Maths/AM key revision

Question 1

sum of the interior angles of polygons

Answer 1

(n-2) x 180

Question 2

exterior angle on any polygon

Answer 2

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

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

Question 3

sum of angles in a regular quadrilateral and triangle

Answer 3

360 and 180 respectively

Question 4

what is the value of sin(30)

Answer 4

1/2

Question 5

what is the value of sin(0)

Answer 5

0

Question 6

what is the value of sin(45)

Answer 6

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

Question 7

what is the value of sin(60)

Answer 7

sqrt(3)/2

Question 8

what is the value of sin(90)

Answer 8

1

Question 9

what is the value of cos(0)

Answer 9

1

Question 10

what is the value of cos(30)

Answer 10

sqrt(3)/2

Question 11

what is the value of cos(45)

Answer 11

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

Question 12

what is the value of cos(60)

Answer 12

1/2

Question 13

what is the value of tan(0)

Answer 13

0

Question 14

what is the value of tan(30)

Answer 14

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

Question 15

what is the value of tan(45)

Answer 15

1

Question 16

what is the value of tan(60)

Answer 16

sqrt(3)

Question 17

what are the formulae for sin, cos, tan

Answer 17

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

Question 18

what is congruence

Answer 18

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

Question 19

what is needed for triangles to be congruent

Answer 19

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

Question 20

what is the multiplication law for logs

Answer 20

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

Question 21

what is the division law for logs

Answer 21

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

Question 22

what is the power law for logs

Answer 22

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

Question 23

what is loga(1)

Answer 23

0

Question 24

what is log(1/a)

Answer 24

-log(a)

Question 25

special properties of a paralellogram

Answer 25

- two pairs of equal sides - opposite sides are parallel - two pairs of equal angles

Question 26

special properties of a rhombus

Answer 26

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

Question 27

special properties of a kite

Answer 27

- 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

Question 28

formula for the nth term of a geometric series

Answer 28

Un = a(r^n-1) | where a is the first term and r is the common multiple/ratio

Question 29

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

Answer 29

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

Question 30

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

Answer 30

S(infinite) = a/1-r

Question 31

what is a function

Answer 31

- 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

Question 32

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

Answer 32

the positive square root

Question 33

best way to find the area of a hexagon

Answer 33

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

Question 34

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

Answer 34

- the chain rule and pascals triangle may need to be used

Question 35

what to do with cubic/quartic

Answer 35

- factor theorem - you have to go the long way round - also sketch

Question 36

what are the first 6 rows of pascals triangle

Answer 36

``` 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 ```

Question 37

volume and S.A of a sphere

Answer 37

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

Question 38

S.A and vol of a cone

Answer 38

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

Question 39

finding the length of the side of a rhombus from diagonals

Answer 39

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

Question 40

name the common Pythagorean triples

Answer 40

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

Question 41

first 17 primes

Answer 41

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

Question 42

what to do on proportionality qs

Answer 42

- find k, if its a nice number

Question 43

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

Answer 43

circle theorems

Question 44

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

Answer 44

- the length scale factor deals with lengths the area scale factor = (length S.F.) ^2 vol S.F. = (length S.F.)^3

Question 45

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

Answer 45

- 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

Question 46

calculating changes in kinetic energy for a ball swinging

Answer 46

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

Question 47

what is a good thing to do on triangle questions

Answer 47

use similarity and ratios

Question 48

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

Answer 48

- let 3^x = Y | solve for Y then substitute back in