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Inequalities - Level 9

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

Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8 Level 9 Exam Menu Help

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.

\( x^2 + 5x + 6\lt 0 \)

Correct Wrong

\( x^2 + 6x + 5\gt 0 \)

Correct Wrong

\( x^2 + 6x + 5\gt 0 \)

Correct Wrong

\( 2x^2 − 11x + 5\lt 0 \)

Correct Wrong

\( -4x^2 + 11x + 3\gt 0 \)

Correct Wrong

\( 2x^2 − 19x + 35\lt 0 \)

Correct Wrong

\( 4x^2 − 16x + 15\gt 0 \)

Correct Wrong

\( -8x^2 − 4x + 12\gt 0 \)

Correct Wrong

\( 8x^2 + 14x + 6\lt 0 \)

Correct Wrong

\( x^2 + 5x \lt 6 \)

Correct Wrong

\( 5x − x^2 \gt 6 \)

Correct Wrong

\( x^2 \lt 6x \)

Correct Wrong

\( 4x^2 \lt 31x − 21 \)

Correct Wrong

\( 5x^2 \lt 21x − 4 \)

Correct Wrong

\( 4x^2 \lt 37x − 40 \)

Correct Wrong

\( 2x^2 \gt 9(x + 2) \)

Correct Wrong

\( (2x + 5)(2 − x) − 4 \lt 0 \)

Correct Wrong

\( x + 4 \lt \frac{21}{x} \)

Correct Wrong


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


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.

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Description of Levels



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.

Level 9 - Quadratic Inequalities

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.

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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.

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