Expand brackets and collect like terms

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Owen Jepps

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Owen Jepps 7 years, 2 months ago

Created this as a copy of Expand brackets and collect like terms.

Name	Status	Author	Last Modified
Expand brackets and collect like terms	Ready to use	Bradley Bush	20/11/2019 14:38
Create an algebraic expression from a word problem, simplify, and evaluate	Ready to use	Bradley Bush	19/12/2022 12:26
Hollie's copy of Expand brackets and collect like terms	draft	Hollie Tarr	17/09/2017 15:18
Raphael's copy of Expand brackets and collect like terms	draft	Raphael Stuhlmeier	23/11/2017 13:28
Expand brackets and collect like terms	draft	Owen Jepps	11/01/2018 06:08
samla lika termer	draft	Ida Landgärds	10/04/2018 14:19
Ida's copy of samla lika termer	draft	Ida Landgärds	10/04/2018 14:21
Ida's copy of samla lika termer	draft	Ida Landgärds	10/04/2018 14:24
Marte's copy of Expand brackets and collect like terms	draft	Marte Bråtalien	12/04/2018 11:01
Marte's copy of Expand brackets and collect like terms	draft	Marte Bråtalien	12/04/2018 11:01
Samantha's copy of Create an algebraic expression from a word problem, simplify, and evaluate	draft	Samantha Konig	28/06/2018 05:55
Samantha's copy of Create an algebraic expression from a word problem, simplify, and evaluate	draft	Samantha Konig	28/06/2018 05:56
Expand brackets and collect like terms	draft	Paul Hancock	24/07/2018 02:40
Expand brackets and collect like terms[L4 Randomised]	Needs to be tested	Matthew James Sykes	25/07/2018 13:56
Heather's copy of Expand brackets and collect like terms[L4 Randomised]	draft	Heather Driscoll	01/10/2018 15:40
Francis's copy of Expand brackets and collect like terms - two questions	draft	Francis Duah	11/11/2018 15:28
Create an algebraic expression from a word problem, simplify, and evaluate in dollars version	Ready to use	Maria Aneiros	18/05/2019 02:13
Maria's copy of Expand brackets and collect like terms	draft	Maria Aneiros	29/05/2019 05:57
Maria's copy of Create an algebraic expression from a word problem, simplify, and evaluate	draft	Maria Aneiros	29/05/2019 05:09
WordProblem01_NL	Ready to use	Paul Verheyen	28/09/2019 18:14
Musa's copy of Expand brackets	draft	Musa Mammadov	01/08/2022 08:17
Musa's copy of Expand brackets and collect like terms 3	draft	Musa Mammadov	27/06/2023 01:45
Musa's copy of 3 Expand brackets	draft	Musa Mammadov	27/06/2023 01:47

There are 86 other versions that do you not have access to.

Question statement

For each expression below, collect like terms and expand brackets.

The * symbol is required between algebraic symbols, e.g. $5ab^2$ should be written 5*a*b^2.

Give any introductory information the student needs.

			Name	Type	Generated Value

a1	integer	9
b1	integer	5
c1	integer	8

			Name	Type	Generated Value

a	list	[ 10, 14, 14, 15, 13 ]
b	list	[ 9, 8, 5, 2, 7 ]
c	list	[ 3, 2, 9, 9, 6 ]
d	list	[ 10, 14, 20, 9, 13, 22 ]
f	list	[ 14, 20, 17, 17, 20, 18, 4 ]
g	list	[ 7, 14, 15, 15, 10, 11, 4 ]
h	list	[ 18, 8, 12, 18, 14, 14, 9 ]
j	list	List of 9 items

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(5..10)

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 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
Part f) Gap-fill
1. Gap Mathematical expression
  Add
Part g) Gap-fill
1. Gap Mathematical expression
  Add
Part h) 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.

$\var{c[0]}x+\var{c[1]}x+\var{c[2]}x=$ Unnamed gap

Advice

When simplifying expressions, only terms of the same type or like terms can be added together.

Algebraic symbols or letters can be added together provided that they are raised to the same power. For example, we can add $x^2+x^2=2x^2$, but we cannot collect both $x^2$ and $x$ into one term.

