Sequences & Functions

Question 1

How might you go about solving a formula questions that doesn’t supply info you can sub in?

Answer 1

Look for unstated equations that are relevant to the formula

I.e. A= 16pidr*2 / x2

Substitute in the formula for area and diameter

Question 2

What should you do if a formula equation asks you to determine the value at which two distinct variables equal one another?

Answer 2

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)

Question 3

What should you be prepared to do when given a formula that contains a constant?

Answer 3

Do 2 substitutions

1 to find the identity of the constant
2 to solve the equation

Question 4

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

Answer 4

Pick values for the altered variables

Solve the formula would a random input
Then solve the formula w the alteration

Question 5

What do you do when you have a problem with multiple constants ?

Answer 5

Plug in thrice

• sub the givens into one and other
• use the solved variables in the original equation to get your answer

Question 6

Functions have two main parts, what are they?

Answer 6

Inputs and outputs

Question 7

The “If..” part of a function is telling you the … and …

Answer 7

Input and output

Question 8

What do you do when there is a coefficient before its header or its input in a function?

Answer 8

Divide out or multiply away the coefficient

Question 9

In the function h(z)=7 . What is the input ? What is the output?

Answer 9

Input is z

Output is 7

Question 10

What is the range of a function?

Answer 10

All of its possible outputs

Question 11

What is the domain of a function?

Answer 11

All of its possible inputs

Question 12

How do you solve embedded functions?

Answer 12

Solve the inside function first

Question 13

How do you answer the question ;

For which of the following functions f is f(x - 1) = f(1-x) for all x ?

Answer 13

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

Question 14

How do you solve an inverse variation function ?

Answer 14

Set the products of two quantities equal to one another

Question 15

Whats the rule for graphing functions?

Answer 15

Replace the f(x) portion of the function with a y

I.e. f(x) = mx + b would become y=mx+b

Question 16

What is the b in a line, y=mx + b ?

Answer 16

The y intercept

Question 17

If you have a repeated symbolism function problem always do what first?

Answer 17

The portion in the parentheses first

Question 18

What is important to remember about solving sequence problems?

Answer 18

You cant solve them without knowing the rule that governs the sequence

Question 19

What is a recursive sequence rule?

Answer 19

When the value of each term in the sequence is defined by the values of the terms around it

Question 20

How do you differentiate between an explicit rule and recursive rule sequence?

Answer 20

An exclusive will just have a subscript

A recursive will have a subscript doing something like subscript minus 1

Question 21

How do you identify a sequence unknown term?

Answer 21

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

Question 22

What should you think about for recursive rules?

Answer 22

Think about the term before i.e. Q subscript t-1 means the term before

And Q subscript t+1 means the term after

Question 23

What must you be told in order to determine the value of an unknown term in a sequence whose rule is unstated?

Answer 23

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

Question 24

What is a linear sequence?

Answer 24

Any sequence in which the difference between any two consecutive terns is the same

I.e. 5,10,15 (difference of 5)

Question 25

What is a ratio sequence?

Answer 25

Any sequence in which the ratio between any two consecutive terms is the same i.e. 3,6,12 (ratio of 2)

Question 26

How do you solve linear sequences w/o rules?

Answer 26

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

Question 27

What is the formula for exponential sequences ?

Answer 27

An=A1(R) ^n-1

Question 28

How do you solve an exponential sequence problem ?

Answer 28

Plug the information you have into the formula

An=A1(R)n-1

Question 29

What is a series?

Answer 29

The sum of the terms in a sequence

Question 30

What must be true to calculate a sequence?

Answer 30

The sequence must be finite

Question 31

How do you determine a linear sequence?

Answer 31

Take the average of the first and last terms of the sequence

Multiply that average by the number of terms in the sequence

Question 32

What is the formula for finding the series of an exponential sequence?

Answer 32

Sn= (A1(1-R^n)/(1-R)

Question 33

Whats an example of a repeating sequence ?

Answer 33

1,3,5,1,3,5

Question 34

How can you go about solving a repeating sequence formula?

Answer 34

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)

Question 35

What can you do if the computational portion of a sequence question seems exceeding complex?

Answer 35

Tease out the first 5 or 6 terms of the sequence and look for a pattern within terms

Question 36

What is a three dimensional shape?

Answer 36

Any shape that has

Height
Width
Depth

Question 37

What is the unit of measurement for volume?

Answer 37

Cubic units

Question 38

What is the formula for volume of a rectangular solid?

Answer 38

Length * width * height

Question 39

How do you find the surface area of a rectangular solid?

Answer 39

Find the sum of the area of its faces

Or

2(lw + wh + hl)

Question 40

Whats the formula for diagonal of a rectangular solid ?

Answer 40

Sq rt of ( l^2 + w^2 + h^2)

Question 41

How do you calculate the volume of a cube ?

Answer 41

S^3

S cubed

Question 42

What information do you need to calculate the surface area, volume and diagonal of a cube ?

Answer 42

Only one side

Question 43

What is the formula for volume of a cylinder?

How should you remember it?

Answer 43

Pi r^2h

Area of the top or bottom circle times the height