Life of Pi
What day is National Pi Day in the U.S.? (Think about pi...)
March 14
Mathematically, in terms of points (a) and (b), how could a straight line segment be defined?
Shortest route through points (a) and (b)
One of the easiest circle theorems to remember is to do with angles in a semi-circle. If two straight lines are drawn from either end of the diameter of a circle and meet at a point on the circumference, what will the angle always be?
90 degrees
The information that is provided at the beginning of a proof is typically called the . . .
givens
What is the supplement of 75 degrees, in radians?
7pi/12
If you were to find the volume of an object, you might use pi. Which of these would not need pi in order to find the volume?
Cube
An important aspect of the straight line is the equation that is derived for use in this particular area of geometry. This is especially so when plotted on to a straight line graph and the co-ordinates of various points on the line are available. What is the general formula commonly accepted in mathematical societies for a straight line?
y=mx + c
When an angle is formed from two points on the circumference and two straight lines drawn from these two points meet at another point on the same circumference, it is said that the angle is ________ by an arc.
Subtended
The first thing we do is to draw a segment from B to D. Items added to a geometric diagram to help with the proof are called . . .
Supplemental
Find all x on [0 degrees, 360 degrees) for which csc(x)=-2.
x=210 degrees, x=330 degrees
Which of these numbers is pi closest to?
22/7
By analysing the equation of a straight line which in this instance will be "y = 3x + 9", what would the gradient be?
3
What is the geometric name given to a straight line which touches the circumference of a circle at one point only?
Tangent
We need to establish that in parallelogram ABCD, AB is parallel to DC and AD is parallel to BC. Our justification is . . .
the definition of a parallelogram
If sin(53 degrees)=N, what does sin(-53 degrees)=?
-N
Which of these letters does the symbol for pi most resemble?
n
From the following equation, what would be the value of the point at where the straight line crosses the y-axis of a graph: y = 4x - 3?
-3
When a straight line touching a circle in exactly one point meets the radius or diameter of a circle, what is the size of the angle always formed?
90 degrees
In parallelogram ABCD, angle ABD is congruent to angle BDC because if we have parallel lines and a transversal, we know . . .
alternate interior angles are congruent
In what quadrant are cos(x) and tan(x) both below zero?
11
Which of these mathematical equations would always have an end result of pi?
Circumference divided by diameter
There is an arithmetic expression available which allows the gradient of a straight line to be found when two co-ordinates of points, for example, (x1/y1) and (x2/y2) are known. What is the described expression?
(y2 - y1) / (x2 - x1)
Two points are marked on the circumference of a circle. A straight line is drawn from each of these points which both meet in the exact centre of the circle. Another straight line is drawn from each point and meet at a certain point on the circumference. How much bigger is the angle formed at the centre compared to the angle formed at the circumference?
Double
Using the transversal BD, we can show that in parallelogram ABCD . . .
angle DBC is congruent to angle ADB
Find a finite, positive x for which csc(26 degrees)=1/cos(2x+12 degrees).
26