:
Original Added Quantity A B A+B % Solution x y z Amount Solution Ax By

n-sided polygon is divided into (n-2) triangles

The number of diagonals that can be drawn from the vertex of an n-sided polygon are: (n-3)

Mixture

z(A+B) =Ax + By

2

María Elena Ortega H.

TRIANGLES Sum of interior angles =180°
f°+g°+ h°= 180° i° = f°+ g°
f° g° h° i°

QUADRILATERALS Sum of interior angles =360° Parallelogram:

The largest side is opposite to the largest angle, and the smallest side is opposite to the smallest angle

2 acute angles & 2 obtuse angles consecutive angles add up to 180° the 2 diagonals bisect each other diagonal divides it into 2 equal size triangles P= 2(l+L) A= bh

Rectangle:

Right...