Simon's copy of Inverse Functions

Error

There was an error loading the page.

Contributors

History

○

Simon Thomas 6 years, 1 month ago

Created this as a copy of Inverse Functions.

Name	Status	Author	Last Modified
Inverse Functions	Ready to use	Katie Lester	01/06/2016 09:47
José's copy of Inverse Functions	Ready to use	Jos Klenner	02/12/2020 15:42
Inverse Functions	draft	steve kilgallon	19/10/2016 15:19
Simon's copy of Inverse Functions	draft	Simon Thomas	21/03/2019 14:52
Maria's copy of Simon's copy of Inverse Functions	Needs to be tested	Maria Aneiros	05/02/2020 07:00

There are 8 other versions that do you not have access to.

Question statement

Rearrange these equations to make $x$ the subject.

Give any introductory information the student needs.

			Name	Type	Generated Value

			c	list	List of 15 items
			x		Definition of variable `x` is empty.

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
repeat(random(-5..5 except 0 except 1 except -1),15)

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, -4, 3, 4, 2, -2, 5, -2, 4, -3, 2, 5, -4, 3, -2 ]

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Mathematical expression
  Add
Part b) Gap-fill
1. Gap Mathematical expression
  Add
Part c) Gap-fill
1. Gap Mathematical expression
  Add
Part d) Gap-fill
1. Gap Mathematical expression
  Add
Part e) Gap-fill
1. Gap Mathematical expression
  Add

Gap-fill

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

$\simplify{y={c[0]}x+{c[1]}}$

$x=$ Unnamed gap

Advice

(a)

$\simplify{y={c[0]}x+{c[1]}}$

$\simplify{y-{c[1]}={c[0]}x}$

$\simplify{(y-{c[1]})/{c[0]}={x}}$ (dividing both sides by $\var{c[0]}$ )

(b)

$\simplify{y={c[2]}x/({c[3]}+x)}$

$\simplify{y*({c[3]}+x)={c[2]}}x$ (multiply both sides by denominator)

$\simplify{y*{c[3]}+x y={c[2]}}x$ (expanding bracket)

$\simplify{y*{c[3]}={c[2]}x- y x}$ (moving all $x$ to the same side)

$\simplify{y*{c[3]}=x({c[2]}- y)}$ (factorising)

$\simplify{(y*{c[3]})/({c[2]}- y)=x}$

(c)

$\simplify{y={c[7]}-{c[8]}/({c[9]}+x)}$

$\simplify{y-{c[7]}=-{c[8]}/({c[9]}+x)}$

$\simplify{({c[9]}+x)=-{c[8]}/(y-{c[7]})}$

$\simplify{x=-{c[9]}-{c[8]}/(y-{c[7]})}$ which is algebraically the same as $\simplify{x=(-{c[9]}(y-{c[7]})-{c[8]})/(y-{c[7]})}=\simplify{(-{c[9]}y+{c[7]*c[9]-c[8]})/(y-{c[7]})}$

(d)

$\simplify{y=sqrt(x+{c[10]})}$

$\simplify{y^2=(x+{c[10]})}$ (squaring both sides)

$\simplify{y^2-{c[10]}=x}$

(e)

$\simplify{y=1/x+{c[11]}}$

$\simplify{y-{c[11]}=1/x}$

$\simplify{x(y-{c[11]})=1}$ (multiply both sides by $x$ )

$\simplify{x=1/(y-{c[11]})}$

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
Gap-fill
Gap-fill		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
Gap-fill
Gap-fill		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

This question is used in the following exam:

Transposition of Formulae by Simon Thomas in Maths support.

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 6 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

Loading...

Error

Simon's copy of Inverse Functions

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 6 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`