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Xiaodan Leng

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Quadratics: Determine the equation of a parabola by Lovkush Agarwal

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College Algebra for STEM

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Xiaodan Leng 5 years, 4 months ago

Created this as a copy of Quadratics: Determine the equation of a parabola.

Name	Status	Author	Last Modified
Quadratic graph - student finds equation	Ready to use	joshua boddy	01/06/2016 09:47
Cubic graph - student finds equation	Ready to use	joshua boddy	01/06/2016 09:47
Quadratic graph - student finds equation	draft	steve kilgallon	24/08/2017 11:30
Graph transforms TEST 1	draft	steve kilgallon	26/10/2016 12:32
Graph transforms TEST 2	draft	steve kilgallon	26/10/2016 12:26
Quadratic graph vertical shift 1 (with answers)	draft	steve kilgallon	17/08/2016 15:16
Quadratic graph horizontal shift 1	draft	steve kilgallon	01/03/2023 09:16
Quadratic graph vertical stretch 1	draft	steve kilgallon	01/03/2023 09:50
Quadratic graph feflection in x-axis 1	draft	steve kilgallon	01/03/2023 09:38
Sin graph vertical shift 1	draft	steve kilgallon	04/08/2016 16:02
Sin graph horizontal shift 1 (with answers)	draft	steve kilgallon	17/08/2016 17:21
MASTER graph examples	draft	steve kilgallon	26/10/2016 12:31
General graph drawing Annimation example	draft	steve kilgallon	17/08/2016 12:19
Francis 's copy of Quadratic graph - student finds equation	draft	Francis Duah	12/08/2016 17:57
Francis 's copy of Quadratic graph - student finds equation	draft	Francis Duah	12/08/2016 17:57
Francis 's copy of Quadratic graph - student finds equation	draft	Francis Duah	12/08/2016 17:58
Cubic graph - student finds equation	draft	steve kilgallon	24/08/2017 11:41
Quadratic graph vertical shift 1	draft	steve kilgallon	27/02/2023 11:57
Sin graph horizontal shift 1	draft	steve kilgallon	18/08/2016 13:02
Sin graph horizontal shift 1 (with answers using script to check)	draft	steve kilgallon	18/08/2016 12:54
Sin graph wavelength and amplitude	draft	steve kilgallon	18/08/2016 13:16
TRIG MASTER GRAPH examples (radians)	draft	steve kilgallon	19/08/2016 12:00
TRIG MASTER GRAPH examples (degrees)	draft	steve kilgallon	21/02/2022 17:29
EXAM 1 Cubic graph - student finds equation	draft	steve kilgallon	30/08/2016 14:09
steve's copy of EXAM 1 Cubic graph - student finds equation	draft	steve kilgallon	30/08/2016 14:16
EXAM 1 Quadratic graph - student finds equation	draft	steve kilgallon	30/08/2016 14:20
Quadratic graph - student finds equation	draft	Marlon Arcila	30/08/2016 17:08
funcion cuadratica	draft	Marlon Arcila	30/08/2016 17:20
funciones plano con eje x en grados	draft	Marlon Arcila	19/09/2016 16:43
grafica con eje en radianes	draft	Marlon Arcila	19/09/2016 16:40
Vekstfart - grafisk og ved regning	draft	Ida Friestad Pedersen	30/09/2016 10:41
Vekstfart - grafisk og ved regning	draft	Morten Brekke	14/10/2016 10:42
quadratic graph eqaution	draft	steve kilgallon	01/03/2023 10:37
Sin graph horizontal shift 1 testing	draft	steve kilgallon	20/10/2016 13:46
Finding multipe solutions of sin(x)= (in degrees -360 to 360) WORKING	draft	steve kilgallon	18/02/2022 16:59
quadratic graph equation	draft	Paul Howes	13/11/2016 18:37
Finding multipe solutions of sin(x)= (in degrees)	draft	steve kilgallon	20/10/2016 22:10
Quadratic graph horizontal stretch 1	draft	steve kilgallon	01/03/2023 09:57
Quadratic horizontal and vertical shift	draft	steve kilgallon	01/03/2023 16:30
Cubic graph eqaution	draft	steve kilgallon	02/03/2023 11:49
Cubic graph vertical shift	draft	steve kilgallon	01/03/2023 16:33