a)

\[
\begin{align}
\var{c[0]}x+\var{c[1]}x+\var{c[2]}x&=(\var{c[0]}+\var{c[1]}+\var{c[2]})x\\
&=\simplify{({c[0]}+{c[1]}+{c[2]})}x
\end{align}
\]

b)

\[
\begin{align}
\var{a[1]}x^2+\var{a[2]}x^2+\var{a[3]}x+\var{a[4]}x +\var{a[0]}&=(\var{a[1]}+\var{a[2]})x^2+(\var{a[3]}+\var{a[4]})x +\var{a[0]}\\
&=\simplify{({a[1]}+{a[2]})}x^2+\simplify{({a[3]}+{a[4]})}x+\var{a[0]}
\end{align}
\]

c)

\[
\begin{align}
\var{b[0]}y^5+\var{b[1]}y^5+\var{b[2]}y^5+\var{b[4]}y^5+\var{b[3]}y^5&=(\var{b[0]}+\var{b[1]}+\var{b[2]}+\var{b[4]}+\var{b[3]})y^5\\
&=\simplify{({b[1]}+{b[2]}+{b[3]}+{b[4]}+{b[0]})}y^5
\end{align}
\]

d)

\[
\begin{align}
\var{d[0]}ab+\var{d[1]}abc+\var{d[2]}a+\var{d[3]}b+\var{d[4]}c+\var{d[5]}abc
&=(\var{d[1]}+\var{d[5]})abc+\var{d[0]}ab+\var{d[2]}a+\var{d[3]}b+\var{d[4]}c\\
&=\simplify{{d[1]}+{d[5]}}abc+\var{d[0]}ab+\var{d[2]}a+\var{d[3]}b+\var{d[4]}c
\end{align}
\]

e)

\[
\begin{align}
\var{f[0]}a^2b+\var{f[1]}ab^2+\var{f[2]}ab+\var{f[3]}a^2b+\var{f[4]}ab^2
&=(\var{f[0]}+\var{f[3]})a^2b+(\var{f[1]}+\var{f[4]})ab^2+\var{f[2]}ab\\
&=\simplify{{f[0]}+{f[3]}}a^2b+\simplify{{f[1]}+{f[4]}}ab^2+\var{f[2]}ab
\end{align}
\]

f)

\[
\begin{align}
\var{g[0]}(\var{g[1]}x+\var{g[2]}y)+\var{g[4]}x+\var{g[5]}y
&=(\var{g[0]}\times \var{g[1]}+\var{g[4]})x+(\var{g[0]} \times\var{g[2]}+\var{g[5]})y\\
&=(\simplify{{g[0]}*{g[1]}}+\var{g[4]})x+(\simplify{{g[0]}*{g[2]}}+\var{g[5]})y\\
&=\simplify{{g[0]}*{g[1]}+{g[4]}}x+\simplify{{g[0]}*{g[2]}+{g[5]}}y
\end{align}
\]

g)

\[
\begin{align}
\var{h[0]}x(\var{h[1]}x+\var{h[2]}z)+\var{h[3]}x+\var{h[6]}z+\var{h[4]}x^2+\var{h[5]}z^2
&=(\simplify[]{{h[0]}{h[1]}}+\var{h[4]})x^2+(\simplify[]{{h[0]}{h[2]}})zx+\var{h[3]}x+\var{h[5]}z^2+\var{h[6]}z\\
&=(\simplify{{h[0]}{h[1]}}+\var{h[4]})x^2+(\simplify[]{{h[0]}{h[2]}})zx+\var{h[3]}x+\var{h[5]}z^2+\var{h[6]}z\\
&=\simplify{{h[0]}*{h[1]}+{h[4]}}x^2+\simplify{{h[0]}*{h[2]}}zx+\simplify{{h[3]}x+{h[5]}}z^2+\var{h[6]}z
\end{align}
\]

h)

\[
\begin{align}
\var{j[0]}(\var{j[1]}x-\var{j[2]}y)+\var{j[3]}(\var{j[4]}x-\var{j[5]}y)+\var{j[6]}(\var{j[7]}x-\var{j[8]}y)
&= (\simplify[]{{j[0]}{j[1]}}+\simplify[]{{j[3]}{j[4]}}+\simplify[]{{j[6]}{j[7]}})x-(\simplify[]{{j[0]}{j[2]}}+\simplify[]{{j[3]}{j[5]}}+\simplify[]{{j[6]}{j[8]}})y\\
&= (\simplify{{j[0]}{j[1]}}+\simplify{{j[3]}{j[4]}}+\simplify{{j[6]}{j[7]}})x-(\simplify{{j[0]}{j[2]}}+\simplify{{j[3]}{j[5]}}+\simplify{{j[6]}{j[8]}})y\\
&= \simplify{({j[0]}*{j[1]}+{j[4]*j[3]}+{j[6]}*{j[7]})x}-\simplify{({j[0]}*{j[2]}+{j[5]}{j[3]}+{j[6]}*{j[8]})y}
\end{align}
\]

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Owen Jepps 7 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

c)

d)

e)

f)

g)

h)

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Error

Expand brackets and collect like terms

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Owen Jepps 7 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

d)

e)

f)

g)

h)

Generated value: `integer`