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Quadratic Equations

Practise solving quadratic equations algebraically with this self-marking exercise.

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This is level 9; Word problems leading to quadratic equations. Use decimals rather than fractions in your answers. You can earn a trophy if you get at least 5 correct.

1

A number is squared and added to seven times that same number to give a sum of one hundred and seventy. Let that number be x. Find the positive value of x.

2

One side of a rectangular garden is x metres long. An adjacent side is five metres longer. The area of the garden is 176 square metres. Find the value of x.

3

A right-angled triangle has one short side x cm long. The other short side is seven centimetres longer, and the hypotenuse is 17 cm long. Find the value of x.

4

A touring cyclist travels 40 km at an average speed of x km/h. If the cyclist had travelled 2 km/h faster, the journey would have taken half an hour less. Find the value of x. Give your answers to three significant figures.

5

In my back garden I have a fish pond in the shape of a perfect square. In the middle of the pond there is an island containing a flower bed, which is also a perfect square. The strip of water between the edge of the pond and the flower bed is exactly one metre wide, as shown in the diagram. If the surface area of the water is the same as the area of the flower bed, calculate the side length of the flower bed in metres correct to the nearest centimetre.
Flower bed in pool

6

The diagram below, a composite of three rectangles, has rotational symmetry of order two. Find the value of x if the area of the composite shape is 342 square units.
Diagram

Check

Can you correct your mistakes in order to get full marks?

This is Quadratic Equations 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.

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?

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"This resource has made a great deal of difference to the standard of starters for all of our lessons. Thank you for being so creative and imaginative."

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Answers

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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.

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Description of Levels

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Factorising - Factorise algebraic expressions in this structured online self marking exercise.

Level 1 - A quadratic equation presented in a factorised form.

Level 2 - Two terms where the unknown is a factor of both. The roots are integers.

Level 3 - Three terms where the squared term has a coefficient of one. The roots are integers.

Level 4 - Three terms where the squared term has a coefficient other than one and the expression factorises.

Level 5 - Quadratic equations that factorise after being rearranged.

Level 6 - The difference between two squares.

Level 7 - Three terms and the roots are not necessarily integers.

Level 8 - Mixed questions on solving quadratic equations

Level 9 - Word problems leading to quadratic equations

Problems - Situations from 1885 which can be described using algebra and explained by solving quadratic equations

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 on this topic 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.

Example

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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