Applications of differentiation

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Nigel Atkins

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Nigel Atkins 8 years, 1 month ago

Created this as a copy of Applications of differentiation .

Name	Status	Author	Last Modified
Leicester: Differentiation 2	draft	Bill Foster	06/08/2020 08:42
Differentiation 15 - Applications	Ready to use	Katie Lester	01/06/2016 09:47
David's copy of Differentiation 15 - Applications	Ready to use	David Mason	01/06/2016 09:47
Jinhua's copy of Differentiation 15 - Applications	Ready to use	Jinhua Mathias	27/08/2024 16:37
CF Maths Differentiation 15 - Applications Finding Gradient	Ready to use	Jinhua Mathias	27/08/2024 16:37
CF Maths In class test two mock paper question 2	Ready to use	Jinhua Mathias	28/08/2024 12:15
Applications of differentiation	draft	Vicky Hall	20/05/2019 14:56
CATORCE CINCO Derivadas aplicaciones	draft	Marlon Arcila	08/09/2021 00:22
OCHO UNO Derivadas valor de f'	draft	Marlon Arcila	08/09/2021 00:45
Applications of differentiation	draft	cormac breen	23/02/2017 18:06
Applications of differentiation	draft	Nigel Atkins	15/03/2017 19:10
Applications of differentiation	draft	Milena Venkova	06/03/2018 15:26
Ida's copy of Applications of differentiation	draft	Ida Landgärds	17/04/2018 15:13
Ida's copy of Applications of differentiation	draft	Ida Landgärds	17/04/2018 15:34
spørsmål 3	draft	Ida Landgärds	02/12/2020 15:42
Harry's copy Applications of differentiation	draft	Harry Flynn	08/05/2018 11:51
Ida's copy of Ida's copy of Applications of differentiation	draft	Ida Landgärds	14/05/2018 09:18
spørsmål 3	draft	Ida Landgärds	02/12/2020 15:42
Blathnaid's copy of Applications of differentiation	draft	Blathnaid Sheridan	11/03/2019 15:07
Christian's copy of Applications of differentiation	draft	Christian Lawson-Perfect	20/05/2019 14:58
Maria's copy of Differentiation 15 - Applications	draft	Maria Aneiros	27/05/2019 05:47
Maria's copy of Christian's copy of Applications of differentiation	draft	Maria Aneiros	27/05/2019 05:47
Exam13 - Differentiation	draft	Michael Proudman	07/12/2021 09:54
nuExam13 - Differentiation	draft	Michael Proudman	07/12/2021 09:54
Differentiation 15 - Applications	draft	Xiaodan Leng	11/07/2019 06:58

There are 27 other versions that do you not have access to.

Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

z	number	22
c	integer	7
b	integer	3
d	integer	5
f	integer	15
w	number	2.4
a	number	8
g	integer	1
h	number	5
t	number	1
maximum	boolean	false

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

Description

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

Can an exam override the value of this variable?

Generated value: `number`

→ Used by:

"Part c)" - prompt
"Part c)" → "Gap 0." - Correct answer
"Part c)" → "Gap 1." - Minimum accepted value
"Part c)" → "Gap 1." - Maximum accepted value

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Mathematical expression
  Add
Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Mathematical expression
  Add
4. Gap Gap 3. Mathematical expression
  Add
5. Gap Gap 4. Choose one from a list
  Add
Part c) Gap-fill
1. Gap Gap 0. Mathematical expression
  Add
2. Gap Gap 1. Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Find the gradient of the curve $y$ at the point $x=\var{d}$ , giving your answer to $2$ decimal places if necessary.

$y = \simplify{ {a}*x^2 + {b}x + {c}}$

Firstly, differentiate.

$\displaystyle \frac{dy}{dx}=$ Gap 1.

Gradient at $x=\var{d}\;$ is Gap 0.

Advice

Parts A and B

Here, the question takes you throught the stages needed to find the solution. The reason we differentiate is that the derivative of a function tells us its gradient at a given point, and we want to find where the function has gradient zero because when the gradient is zero we either have a maximum or a minimum point.

Part C

The first part of this question is similar to parts A and B. The tricky bit is the second part! You need to work out the value of $t$ that produces the maximum piont but that is not the final answer - you need to use that value of $t$ to find the maximum height, which you do by substituting $t$ into the original function to find $y$ .

Give a worked solution to the whole question.

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

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

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

LS4003 Maths Test 2D (2018-19) by Nigel Atkins in Nigel's workspace.
Maths Test 2D (2019-20) by Nigel Atkins in Nigel's workspace.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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History

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Checkpoint description

Nigel Atkins 8 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: `number`

Parts

Gap-fill

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Applications of differentiation

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Nigel Atkins 8 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`