Calculating area and perimeter using simultaneous equations

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Vicky Hall

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Vicky Hall 8 years, 9 months ago

Created this as a copy of Q4 (Calculating area using algebraic equations).

Name	Status	Author	Last Modified
Q1 (Simplify algebra equations)	Ready to use	TEAME CIT	06/10/2016 16:13
Q2 (Algebra equations solve for x)	draft	TEAME CIT	06/10/2016 16:13
Q4 (Calculating area using algebraic equations)	Ready to use	TEAME CIT	06/10/2016 16:14
Calculating area and perimeter using simultaneous equations	draft	Vicky Hall	06/02/2018 13:12
Bokstavregning og parenteser 1	draft	Ida Friestad Pedersen	15/07/2016 11:12
Bokstavregning og parenteser 2	draft	Ida Friestad Pedersen	15/07/2016 11:11
Simplify algebra equations	draft	steve kilgallon	24/08/2017 16:02
Simplify algebra equations	draft	steve kilgallon	23/08/2017 11:19
Simplify algebra equations	draft	steve kilgallon	08/08/2016 15:18
Bokstavregning og parenteser 2	draft	Ida Friestad Pedersen	15/08/2016 14:06
Algebra : Solving Linear Equations (2)	Ready to use	Nasir Firoz Khan	21/11/2016 09:46
Simplify algebra equations L1	draft	steve kilgallon	16/10/2016 10:59
Rational Equation..becomes Linear	draft	Clare Lundon	13/10/2016 10:11
Morten's copy of Bokstavregning og parenteser 1	draft	Morten Brekke	13/10/2016 15:13
Bokstavregning og parenteser 1	draft	Morten Brekke	03/11/2017 08:32
Mock exam 1 Simplify algebra equations L1	draft	steve kilgallon	04/11/2017 14:23
Algebra and parenthesis 1	draft	Robert Førland	04/11/2016 23:35
Herleiden met vereenvoudigingsregels	draft	Johan Maertens	11/02/2017 09:16
Rachel's copy of Algebra and parenthesis 1	draft	Rachel Staddon	20/04/2017 15:04
Brackets	draft	Harry Flynn	30/05/2017 13:10
Regina's copy of Mock exam 1 Simplify algebra equations L1	draft	Regina Kobus	07/11/2017 01:48
Simplify algebra equations BY138	Ready to use	steve kilgallon	12/01/2021 10:29
Marte's copy of Bokstavregning og parenteser 1	draft	Marte Bråtalien	12/04/2018 10:42
Amanda's copy of Morten's copy of Bokstavregning og parenteser 1	draft	Amanda Haslemo	09/11/2018 09:22
mengeling veeltermen	draft	Johan Maertens	03/05/2023 14:24
Simon's copy of Q4 (Calculating area using algebraic equations)	draft	Simon Thomas	25/03/2019 09:59

There are 47 other versions that do you not have access to.

Question statement

Solve the following correct to $1$ decimal place:

Give any introductory information the student needs.

			Name	Type	Generated Value

lent1	integer	18
red1	integer	10
area1	number	459.5
ans11	number	35.5277777778
ans12	number	639.5
per2	integer	52
ratio2	number	4.5
ans21	decimal	dec("4.727272727272727272727272727272727272727")
ans22	number	21.2727272727
ans23	decimal	dec("1.005619834710743814545454545454545454545e+2")
lent3	integer	20
per3	number	3.6
ans31	decimal	dec("9.818181818181819818181818181818181818182e-1")
ans32	decimal	dec("8.181818181818183181818181818181818181818e-1")
ratio4	number	3.25
per4	number	23.2
ans41	number	2.7294117647
ans42	number	8.8705882353
ans43	number	24.2114878893
dec	rational	6/5

Automatically regenerate variables?

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Data type

Value

xxxxxxxxxx
 
random(15..35)

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: `integer`

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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1. Step Information only
Part b) Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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Part c) Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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Gap-fill

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

A rectangle has a length of $\var{lent1} cm$ and a width of $x cm$ . If the width was reduced by $\var{red1} cm$ but the length remained the same, the area would be $\var{area1} cm^2$ . Find the original width and area of this rectangle.

Width: Gap 0. $cm$

Area: Gap 1. $cm^2$

Advice

Have a look at this youtube video to understand simultaneous equations better: Simultaneous Equations

Part 1:

Width is represented by the variable $x$ so if the width is reduced by $\var{red1}$ then we can say the new width is $x-\var{red1}$ . So the formula for the area of the new rectangle is given by

$\var{lent1} \times (x - \var{red1}) = \var{area1}cm$

$x - \var{red1} = \displaystyle \frac{\var{area1}}{\var{lent1}}$

$x = \displaystyle \frac{\var{area1}}{\var{lent1}} + \var{red1} = \simplify{{area1/lent1+red1}}$

The area of the original rectangle is given by $\var{lent1}x$ .

Part 2:

We have two equations:

$(2 \times length)+ (2 \times width) = \var{per2}$

and

$length = \var{ratio2} \times width$

Substitute the value for the length from the second equation into the first equation and solve to find the width.

Once you have the value for width, substitute this into the second equation to find the length.

Part 3:

Instead of being told that the length is so many times greater than the width, we've been given that it is a percentage greater than the width. But this percentage can be turned into a number. For example, if the length is $50$ % greater than the width, then we could multiply the width by $1.5$ to find the length.

Call the width $w$ and the length $l$ .

For any rectangle, perimeter = $2w + 2l$ .

We also know that $l=\var{dec}w$ . Substitute this value for $l$ into the equation for perimeter and solve for $w$ .

Give a worked solution to the whole question.

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

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Calculating area and perimeter using simultaneous equations

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

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Checkpoint description

Vicky Hall 8 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Calculating area and perimeter using simultaneous equations

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Vicky Hall 8 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`