Math Foundations Flashcards
First 10 prime numbers.
2,3,5,7,11,13,17,19,23,29
Is zero even, odd, or neither?
Even
An integer is divisible by two if:
It’s last digit is divisible by two
An integer is divisible by three if:
Its digits add up to a multiple of three.
An integer is divisible by four if:
Its last two digits are a multiple of four.
Integer is divisible by five if
Its last digit is a zero or five.
An integer is divisible by six if:
It is divisible by both two and three.
An integer is divisible by nine if:
Its digits add up to a multiple of nine.
Greatest common factor (divisor)
The largest factor a pair of integers share. To find it, break down both integers into their prime factorizations and multiply all prime factors they have in common.
Prime Number
An integer greater than one that has only two factors: itself and 1. The number 1 is not a prime, because it is divisible only by itself.
The least common multiple of two or more integers is…
The smallest number that is a multiple of each of the integers.
1. Determine the prime factorization of each
2. Multiply each prime number maximum number of times it appears (in any one)
It will be less than, or equal to, the product of both numbers
Multiply or divide powers with the same base
Add or subtract exponents
To raise a power to another power
Multiply exponents
Percent increase and decrease formula
%increase= increase(100%)/original
%decrease=decrease(100%)/original
Part-Whole problems
Part/whole=fraction
Is(are)=part
Of=whole
Work problem
1/a+1/b+1/c=1/T
where a, b, c= units of time to complete a job independently and T= The time it takes all three working together to complete the job.
Complementary angles
Angles that add up to 90°
Supplementary angles
Angles that add up to 180°
Angle bisectors
Splits the angle into two smaller equal angles
Adjacent angles (formed by two intersecting lines)
Next to each other, supplementary
Vertical angles (formed by two intersecting lines)
Are opposite each other and equal in measure (they are supplementary to the same adjacent angle)
Transversal
A line that intersects two parallel lines
Calculate the sum of the interior angles of a polygon
Draw diagonals from any vertex to all non-adjacent vertices. Then multiply the number of triangles formed by 180°
Isosceles triangle
A triangle with two equal sides (legs), which are opposite to equal angles (The third, unequal side is called the base)
Equilateral triangle
A triangle whose three sides are all equal in length and whose three interior angles each measure 60°
Exterior angles
The angle formed between any side of a polygon, and the line extended from the adjacent side (always sum to 360°)
Right triangle
A triangle with one interior angle of 90°
Special right triangles
3, 4, 5
5, 12, 13
30/60/90
45/45/90
Sides of an Isosceles right triangle (45/45/90)
x/x/x(square root of two)
Sides of a 30/60/90 triangle
x:x(3)^(1/2):2x
Quadrilateral
A four-sided polygon
Parallelogram
A quadrilateral with two pairs of parallel sides. Opposite sides are equal in length: opposite angles are equal and measure: angles that are not opposite are supplementary to each other.
Rhombus
A parallelogram with four equal sides
Circle
The set of all points in a plane at the same distance from a certain point, the center. A circle is labeled by it’s Center point.
Central angle
An angle formed by two radii of a circle
Chord
A line segment that joins two points on a circle. The longest is the diameter.
Tangent line
A line that touches only one point on the circumference of a circle. It is perpendicular to the radius at the point of tangency.
Pi
The ratio of the circumference of the circle to its diameter. C/d=3.14
Arc
Is section of the circumference of a circle; the portion of a circle cut off by a particular central angle.
Degree of arc=measure of central angle
Arc length
Same as the fraction of the arc’s measure multiplied by the circumference
=(arc n)°/360° x 2 pi r
Sector of a circle
A portion of a circle’s area that is bound by two radii and an arc
Area of a sector
(Measure of central angle)°/360° x pi.r^2
Inscribed
Polygon inside a circle such that all the vertices of the polygon lie on the circle.
Circumscribed
A circle in a polygon such that all sides of the polygon are tangent to the circle.
The formula for number of different subgroups containing k different objects that can be selected from a group of n different objects (nCk)
nCk=n!/{k!(n-k)!}
n is positive
k is non-negative
0!=1
Laws of exponents
- (a^x)^y=a^xy
2. (a^x)(a^y)=a^(x+y)
Standard deviation percentages
~2, (2SD), ~14, (1SD), ~34
Pythagorean tripples
3: 4:5
5: 12:13
8: 15:17
7: 24:25
Permutation
The number of ways to arrange elements sequentially (order matters)
nPk=n!/(n-k)!
Combinations
Small group from a large group (order does not matter)
nCk=n!/{k!(n-k)!}
n is positive
k is non-negative
0!=1
Combinations short-cut
nCk=nCn-k (e.g. 10C3=10C7)
List all prime numbers
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59
11^2
121
13^2
169
14^2
196
15^2
225
0.2
1/5
0.16667…
1/6
0.83333…
5/6
0.1429…
1/7
0.2857…
2/7
0.4286…
3/7
0.5714…
4/7
0.7143…
5/7
0.8571…
6/7
0.125
1/8
0.375
3/8
0.625
5/8
0.875
7/8
0.1111…
1/9
