standard form homework

Standard Form: Worksheets with Answers

Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. And best of all they all (well, most!) come with answers.

Mathster keyboard_arrow_up Back to Top

Mathster is a fantastic resource for creating online and paper-based assessments and homeworks. They have kindly allowed me to create 3 editable versions of each worksheet, complete with answers.

Corbett Maths keyboard_arrow_up Back to Top

Corbett Maths offers outstanding, original exam style questions on any topic, as well as videos, past papers and 5-a-day. It really is one of the very best websites around.

Standard Form Practice Questions

Click here for questions, click here for answers, gcse revision cards.

5-a-day Workbooks

Primary Study Cards

Privacy Policy

Terms and Conditions

Corbettmaths © 2012 – 2024

Standard Form Worksheet and Answer Key

Students will practice working with the Standard Form Equation of a Line including finding the X and Y-intercept s, Graphing Standard Form Equations and converting Slope Intercept to Standard Form .

Example Questions

Find the x - and y - intercepts of the Standard Form Linear Equations below.

Write each equation in Standard Form using integer coefficients for A, B and C.

Graph each line using intercepts.

Other Details

This is a 4 part worksheet:

• Part I Model Problems
• Part II Practice
• Part III Challenge Problems
• Part IV Answer Key
• Slope Intercept Form to Standard Form
• Slope Intercept to Standard Form
• Standard to Slope Intercept
• Equation of Line Formulas
• Linear Equation Links, Lessons and Tutorials
• Standard Form to Point Slope Form
• Point Slope to Standard Form

Ultimate Math Solver (Free) Free Algebra Solver ... type anything in there!

Popular pages @ mathwarehouse.com.

• Shape and space
• Data handling
• Graph Paper

Standard Form worksheets

Convert numbers to standard form, convert standard form to numbers, convert between ordinary numbers and standard form, adding in standard form, subtracting in standard form, add and subtract in standard form, multiply standard form, divide standard form, multiply and divide standard form, add, subtract, multiply and divide in standard form.

Standard Form

What is "Standard Form"?

that depends on what you are dealing with!

I have gathered some common "Standard Form"s here for you..

Note: Standard Form is not the "correct form", just a handy agreed-upon style. You may find some other form to be more useful.

Standard Form of a Decimal Number

In Britain this is another name for Scientific Notation , where you write down a number this way:

In other countries it means "not in expanded form" (see Composing and Decomposing Numbers ):

Standard Form of an Equation

The "Standard Form" of an equation is:

(some expression) = 0

In other words, "= 0" is on the right, and everything else is on the left.

Example: Put x 2 = 7 into Standard Form

x 2 − 7 = 0

Standard Form of a Polynomial

The "Standard Form" for writing down a polynomial is to put the terms with the highest degree first (like the "2" in x 2 if there is one variable).

Example: Put this in Standard Form:

3 x 2 − 7 + 4 x 3 + x 6.

The highest degree is 6, so that goes first, then 3, 2 and then the constant last:

x 6 + 4 x 3 + 3 x 2 − 7

Also, within each term, it is nice to have the variables in alphabetical order (if it does not make things more confusing):

yzx 2 + 4 yx 3

The highest degree is 3, so that goes first, also put the variables in alphabetical order

4 x 3 y + 3 x 2 yz

Standard Form of a Linear Equation

The "Standard Form" for writing down a Linear Equation is

Ax + By = C

A shouldn't be negative, A and B shouldn't both be zero, and A , B and C should be integers.

Bring 3x to the left:

−3x + y = 2

Multiply all by −1:

3x − y = −2

Note: A = 3, B = −1, C = −2

Ax + By + C = 0

is sometimes called "Standard Form", but is more properly called the "General Form".

Standard Form of a Quadratic Equation

The "Standard Form" for writing down a Quadratic Equation is

( a not equal to zero)

Expand "x(x−1)":

x 2 − x = 3

Bring 3 to left:

x 2 − x − 3 = 0

Note: a = 1, b = −1, c = −3

Standard Form of a Circle Equation

With a circle like this:

The Standard Form is this:

(x−a) 2 + (y−b) 2 = r 2

See Circle Equations for more details.

