All

Question 1

When dividing or multiplying inequalities, remember to…

Answer 1

Flip the sign

Question 2

A^5 x b^6 > 0, how can we simplify?

Answer 2

Ignore b^6. A^5 > 0

Question 3

Quadratic inequalities

Solve for x^3 - 4x < 0?

Answer 3

Get all variables on the left side < 0 and solve for x

Question 4

Where X>1, what is the order of values?

Answer 4

1/x, 1, root x, x, x^2, x^3

Question 5

Where X is b/w 0 and 1, what is the order of values?

Answer 5

0, x, 1, x^3, x^2, x, root x, 1, 1/x

Question 6

To solve an inequality with a variable in the divisor…

Answer 6

Multiply by x squared so no negative number in bottom

Question 7

What is the greatest common divisor of two consecutive numbers?

Answer 7

One

Question 8

|A| = |B|

Simplify?

Answer 8

A = +/- B

|X-4| = 8

X - 4 = +/- 8
X = 12, -4

Question 9

|ab| =?

Answer 9

|a| x |b|

Question 10

|x| = a

–> inequality form?

Answer 10

-a < x < a

Question 11

|a + b | < |a| + |b|, then?

Answer 11

Ab < 0

Question 12

|a + b | = |a| + |b|l then?

Answer 12

Ab > or = to 0

Question 13

|a-b| > 0 AND (a-b)^2 is <0, then…

Answer 13

A does not equal B

Question 14

If |a-b| is < or = 0 and (a-b)^2 is < or = 0, then…

Answer 14

A = B

Question 15

A ^ 2 + b ^ 2 = 0 
AND / or 
|a| + |b| = 0 
And / or 
Root A + Root B = 0, 

Then

Answer 15

A = b = 0

Question 16

|x-y| =?

Answer 16

|y-x|

Distance between two points on a number line

Square both sides, cancel like items and solve for X

Question 17

|x| > or = to X

Answer 17

X < |x|, then x<0

X = |x|, then x > or = 0

Question 18

Data Sufficiency Strategy

Triangle perimeter or angle questions have how many variables?

Answer 18

3

Question 19

3 side lengths

2 lengths, 1 angle

1 length, 2 angles

Answer 19

Each set is 3 distinct equations for perimeter or area of triangle

Question 20

Quadrilateral

DS variables?

Answer 20

Four sided figure

Likely 4

5 variables

Question 21

Parallelogram

Answer 21

2 sets of parallel sides
Not necessarily same angles
3 variables
Likely E

Question 22

Rectangle

Answer 22

4 90 degree angles
2 variables
Likely C

Question 23

Rhombus

Answer 23

4 equal sides, not necessarily 90 degree angles
Likely C
2 variables

Question 24

Square

Answer 24

4 equal sides, 90 degree angles
1 variable
Likely D

Question 25

DS -

Triangles w/ angles

Answer 25

3 variables, 1 equation

X + y + z = 180

(Right Triangle, isosceles are 2)

(Equilateral are known - 60)

Question 26

Quadrilateral angles - number of variables

Answer 26

4

Question 27

Parallelogram angles - number of variables

Answer 27

2

Question 28

Units digit reoccurs after ever ____ the Power

Answer 28

4th power

Question 29

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 ?

Answer 29

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

Question 30

Solving for a remainder when you have to sets of divisors and remainders but neither is sufficient

Answer 30

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

Question 31

Remainder for numbers divided by 3 or 9

Answer 31

Add the sum of all digits in the number

Question 32

Remainder after division by 4 or 8

Answer 32

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)

Question 33

Determining number of factors

Answer 33

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

Question 34

GREAT COMMON DIVISOR

Answer 34

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

Question 35

LCM least common multiple

Answer 35

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

Question 36

For two numbers A and B . . .

Answer 36

A = a x GCD and B = b x GCD, where a and b are relative prime numbers

LCM = abG

AB = LG

Question 37

Terminating Decimal . . .

Answer 37

Only prime factors in the denominator are 2 or 5