Cubic graph horizontal shift	draft	steve kilgallon	01/03/2023 16:45
Finding multipe solutions of sin(x)= (in degrees 0 to 360) WORKING	Ready to use	steve kilgallon	11/01/2024 11:06
Growth rate - by graph and calculating	draft	Robert Førland	05/11/2016 12:29
Hannah's copy of Quadratic horizontal and vertical shift	draft	Hannah Bartholomew	02/11/2016 11:37
Quadratic graph - student finds equation	draft	Morten Brekke	02/11/2016 14:33
mock_exam Quadratic graph - student finds equation	draft	steve kilgallon	06/11/2016 13:07
mock_exam Cubic graph - student finds equation	draft	steve kilgallon	06/11/2016 13:07
mock_exam Finding multipe solutions of sin(x)= (in degrees 0 to 360) WORKING	draft	steve kilgallon	27/11/2017 12:42
mock_exam Finding multipe solutions of sin(x)= (in degrees -360 to 360) WORKING	draft	steve kilgallon	27/11/2017 12:43
exam Finding multipe solutions of sin(x)= (in degrees 0 to 360) WORKING	draft	steve kilgallon	07/11/2016 08:25
Amplitude, periode og likevektslinje	draft	Ida Friestad Pedersen	11/11/2016 08:47
a sin(bx) graph	draft	Paul Howes	01/10/2020 12:45
a cos(bx) graph	draft	Paul Howes	14/11/2016 11:23
slope of graph multi choice	draft	Paul Howes	14/11/2016 18:08
Quadratic graph equation	draft	Hannah Bartholomew	02/12/2016 10:05
QM101_REFERRAL_exam_2016_17 Cubic graph - student finds equation	draft	steve kilgallon	05/01/2017 11:25
BY138_referral_exam Cubic graph - student finds equation	draft	steve kilgallon	05/01/2017 14:49
Quadratics: Determine the equation of a parabola	Ready to use	Lovkush Agarwal	18/06/2018 12:55
Differentiation, graphs: Number of roots and stationary points of a graph	Ready to use	Lovkush Agarwal	18/06/2018 13:23
Algebra: functions, determining function values from graph	Ready to use	Lovkush Agarwal	13/11/2018 14:30
Straight lines, functions: Reading a graph of a straight line.	Ready to use	Lovkush Agarwal	18/06/2018 12:54
Differentiation: coordinates of stationary points from a graph	Ready to use	Lovkush Agarwal	18/06/2018 12:56
Differentiation: gradient positive or negative	Ready to use	Lovkush Agarwal	18/06/2018 12:58
Paul 's copy of Reading a graph of a function.	draft	Paul Howes	08/02/2017 14:40
Integrasjon og areal 1	draft	Ida Friestad Pedersen	20/02/2017 17:01
Ethan's copy of Equation of a Quadratic Graph	draft	Ethan Smith	22/02/2017 03:33
Hina's copy of MASTER graph examples	draft	Hina Ahmed	24/03/2017 16:00
Maximum and Minimum points on a curve	draft	David Rickard	05/05/2017 22:42
Algebra: graphs of functions, straight line	draft	Lovkush Agarwal	20/06/2018 14:20
Algebra: Functions, inverses and compositions	draft	Lovkush Agarwal	25/11/2018 11:41
Algebra. Procedures. Version 1	draft	Lovkush Agarwal	20/06/2018 15:00
Algebra. Procedures. Version 2	draft	Lovkush Agarwal	20/06/2018 15:00
Algebra. Procedures. Version 3	draft	Lovkush Agarwal	20/06/2018 15:00
Algebra. Procedures. Version 4	draft	Lovkush Agarwal	20/06/2018 15:00
Algebra: solving equations graphically. Version 1	Ready to use	Lovkush Agarwal	20/06/2018 14:14
Algebra: solving equations graphically. Version 2	Ready to use	Lovkush Agarwal	20/06/2018 14:14
Algebra: solving equations graphically. Version 3	Ready to use	Lovkush Agarwal	20/06/2018 14:14
Algebra: solving equations graphically. Version 4	Ready to use	Lovkush Agarwal	20/06/2018 14:14
George's copy of Equation of a Quadratic Graph	draft	George Loughlin	06/07/2017 15:09
Differentiation: Derivative of a graph. I	Ready to use	Lovkush Agarwal	19/06/2018 15:50
Differentiation: Derivative of a graph. III	Ready to use	Lovkush Agarwal	19/06/2018 15:51
Differentiation: Derivative of a graph. II	Ready to use	Lovkush Agarwal	19/06/2018 15:51
