Stationary Points

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Matthew Mears

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Matthew Mears 6 years, 5 months ago

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Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

z	number	27.5
c	integer	7
b	integer	4
d	integer	4
f	integer	-1
w	number	4.2
a	number	9.5
g	integer	-10
h	number	0.5
t	number	0.5
maximum	boolean	true

Automatically regenerate variables?

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A random number between and (inclusive) with step size

Description

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Generated value: `number`

27.5

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Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Mathematical expression
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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

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 $y$ .

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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

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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History

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Checkpoint description

Matthew Mears 6 years, 5 months ago

Error in variable testing condition

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Warning

Generated value: `number`

Parts

Gap-fill

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Stationary Points

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Matthew Mears 6 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`