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?

### Feedback

From users who are members of Transition to university :

### History

#### Checkpoint description

Describe what's changed since the last checkpoint.

#### Christian Lawson-Perfect3 years ago

Saved a checkpoint:

Whoops - the prompt had the constant term as $c \times d$ instead of $b \times d$. Thanks for pointing this out!

#### Christian Lawson-Perfect3 years ago

Gave some feedback: Ready to use

#### Christian Lawson-Perfect3 years ago

Gave some feedback: Has some problems

#### Katherine Tomlinson3 years ago

Has some problems.  I was given the equation 24x^2 - 37x - 8 and it said that factorised this was (3x+5)(8x-1).

#### Christian Lawson-Perfect3 years ago

Gave some feedback: Ready to use

#### Christian Lawson-Perfect3 years ago

Saved a checkpoint:

Removed a lot of rubbish which must have come from a previous question, and renamed the variables so they make sense.

It's important that the coefficients of $x$ in the two factors aren't the same - otherwise, the order of the factorisation would be ambiguous.

Published this.

#### Hannah Aldous3 years, 1 month ago

Gave some feedback: Needs to be tested

#### Christian Lawson-Perfect3 years, 1 month ago

Gave some feedback: Has some problems

#### Christian Lawson-Perfect3 years, 1 month ago

Saved a checkpoint:

The statement says you can factorise as $(ax+m)(bx+n)$ but then part a asks you to factorise in the form $a(x+m)(x+n)$. Should this be a separate question, since spotting a common factor of all the coefficients is a fairly simple corollary of factorising a quadratic with leading coefficient 1?

In fact, part b is the same! I was shown $8x^2+240x+1600=0$, which factorises as $8(x+10)(x+20) = 0$. The expected answer had roots $-5/4$ and $-5/2$, which is equivalent to $8x^2+30x+25=0$. So is it the displayed equation that's wrong?

The marking for part a is wrong - I think the wrong variable is used somewhere, but it's not obvious where.

Part b could begin by asking you to find the factorisation.

In part c, I got $2x^2+13x+20$, so a particularly pedantic student might want to leave the second gapfill empty, since the coefficient of $x$ in the second part is $1$. Can you make sure that the coefficient of $x^2$ in the equation is greater than $2$?

I got $-5/3$ as one of my roots in part d, so I've enabled "allow the student to enter a fraction".

Parts c and d could use the same equation - why not? That would make a nice, self-contained question.

So, in summary:

• Fix the marking in parts a and b.
• If they use the same equation rather than a new one in each part, I think parts (a,b) make a self-contained question, and (c,d) another.

#### Hannah Aldous3 years, 1 month ago

Gave some feedback: Needs to be tested

#### Elliott Fletcher3 years, 1 month ago

Gave some feedback: Has some problems

#### Elliott Fletcher3 years, 1 month ago

I think the questions here are good and will be reasonably challenging for the students, there are just a few errors that i noticed.

Main Parts

a) the correct numbers that you put into the answer box are marked correct, but the expected answer comes up as somethinwe g else which would be incorrect. For example, i was given the equation 2x^2+12x+10 =0, which factorises to 2(x+5)(x+1) = 0, which is marked correct, however the expected answer comes up as 2(x+4)(x+3) = 0.

b) Here the correct answer is marked incorrect,

i had 8x^2+112x+320=0 which factorises to 8(x+10)(x+4) = 0. Thus x1 = -10 and x2=-4. However this is marked wrong and the expected answer is x1=-5 and x2= -1, which wouldn't be right.

c) good

d) i would write "in order to calculate the possible values of x that satisfy the equation" instead of "in order to calculate the possible values of x".

Again, the correct answer is marked incorrect. The expected answer shows different values which would be incorrect.

a)

I don't think you need a comma after "with" on the first line here.

I think there should be a 2 in front of the brackets in the final answer, as you have done in the question itself.

b)

I don't think you need a comma after "with" on the first line here.

I think you need a full stop after the factorised equation on the 7th line.

c)

The equation here shows the wrong coefficient of x in the second factor, for example for

6x^2+5x+1 = 0, you have

"This means our factorised equation must take the form (3x+a)(3x+b) = 0" whereas the equation should be "(3x+a)(2x+b) =0".

On that note i think it should be 3b+2a = 5 instead of 3a+2b=5.

I would put the multiplications in brackets here when you write when you multiply the values of a and b by 3 and 2.

d)

I think you should just write "we need to find two values that add together to make 5 and multiply to make 6" as one line instead of two.

Typo: "mutipy" should be "multiply"

I think this part needs more explanation for how you obtain each of the numbers for the factorised expression, something like you have done in part c)

Although the way you find the final answer does make sense and does work, i don't really see why you need to find the previously mentioned values like 3 and 2 that add and multiply to make a certain number to do this. I think you'd be better answering this question in the same way as you answered part c.

