Math Final

What is the Pascal Triangle?

Pascal triangle is a system of numbers arranged in rows resembling a triangle with each row consisting of the coefficients in the expanded form.

To divide fractions we normally divide by the reciprocal. Is it possible to divide in a straight line?

Yes it is possible, however I am unsure if it will work for every single function. It is possible though! It worked for the fractions 2/3 and 2/1. I have shown my calculations above.

Why are triangular numbers called that way?

triangular numbers are the addition of consecutive numbers. When you put a pictorial representation it appears to look like a triangle.

Are numbers in binary different from numbers in base 5?

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What is a function?

A function is an equation that has a dependent variable and an independent variable. It has a domain expressed as x, and a range expressed as y. These values produce coordinates that we can graph ex: f(x)=2x+1. Every x can only have one y.

What is the relation between patterns and functions?

A function is described as having one or more variables, which is similar to a pattern which has a repeated process or sequence in the same way a function is also a form of a sequence or process.

What is the difference between linear and quadratic functions?

A linear function can be drawn as a line like y=mx+b. A quadratic function can be drawn as a parabola which is a curved shape and is y=ax^2+bx+c

What is a linear function? Explain

A linear function is a function that when graphed displays a line. For example, there are no turns or loops or curves in this function. Usually to the first degree exponent. f(x)=5x^1+2 x:0,1,2 y: 2,7,12

What is a pattern?

A pattern is repetitive, predictable process of sequence. ex: abcabcabc or 2468101214

Why are prime numbers important?

A prime number is important because it can only be divided by one and itself, but must be greater than one. In the lesson about opening and closing the lockers, identifying the pattern of prime numbers helped us solve the equation.

What is a sequence?

A sequence is a set of numbers or objects in order

What is an algorithm?

An algorithm is a sequence of steps to perform a task. We use these in everyday mathematics such as multiplication and division.

What is an exponential function?

An exponential function is a function whose value is a constant raised to the power of the argument.

Why do we say that division can be thought of as repeated subtraction?

Because we are continuously subtracting quantities away from the original number until we have no numbers or a remainder leftover.

What is better? To have a discount before or after taxes? Explain

Both methods are correct and yield exactly the same result

Draw a visual pattern and describe it.

Can draw hearts and squares and circles.

Give an example of a function that does not involve numbers?

First Name: Sarah, Victoria, Lucy, Eric Last Name: Smith, Dobbs, Black, Fintel

Draw the graph of a function and something that fails to be a function. Explain why.

Graph that is a function: I drew a straight diagonal line. Graph that isn't a function: I drew a squiggly line. In a function x variables cannot be the same

Why do we say fractions have a counting part and a measuring part?

In a fraction there is a numerator and a denominator. The denominator measures the amount that we are comparing and the numerator counts how many things are in the total, or measured part. Ex: a/b. a=girls in 3rd grade. b=total students in 3rd grade

What is the difference between a power function and an exponential function?

In a power function the independent variable (x) is raised to a constant power. In an exponential function the independent variable is the exponent while the base is a constant.

What is the requirement for a function to have an inverse?

It has to pass the horizontal line test. If it doesn't then when inversed, it won't pass the vertical line test to make it a function. The function and its inverse must be functions.

What is a binomial coefficient?

It is number of ways of picking unordered outcomes from possibilities

What geometric property does the leading coefficient of a quadratic function represent?

Leading coefficient tells us how skinny or wide the graph will be (the parabola) and also, if the leading coefficient is negative, it tells us the graph will open down like an upside down U. If the leading coefficient is larger, the graph will look skinnier.

What are the most important types of functions?

Linear, quadratic, power, exponential, and log

Why do we say that multiples don't affect residue?

Multiples do not affect residue because residues are the leftovers of integers after DIVISION.

Can we add percentages? Explain.

No you can't because a percentage is a way to measure or represent a ratio/proportion/quantity in comparison to 100. If you add percentages, you are comparing two completely unrelated equations and you just can't add them.

Can we have residue when dividing by decimals?

No, because when you divide a decal, whatever "residue" is left at the end of your long division sequence would just be included in the decimal.

Could we have a negative remainder in division?

No. One way we can look at remainders is as if they are extra, or left overs. We learned about remainders when solving the extra amount of coins that the pirates had. According to the definition of remainder, it says what is leftover of an integer. If you have zero leftovers or less than zero, you do not have a remainder at all.

Can every decimal be written as a fraction?

No. irrational numbers cannot be written in the form of a fraction. This includes non termination, non repeating decimals.

Why do we have different number representations?

Number representations are simply different ways to write a quantity. Depending on the subject matter, we can choose the best way to represent a quantity. For example, if I write 125 dogs, you know that I have one hundred twenty-five dogs. But if I write $1.25 you know that I have one dollar and twenty-five cents.

What is the advantage of Binary representations?

One advantage of the binary representation is its simplicity. The binary number system requires the smallest possible number of distinct digits. As a result, the rules for doing arithmetic on binary numbers only have a very small number of cases.

What is parity?

Parity is the property of an integer being odd or even. We learned about/used parity in the homework where we were given an 8x8 grid but 2 tiles were removed and we had to fit domino shaped pieces into the manipulated grid.

Why is rounding important?

Rounding is altering a number for the convenience of solving an equation. It is important because some problems, for example, that have repeated decimals, there will be an infinite amount of numbers. In order to solve problems like that, it is best to round your numbers for your convenience.

Give an example of something that is not a function.

Something that does not pass the vertical line test and has more than one y value for a given x value.

There are fifteen people at a business meeting. Everybody shakes hands and exchange business cards. What is bigger, the total number of handshakes or the total number of business cards?

There are more business cards because for each interaction, one handshake is given but two business cards are exchanged.

Give an example of a function that does not have an inverse.

Upside down U graph. It doesn't have an inverse because it doesn't pass the horizontal line test when flipped/inverted. It would then fail the vertical line test which is whats used to determine a function

Can we have a function that does not follow a pattern?

Yes. For example, in class we saw a pattern that required 2 equations to describe it. 2^x and x^2. Not all of the values in this function met the equation for a single pattern.

How many symbols do we need for a numerical system base 12?

You would need one for number ten and one for number 11. Once you get to number 12, you would actually be in the next level.

Can we divide by zero? Explain why or why not?

no you cannot divide by zero because there is no quantity to divide by or "take away" Zero has no factors and cannot be divided in any way