Math Review Flashcards
Order of operations
PEMDAS
Is zero positive or negative?
Neither
How to find a remainder
If m and n are positive integers and if r is the remainder when n is divided by m, then n is r more than a multiple of m.
That is, n = mq + r where q is an integer and 0 < m
Is 1 prime?
No
First ten prime numbers
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Relationship between GCF and LCM
The product of the GCF and LCM of two numbers is equal to the product of the two numbers.
GCF x LCM = ab
Laws of exponents
For any numbers b and c and positive integers m and n:
```
b^m)(b^n) = b^(m+n
(b^m)/(b^n) = b^(m-n)
(b^m)^n = b^mn
(b^m)(c^m) = (bc)^m
~~~
Laws of radicals
For any positive numbers a and b:
√(ab) = √a x √b √(a/b) = √a/√b
Distributive Property
a(b + c) = ab + ac
a(b - c) = ab - ac
(b + c)/a = b/a + c/a
(b - c)/a = b/a - c/a
Fractions and inequalities
If 0 < x < 1, and a is positive, then xa < a
If 0 < x < 1, and m and n are positive integers with m > n, then x^m < x^n < x
If 0 < x x
If 0 < x x and (1/x) > 1
Is 0 even or odd?
Even
Comparing fractions
Cross-multiply:
To compary (1/3) and (3/8), multiply 3 x 3 and 8 x 1.
3 x 3 > 8 x 1, so (3/8) > (1/3)
Dividing by fractions
To divide any number by a fraction, multiply that number by the reciprocal of the fraction.
Convert a fraction to a percent
Convert the fraction to a decimal, then convert the decimal to a percent.
Which is greater: a% of b or b% of a?
a% of b = b% of a
Percent increase and percent decrease
If a < b, the percent increase in going from a to b is always greater than the percent decrease going from b to a.
An increase of k% followed by a decrease of k% is equal to a decrease of k% followed by an increase of k%, and is always less than the original value.
(x + y)(x - y)
x^2 - y^2
(x - y)^2
x^2 - 2xy + y^2
(x + y)^2
x^2 + 2xy + y^2
How to solve a system of equations
Add or subtract them
Distance
rate x time
Vertical angles
Have equal measure.
Transversal
A line that transects two lines. If those lines are parallel, the four acute angles are equal and the four obtuse angles are equal.
The measure of an exterior angle
Is equal to the sum of the measures of the two opposite interior angles.
Measures of the sides of triangles
a^2 + b^2 = c^2 for a right triangle
a^2 + b^2 < c^2 if angle C is obtuse
a^2 + b^2 > c^2 if angle C is acute
Common right triangles
3-4-5 and 5-12-13
Sides of a 45-45-90 triangle
x - x - x√2 (hypotenuse)
Sides of a 30-60-90 triangle
x - x√3 - 2x (hypotenuse)
Sum of the sides of a triangle
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
The difference of the lengths of any two sides of a triangle is less than the length of the third side
Area of a triangle
A = (1/2)bh
Area of an equilateral triangle
A = (s^2√3)/4
Sum of the angles in a quadrilateral
360
Sum of the angles in a polygon with n sides
(n - 2) x 180
Sum of exterior angles in a polygon
360
Area of a square
A = s^2 OR A = (1/2)d^2
Relationship between circumference and diameter of a circle
C = πd
Area of a circle
A = πr^2
Surface area of a rectangular solid
A = 2(l + w + h)
Surface area of a cube
A = 6e^2
Diagonal of a box
d^2 = l^2 + w^2 + h^2
Volume of a cylinder
V = π(r^2)h
Surface area of a cylinder
A = 2πrh
Total area of a cylinder
T = 2πrh + 2π(r^2)
Finding the distance between two points
d = √((x2-x1) + (y2 - y1))
Essentially the Pythagorean Theorem
Midpoint of any two points
The average of the x coordinates and the average of the y coordinates
(x1 + x2)/2, (y1 + y2)/2
Slope
(y2 - y1)/(x2 - x1)
The counting principle
If two jobs need to be completed and there are m ways to do the first job and n ways to do the second job, then there are m x n ways to do one followed by the other.
Probability
If an experiment is done two or more times, the probability that the first one event will occur and then a second event will occur is the product of the probabilities.
