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Using Graphs to Solve Equations

Using and creating graphs to solve quadratics and pairs of simultaneous equations.
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For this level you will draw graphs on graph paper using a very sharp pencil and nice ruler.

TI-nSpire

If you don't have graph paper you can print a sheet from this Graph Paper page.

Take a full, fresh sheet of graph paper and place it on a clear desk, in a good light portrait way round.

Using a scale of 2cm to represent one unit draw an x-axis from -4 to 4
Add a y-axis from -8 to 5

Draw accurate graphs then use them to find a solution to the following simultaneous equations:

\( \quad \quad y=x-4\)
\( \quad \quad y=1-x\)

\(x =\) ☐ ✓ ✗ ☐\(y =\) ☐ ✓ ✗

3

Using a scale of 2cm to represent one unit draw an x-axis from -2 to 4
Add a y-axis from -5 to 5

Draw accurate graphs then use them to find the largest value of \(x\) which is a solution to these simultaneous equations:

\( \quad \quad 2y=x+2\)
\( \quad \quad y=x^2-2x-3\)

Type in the answer correct to one decimal place:

☐\(x =\) ☐ ✓ ✗

4

Using a scale of 4cm to represent one unit draw an x-axis from 0 to 3
Add a y-axis from 0 to 3

Draw accurate graphs within the scope of these axes to find a value of \(x\) which is a solution to these simultaneous equations:

\( \quad \quad y=x^2+3x-4\)
\( \quad \quad y=2-(x-1)^2\)

Type in the answer correct to one decimal place:

☐\(x =\) ☐ ✓ ✗

5

Using a suitable scale (to make the graphs as large as possible) draw an x-axis from -2 to 2
Add a y-axis from -2 to 2

Draw accurate graphs within the scope of these axes to find the largest value of \(y\) which is a solution to these simultaneous equations:

\( \quad \quad y=x^3-2x-1\)
\( \quad \quad y=2^x - 2\)

Type in the answer correct to one decimal place:

☐\(y =\) ☐ ✓ ✗

6

The graphs of the following equations intersect in the region \(0 \le x \le 4\):

\( \quad \quad y=x^3-3x^2\)
\( \quad \quad y=\frac{1}{x+5}\)

By drawing graphs (choose your own scale for each of the axes) find the value of \(x\) at the point where this intersection occurs correct to one decimal place:

☐\(x =\) ☐ ✓ ✗

Check

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

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.
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Description of Levels

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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.

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Help Video

Help plotting graphs 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

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