Final Exams Notes Flashcards
What does a sign change signify in iteration?
That there is a solution between the two values you have just put in, therefore you must try more values between those two.
When you use an iteration machine, when do you know when you have found the solution?
When you find two values that are equal when rounded to the desired number of decimal places.
What is the equation for a circle with centre (0,0) and radius r?
r^2= x^2 + y^2
Write out the initial bracket for completing the square
(x + b/2)^2 - (balancing number)
When a is positive what does the completing the square balancing number tell you?
the minimum y point.
The minimum y point is (-b/2, balancing number)
If the balancing number is positive, what does this tell you?
There are no real roots
What is the difference of two squares?
a^2-b^2 = (a + b)(a - b)
What is a geometric sequence?
One where the term to term rule is to multiply or divide by the same value.
How do you find the multiplier or divider in a geometric sequence?
Divide a term by the previous term
What are the equations for exponential graphs?
y= k^x y= k^-x
Under what conditions do exponential graphs curve up?
If k>1 and the power is positive
If x^2 > a^2
x > a or x < -a
If x^2 < a^2
-a < x < a
Explain the graph transformation: y = f (x-1)
Shifts to the right
Explain the graph transformation: y = f (x) -1
Shifts down
Explain the graph transformation: y = f (-x)
Reflects in the x axis
Explain the graph transformation: y = f (2x)
Squashed by stretch factor 2
Explain the graph transformation: y = 2f (x)
Height doubles
State the alternate segment theorem
The angle between a tangent and a chord is always equal to the angle made at the circumference by the two lines drawn from the ends of the chord.
What does “the angle subtended at” mean
The angle made at
How do you read column vectors?
The numerator is the horizontal movement
The denominator is the vertical movement
How should you write vectors?
Underline them
What does
—>
AB
mean?
Go from point A to point B
What is the consequence of multiplying a vector by a positive number?
Magnitude is changed
What are the consequences of multiplying a vector by a negative number?
Direction and magnitude may change
How do you add column vectors?
Add the tops then add the bottoms
How do you find an unknown vector?
Find any route there made up of known vectors then simplify
How do you show vectors to be on a straight line?
Show that the vectors are all in the same direction by showing that they are multiples of each other.
How do you prove congruency?
SSS, AAS, SAS, RHS
How do you prove similarity?
All the sides are proportional,
All the angles are the same,
Any two sides are proportional and the angle between them the same.
How are scale factors calculated?
old length
Explain scale factors for sides, areas and volumes
The sides are n times bigger
The areas are n^2 times bigger
The volumes are n^3 times bigger
How do you calculate scale factor n^2
Old area
How do you calculate scale factor n^3
Old volume
What is the lower quartile?
The value 25% of the way through a data set
What is the median?
The value 50% of the way through the data set
What is the upper quartile?
The value 75% of the way through the data set
In probability, how is “and” written?
n
In probability, how is “or” written?
u
How is relative frequency calculated?
Total no. outcomes
How many probabilities when rolling 4 dice?
6 x 6 x 6 x6
How do you add and subtract in standard form?
Make sure the powers are all the same
Define equation
A statement that the values of two expressions are equal
Define formula
A rule written with mathematical symbols
Define identity
An equation that is true regardless of the values chosen
Define term
A single number or variable
Define expression
Numbers, symbols and operators grouped together to show the value of something.
Define inequality
An equation that uses < and > rather than =
Define factor
A number that multiplies with another number to produce a multiple
What do functions mean?
The function f takes a value for x, multiplies it by 5 then adds 2
Equation for a line (not y = mx +c)
y - y1 = m (x - x1)
For inequalities on number lines, when do you use dotted and filled lines?
Solid lines means including points on the line
Dotted lines means not including points on the line
For inequalities on graphs, when do you use open and closed dots
Open dots, not including the values
Closed dots, including the values
How do you calculate the sum of the internal angles of any polygon with n sides
180(n-2)
What is the sine rule?
a/sinA = b/sinB = c/sinC
What is the normal cosine rule?
a^2 = b^2 + c^2 - 2bc cos A
What is the cosine rule for finding angles?
Cos A = b^2 + c^2 - a^2
—————————–
2bc
How do you calculate the area of a triangle?
0.5 ab sin c