Differentiation: Derivative of a graph. IV	Ready to use	Lovkush Agarwal	19/06/2018 15:51
Integration: Integral of a graph. Version IV	Ready to use	Lovkush Agarwal	20/06/2018 17:24
Integration: Integral of a graph. Version II	Ready to use	Lovkush Agarwal	20/06/2018 17:24
Integration: Integral of a graph. Version I	Ready to use	Lovkush Agarwal	20/06/2018 17:24
Integration: Integral of a graph. Version III	Ready to use	Lovkush Agarwal	20/06/2018 17:24
Reading a graph of a straight line.	Ready to use	Beka Zarnadze	09/08/2017 11:06
Gradient positive or negative.	draft	Adrian Jannetta	16/08/2023 14:56
Algebra: functions, determine coordinates of graph algebraically	draft	Lovkush Agarwal	03/04/2020 17:14
Adrian's copy of Quadratic graph - student finds equation	draft	Adrian Jannetta	16/08/2023 14:56
Helge's copy of Adrian's copy of Quadratic graph - student finds equation	draft	Helge Münnich	09/10/2017 21:20
Sketching graph: which graphs are quadratic graphs	draft	Lovkush Agarwal	23/10/2019 11:17
Algebra: number of solutions of quadratic based on graph	draft	Lovkush Agarwal	24/10/2018 10:31
Sketching graphs: quadratics	draft	Lovkush Agarwal	08/11/2019 14:12
Differentiation: Displacement-time to velocity-time graphs	Ready to use	Lovkush Agarwal	11/02/2021 10:03
Differentiation: Anti-differentiation of constant function, graphically.	draft	Lovkush Agarwal	19/06/2018 16:09
Algebra: trig, graphs, solving equations	draft	Lovkush Agarwal	20/06/2018 12:57
W1 Copy of Displacement-time to velocity time graphs	draft	Stuart Turner	09/11/2017 16:17
Algebra: exp and log, graphs, solving equations	draft	Lovkush Agarwal	15/04/2020 10:01
Sketching graphs: which graphs are quadratic graphs	draft	Lovkush Agarwal	19/06/2018 16:41
Sketching graphs: which graphs are cubic graphs	draft	Lovkush Agarwal	19/06/2018 16:41
Sketching graphs: which graphs are exponentials	draft	Lovkush Agarwal	29/11/2019 12:42
Sketching graphs: which graphs are logarithmic	draft	Lovkush Agarwal	19/06/2018 16:41
Sketching graphs: which graphs are sine and cosine	draft	Lovkush Agarwal	02/04/2020 10:40
Differentiation: Equation of tangent. Quadratic	draft	Lovkush Agarwal	19/06/2018 15:40
Grainne's copy of Derivative of a graph, multiple choice. Version IV	draft	Grainne Scanlon	16/01/2018 13:43
Differentiation: Equation of tangent. Chain rule.	draft	Lovkush Agarwal	12/01/2023 10:35
Number of Stationary Points of a Cubic	draft	Lovkush Agarwal	19/06/2018 10:21
Differentiation: coordinates of stationary points from a graph	draft	Lovkush Agarwal	28/01/2019 08:47
Gradient positive or negative.	draft	Lovkush Agarwal	19/06/2018 10:21
Differentiation: Equation of tangent. Chain rule. Shorter	draft	Lovkush Agarwal	19/06/2018 09:50
Julie's copy of Helge's copy of Adrian's copy of Quadratic graph - student finds equation	draft	Julie Crowley	03/04/2018 23:27
Marte's copy of Quadratic graph - student finds equation	draft	Marte Bråtalien	12/04/2018 15:07
Quadratic graph - student finds equation	draft	David Goulding	27/04/2018 14:27
Shan's copy of Integration: Integral of a graph. Version III	draft	Shan Lou	21/06/2018 11:30
Shan's copy of Shan's copy of Integration: Integral of a graph. Version III	draft	Shan Lou	21/06/2018 11:30
Nick's copy of Differentiation: Displacement-time to velocity-time graphs	draft	Nick Walker	22/06/2018 00:40
Nick's copy of Differentiation: Derivative of a graph. IV	draft	Nick Walker	22/06/2018 00:42
Nick's copy of Differentiation: coordinates of stationary points from a graph	draft	Nick Walker	22/06/2018 00:43
Nick's copy of Differentiation, graphs: Number of roots and stationary points of a graph	draft	Nick Walker	22/06/2018 00:43
