Basic rules Flashcards
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
volume of cylinder
πr^2 x height
surface area of cylinder
2πr^2 + 2πrh
circumference of circle
πd
or
2πr
area of circle
πr^2
If one side of an inscribed triangle is the diameter of a circle…
the opposite angle is 90°
sector area in a circle
proportionate to angle size: how much is the angle out of 180°? The sector is that much of the total area
When a line intersects two other, parallel lines…
The corresponding angles are equal
When two lines intersect, what do you know about their angles?
Opposite angles are equal
Calculate slope of a line from two points
slope = rise/run = (y2 - y1)/(x2 - x1)
midpoint between two points on a line in the coordinate plane
((x1 + x2)/2) , ((y1 + y2)/2)
distance between two points in the coordinate plane
sq((x2 - x1)^2 + (y2 - y1)^2))
