Maths - Half Yearly

Question 1

if Sin € = AB/AC

Find AB
Find AC

Answer 1

AB=AC*Sin €

AC=AB/Sin €

Question 2

angles of elevation/ depression.

Answer 2

angle of elevation: when looking up the angle between line of sight and horizontal
angle of depression: when looking down angle between line of sight and horizontal. alt. angle to angle of elevation

Question 3

Explain Three figure bearings.

Answer 3

aka true bearings, written as 000-360 degrees. measures degrees clockwise from north.

Question 4

Explain compass bearings.

Answer 4

written as a measurement between 0 and 90 degrees east or west from north or south. eg N80E

Question 5

the two triangles needed to find exact ratios of 30, 60 and 45.

Answer 5

draw an equilateral triangle with all sides 2. split down the middle. the triangle now has sides 1, 2 and (root)3 and angles 90, 60 and 30.

draw an isosceles, right angle triangle with two sides 1 and hypotenuse (root)2.

Question 6

the three types of clusters and what they look like.

Answer 6

symmetrical: .-/-.
positively skewed: ./|:~.
negatively skewed: .~:/|.

Question 7

2 properties of trapeziums:

Answer 7

one pair of parallel sides

no symmetry

Question 8

4 properties of a kite:

Answer 8

2 pairs of adj. sides equal
one pair of opp. angles equal
1 axis of symmetry
diagonals intersect at right angles

Question 9

4 properties of a parallelogram:

Answer 9

opp. sides equal and parallel
opp. angles equal
no symmetry
diagonals bisect each other

Question 10

6 properties of a rhombus:

Answer 10

all sides are equal
opp sides are parallel
opp. angles are equal
2 axis of symmetry 
diagonals bisect at right angles
diagonals bisect angles of rhombus

Question 11

how do you test for parallel lines

Answer 11

prove alt. angles, corresp. angles or co-int. angles

Question 12

what is the proof for the angle sum of a triangle?

Answer 12

draw a triangle and draw a line parallel to one of the sides on one of the corners and then use alternate angles and shit

Question 13

/__ < that’s a really bad exterior angle. what’s the proof?

Answer 13

just know it ceebs drawing it

Question 14

angles sum of a polygon?

Answer 14

A=(n-2)*180

Question 15

what is an outcome?

Answer 15

a result

Question 16

what is a sample space and how do you write one?

Answer 16

all possible outcomes: {1,2,3,4,5,6}

Question 17

what is an event?

Answer 17

a possible outcome.

p(event)=number of outcome matching event / total number of outcomes.

Question 18

complimentary event?

Answer 18

the complimentary of an event is the rest of the outcomes in the sample space. the compliment of E is written as
_
E

Question 19

what is a mutually exclusive event:

Answer 19

when if one event occurs the other cannot eg odd and even numbers

Question 20

non mutually exclusive events?

Answer 20

e.g prime and odd numbers, in a venn diagram there would be an overlap

Question 21

relative frequency is?

Answer 21

the number of times an event occurred compared to the total frequency of outcomes.

Question 22

independent and dependent events?

Answer 22

when the outcome of one event depends on the other it is dependent

eg without replacement

Question 23

what are the 3 ways to work out 2 stage events?

Answer 23

list, table and tree diagram

Question 24

when do you change the direction of the sign in linear inequations?

Answer 24

when multiplying or dividing by a negative or reversing the sides.

Question 25

what are the three ways of solving quadratics?

Answer 25

factorizing, completing the square and the quadratic formula.

Question 26

what are the steps to completing the square?

Answer 26

1. move the constant to the RHS
2. divide by the coefficient of x^2
3. half the coefficient of x, square it and add it to both sides
4. write LHS as a perfect square
   5 square root all tha shit

Question 27

what is the quadratic formula?

Answer 27

x=(-b+-|b^2-4ac|)/2a

|= square root

Question 28

what are the 3 ways of solving simultaneous equations with a brief description

Answer 28

graphically: draw it on a graph and write the coordinates where the two lines meet.
substitution: sub in the value of one pro-numeral into the equation
elimination: add or subtract the two equations.