Jasmine's copy of Integration: Integral of a graph. Version IV	draft	Jasmine Zhang	28/06/2018 01:06
Jan's copy of Integration: Integral of a graph. Version IV	draft	Jan Harte	28/06/2018 01:06
Daniel's copy of Integration: Integral of a graph. Version IV	draft	Daniel Mansfield	28/06/2018 01:07
Praneetha's copy of Integration: Integral of a graph. Version III	draft	Praneetha Singh	28/06/2018 01:06
Sara's copy of Sketching graph: which graphs are quadratic graphs	draft	Sara Waugh	28/06/2018 01:07
Praneetha's copy of Integration: Integral of a graph. Version IV	draft	Praneetha Singh	28/06/2018 01:07
Jasmine's copy of Daniel's copy of Integration: Integral of a graph. Version IV	draft	Jasmine Zhang	28/06/2018 01:09
test #1	draft	Praneetha Singh	28/06/2018 01:12
Jasmine's copy of Jasmine's copy of Integration: Integral of a graph. Version IV	draft	Jasmine Zhang	28/06/2018 01:13
Shantha's copy of Sara's copy of Sketching graph: which graphs are quadratic graphs	draft	Shantha Bose	28/06/2018 01:16
Integration: Integral of a graph. Version IV	Ready to use	Jasmine Zhang	28/06/2018 01:22
Jasmine's copy of Integration: Integral of a graph. Version IV	draft	Jasmine Zhang	28/06/2018 01:28
Integration: Integral of a graph. Version IV	draft	Stephen Face	28/06/2018 05:06
Praneetha's copy Sara's copy of Sketching graph: which graphs are quadratic graphs	draft	Praneetha Singh	28/06/2018 05:45
Jasmine's copy of Jasmine's copy of Jasmine's copy of Integration: Integral of a graph. Version IV	draft	Jasmine Zhang	22/07/2018 09:15
Algebra: Functions, inverses and compositions [L3 Randomised]	Needs to be tested	Matthew James Sykes	25/07/2018 10:48
Algebra: graphs of functions, straight line [L2 Randomised]	Needs to be tested	Matthew James Sykes	25/07/2018 10:46
Integration: Integral of a graph [L10 Randomised]	Needs to be tested	Matthew James Sykes	25/07/2018 10:46
Number of roots	draft	Vicky Mason	11/09/2018 14:26
Vicky's copy of Functions: Reading a graph of a function	draft	Vicky Mason	11/09/2018 14:29
Algebra: Graphs of functions, straight line	draft	Clare Lundon	05/10/2018 22:36
Differentiation: Equation of tangent to Quadratic	Ready to use	Clare Lundon	21/02/2023 20:08
Algebra: solving a quadratic equation graphically.	draft	Lovkush Agarwal	07/04/2020 10:05
Algebra: functions, determining function values from graph	draft	Lovkush Agarwal	03/04/2020 17:12
Algebra: solving a (quadratic) function graphically	draft	Lovkush Agarwal	13/11/2018 14:50
Algebra: trig graphs, sin, basic	draft	Lovkush Agarwal	02/04/2020 10:46
Algebra: trig graphs, cos, basic	draft	Lovkush Agarwal	15/11/2019 18:27
Algebra: number of solutions of quadratic based on graph	draft	Clare Lundon	19/11/2018 09:57
Algebra: Equation of tangent. Quadratic	draft	Lovkush Agarwal	10/04/2020 09:46
Differentiation: Equation of tangent. Quadratic	Ready to use	Johnny Yi	26/11/2018 05:27
Barry's copy of Sketching graphs: quadratics	draft	Barry Zhang	29/11/2018 05:23
Johnny's Differentiation: Equation of tangent. Quadratic	draft	Johnny Yi	03/12/2018 06:05
David's copy of Sin graph wavelength and amplitude	draft	David Rickard	03/12/2018 21:31
Function composition (numerical)	draft	Daniel Mansfield	26/01/2020 04:30
Differentiation: Graphically determine derivative	draft	Lovkush Agarwal	13/12/2022 13:04
Differentiation: Equation of tangent. Quadratic	draft	Lovkush Agarwal	20/04/2020 14:26
Prerequisites: reading graph and symmetry	draft	Lovkush Agarwal	23/01/2019 17:43
Differentiation: Equation of Tangent- Quadratic	draft	Clare Lundon	03/02/2020 10:04
Laura's copy of Sketching graphs: quadratics	draft	Laura Horton	07/02/2019 13:25
Integrasjon og areal 1	draft	Ida Friestad Pedersen	22/02/2019 13:21
