Formulas Flashcards
What is the formula for the area, perimeter and diagonal of a rectangle?
Area=widthxlength Ex: width=5cm length=4 cm 5x4=20 Perimeter=2x(w+l) Ex:w=6 l=7 2x13 26 Diagonal=square root of(w squared+l squared) Ex:w=3 l=4 Square root of (9+16) Square root of 25 5
What is the formula for the area of a triangle?
basexheight:2 Ex: base =5 cm height=4 cm 5x4:2 20:2 10
What is the formula for the area of a square?
Area=sidexside
Ex:s=4
4x4=16
What is the formula for the area and circumference(perimeter)of a circle?
Area=pix(radius squared) Ex:r=5 25xpi Circumference=pixradiusx2 Ex:r=5 Pix5x2 Pix10
What is a triangle number?
A triangle number is the number of objects you need to shape them into a triangle.
Ex:
3 balls can be arranged to form a triangle. 3 is a triangle number. The next triangle number is 6…
What is the formula for a triangle number?
(nx(n+1)):2 Ex:to find the 100th triangle number, you put 100 for n. 100x101:2 10 100:2 5050 The 100th triangle number is 5050. You'll notice that the other way to find triangle numbers is to add up all the numbers that come before it. Ex:1+2+3+4+5...+99+100=5050
What is a tetrahedral number?
A tetrahedral number is the number of objects it takes to build a tetrahedral(a three-sided pyramid).
Ex: using three balls as a base and putting another on top, you get a tetrahedral. 3+1=4. 4 is a tetrahedral number. The next tetrahedral number is 6…
What is the formula for tetrahedral numbers?
To find the nth tetrahedral number you must do…
((n cubed)+(3x(n squared))+(2xn)):6
Ex: the 5th tetrahedral number
(25+75+10):6
110:6
~18.3
The 5th tetrahedral number is about 18.3.
What is the formula for centred hexagonal numbers?
3x(n squared)-(3xn)+1 Ex:n=3 3x9-9+1 27-9+1 18+1 19 The 3rd centred hexagonal number is 19.
What is the formula for pentagonal numbers?
(nx(3xn-1)):2 Ex:n=4 4x(12-1):2 4x11:2 44:2 22 The 4th pentagonal number is 22.
What is the formula for squares?
n squared Ex:n=6 6 squared 36 The 6th square is 36.
What is the formula for square pyramid numbers?
(2x(n cubed)+3x(n squared)+n):6 Ex:n=5 2x125+3x25+5:6 250+75+5:6 330:6 55 The 5th square pyramid number is 55.
How do you write triangle numbers without knowing what they are equal to?
T3 is the third triangle number
T7 is the seventh triangle number
t7 does not mean anything.
What is the link between squares and triangle numbers?
n squared=Tn+T(n-1)
Ex:n=4
4 squared=T4+T3
16=10+6
If you have a sheet of stamps with f number of stamps on the length and g number of stamps on the width, what is the TOTAL number of squares and rectangles that you can make with the stamps?
TfxTg
Ex:f=3 g=4
6x10=60
You can make a total of 60 different squares and rectangles from a sheet of stamps of 3 on 4.
If you have an l number of objects, and you have to link all of these objects to one another, how many links must you use?
T(l-1) Ex:l=20 T19 19x20:2 190 To link up 20 objects, you must use 190 links.
To cut up a circle into different parts (that do not have to be equal), what is the maximum pieces you can cut using c lines?
Tc+1 Ex:c=4 T4+1 10+1 11 You can make a maximum of 11 parts using 4 lines.
To cut up a crescent shape in c lines, what is the maximum of parts you can make?
(cx(c+3)):2+1 Ex:c=4 4x7:2+1 28:2+1 14+1 15 You can make a maximum of 15 parts using 4 lines.
If you have a cube and you cut it up in c cuts, what is the maximum of parts you can make?
((c cubed)+5xc):6+1 Ex:c=3 27+15:6+1 42:6+1 7+1 8 You can make a maximum of 8 parts with 3 cuts.
What are the formulas for calculating distance,speed and time?
d=sxt Ex:s=5 t=4 5x4=20 s=d:t Ex:d=6 t=3 6:3=2 t=d:s Ex:d=8 s=2 8:2=4
What is the formula for acceleration?
a=acceleration s=final speed t=time you’ve been accelerating
a=s:t
Ex:s=50 t=25
50:25=2
When you’ve accelerated to 50 mps in 25 seconds, you have accelerated 2 mph every second.
What is the formula for the distance where you have accelerated?
d=(ax(t squared)):2 Ex:a=5 t=7 5x49:2 245:2 122.5 If you accelerate 5 mps for 7 seconds, you will have traveled 122.5 m.
What is the formula for the time during which you have accelerated?
t=square root of (2xd:a) Ex:d=19.5 a=3 square root of 39:3 square root of 13 ~0.114 If you travel 19.5 miles and you have been accelerating at 3 mps,you have travelled for about 0.114 seconds.
What is the formula to find your final speed when you are accelerating?
s2=s1+axt
s2=final speed s1=first speed a=acceleration t=time
Ex:s1=10 a=2 t=7
10+14
24
If you were going at 10 mph and you accelerated by 2 mph every second for 7 seconds, your final speed would be 24 mph.
What is the formula for calculating your final speed while decelerating?
It’s the same as the one for accelerating, except that a is negative.
Ex:s1=15 a=-3 t=4
15+-3x4
15+-12
3
If you were going at 15 mph and you decelerated by 3 mph every second for 4 seconds, your new speed would be 3 mph.
