Maths Flashcards
When is Arc Length used?
What is the formula?
To find the length of a side of a part of the circumference of a circle
To calculate it we use the formula
AL= angle/360 x PIE D
When is Sector Area used?
What is the formula?
Sector Area is used to calculate the area (not length- that would be arc length) of a major or minor section of a circle
The formula is
SA= angle/ 360 x PIE R squared
When Pythagoras used ?
What is the formula?
Pythagorus is used to calculate the length of a side of a right angled triangle
c2= a2 + b2
How do you find the angle, when given a percentage, using a pie chart and vice versa
To find an angle you do
percentage / 100 x 360
to find the percentage you use # / 100 x 360
When is standard deviation used?
What is the formula - will be given on formula sheet.
Standard deviation finds the average distance each data point is from mean
The formula is
SD= squareroot of E(x- mean) squared / n-1
how do you ‘draw the line if y=2x-3 or y=3x+2 or y=-2+2’ ?
Set up a table of x values and use formula to find y values
plot the points on your graph
draw the lines through the points
when is y=mx+c used?
When we have the gradient and y intercept
When is m= v/h used?
what’s used otherwise?
If we are given a triangle but if given a coordinate we use :
m= y2-y1 / x2-x1
When two perpendicular gradients are multiplied, what do we get?
-1
If you only have one point and a gradient, how do you find the equation of a straight line?
y-b = m(x-a)
What is Simple Interest?
How do we find it?
Simple Internet is the money paid out each year buts not added to your account.
We find it using
SI= % for one year x #of years
What is compound interest?
How do we find it?
Compound interest is used when the interest that is calculated is added to your account each year.
We find it using a calculator by
CI= amount invested x % increase or decrease squared to the amount of years
What is simultaneous equations?
How do we find it by graph?
Simultaneous equations are used to find the solution that fits both equations given.
By graph we find them by looking for the point of intersection
- draw both lines
- find the coordinate of the POI
How do we find simultaneous equations algebraically?
Crate equal Coefficients by multiplying
Take one equation away from the other
Substitution the answer you just got into one of the equations
MAKE ANSWERS CLEAR
a transformation of (x+b) squared moves the graph where?
In x direction and -b places
How do you sketch quadratics in the form of y=(x-a) (x+b)
state the roots
Find the axis of symmetry (add routes and divide by 2)
Find the turning point (sub axis of symmetry into equation)
Find y intercept (sub x=0)
Draw
If a quadratic equation can not be factorised, what do we use? Usually in the form
ax squared + bx + c= 0
The Quadratic Formula
What are the 3 conditions for crossing the x axis?
How do we know which is which?
Two real and distinct roots
- If b squared - 4ac is more than 0
Two real and equal roots
- If b squared - 4ac is equal to 0
No real roots
- If b squares - 4ac is less than zero
What is the discriminant?
The discriminant is the part of the quadratic formula in the square root. It is used to find the condition of crossing the x axis.
example - determine the nature of the roots.
Key features of the Sine graph
maximum value is 1
Minimum value is -1
period is 360 degrees
in the shape of a N
Key features of a cosine graph
Maximum value if 1
Minimum value of -1
Period is 360
In the shape of a V
y= a sin/cos b x +/- c
what does a, b and c affect
a affects the height of the graph.
b affects how many waves are on the graph ( length of a period)
c moves the graph up or down by the number
