Try to answer the following questions here:

• What is this question used for?
• What does this question assess?
• What does the student have to do?
• How is the question randomised?
• Are there any implementation details that editors should be aware of? Solving linear inequalities by Bradley Bush

### History and Feedback

#### Checkpoint description

Describe what's changed since the last checkpoint.

Published this.

#### Christian Lawson-Perfect2 years, 4 months ago

Gave some feedback: Ready to use

#### Christian Lawson-Perfect2 years, 4 months ago

Saved a checkpoint:

I've fixed a couple of typos, but otherwise this is OK!

#### Bradley Bush2 years, 4 months ago

Thank you for the feedback, I can see your logic, so I've changed it to your way of asking.

The inequality signs have been swapped to make sure the student is paying attention to their direction because of it's significance to the question.

Both graphs struggled to fit on the same figure so I have added another graph at the end with an brief bit of text to justify that both x ranges are the same.

#### Bradley Bush2 years, 4 months ago

Gave some feedback: Needs to be tested

#### Christian Lawson-Perfect2 years, 4 months ago

(I realise I contradicted Vicky's suggestion. Not sure if what you've done is exactly what she imagined, but it doesn't read clearly to me!)

#### Christian Lawson-Perfect2 years, 4 months ago

Gave some feedback: Has some problems

#### Christian Lawson-Perfect2 years, 4 months ago

The prompt doesn't actually say what should go in the first gap for each part. I know the statement says factorise first, but you should be absolutely clear what you want.

I'd have:

"Factorise $f(x)$:

$x^2+ax+b =$ [[gap]]

Hence, find the range of values for $x$ such that $x^2+ax+b \gt 0$."

You need a conjunction between the two inequalities at the end of parts a and b: "$x \gt ??$ OR $x \lt ??$" in part a, and $x \gt ??$ AND $x \lt ??$" for part b. If you want, you can make that a dropdown.

The inequality signs for part b are the other way round to part a. Why?

Part c doesn't make sense - you can't rearrange an inequality to get an equality. I'd ask them to rearrange to get something $\gt 0$ - this also makes sure they don't give the negation of what you're expecting - and then say "by factorising or otherwise, give the range of values for which $ax + b \gt x^2$. Keeping track of the inequality makes it easier to work out which way round the upper and lower bounds should go.

In the advice, I'd give examples of some values of $x$ that satisfy the inequality - in part a, a big negative value and a big positive value, and in part b a vlaue between the roots. For part c, I think it would be very helpful to show the graphs of $x^2$ and $ax+b$ on top of the graph of $x^2-ax-b$ to show that the inequality holds for the same values in both arrangements - i.e., $x^2 \gt ax+b$ exactly when $x^2-ax-b \gt 0$.

#### Bradley Bush2 years, 4 months ago

Gave some feedback: Needs to be tested

#### Bradley Bush2 years, 4 months ago

Gave some feedback: Has some problems

#### Bradley Bush2 years, 4 months ago

Gave some feedback: Needs to be tested

#### Bradley Bush2 years, 4 months ago

Thank you for the feedback, those typos were careless and hopefully they are all sorted now, I have also reworded the question for you.

I hate to disagree but I think that it would be useful for students who are struggling in particular to have the factorise step left in the question to give the student a mid way point. But if there is more logic behind removing the gap, I am happy to take it out.

#### Vicky Hall2 years, 4 months ago

Gave some feedback: Has some problems

#### Vicky Hall2 years, 4 months ago

Reword the questions here to say something like: find the range of values of $x$ for which ${function}>0$. You have told the student to factorise in the statement so you don't need to say it again. I would also remove the gap asking them to give the factorised form.

Have a check through the advice as I noticed a couple of typos and a rogue part d).

#### Bradley Bush2 years, 4 months ago

Gave some feedback: Needs to be tested

#### Bradley Bush2 years, 5 months ago

How do I allow either or answers for the gap in part a?

#### Bradley Bush2 years, 5 months ago

Created this as a copy of Solving linear inequalities.
Solving linear inequalities draft Adrian Jannetta 21/10/2018 10:22
Ida's copy of Solve quadratic inequalities draft Ida Landgärds 13/04/2018 09:16
Ida's copy of Solving linear inequalities draft Ida Landgärds 13/04/2018 09:16
Solving linear inequalities [L5 Randomised] Needs to be tested Matthew James Sykes 25/07/2018 10:51
cormac's copy of Solving linear inequalities draft cormac breen 24/10/2018 13:44
cormac's copy of Solve quadratic inequalities draft cormac breen 24/10/2018 13:46
Solving linear inequalities draft Xiaodan Leng 11/07/2019 01:43
Quiz: Solving linear inequalities draft Electronics Leeds 01/10/2019 21:06

Give any introductory information the student needs.

No variables have been defined in this question.

(a number)

Numbers between and (inclusive) with step size
A random number between and (inclusive) with step size

(text string)

(numbers)

(text strings)

This variable is an HTML node. HTML nodes can not be relied upon to work correctly when resuming a session - for example, attached event callbacks will be lost, and mathematical notation will likely also break.

If this causes problems, try to create HTML nodes where you use them in content areas, instead of storing them in variables.

Describe what this variable represents, and list any assumptions made about its value.

This variable doesn't seem to be used anywhere.

Name Type Generated Value

#### Error in variable testing condition

There's an error in the condition you specified in the Variable testing tab. Variable values can't be generated until it's fixed.

Error:

for seconds

Running for ...

No parts have been defined in this question.

Select a part to edit.

The correct answer is an equation. Use the accuracy tab to generate variable values satisfying this equation so it can be marked accurately.

#### Checking accuracy

Define the range of points over which the student's answer will be compared with the correct answer, and the method used to compare them.

#### Variable value generators

Give expressions which produce values for each of the variables in the expected answer. Leave blank to pick a random value from the range defined above, following the inferred type of the variable.

#### String restrictions

Both choices and answers must be defined for this part.

Help with this part type

##### Base marking algorithm

#### Test that the marking algorithm works

Check that the marking algorithm works with different sets of variables and student answers using the interface below.

Create unit tests to save expected results and to document how the algorithm should work.

There's an error which means the marking algorithm can't run:

Name Value

Note
Value Feedback

Click on a note's name to show or hide it. Only shown notes will be included when you create a unit test.

#### Unit tests

No unit tests have been defined. Enter an answer above, select one or more notes, and click the "Create a unit test" button.

The following tests check that the question is behaving as desired.

### This test has not been run yet This test produces the expected output This test does not produce the expected output

This test is not currently producing the expected result. Fix the marking algorithm to produce the expected results detailed below or, if this test is out of date, update the test to accept the current values.

One or more notes in this test are no longer defined. If these notes are no longer needed, you should delete this test.

Name Value

 This note produces the expected output

This test has not yet been run.

When you need to change the way this part works beyond the available options, you can write JavaScript code to be executed at the times described below.

Run this script the built-in script.

This script runs after the built-in script.

To account for errors made by the student in earlier calculations, replace question variables with answers to earlier parts.

In order to create a variable replacement, you must define at least one variable and one other part.

The variable replacements you've chosen will cause the following variables to be regenerated each time the student submits an answer to this part:

These variables have some random elements, which means they're not guaranteed to have the same value each time the student submits an answer. You should define new variables to store the random elements, so that they remain the same each time this part is marked.

### Parts

Give a worked solution to the whole question.

### Preamble

This script will run after the question's variable have been generated but before the HTML is attached.
Apply styling rules to the question's content.

This question is used in the following exams: