All Flashcards
When dividing or multiplying inequalities, remember to…
Flip the sign
A^5 x b^6 > 0, how can we simplify?
Ignore b^6. A^5 > 0
Quadratic inequalities
Solve for x^3 - 4x < 0?
Get all variables on the left side < 0 and solve for x
Where X>1, what is the order of values?
1/x, 1, root x, x, x^2, x^3
Where X is b/w 0 and 1, what is the order of values?
0, x, 1, x^3, x^2, x, root x, 1, 1/x
To solve an inequality with a variable in the divisor…
Multiply by x squared so no negative number in bottom
What is the greatest common divisor of two consecutive numbers?
One
|A| = |B|
Simplify?
A = +/- B
|X-4| = 8
X - 4 = +/- 8
X = 12, -4
|ab| =?
|a| x |b|
|x| = a
–> inequality form?
-a < x < a
|a + b | < |a| + |b|, then?
Ab < 0
|a + b | = |a| + |b|l then?
Ab > or = to 0
|a-b| > 0 AND (a-b)^2 is <0, then…
A does not equal B
If |a-b| is < or = 0 and (a-b)^2 is < or = 0, then…
A = B
A ^ 2 + b ^ 2 = 0 AND / or |a| + |b| = 0 And / or Root A + Root B = 0,
Then
A = b = 0
|x-y| =?
|y-x|
Distance between two points on a number line
Square both sides, cancel like items and solve for X
|x| > or = to X
X < |x|, then x<0
X = |x|, then x > or = 0
Data Sufficiency Strategy
Triangle perimeter or angle questions have how many variables?
3
3 side lengths
2 lengths, 1 angle
1 length, 2 angles
Each set is 3 distinct equations for perimeter or area of triangle
Quadrilateral
DS variables?
Four sided figure
Likely 4
5 variables
Parallelogram
2 sets of parallel sides
Not necessarily same angles
3 variables
Likely E
Rectangle
4 90 degree angles
2 variables
Likely C
Rhombus
4 equal sides, not necessarily 90 degree angles
Likely C
2 variables
Square
4 equal sides, 90 degree angles
1 variable
Likely D
DS -
Triangles w/ angles
3 variables, 1 equation
X + y + z = 180
(Right Triangle, isosceles are 2)
(Equilateral are known - 60)
Quadrilateral angles - number of variables
4
Parallelogram angles - number of variables
2
Units digit reoccurs after ever ____ the Power
4th power
Finding a remainder? List steps where one other remainder and divisor is given
If N/8 has a remainder of 1, what is the remainder when n/4 ?
N/8 r 1
N = 8p + 1
80 + 1 = 1
81 + 1 = 9
8*2 + 1 = 17
Etc.
Check whether 4xp + ___ is the same for each
Solving for a remainder when you have to sets of divisors and remainders but neither is sufficient
Find the overlapping first number of both
Add the least common multiple of the divisors to the overlapping number and keep adding the LCM to see if there is consistent remainder
Remainder for numbers divided by 3 or 9
Add the sum of all digits in the number
Remainder after division by 4 or 8
For 4, same as the 10s (e.g., 398, look at 98)
For 8, same as the 100s (e.g., 24,899, look at 899)
Determining number of factors
Take the distinct prime factors, list out their exponents to make the number
Add 1 to each exponent
Multiply the resulting numbers together
MAKE SURE THAT THE PRIME FACTORS ARE NOT EQUAL TO EACH OTHER, IN CASE OF VARIABLES
GREAT COMMON DIVISOR
Minimum value of all exponents of the numbers
E.g, take the prime factorization of each number
Prime numbers not shared between the numbers will drop out
Prime numbers that are shared will use the prime number with the smaller exponent
LCM least common multiple
Max value of the exponents
If a prime isn’t shared between them, it will be included
For primes that are shared, the one with the larger exponent will be included
For two numbers A and B . . .
A = a x GCD and B = b x GCD, where a and b are relative prime numbers
LCM = abG
AB = LG
Terminating Decimal . . .
Only prime factors in the denominator are 2 or 5
