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Standard Form Algebra

Deeply test your understanding of standard form (scientific notation) by involving a little algebra.
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This is level 3: mixed standard form questions. You will be awarded a trophy if you get at least 7 correct and you do this activity online. All answers should be given in standard form. To type indices or exponents use the up arrow key ^ then type the index. Use the button provided to insert a multiplication sign.

1

Simplify

\(\sqrt{16 \times 10^{2p}}\)




= Correct Wrong

2

Simplify

\(\sqrt{a^2 \times 10^{6}}\)

when

\(1 \le a \lt 10\)

= Correct Wrong

3

Simplify

\(\sqrt{9a^2 \times 10^{2p+4q}}\)

when

\(\frac13 \le a \lt \frac{10}{3}\)

= Correct Wrong

4

Simplify

\(\sqrt{a^4b^6 \times 10^{-6}}\)

when

\(10 \le a^2b^3 \lt 100\)

= Correct Wrong

5

Simplify

\((a \times 10^{3})^2\)

when

\(\sqrt{10} \le a \lt 10\)

= Correct Wrong

6

Simplify

\((a \times 10^{p})^q\)

when

\(100 \le a^q \lt 1000\)

= Correct Wrong

7

Simplify
$$ \frac{a \times 10^5 \times b \times 10^p}{b \times 10^q} $$
where

\(1 \le a \lt 10\)

= Correct Wrong

8

Simplify
$$ \frac{a^2 \times 10^{2p} \times b^3 \times 10^{-3q}}{a^2b^2 \times 10^{5q+2p-8}} $$
where

\(1000 \le b \lt 10000\)

= Correct Wrong

9

Simplify

\((a \times 10^3) + (10a \times 10^2)\)


where


\(0.5 \le a \lt 5\)

= Correct Wrong

Check

This is Standard Form Algebra level 3. You can also try:
Level 1 Level 2

The questions in this exercise have been adapted from an exercise created by Transum subscriber Chris Boardman.

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.
Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 26 March 'Starter of the Day' page by Julie Reakes, The English College, Dubai:

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Comment recorded on the 11 January 'Starter of the Day' page by S Johnson, The King John School:

"We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory."

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Description of Levels

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Standard Form - Begin here if you prefer your standard form to come without algebra.

Level 1 - Simplifying expressions in standard form

Level 2 - Multiplication and division of numbers in standard form

Level 3 - Mixed standard form questions

More Indices including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Standard Form

Standard form, also known as scientific notation, is a way of conveniently writing numbers that accommodates values too large or small to be conveniently written in standard decimal notation.

Standard Form

Examples

3.48 x 104

= 3.48 x 10 x 10 x 10 x 10

= 3.48 x 10000

= 34800

 

3.48 x 10-2

3.48 x 1⁄100

= 3.48 ÷ 100

= 0.0348

 

Finally note that any number raised to the power zero is 1 so:

3.48 x 100

= 3.48 x 1

= 3.48

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Typing Mathematical Notation

These exercises use MathQuill, a web formula editor designed to make typing Maths easy and beautiful. Watch the animation below to see how common mathematical notation can be created using your keyboard.

MathQuill Animation

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