Maths/AM key revision Flashcards
sum of the interior angles of polygons
(n-2) x 180
exterior angle on any polygon
360/n to find angle between extended edge and next edge
180+(360/n) to find total ext. angle
sum of angles in a regular quadrilateral and triangle
360 and 180 respectively
what is the value of sin(30)
1/2
what is the value of sin(0)
0
what is the value of sin(45)
1/sqrt(2)
or
sqrt(2)/2
what is the value of sin(60)
sqrt(3)/2
what is the value of sin(90)
1
what is the value of cos(0)
1
what is the value of cos(30)
sqrt(3)/2
what is the value of cos(45)
1/sqrt(2)
or
sqrt(2)/2
what is the value of cos(60)
1/2
what is the value of tan(0)
0
what is the value of tan(30)
1/sqrt(3)
or
sqrt(3)/3
what is the value of tan(45)
1
what is the value of tan(60)
sqrt(3)
what are the formulae for sin, cos, tan
sin = O/H cos = A/H tan = O/A
what is congruence
Two shapes that are the same size and the same shape are congruent.
what is needed for triangles to be congruent
SSS, SAS, AAS,
or
right angle, hypotenuse and another side (RHS)
what is the multiplication law for logs
loga(X) + loga(Y) = loga(XY)
what is the division law for logs
loga(X) - loga(Y) = loga(X/Y)
what is the power law for logs
a*Logb(x) = Logb(x^a)
what is loga(1)
0
what is log(1/a)
-log(a)
special properties of a paralellogram
- two pairs of equal sides
- opposite sides are parallel
- two pairs of equal angles
special properties of a rhombus
- two pairs of equal sides
- opposite sides are parallel
- opposite angles are equal
- diagonals bisect each other at right angles (only difference to parallelogram)
special properties of a kite
- two pairs of equal sides (bottom two are =, top two are =)
- two side angles are equal
- diagonals bisect at right angles
- distances to diagonals’ bisector is equal from both sides but not from both ends
formula for the nth term of a geometric series
Un = a(r^n-1)
where a is the first term and r is the common multiple/ratio
what is the formula for the sum of the first n numbers in a geometric series
Sn = (a(1-r^n)) / (1-r)
what is the formula for the infinite sum of a convergent series where mod(r)<1
S(infinite) = a/1-r
what is a function
- a function is a mapping where every input has a distinct output
- that is to say it is many-to-one or one-to-one but never one-to-many
what is the true meaning of f(x) = sqrt(x)
the positive square root
best way to find the area of a hexagon
split it into 6 equilateral triangles, e.g. if you are given height (h), you know the height of one of the triangles is (h/2) then use
6(h/2)^2 (tan30) = A
what to do on questions asking about coefficients of dy/dx
- the chain rule and pascals triangle may need to be used
what to do with cubic/quartic
- factor theorem
- you have to go the long way round
- also sketch
what are the first 6 rows of pascals triangle
1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1
volume and S.A of a sphere
vol = 4/3 (pi) (r^3) S.A. = 4 (pi) (r^2)
S.A and vol of a cone
S.A. = (pi) r L + (pi) r^2 Vol = 1/3 (pi) (r^2) (H)
finding the length of the side of a rhombus from diagonals
length of sides = sqrt((D/2)^2 + (d/2)^2)
name the common Pythagorean triples
3,4,5 6,8,10 5,12,13 10,24,26 7,24,25 14,48,50
first 17 primes
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59
what to do on proportionality qs
- find k, if its a nice number
what might be needed if you see a question including circles and triangles
circle theorems
what is the difference between a length scale factor and an area/volume scale factor
- the length scale factor deals with lengths
the area scale factor = (length S.F.) ^2
vol S.F. = (length S.F.)^3
how to find the shortest distance from a circle to a point
- form a tangent with the circle from the point
- find out the hypotenuse length, i.e. the length from the circle centre to the point
hypotenuse length - radius = shortest distance
calculating changes in kinetic energy for a ball swinging
- calculate the change in GPE using right angles triangles
- set this equal to KE (assuming at rest at start)
- find V
what is a good thing to do on triangle questions
use similarity and ratios
what is a good thing to do where an equation is in the form 3^2x + 3^x + 5
- let 3^x = Y
solve for Y then substitute back in
