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University Prep > Maths/AM key revision > Flashcards

Maths/AM key revision Flashcards

1
Q

sum of the interior angles of polygons

A

(n-2) x 180

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2
Q

exterior angle on any polygon

A

360/n to find angle between extended edge and next edge

180+(360/n) to find total ext. angle

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3
Q

sum of angles in a regular quadrilateral and triangle

A

360 and 180 respectively

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4
Q

what is the value of sin(30)

A

1/2

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5
Q

what is the value of sin(0)

A

0

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6
Q

what is the value of sin(45)

A

1/sqrt(2)
or
sqrt(2)/2

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7
Q

what is the value of sin(60)

A

sqrt(3)/2

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8
Q

what is the value of sin(90)

A

1

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9
Q

what is the value of cos(0)

A

1

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10
Q

what is the value of cos(30)

A

sqrt(3)/2

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11
Q

what is the value of cos(45)

A

1/sqrt(2)
or
sqrt(2)/2

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12
Q

what is the value of cos(60)

A

1/2

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13
Q

what is the value of tan(0)

A

0

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14
Q

what is the value of tan(30)

A

1/sqrt(3)
or
sqrt(3)/3

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15
Q

what is the value of tan(45)

A

1

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16
Q

what is the value of tan(60)

A

sqrt(3)

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17
Q

what are the formulae for sin, cos, tan

A 
sin = O/H
cos = A/H
tan = O/A
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18
Q

what is congruence

A

Two shapes that are the same size and the same shape are congruent.

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19
Q

what is needed for triangles to be congruent

A

SSS, SAS, AAS,
or
right angle, hypotenuse and another side (RHS)

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20
Q

what is the multiplication law for logs

A

loga(X) + loga(Y) = loga(XY)

21
Q

what is the division law for logs

A

loga(X) - loga(Y) = loga(X/Y)

22
Q

what is the power law for logs

A

a*Logb(x) = Logb(x^a)

23
Q

what is loga(1)

A

0

24
Q

what is log(1/a)

A

-log(a)

25
Q

special properties of a paralellogram

A
  • two pairs of equal sides
  • opposite sides are parallel
  • two pairs of equal angles
26
Q

special properties of a rhombus

A
  • two pairs of equal sides
  • opposite sides are parallel
  • opposite angles are equal
  • diagonals bisect each other at right angles (only difference to parallelogram)
27
Q

special properties of a kite

A
  • 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
28
Q

formula for the nth term of a geometric series

A

Un = a(r^n-1)

where a is the first term and r is the common multiple/ratio

29
Q

what is the formula for the sum of the first n numbers in a geometric series

A

Sn = (a(1-r^n)) / (1-r)

30
Q

what is the formula for the infinite sum of a convergent series where mod(r)<1

A

S(infinite) = a/1-r

31
Q

what is a function

A
  • 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
32
Q

what is the true meaning of f(x) = sqrt(x)

A

the positive square root

33
Q

best way to find the area of a hexagon

A

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

34
Q

what to do on questions asking about coefficients of dy/dx

A
  • the chain rule and pascals triangle may need to be used
35
Q

what to do with cubic/quartic

A
  • factor theorem
  • you have to go the long way round
  • also sketch
36
Q

what are the first 6 rows of pascals triangle

A 
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
37
Q

volume and S.A of a sphere

A 
vol = 4/3 (pi) (r^3)
S.A. = 4 (pi) (r^2)
38
Q

S.A and vol of a cone

A 
S.A. = (pi) r L + (pi) r^2
Vol = 1/3 (pi) (r^2) (H)
39
Q

finding the length of the side of a rhombus from diagonals

A

length of sides = sqrt((D/2)^2 + (d/2)^2)

40
Q

name the common Pythagorean triples

A 
3,4,5
6,8,10
5,12,13
10,24,26
7,24,25
14,48,50
41
Q

first 17 primes

A

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59

42
Q

what to do on proportionality qs

A
  • find k, if its a nice number
43
Q

what might be needed if you see a question including circles and triangles

A

circle theorems

44
Q

what is the difference between a length scale factor and an area/volume scale factor

A
  • the length scale factor deals with lengths

the area scale factor = (length S.F.) ^2

vol S.F. = (length S.F.)^3

45
Q

how to find the shortest distance from a circle to a point

A
  • 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

46
Q

calculating changes in kinetic energy for a ball swinging

A
  • calculate the change in GPE using right angles triangles
  • set this equal to KE (assuming at rest at start)
  • find V
47
Q

what is a good thing to do on triangle questions

A

use similarity and ratios

48
Q

what is a good thing to do where an equation is in the form 3^2x + 3^x + 5

A
  • let 3^x = Y

solve for Y then substitute back in

University Prep (6 decks)

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