Gizem's example for multiple answers to a question	draft	Gizem Intepe	02/03/2019 05:15
Gizem's copy of Algebra: solving a quadratic equation graphically.	draft	Gizem Intepe	02/03/2019 05:48
Differentiation: Equation of tangent. Quadratic	draft	Lovkush Agarwal	23/03/2020 09:13
Finding Derivative From a Graph, for W6 tute	draft	Joshua Calcutt	25/08/2020 09:21
Derivative Question 3 (Select the graph that shows the derivative of the graph above)	draft	Joshua Calcutt	25/08/2020 00:25
John's copy of Derivative Question 3	draft	John Wick	29/04/2019 12:09
Vertical Shift	draft	Johnny Yi	30/04/2019 03:35
Maria's copy of Laura's copy of Sketching graphs: quadratics	draft	Maria Aneiros	25/05/2019 07:26
Maria's copy of Algebra: functions, determining function values from graph	draft	Maria Aneiros	25/05/2019 07:26
Maria's copy of W1 Copy of Displacement-time to velocity time graphs	draft	Maria Aneiros	27/05/2019 04:31
Maria's copy of Algebra: Functions, inverses and compositions	Needs to be tested	Maria Aneiros	05/02/2020 06:56
Quadratic Graphs	draft	Kevin Bohan	05/06/2019 10:21
Shivendra's copy of Integration: Integral of a graph [L10 Randomised]	draft	Deactivated user	05/01/2020 16:21
Exam09 - sine and cosine	draft	Michael Proudman	07/12/2021 09:54
nuExam09 - sine and cosine	draft	Michael Proudman	07/12/2021 09:54
Differentiation: Equation of tangent. Quadratic	draft	Xiaodan Leng	10/07/2019 23:02
Algebra: functions, determining function values from graph	draft	Xiaodan Leng	10/07/2019 23:08
Integration: Integral of a graph. Version IV	draft	Xiaodan Leng	11/07/2019 00:00
Integral of a graph. Version IV	draft	Xiaodan Leng	11/07/2019 00:01
Integral of a graph. Version III	draft	Xiaodan Leng	11/07/2019 00:02
Integral of a graph. Version II	draft	Xiaodan Leng	11/07/2019 00:02
Integral of a graph. Version I	draft	Xiaodan Leng	11/07/2019 00:03
solving equations graphically. Version 4	draft	Xiaodan Leng	11/07/2019 00:04
solving equations graphically. Version 3	draft	Xiaodan Leng	11/07/2019 00:04
solving equations graphically. Version 3	draft	Xiaodan Leng	11/07/2019 00:05
solving equations graphically. Version 2	draft	Xiaodan Leng	11/07/2019 00:05
solving equations graphically. Version 1	draft	Xiaodan Leng	11/07/2019 00:06
Differentiation: Derivative of a graph. IV	draft	Xiaodan Leng	11/07/2019 00:06
Differentiation: Derivative of a graph. III	draft	Xiaodan Leng	11/07/2019 00:07
Differentiation: Derivative of a graph. II	draft	Xiaodan Leng	11/07/2019 00:07
Differentiation: Derivative of a graph. I	draft	Xiaodan Leng	11/07/2019 00:08
Differentiation, graphs: Number of roots and stationary points of a graph	draft	Xiaodan Leng	11/07/2019 00:09
Differentiation: gradient positive or negative	draft	Xiaodan Leng	11/07/2019 00:09
Differentiation: coordinates of stationary points from a graph	draft	Xiaodan Leng	11/07/2019 00:10
Quadratics: Determine the equation of a parabola	draft	Xiaodan Leng	11/07/2019 00:11
Quadratic graph - student finds equation	draft	Xiaodan Leng	11/07/2019 06:40
Thomas's copy of Nick's copy of Differentiation, graphs: Number of roots and stationary points of a graph	draft	Thomas Waters	11/09/2019 22:19
Number of roots and stationary points of a graph	Ready to use	Thomas Waters	08/06/2021 13:35
Musa's copy of 3 solving equations graphically, x-y intercepts	draft	Musa Mammadov	27/06/2023 01:27
Musa's copy of 3 Number of roots and stationary points of a graph	draft	Musa Mammadov	27/06/2023 01:35
Musa's copy of 5 Number of roots and stationary points of a graph	draft	Musa Mammadov	20/07/2023 01:38
T1	Ready to use	Shaheen Charlwood	16/05/2022 14:22
C7	Has some problems	Shaheen Charlwood	24/07/2022 14:12

