Transum Software

Using Graphs to Solve Equations

Using and creating graphs to solve quadratics and pairs of simultaneous equations.
  Menu   Level 1 Level 2 Level 3 Level 4 Exam-style   Help     More  

A Graphic Display Calculator is require for this level.

TI-nSpire

If you don't have a GDC try this Graph Plotter.

Use your GDC to find a solution to the following simultaneous equations:

\( \quad \quad y=2.9x-40\)
\( \quad \quad y=23-1.1x\)

Give your answers correct to three significant figures.

\(x =\) ☐ ✓ ✗ ☐\(y =\) ☐ ✓ ✗

3

Solve the following simultaneous equations when \( 0 \lt x \lt 10\):

\( \quad \quad y=\log{x}\)
\( \quad \quad y=\frac{5}{x-7}+3\)

Give the y value correct to three significant figures.

☐\(y =\) ☐ ✓ ✗

4

Solve the following simultaneous equations where \(x\) is measured in degrees:

\( \quad \quad y=2\sin{(x+25)}\)
\( \quad \quad y=3x\)

Give the x value correct to three significant figures.

☐\(x =\) ☐ ✓ ✗

5

Solve the following simultaneous equations where \(x\) is measured in radians:

\( \quad \quad y=2\sin{(x+25)}\)
\( \quad \quad y=3x\)

Give the x value correct to three significant figures.

☐\(x =\) ☐ ✓ ✗

6

Solve the following simultaneous equations where \(x\) is measured in degrees:

\( \quad \quad y=3^x-10\)
\( \quad \quad xy=\cos{x}\)

Give the y value of the solution that has a positive x value correct to three significant figures.

☐\(y =\) ☐ ✓ ✗

Check

This is Using Graphs to Solve Equations level 4. You can also try:
Level 1 Level 2 Level 3

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 1 May 'Starter of the Day' page by Phil Anthony, Head of Maths, Stourport High School:

"What a brilliant website. We have just started to use the 'starter-of-the-day' in our yr9 lessons to try them out before we change from a high school to a secondary school in September. This is one of the best resources on-line we have found. The kids and staff love it. Well done an thank you very much for making my maths lessons more interesting and fun."

Comment recorded on the 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College:

"Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work"

Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month.

The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing.

Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.
Featured Activity

Lemon Law

Lemon Law

A fascinating digit changing challenge. Change the numbers on the apples so that the number on the lemon is the given total. Can you figure out, by understanding place value, how this works?

Answers

There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.

Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now:

Subscribe

Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if Transum.org should go offline for whatever reason, there is a mirror site at Transum.info that contains most of the resources that are available here on Transum.org.

When planning to use technology in your lesson always have a plan B!

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

For Students:

 

For Teachers:

For All:

Transum.org is a proud supporter of the kidSAFE Seal Program
©1997-2024 WWW.TRANSUM.ORG

© Transum Mathematics 1997-2024
Scan the QR code below to visit the online version of this activity.

This is a QR Code

https://www.Transum.org/go/?Num=373

Description of Levels

Close

❎

Level 1 - The original basic exercise

Level 2 - A collection of graphs already drawn with related questions

Level 3 - Graphs to draw with pencil and paper in order to find solitions

Level 4 - For older students who have access to a Graphic Display Calculator (GDC).

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

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

More Simultaneous Equations 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.

Log in Sign up

Help Video

Instructions for using the TI-Nspire GDC can be found here.

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.

Log in Sign up

Close

❎