What is the formula for finding out how much time does it take to stop?
t=s:a s=original speed a=deceleration Ex:s=6 a=2 6:2=3 If you were going at 6 mps and your deceleration was of 2 mps, you would stop after 3 seconds.
What is the formula for calculating the distance travelled before stopping?
d=s squared:(2xa)
Ex:s=12 a=3
144:6=26
If you were going at 12 mph and your deceleration was of 3 mph every second, you would stop after having travelled 26 m.
What is the formula for calculating the time it takes to drop something from a certain height?
t= square root of(2xh:g) h=height g= gravitational acceleration(~10) Ex:h=80 square root of 2x80:10 square root of 160:10 square root of 16 4 If you dropped something by a height of 80 metres, it would take 4 seconds to hit the earth (providing it is at sea level).
What is the formula for calculating the maximum height that can be reached when throwing an object vertically in the air?
h=v squared:2xg v=velocity g=gravitational deceleration Ex:v=40 160:20 8 If you throw something in the air with a velocity of 40 mps, it would go up to a maximum height of 8 m.
What is the formula for calculating how much time does it take for an object to reach its maximum height when thrown?
v:g Ex:v=40 40:20 2 If you throw an object in the air with a velocity of 40 mps, it will take 2 seconds to reach its maximum height.
What is in common with the initial speed of an object thrown in the air and its final speed when it goes back down?
They are both exactly the same. If you throw something vertically up in the air, it will come back down at exactly the same speed as the one with which you threw it.
What is the formula for calculating the distance of planets from the sun?
T squared: d cubed=k
T=time to go around the sun d=average distance of planet
k=don’t worry about that, it disappears soon.
Ex:t=time for Earth to go around the sun=1 year
d=average distance of the Earth=150 (million km)
1 squared:150 cubed=k
Mars takes 1.88 years to go around the sun, and we’ll call the distance m.
1.88 squared:m cubed=k=1 squared:150 cubed
1.88 squared:m cubed=1 squared:150 cubed
By using cross multiplication,you get:
m cubed=1.88 squaredx150 squared
m cubed=11 928 600
m=~228
Mars is about 228 million km from the sun.
What is the formula for calculating the gravitational force that attracts two objects?
F=Gx(m1xm2:d squared) m1=mass (first) m2=mass (second) d=distance G=gravitational constant=0.000000000067 Ex:m1=60 m2=50 d=1 0.000000000067x60x50x1 squared 0.0000002001 newtons
What is the formula for calculating the time it takes for a pendulum to swing back and forth?
2xpix(square root of l:g) l=length of pendulum g=gravitational acceleration(9.81) Ex:l=1 2xpix(square root of 1:9.81) 2x3.1416x0.3193=2.0065 seconds.
Define permutations:
A permutation is the number of ways in which you can arrange different objects.
What is the formula for calculating permutations when all the objects are different?
n!
Ex:5 different objects. Number of ways to arrange them in a straight line=5!=120
What is the formula for finding permutations when not all of the objects are different?
n!/l!
n=total number of objects l=number of objects that are different
Ex:n=5 l=3
5!/3!
120/6
20
If you line up 5 objects, but 3 of the objects are the same, you can line them up in 20 different ways.
What is the formula for calculating permutations when there are several groups of identical objects?
n!:(a!xb!xc!x...) n=total number of objects a=number of obects in group a b=number of objects in group b c=" " c ... Ex:n=6 a=3 b=2 c=1 6!:(3!x2!x1!) 720:(6x2x1) 720:12 60 If you have 6 objects, 3 are identical, another 2 are the same, and 1 is unique, you have 60 different ways of lining them up.
You have n different cards to choose from, and you can choose p number of them. How many combinations of cards can you get when the order matters?
n!:(n-p)! Ex:n=7 p=4 7!:3! 5040:6 840 If you can choose 4 out of 7 cards, there are 840 ways to pick them when the order matters.
If you have n cards and can choose p of them, how many combinations can you get when the order does not matter?
n!:p!x(n-p)! Ex:n=7 p=4 7!:4!x3! 5040:24x6 5040:144 35 If you can choose 4 cards out of 7 and the order does not matter, you can have 35 different combinations. or you can say that 7C4=35
What are the chances of winning the lottery(49C6)?
1 in 13 983 816
~1/14 million
If you can throw p dice and the order matters,how many different combinations can you get?
(LOOK OUT! The same number can repeat itself)
n to the power of p n=the number of possibilities that can come out from one die=6 p=the number of die you are throwing Ex:p=4 6 to the power of 4 6x6x6x6 1296 If you are throwing 4 die and the order matters, you can have 1296 combinations.
If you are throwing p die and the order does not matter,how many combinations can you get?
(p+n-1)!:p!x(n-1)! Ex:p=4 (4+6-1)!:4!x(6-1)! 9!:4!x5! 126 If you are throwing 4 die and the order does not matter, you can have 126 different combinations.
What is a circumscribed circle?
A circumscribed circle of a shape is the smallest circle that this shape can fit in.
What is the formula for the radius of a circumscribed circle in a rectangle?
(square root of a squared + b squared):2 Ex:a=3 b=5 square root of 9+25:2 square root of 34:2 ~5.83:2 2.915 If you have a rectangle of 3 on 5, the radius of the circumscribed circle will be about 2.915.
What is an inscribed circle?
The inscribed circle of a shape is the smallest circle that can fit inside the shape.
What is the formula for the radius of an inscribed circle of a square?
What is the formula for the circumscribed circle of a square?
a:2 a=side a:square root of 2(~1.41) Ex:a=2 2:2=1 2:1.41=1.41 If you have a square of side 2, the inscribed circle will be 1 and the circumscribed circle will be about 1.41.
