Shape Flashcards
How do you know if two vectors are parallel to each other?
They will be multiples of each other e.g.
3a+2b and 6a+4b
If you have a vector question and need to prove that a line is straight, what do you do?
Find and prove that the gradients of two lines are parallel and that they go through the same point.
If for example, you had to prove line ABC was straight, find the vector of AB and BC. They both go through B and should be parallel
What must you always remember with bearings?
Always have a north line.
Always go clockwise.
Always have a 3 figure bearing e.g. 004 ,076 ,174
What do you do if you have to find put if two lines intersect?
Find the gradient of both. If they are the same, they won’t.
How is the exterior angle calculated?
360 divided by the number of sides.
How is the interior angle calculated ?
180 - the exterior angle.
How is the sum of the exterior angles calculated ?
It is always 360
How is the sum of the interior angles calculated?
First take away 2 from the number if sides.
Then times the result of this by 180
How do you find the magnitude of a vector?
Imagine it as a right angled triangle and calculate the hypotenuse.
Square the numbers, add them togethers and find the square root. Do this even with negative numbers.
What is a basic version of the cosine rule for angles?
CosA = b + c -a over 2bc
How do you find the gradient of a line?
The distance travelled up divided by the distance traveled to the right.
Y=mx+c
What do all the bits mean?
The m is the gradient.
The c is the Y intercept.
If you have the gradient of a line, and need to find the gradient of the perpendicular bisector of that line, what do you do?
Find the reciprocal of the original gradient and put a minus sign in front of it.
The two gradients should multiply to get -1
A straight line passes thorough the points (0,3) and (4,5)
Find the equation of the straight line.
The Y intercept is 3
It went across two and four up. 2/4=0.5
Y=0.5x+3
A straight line, L passes through the point with the coordinates (4,1) and is perpendicular to the line with the equation y=2x-5
Find the equation of line L.
First we change the gradient so it is perpendicular.
Y=-0.5x-5
Look at the coordinates. The x value is 4 and the y value is 1
Substitute this into your equation.
1=-0.5 X 4 + c. ( you can forget the -5 and remember to have a y intercept)
1=-2+c. c must be 3
Put it together and the answer is y=-0.5x+3
How do you find the volume of a cone or pyramid?
One third X area of base X height.
If you have to talk about geometric facts about two vectors, what might you talk about?
Whether they have the same gradient or magnitude.
What are the 8 circle theorems?
The perpendicular bisector of a chord goes through the centre.
The angle between a tangent and a radius is 90
The length of two tangents from a point are equal.
The angle in a semicircle is always a right angle.
The angle at the centre is twice the angle at the circumference.
Angles in the same segment are equal.
Opposite angle of a cyclic quadrilateral equal 180
The alternative segment theorem.
Explain the alternative segment theorem.
The angle between a tangent and its chord is equal to the angle in the alternative segment.
How is a specific arc length calculated?
Do the angle divided by 360
Then times this by the diameter and by pi.
How is the area of an ark length calculated ?
Angle divided by 360
Multiply this by pi and the radius squared.
