# Inequalities - Level 9

## Practise solving two and three part inequalities in this self marking exercise.

##### Level 1Level 2Level 3Level 4Level 5Level 6Level 7Level 8Level 9ExamMenuHelp

This is level 9, Quadratic Inequalities. For each inequality can you find the range of values for x which makes the statement true. The first two questions have been done for you so that you can see the format your answers must be in for the computer to mark them correct.

 $$x^2 + 5x + 6\lt 0$$ $$x^2 + 7x + 10\gt 0$$ $$x^2 + 7x + 10\gt 0$$ $$5x^2 − 26x + 5\lt 0$$ $$-5x^2 + 22x + 15\gt 0$$ $$2x^2 + 7x + 6\gt 0$$ $$4x^2 − 22x + 30\lt 0$$ $$-4x^2 − 4x + 3\gt 0$$ $$25x^2 − 15x + 2\lt 0$$ $$x^2 + 5x \gt 6$$ $$5x − x^2 \lt 6$$ $$x^2 \gt 6x$$ $$5x^2 \lt 23x − 12$$ $$4x^2 \gt 7x + 2$$ $$2x^2 \gt 7x − 3$$ $$2x^2 \gt 9(x + 2)$$ $$(2x + 5)(2 − x) − 4 \lt 0$$ $$x + 4 \lt \frac{21}{x}$$
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This is Inequalities level 9. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8

## 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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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?

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"A really useful set of resources - thanks. Is the collection available on CD? Are solutions available?"

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#### Nine Digits

Arrange the given digits one to nine to make three numbers such that two of them add up to the third. This is a great puzzle for practicing standard pen and paper methods of three digit number addition and subtraction.

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## 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.

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## Description of Levels

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Level 1 - Comparing positive integers

Level 2 - Comparing positive and negative decimal numbers

Level 3 - Comparing positive and negative fractions

Level 4 - Comparing metric measures

Level 5 - Matching statements to number line diagrams.

Level 6 - Solving linear inequalities.

Level 7 - Solving linear two part inequalities.

Level 8 - Matching statements to graphs.

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

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.

## Hints

Rearrange the inequality so that all of the terms are on the left of the inequality sign and zero is on the right.

Sketch the graph of the function on the left of the inequality sign.

Determine the roots of the function you have sketched by solving the quadratic.

Use your sketch (and the roots) to determine the format of the answer.

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.

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