Sequences & Functions Flashcards
How might you go about solving a formula questions that doesn’t supply info you can sub in?
Look for unstated equations that are relevant to the formula
I.e. A= 16pidr*2 / x2
Substitute in the formula for area and diameter
What should you do if a formula equation asks you to determine the value at which two distinct variables equal one another?
Set the two variables equal to one another and substitute the info into the provided formula
I.e. c= 5/9 (f-32)
To find the temp at which c = f
Do f= 5/9 (f-32)
What should you be prepared to do when given a formula that contains a constant?
Do 2 substitutions
1 to find the identity of the constant
2 to solve the equation
How to you solve a question in which the value of a given formula is increased or decreased by the alteration of its variable?
I.e. in the formula A=3/(2z) and z is tripled, by what amount is A multipled
Pick values for the altered variables
Solve the formula would a random input
Then solve the formula w the alteration
What do you do when you have a problem with multiple constants ?
Plug in thrice
- sub the givens into one and other
- use the solved variables in the original equation to get your answer
Functions have two main parts, what are they?
Inputs and outputs
The “If..” part of a function is telling you the … and …
Input and output
What do you do when there is a coefficient before its header or its input in a function?
Divide out or multiply away the coefficient
In the function h(z)=7 . What is the input ? What is the output?
Input is z
Output is 7
What is the range of a function?
All of its possible outputs
What is the domain of a function?
All of its possible inputs
How do you solve embedded functions?
Solve the inside function first
How do you answer the question ;
For which of the following functions f is f(x - 1) = f(1-x) for all x ?
Let x equal a random number
Put it into both functions
Test the two inputs into each answer choice
The choice where the answers are identical is the correct choice
How do you solve an inverse variation function ?
Set the products of two quantities equal to one another
Whats the rule for graphing functions?
Replace the f(x) portion of the function with a y
I.e. f(x) = mx + b would become y=mx+b
What is the b in a line, y=mx + b ?
The y intercept
If you have a repeated symbolism function problem always do what first?
The portion in the parentheses first
What is important to remember about solving sequence problems?
You cant solve them without knowing the rule that governs the sequence
What is a recursive sequence rule?
When the value of each term in the sequence is defined by the values of the terms around it
How do you differentiate between an explicit rule and recursive rule sequence?
An exclusive will just have a subscript
A recursive will have a subscript doing something like subscript minus 1
How do you identify a sequence unknown term?
For explicit rules: set the rule of the sequence equal to the value of unknown terms
For recursive rules flesh out the sequence until the value of the desired term appears
What should you think about for recursive rules?
Think about the term before i.e. Q subscript t-1 means the term before
And Q subscript t+1 means the term after
What must you be told in order to determine the value of an unknown term in a sequence whose rule is unstated?
You must be told something specific about the sequence such as the difference between successive teams is constant or the ratio between successive teams is constant
What is a linear sequence?
Any sequence in which the difference between any two consecutive terns is the same
I.e. 5,10,15 (difference of 5)
What is a ratio sequence?
Any sequence in which the ratio between any two consecutive terms is the same i.e. 3,6,12 (ratio of 2)
How do you solve linear sequences w/o rules?
Find the number of moves from given term and desired term
Multiply that number by the constant
Add the product to the given term
I.e. given s5=15 and s6=18 , constant is 3
Find the value of s38
Do 38-3= 32
32*3=96
18+96=114
Answer is 114
What is the formula for exponential sequences ?
An=A1(R) ^n-1
How do you solve an exponential sequence problem ?
Plug the information you have into the formula
An=A1(R)n-1
What is a series?
The sum of the terms in a sequence
What must be true to calculate a sequence?
The sequence must be finite
How do you determine a linear sequence?
Take the average of the first and last terms of the sequence
Multiply that average by the number of terms in the sequence
What is the formula for finding the series of an exponential sequence?
Sn= (A1(1-R^n)/(1-R)
Whats an example of a repeating sequence ?
1,3,5,1,3,5
How can you go about solving a repeating sequence formula?
Tease out the sequence until you see it repeat
Count the number of terms that repeat
Divide the place number of the term that you are seeking to identify by the number of terms found in step 1
The remainder determines the value of the answer term (no remainder=same value as the last term)
What can you do if the computational portion of a sequence question seems exceeding complex?
Tease out the first 5 or 6 terms of the sequence and look for a pattern within terms
What is a three dimensional shape?
Any shape that has
Height
Width
Depth
What is the unit of measurement for volume?
Cubic units
What is the formula for volume of a rectangular solid?
Length * width * height
How do you find the surface area of a rectangular solid?
Find the sum of the area of its faces
Or
2(lw + wh + hl)
Whats the formula for diagonal of a rectangular solid ?
Sq rt of ( l^2 + w^2 + h^2)
How do you calculate the volume of a cube ?
S^3
S cubed
What information do you need to calculate the surface area, volume and diagonal of a cube ?
Only one side
What is the formula for volume of a cylinder?
How should you remember it?
Pi r^2h
Area of the top or bottom circle times the height
