Turning points

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Xiaodan Leng 5 years, 10 months ago

Created this as a copy of Turning points.

Name	Status	Author	Last Modified
Turning points	Ready to use	Frank Doheny	13/03/2019 15:21
Katy's copy of Turning points	Ready to use	Katy Dobson	09/01/2024 11:42
Simon's copy of Turning points	draft	Simon Thomas	14/03/2019 11:07
Turning points	draft	Xiaodan Leng	10/07/2019 22:14

There are 7 other versions that do you not have access to.

Question statement

The function $f(x)=2x^3-\simplify{3*({a}+{b})x^2+6*{a}*{b}x}+\var{c}$ has two turning points.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	1
b	integer	9
c	integer	1

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: `integer`

→ Used by:

Statement
Advice
"Unnamed part" → "Gap 0." - Minimum accepted value
"Unnamed part" → "Gap 0." - Maximum accepted value

Parts

Gap-fill
1. Gap Gap 0. Number entry
  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.

Input the smaller of the two $x$ values.

$x=$ Gap 0.

Input the larger of the two $x$ values.

$x=$ Gap 1.

Advice

$f(x)=2x^3-\simplify{3*({a}+{b})x^2+6*{a}*{b}x}+\var{c}$

To locate a turning point, differentite the function, set equal to zero and solve.

$f'(x)=6x^2-\simplify{6*({a}+{b})x+6*{a}*{b}}=0$

Divide across by 6 to get the quadratic equation

$x^2-\simplify{({a}+{b})x+{a}*{b}}=0$

This has factors

$(x-\var{a})(x-\var{b})=0$

$x-\var{a}=0$ or $x-\var{b}=0$

$x=\var{a}$ or $x=\var{b}$

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
Number entry
Number entry		Hasn't run yet

This question is not used in any exams.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

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Checkpoint description

Xiaodan Leng 5 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Turning points

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Xiaodan Leng 5 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`