Sorry for all the feedback!

#### Hannah Aldous3 years, 1 month ago

Gave some feedback: Needs to be tested

#### Vicky Hall3 years, 1 month ago

Gave some feedback: Has some problems

#### Vicky Hall3 years, 1 month ago

The statement is exactly the same as the other quadratic equations questions, but this time its not true that $ax^2+bx+c$ factorises to $(x+m)(x+n)$ - the $x$s need coefficients.

I think there should be two more parts to this question, a question at the beginning that only wants to students to factorise, and a question at the end that doesn't give them one of the $x$ coefficients.

It would also be very helpful to tell students in the statement that we can sometimes divide through by the $x^2$ coefficient to obtain a simpler equation, but sometimes the coefficent is not a factor of all terms so we can't. (I know you show this in the advice but it would be nice for the student to see this before they try the question as otherwise they will start looking for factors of the existing numbers).

#### Hannah Aldous3 years, 1 month ago

Gave some feedback: Needs to be tested

#### Hannah Aldous3 years, 1 month ago

Gave some feedback: Has some problems

#### Hannah Aldous3 years, 1 month ago

Gave some feedback: Needs to be tested

#### Hannah Aldous3 years, 1 month ago

Gave some feedback: Has some problems

#### Chris Graham3 years, 1 month ago

In part a), i),ii) should be in italics, and I would start a new line afterwards.

You need some string restrictions in part (a), for example I can enter the expression into the gap as given, and get full marks. See the bottom of the Numbas tutorial.

In (b) and (c) "values of x in the following equation" would be better expressed as "values of x which satisfy the following equation".

In the advice, put a),b)... on a new line, and preferably set the style using format->Formats->Headings->Heading 4

The advice is not easy to scan, and unfortunately students will not take care to read the whole thing. Help them out by placing any important equations on a new line, so that the student can easily see how the solution develops. And as a general rule, use display style for any equations on their own line.

In part (d) of the advice you obtain the possible values of x, however this is not asked in the question. Did you intend to include this? If you do so you will need to think about the precision that you would like, and formatting in the advice (see e.g. dpformat on the jme reference page).

#### Hannah Aldous3 years, 1 month ago

Gave some feedback: Needs to be tested

#### Hannah Aldous3 years, 1 month ago

Created this.
Factorising Quadratic Equations with $x^2$ Coefficients Greater than 1 Ready to use Hannah Aldous 20/11/2019 14:39
Simplifying and Factorising Quadratic Equations with $x^2$ Coefficients Greater than 1 Should not be used Hannah Aldous 20/11/2019 14:42
Factorising Quadratic Equations with $x^2$ Coefficients Greater than 1 draft Breanne Chryst 23/08/2017 14:40
Factorising Quadratic Equations with $x^2$ draft Breanne Chryst 23/08/2017 14:39
Factorising Quadratic Equations with $x^2$ coefficient of 1 draft Lyn Gardner 09/10/2017 11:33
Lyn's copy of Factorising Quadratic Equations with $x^2$ coefficient of 1 draft Lyn Gardner 09/10/2017 13:17
Lyn's copy of Factorising Quadratic Equations with $x^2$ Coefficients Greater than 1 draft Lyn Gardner 09/10/2017 13:21
MATH6058 Factorising Quadratic Equations with $x^2$ Coefficients Greater than 1 draft Catherine Palmer 25/01/2018 09:18
cormac's copy of MATH6058 Factorising Quadratic Equations with $x^2$ Coefficients Greater than 1 draft cormac breen 24/10/2018 13:36
Factorising Quadratic Equations with $x^2$ Coefficients Greater than 1 draft Ed Southwood 05/11/2018 13:17
Factorising Quadratic Equations with $x^2$ Coefficients Less than 1 draft Ed Southwood 05/11/2018 13:19
Simon's copy of Factorising Quadratic Equations with $x^2$ Coefficients Greater than 1 draft Simon Thomas 07/03/2019 09:41
Factorización de cuadrado de binomio draft Guillermo Bernardo DURÁN GONZÁLEZ 28/03/2020 03:25
Factorising Quadratic Equations with $x^2$ Coefficients Greater than 1 Ready to use John Ian Keng 01/07/2020 14:59

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 ...

Name Limit

### Penalties

Name Limit

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

#### 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

Alternative used:

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.

This part can't be reached by the student.

Add a "next part" reference to this part from another part.

None of the parts which can lead to this part are reachable either.

### Next part options

Define the list of parts that the student can visit after this one.

• #### Variable replacements

No variable replacements have been defined for this next part option.
Variable Value

### Previous parts

This part can follow on from:

This part doesn't follow on from any others.

### Parts

#### Steps

Give a worked solution to the whole question.