Differentiation 19 - Finding Tangent and Normal

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Katie Lester

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Name	Status	Author	Last Modified
Differentiation 19 - Finding Tangent and Normal	Has some problems	Katie Lester	13/11/2020 20:13
Gareth's copy of Differentiation 19 - Finding Tangent and Normal	draft	Gareth Woods	08/07/2016 11:14
OCHO CUATRO Derivadas valor de f'	draft	Marlon Arcila	08/09/2021 00:47
Denis's copy of Gareth's copy of Differentiation 19 - Finding Tangent and Normal	draft	Denis Flynn	29/03/2017 15:12
Differentiation 19 - Finding Tangent and Normal	draft	Xiaodan Leng	11/07/2019 07:00

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Question statement

Find the following.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	list	[ 3, 2 ]
b	list	[ -5, -7 ]
c	list	[ 10, -8 ]
d	integer	-1

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
repeat(random(2..4),2)

JME function reference

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: `list`

[ 3, 2 ]

→ Used by:

"Part a)" - prompt
"Part a)" → "Gap 0." - Correct answer
"Part b)" - prompt
"Part b)" → "Gap 0." - Correct answer
"Part b)" → "Gap 1." - Minimum accepted value
"Part b)" → "Gap 1." - Maximum accepted value
"Part b)" → "Gap 2." - Minimum accepted value
"Part b)" → "Gap 2." - Maximum accepted value
"Part b)" → "Gap 3." - Correct answer
"Part b)" → "Gap 4." - Minimum accepted value
"Part b)" → "Gap 4." - Maximum accepted value

Parts

Part a) Gap-fill
1. Gap Gap 0. Mathematical expression
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Mathematical expression
  Add
Part b) Gap-fill
1. Gap Gap 0. Mathematical expression
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Mathematical expression
  Add
5. Gap Gap 4. Number entry
  Add

Gap-fill

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

Find an equation for the tangent to the curve $\simplify{y={a[0]}x^2+{b[0]}x+{c[0]}}$ at the point at which it crosses the y-axis.

$\frac{dy}{dx}=$ Gap 0.

Therefore, the gradient of the tangent at $x=0$ is Gap 1.

When $x=0$ , $y=$ Gap 2.

Hence, the equation for the tangent is:

So, $y=$ Gap 3.

Advice

The differentiate of a function gives the gradient of the original function at the point $x$ .

The tangent to a line is the gradient of the curve at the point, and the normal is the reciprocal of this value (the perpendicular line intersecting the curve).

The equation of a line can be found in many ways, but given a point and gradient for a straight line, two of the simple manipulations are:

Using $y=mx+c$ and substituting in to find $c$

Using $\frac{y_2-y_1}{x_2-x_1}=m$ and rearranging.

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
Mathematical expression
Mathematical expression		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
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		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
Number entry
Number entry		Hasn't run yet

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Differentiation 19 - Finding Tangent and Normal

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

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Checkpoint description

Deactivated user 4 years, 4 months ago

Katie Lester 9 years, 6 months ago

Katie Lester 9 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

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Error

Differentiation 19 - Finding Tangent and Normal

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Deactivated user 4 years, 4 months ago

Katie Lester 9 years, 6 months ago

Katie Lester 9 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`