Math Shortcuts Flashcards
two digit number divided by 99
becomes a decimal with that two digit number repeating. For instance –> 49/100 = 0.494949….
FDP: Scientific Notation
FDP: Compensating Decimals
FDP: Solution Less Traveled
Quadratic Formula
The discriminant (b^2 - 4ac) which is under the radical in the quadratic formula can tell you how many solutions.
b^2 - 4ac > 0 –> 2 solutions
b^2 - 4ac = 0 –> 1 solutions
b^2 - 4ac = 0 –> 0 solutions
Conjugate of square root expression involving addition or subtraction
multiply by a negative number in an inequality
flip the sign
On test cases, when I see |x|, I will try
absolute value: + and -
On test cases, when I see x^2, I will try
exponents: 0, 1, and fractions
On smart numbers, I will avoid…
0 and 1 and usually #s that appear in the problem
On smart numbers when choosing 2 variables, I will…
pick two differen tnumbers
decimal raised to exponent = how many decimal places?
of decimals * exponent
decimals for a root = how many decimal places
of decimals / root
=# of decimals * (1/root)
What is the pattern if the denominator is a number equal to a power of 10 - 1 (eg 9, 99, 999, etc)
then the numerator is repeating
How to check if a number will terminate?
The denominator only has 2 and 5 as prime factors once fraction is in smallest form
Digit Place Value questions
example two digit number -A -> how to represent this
A = 10x + y
Find units digit or a remainder after division of 10
you can pay attention to only the digits
x^2 - y^2
(x+y)(x-y)
x^2 + 2xy + y^2
(x+y)(x+y) = (x+ y)^2
x^2 - 2xy - y^2
(x-y)(x-y) = (x+ y)^2
inequality statement –> what is the implication?
xy>0
x and y are both positive or negative
inequality statement –> what is the implication?
xy < 0
one positive, one negative
inequality statement –> what is the implication?
x^2 - x < 0
x^2 < x
0 < x < 1
When combining inequalities can yo subtract?
NO
direct proportions > what to use?
ratios