What is standard form?

Standard form helps us represent numbers and equations clearly and consistently. Let’s explore the concept in more detail!

Author Michelle Griczika

Published Sep 22nd, 2023

• Key takeaways
• Standard form is a concept that helps us to consistently represent numbers and equations
• Fractions and equations can be written in standard forms

Table of contents

• Standard form explained

How to write numbers in standard form

Standard form is an important mathematical concept that helps us represent numbers and equations clearly and consistently. It may sound a bit technical, but don’t worry! In this article, we’ll explore standard form in a simple and clear way. Let’s get started!

Let’s start by understanding what standard form really means. 

Standard form is a special way of writing numbers or equations that helps us easily compare and work with them . 

In standard form, numbers are written as a multiplication of two parts: a number between 1 and 10 and a power of 10.  Let’s break it down with some examples.  

To write numbers in standard form, we follow a simple process. 

First, we identify the number between 1 and 10 and then determine how many times we need to multiply it by 10 to get the original number. 

Let’s take the number 5,000 as an example. We can write it in standard form as 5 x 10^3. The number 5 is between 1 and 10, and we multiply it by 10 three times to get 5,000.

Unlock unlimited maths questions

Put your skills to the test with fun exercises + maths games that are proven to boost ability!

Get 2 FREE weeks of Doodle!

Use code 2WKS_AUTUMN  to enjoy unlimited questions and games

Use code 2WKS_AUTUMN to get 2 FREE weeks of Doodle!

Try DoodleMaths for free!

Select a year group

• Early Years

Shape, space and measure

Number and place value, addition and subtraction, multiplication and division, operations (asmd), shape/geometry, ratio and proportion, probability, sample questions, advanced topics in standard form.

Now, let’s explore some advanced topics in standard form. Don’t worry if it seems a little challenging at first; understanding these concepts will help you as you progress in your mathematical journey.

Standard form of fractions

You can use standard form with fractions. When dealing with fractions, we can write the numerator and denominator in standard form separately. 

Here’s one example of standard format: the fraction 3/20 can be expressed as 3 x 10^0 / 2 x 10^1. When we simplify it, we get 1.5 x 10^-1. It’s like magic!

Explore standard form with DoodleMaths

DoodleMaths  is an award-winning app that’s filled with fun, interactive questions exploring standard form and beyond!  

Created by teachers, DoodleMaths creates every child a personalised learning experience tailored to their needs, boosting their confidence and ability in maths.

Designed to be used for 10 minutes a day , it automatically targets tricky topics, tops up knowledge and introduces new areas, helping kids get ahead in their learning.  Try it for free  today!

Standard form of equations

Equations can also be written in standard form.  Let’s start with linear equations. 

In standard form, a linear equation looks like this: Ax + By = C. The letters A, B, and C represent numbers we need to find. 

Quadratic equations also have a standard form, written as Ax^2 + Bx + C = 0.

Linear equation standard form

The standard form is represented in linear equations as Ax + By = C, where A, B, and C are constants. This form clearly lets us see the coefficients (the numbers multiplying x and y). 

For example, the equation 2x + 3y = 7 is in standard form. Therefore, we can easily compare the coefficients by writing equations in this form and see how x and y are related!

Quadratic equation standard form

Quadratic equations also have a standard form, written as Ax^2 + Bx + C = 0. This form helps us identify the quadratic, linear, and constant coefficients. 

For instance, the equation x^2 – 5x + 6 = 0 is in standard form. By expressing quadratic equations this way, we can quickly recognise the coefficients and understand the behaviour of the quadratic function.

Standard form of polynomials

You can write polynomials with multiple terms in standard form, too. We arrange the terms in descending order of their degree, which means the highest power comes first, followed by the others. 

For example, the polynomial 5x^2 – 2x^3 + 3x^4 – 7x + 1 can be written in standard form as 3x^4 – 2x^3 + 5x^2 – 7x + 1.