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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:

This is an extension type part. There is no expected answer, and it's assumed that the marking depends on interactions within the part's prompt.

You can test this part's marking algorithm by interacting with the rendering of the part's prompt below.

Gap	Expected answer	Student's answer

Feedback

Score:

Question variables

These variables are available within the marking algorithm.

	Name	Value

Marking parameters

These values are available as extra variables in the marking algorithm.

Name	Value

Part settings

These values are available as entries in the settings variable.

Name	Value

This feedback is based on your last submitted answer. Submit your changed answer to get updated feedback.

Warnings:

Alternative used:

These are the notes produced by this part's marking algorithm.

Note	Value	Feedback

Click on a note's name to show or hide it.

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

	Note		Value	Feedback
This note produces the expected output		Current:		Messages No feedback messages. Warnings No warnings.
This note produces the expected output		Expected:		Messages A difference in feedback messages does not cause this test to fail. No feedback messages. Warnings A difference in warnings does not cause this test to fail. No warnings.

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.

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.

Variable	Answer to use	Must be answered?

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.

Next part options

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

Label

Lock this part?

Availability

Available if

Penalty to apply when visited

Amount of penalty

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Variable replacements

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

Variable	Value

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by	More information

Advice

Give a worked solution to the whole question.

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Define rulesets for simplification and display of mathematical expressions.

Name

Definition

Functions

Define functions to use in JME expressions.

Select a function to edit.

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Name

Language

Parameters

Name	Type
	of
Output type

Definition

Built-in constants

Tick the built-in constants you wish to include in this question.

Custom constants

You can define constants in terms of the built-in constants, even if they're disabled.

Names	Value	LaTeX

Add styling to the question's display and write a script to run when the question is created.

URL

Text alternative

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

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Checkpoint description

Xiaodan Leng 5 years, 4 months ago

Error in variable testing condition

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Advanced settings

Advanced settings

Advanced settings

Advanced settings

Advanced settings

Base marking algorithm

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Test that the marking algorithm works

Feedback

Question variables

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Warnings:

Unit tests

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

Next part options

Variable replacements

Previous parts

to

Functions

Built-in constants

Custom constants