Basic rules Flashcards
(35 cards)
Strategy for solving an absolute value equation
Solve once for the positive value, then again for the negative. You get two answers.
Algebraic inequality with negatives: don’t forget to do this
When multiplying or dividing by a negative, flip the sign
Formula for overlapping sets
Total = Group 1 + Group 2 - Both + Neither
Order of ops
PEMDAS: parentheses exponents multiply and divide add and subtract
FOIL method
When multiplying algebraic terms in parentheses, multiply the First, Outside, Inside, then Last terms.
When multiplying two exponents with the same base…
Add the powers
When dividing two exponents with the same base…
Subtract the powers
When raising an exponent to another power…
Multiply the exponents
Simplifying a negative exponent
Reciprocate: 5^-9 = 1/5^9
Dividing fractions
Multiply by the reciprocal (flip denominator upside-down and multiply)
An odd number to any power is…
odd
Combinatorics when order matters
E.g. How many ways can 3 medals be awarded to 7 competitors?
(Pool!)/(Out!)
E.g. the number of options factorial over the number of unchosen options factorial
Combinatorics when order doesn’t matter
E.g. How many teams of 3 can be picked from 7 people?
(Pool!)/(In!)(Out!)
% of values within 1 SD of the mean
68%
% of values within 2 SD of the mean
95%
% of values within 3 SD of the mean
99.7%
area of triangle
0.5 x base x height
similar triangles
have the same angles, and the sides are proportionate
The third side of a triangle…
Is greater than the difference of the other two sides, but less than their sum.
Pythagorean theorem
a^2 + b^2 = c^2
Isosceles triangle
two equal sides
equilateral triangle
3 equal sides, all angles are 60°
area of a parallelogram
base x height
sum of angles in a polygon
180(n-2)
n = number of sides
