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Gravity
Terms in this set (43)
When asked to round a place, only look at the digit next to the place.
Rounding
{3,4,5}
{5,12,13}
{8,15,17}
{7,24,25}
Pythagorean Triplet
If the sides given are larger, divide down by the greatest common factor. Do the computations in the smaller triangle and then scale back up.
Right angled Triangle
Similar figures have the same shape but different sizes.
The angles in similar figures are always equal.
We can prove two triangles are similar if they simply share two angles.
Sides in similar figures are proportional.
The scale factor k, is the factor by which all lengths in the smaller figure were multiplied to arrive at the lengths in the larger figure.
If all the lengths are multiplied by k, then the area is multiplied by k squared, the scale factor squared.
Similar Triangles
Angles= 45-45-90; sides= 1-1-√(2)
Isosceles Right Triangle
We get this by diving an equilateral triangle in half.
Has sides 1-√(3)-2.
30-60-90 triangle
The average of a group of consecutive integers is equal to the average of the smallest and largest numbers.
Average(Arithmetic Mean) Tips
A=RT
For problems with multiple workers or machines, create rates for each one and then add the rates.
Work Problems
All even numbers(last digit is even)
Divisibility rule for 2
If the sum of the digits is divisible by 3 then the number is divisible by 3
Divisibility for 3
If last two digits are divisible by 4 then the whole number is divisible by 4.
divisibility for 4
Last digit is 5 or 0
Divisibility by 5
No. should be divisible by 2 and 3
Divisibility by 6
If the sum of the digits is divisible by 9 then the number is divisible by 9
Divisibility by 9
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59
1 is not a prime number
2 is the only even prime number
to check if a no. <100 is prime check whether it is divisible by 2 3 5 and 7.
Prime numbers
D= RT
Motion Problems
20% : 0.2: 1/5
25%: 0.25: 1/4
50%: 0.5: 1/2
60%: 0.6: 3/5
75%:0.75:3/4
Percentage:decimal:fraction
nCr= (first r values of n!)/r!
Easy nCr formula
n!=n(n-1)!
nCr=nCn-r
nC1= n
Factorials
If there are n items with b identical items then the total no. of arrangements is,
N=n!/b!
or if there are b identical items,different group of c identical items,d identical items then,
N=n!/(b!c!d!)
Counting with identical items
(n-2)*180
the sum of angles in an n sided polygon
The measure of the inscribed angle is half the measure of the arc it intercepts.
If two inscribed angles in the same circle intercept the same arc or the same chord and intersect the same chord on the same side, then the two inscribed angles are equal.
Inscribed angle of a circle
If we draw a radius to the point of tangency, then the radius and the tangent line are perpendicular.
Tangents
Cube volume of side s
s^(3)
Each face of a cube has area s^(2) thus total surface area is
6s^(2)
Volume of a rectangular solid is
l
b
h
Surface area of rectangular solid is
2lb+2bh+2lh
Diagonal length in a rectangular solid from one vertex to opposite vertex is
ad^2= (edge)^2+(edge)^2+(edge)^2
diagonal in a cube with length s is
ad^2=s^2+s^2+s^2
Volume of a cylinder is
pi r^2 h
surface area of a cylinder is
2pi r^2+ 2pi r h
1 foot
12 inches
1 meter
100cm
If A*B=C then A and B are factors of C
A is a factor of c implies that we can multiply a by some other number to get c
Factor
Always plug in the roots and check the equation as one or both the roots might not satisfy the equation.
Absolute value equation
If a>b and c>d then, (same direction >)
a+c> b+d
If a>b and d<c then, (different direction)
a-d>b-c
|x|=
distance of x from zero
|x-5|=
distance of x from 5
|x+3|=
distance of x from -3
Changing the highest or lowest number will not change the median
Median
if the list consists of evenly spaced numbers, then the mean equals the median. Consecutive integers and consecutive multiples of the same number are examples of evenly spaced lists.
mean and median are equal whenever the list is entirely symmetrical.
Same mean and median
Mean follows the outliers.
High-value outliers cause the mean to be higherr than the median and vice versa
To know about mean of large numbers
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