# The Basics Of Eleventh Grade Math On One Page

Don’t know what’s going on with your kid’s math homework? Let’s make this easy on you. Here’s a resource for parents who want to teach their eleventh grade kid some math over the summer, or whenever. It covers the key stuff in your local grade 11 curriculum. Read through the sections and download the workbooks, or review a prior Grade 11 Final Exam. Try to have as much fun with it as you can because the key to learning is feedback. Make some rules, offer rewards, and make it a game. If you can make practice fun and challenging, your child will thrive!

Mastered Eleventh-grade math? Check out our Grade 12 Math Curriculum resource page (coming soon).

Introduction To Math Education

Like building a house, there are no shortcuts to learning math. All new math is build on top of an existing math foundation. Sir Isaac Newton, the inventor of calculus once wrote: “If I have seen further, it is by standing on the shoulders of giants.”. We discover new things by building on previous things. It is important that our the foundation is strong. This makes learning advanced math easier. Knowing the prerequisite knowledge unlocks paths and makes learning the new stuff easier. Without a strong foundation anyone will find it difficult to follow the new material. This causes stress and confusion in later years. Like building a house, we should aim to have the most complete foundation we can. Get the cracks fixed and you will build a beautiful house. Think of educational learning as a pyramid. The foundation is Elementary School Math and the Pinnacle being a pHD. A knowledge gap at the base affects your ability to learn at the top.

It is very important for parents to be aware of what their child is learning in school.

Your school gets its direction from a governing body. The school board issues a curriculum (or math standards) for schools to follow. The curriculum varies across the world. For example, in Saudi Arabia, algebra starts in Grade 1, while in Ontario it starts in Grade 8. That means your school’s curriculum differs from what you may find online. In this article, we cover an estimation of what you can expect from your school’s curriculum.

• Solving Linear Systems (Graphing, Substitution Method, Elimination Method)
• Factoring Quadractics, Completing The Square, Applications
• Graphing Geometry: Trigonometric Identities, Special Triangles, Area Problems, Volume And Surface Area.
• Probability & Statistics: Basic Probability, Probability Models, Sample Spaces, Comparing Spaces

Find an online math tutor today! ## What’s a Relation? What’s a function?

What’s a Relation? What’s a function? A relation is a way that two objects relate.

Here are a few relations you may have seen:

• = means ” this is the same as that”.
• > means “this is greater than that”.
• < means ” this is the less than that”.

If we have an equation. Like Y = X squared.

That is a relation. But it is also a function

If we had another relation, like y squared = x squared.Would it be a relation? Yes, it would be. It would not be a function.

How do you tell what’s the relation and what’s a function? That’s where the vertical line test can help you out.

The vertical line test is when. You imagine scanning the function with a vertical line. And if ever the vertical line passes through the function twice then the function has two Y values for one X value. Since functions are 1-1 mappings of x-values to y-values then it is not a function.

The vertical line test is a simple test that will tell you. By looking at the graph if something is a function.

To recap a function is a relation, but a relation is not always a function.

A relation is like a function with less restrictions. And the restriction is that a function can only have a one to one mapping of X values to Y values.

Analogy to a vending machine

Think of a function, like a vending machine. If you press Pepsi and do you get Pepsi? Then it’s a function. If you press Pepsi and you get Pepsi and Coke. Then it’s not a function. Because there should only be a one-to-one mapping from a button to a drink.

So that is the difference between functions and relations, and how to use the vertical line test.

## Set Notation. What Is A Set And How To Write One Think of a set as a bag. Whenever you see this { } that means it is a set. Putting numbers in a set is like having a collection of numbers. {1, 2, 3} is a set containing 3 elements: the numbers 1, 2, 3.

Sometimes we want to put infinite numbers in a set. We can do that by using variables. X element of R means x is a number belonging to the real numbers. That could be an any number, so there are infinite possibilities. Put that statement in a set, and you have {X element of R}. This set of numbers is infinitely big.

We can be more specific about the set with conditions. The symbol | means “such that”. If we say X element of R such that x <= 3, that means that x has to be less than or equal to 3. Put that in a set and we have an infinite set of elements where all elements are less than or equal to 3. It is writer {x element of R | x <= 3}

### The Domain Of A Function And How To Write It

What values of x can the relation take? It’s the knob that you turn, or the buttons on the vending machine.

Practice naming the domain of these functions:

X = { x element R | x<=3 }

For example,

the domain can be the same as all the real numbers.
The domain can be all the real numbers except for 1.
The domain can be all the real numbers less than 1
The domain can be all the real numbers between 0 and 1.

As you can see there are many ways to describe the domain. You will have to learn how to analyze the function to determine what is the domain. ## The Range Of A Function And How To Write It What values of y can the relation make? Its the output that happens when you turn the knob. It’s all the possible drinks in the vending machine that you can buy.

Practice naming the range of these functions (Where the points are vertically)

Similarly, the range is all the possible y values that the function can create.

The range can be all the real numbers
The range can be all the real numbers except for 1.
The range can be all the real numbers less than 1
The range can be all the real numbers between -1 and 1. (Sin)

### Function Notation

In the past you learned to write equations like y=mx+b. Now we will change the notation. That means everything will be the same, but written in a different way. The only change is that instead of “y” you now write “f(x)”. F(x) means “function  with respect to x”. X is the input and f(x) is the output. This is the same as the relationship with y and x!

### Finding The Vertex Of A Quadratic

The vertex is the point where the function changes direction. In a quadratic there’s 1 vertex. For example x^2 has one vertex. As you add more degrees, you will have more vertices. Sometimes functions are special and do not have a vertex. They dont change direction. Instead it’s called a “critical point”. It looks as if it will change direction, but it just stops then continues in the same direction.

Solving a quadratice usually means finding the values of x where the function is equal to zero. That means, find the values of x where the function crosses the x axis. There are many ways to solve a quadratic. If you have a graph, you can just see with your eye where the point is that the function crosses the zero. You can use “The Quadratic Formula” to get the values of x. You may also just recognize from looking at the equation where the solution is.

### Operations With Rational Expressions

You can do all kinds of things with rational expressions:

• Subtract them
• Stick-em-in-a-Stew… Just kidding!

## Eleventh Grade Math Problem Worksheets

Are you looking for something you can hand to your kid to start learning? Check out our free 11th grade math worksheets. You can download or try out our math problem generator to learn online.  You can make a copy, download, and print these problems. Make it an exciting game and start learning Grade 11 math today! If you don’t have a printer, open it with the iPad/Tablet. 1

We also love to write blogs about learning. check out our blog on 6 free back to school math activities to get to the next level.

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