FAQs about standard form

Standard form in maths refers to representing numbers or equations in a consistent format that includes a coefficient and a power of 10.

An example of standard form is 4.2 x 10^2, which represents the number 420.

Yes, standard form and scientific notation are the same concepts! Both involve writing numbers as a coefficient multiplied by a power of 10.

In summary...

Congratulations! You’ve now gained a solid understanding of standard form — a powerful tool in maths. 

Remember, standard form is all about breaking down numbers and equations into parts that are easy to understand and work with.  Whether writing numbers in standard form or expressing fractions, standard form simplifies how we communicate and solve mathematical problems.

If you want to further enhance your skills, be sure to check out the DoodleMaths app . It’s filled with  engaging activities and exercises that will help reinforce your understanding of standard form and many other mathematical concepts!

Related posts

Rational vs irrational numbers

Learn about the differences between rational and irrational numbers

What are odd and even numbers?

We explore examples of odd and even numbers from 1 to 100

Roman numerals from 1 to 100

Learn the Roman numerals from 1 to 100 and have a go at some questions!

Lesson credits

Michelle Griczika

Michelle Griczika is a seasoned educator and experienced freelance writer. Her years teaching first and fifth grades coupled with her double certification in elementary and early childhood education lend depth to her understanding of diverse learning stages. Michelle enjoys running in her free time and undertaking home projects.

What we offer

Quick links

All rights reserved. 

Book a chat with our team

I’m new to Doodle

My school is already using Doodle

Are you a parent, teacher or student?

Get started for free!

Maths information pack

We ask for your contact info so we can send our info pack directly to your inbox for your convenience, exam prep information pack, case studies information pack, information pack, we ask for your contact info so that our education consultants can get in touch with you and let you know a bit more about doodle., student login, which programme would you like to use.

DoodleMaths

DoodleTables

DoodleEnglish

DoodleSpell

If you’d like to use Doodle’s browser version, please visit this page on a desktop.

To log in to Doodle on this device, you can do so through our apps. You can find out how to download them here:

Standard Form

Learn about standard form., standard form lesson, definition of standard form.

Standard form is the standard way of writing something. In mathematics, there are many different standard forms. For example, there is a standard form for writing a number, an equation, a polynomial, and so forth.

We will go through the most common algebraic standard forms in this lesson.

Standard Form of a Number

Writing numbers in standard form is also known as scientific notation. The form is given as:

Where C is a decimal number between 0 and 10, such as 6.35. C is shown with two decimal places in the following example. However, we can write out as many decimal places as necessary.

Example problem:

Write the number 36,500 in standard form, also known as scientific notation.

• Let's move the decimal to the left 4 places so that C = 3.65. C will need to be multiplied by 10 4 to equal 36,500.
• The number is written in standard form as 3.65 x 10 4 .

Standard Form of a Polynomial

A polynomial is in standard form if the terms' exponents are in descending order. In other words, the term with the highest power should be furthest to the left and the term with the lowest power should be furthest to the right.

Rewrite the polynomial 3x 2 + x - 2x 3 + 6 in standard form.

• Let's rearrange the terms so that the exponents are in descending order.
• 3x 2 + x - 2x 3 + 6 → -2x 3 + 3x 2 + x + 6
• The polynomial is rewritten in standard form as -2x 3 + 3x 2 + x + 6.

Standard Form of an Equation

An equation is in standard form if it is set equal to zero. For example, the equation 4y 3 + y = 5 can be rearranged to standard form by moving the 5 to the left side of the equals sign. Standard form of this equation is 4y 3 + y - 5 = 0.

Standard Form of a Linear Equation

The standard form of a linear equation is given as:

Ax + By = C

Where A , B , and C are constants, and x and y are variables. This standard form is only applicable for the equation of a line.

Rewrite the equation y = 4x + 2 in standard form.

• The equation is currently in slope intercept form. Let's move the term 4x over to the left side of the equals sign.
• y = 4x + 2 → -4x + y = 2
• The linear equation is written as -4x + y = 2 in standard form.

Standard Form of a Quadratic Equation

The standard form of a quadratic equation is given as:

ax 2 + bx + c = 0

Where a , b , and c , are constants, and x is a variable.

Rewrite the quadratic -4x - 12 = 2x 2 in standard form.

• We must have all nonzero terms on one side of the equals, and the zero term on the other side of the equals. The nonzero terms must also be in descending order of exponent power.
• -4x - 12 = 2x 2 → 2x 2 + 4x + 12 = 0
• The quadratic is written as 2x 2 + 4x + 12 = 0 in standard form.

Learning math has never been easier. Get unlimited access to more than 168 personalized lessons and 73 interactive calculators. Join Voovers+ Today 100% risk free. Cancel anytime.

Insert/edit link

Enter the destination URL

Or link to existing content

• International
• Education Jobs
• Schools directory
• Resources Education Jobs Schools directory News Search

Standard form - homework

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

Last updated

4 June 2024

• Share through email
• Share through twitter
• Share through linkedin
• Share through facebook
• Share through pinterest

This homework is designed to support GCSE pupils learning of standard form. The exercise is suitable for all abilities and will help students retain the information learned from the lesson. I put these two topics together to fit in with Exam-boards scheme of work.

This resource will take students through writing standard and ordinary form as well as testing their ability on adding, subtracting, multiplying and dividing standard form. The homework offers questions that increase in difficulty allowing accessibility and challenge. Exam and more problem solver type questions are also included. The sheet also gives the students a chance to reflect on their learning.

Homework includes

Recall questions (previous topic) Topic skill questions Applied questions/ Exam questions Random problem solver Reflection page Solutions, solutions, solutions

Creative Commons "Sharealike"

Your rating is required to reflect your happiness.

It's good to leave some feedback.

Something went wrong, please try again later.

This resource hasn't been reviewed yet

To ensure quality for our reviews, only customers who have downloaded this resource can review it

Report this resource to let us know if it violates our terms and conditions. Our customer service team will review your report and will be in touch.

Not quite what you were looking for? Search by keyword to find the right resource:

Standard form

Standard form is a term commonly used to describe the most typical form of an object (like a number, expression, equation, etc.) used in a number of different topics. In this case, standard form refers to the standard form of a linear equation. The standard form of a linear equation is given by the equation:

Ax + By = C

where A, B, and C are constants.

Standard form is useful because the x- and y-intercepts of the line can be easily found by setting x or y equal to 0, then solving for the desired variable. Doing so results in the general formulas for finding the x and y-intercept given a linear equation in standard form:

One of the key benefits of the standard form of a linear equation over point-slope form and slope-intercept form is the ease with which it can be used to find the x-intercept. Finding the x-intercept using either of these two other forms is more tedious than it is with standard form.

Once the x and y-intercepts are found, the line can be graphed by plotting the x and y-intercepts then drawing a line connecting the intercepts.

3x + 2y = 6

Depending on the linear equation, it can be easier to graph a line given an equation in slope-intercept or point-slope form, since it can be tedious to calculate the x and y-intercepts given an equation in standard form. Equations in slope-intercept and point-slope form include the slope of the line, and a point on the line, which can be immediately read from the equation. Thus, plotting the line doesn't require any calculation of the intercepts.

Converting to standard form

Different forms of linear equations are useful for different applications. For example, when solving systems of linear equations, it is helpful to first convert the equation into standard form. Slope-intercept and point-slope form are two commonly used forms of a linear equation that, while useful for graphing, are not useful for solving systems of linear equations. It is therefore important to know how to convert between various forms of linear equations to best suit the application.

Converting from point-slope or slope-intercept form to standard form involves moving all the variables to one side of the equation, moving the constant to the other side, then manipulating the equation as necessary such that the coefficients of the terms of the equation are integers.

Convert the following linear equations to standard form.

1 . y = -3/4x + 2:

3/4x + y = 2

3x + 4y = 8

2 . y - 2 = 3/4(x - 8):

y - 2 = 3/4x - 6

-3/4x + y = 4

-3x + 4y = 16

Other forms of a linear equation also exist, but the above are a few of the most common.