Copy of Q2 Adding and subtracting surds

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Don Shearman 3 years, 9 months ago

Published this.

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Jim Pettigrew 4 years, 4 months ago

Created this as a copy of Q2 Adding and subtracting surds.

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Question statement

To include a square root sign in your answer use sqrt(). For example, to write $\sqrt{3}$ , type sqrt(3) into the answer box. If you are entering a number multiplied by the square root of some other number, for example $3\sqrt{5}$ , type 3sqrt(5) into the answer box.

Give any introductory information the student needs.

			Name	Type	Generated Value

d	integer	6
n	integer	5
b	integer	5
a	integer	5
v	integer	2
m	integer	3

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..7 except 4)

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`

→ Used by:

Advice
"Part a)" - prompt
"Part a)" → "Unnamed gap" - Correct answer
"Part b)" - prompt
"Part b)" → "Unnamed gap" - Correct answer
"Part c)" - prompt
"Part c)" → "Unnamed gap" - Correct answer

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

Gap-fill

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

Simplify $\simplify[!cancelTerms]{{d}sqrt({a}) - sqrt({a})+{n}sqrt({a})}$ .

$\simplify[!cancelTerms]{{d}sqrt({a}) - sqrt({a})+{n}sqrt({a})}$ = Unnamed gap.

Advice

Simplify $\simplify[!cancelTerms]{{d}sqrt({a}) - sqrt({a})+{n}sqrt({a})}$ .

The surds are all like surds, so we can collect like surds.

$\simplify[!cancelTerms]{{d}sqrt({a}) - sqrt({a})+{n}sqrt({a})={d-1+n}sqrt({a})}$ .

$\simplify[!cancelTerms]{{d}sqrt({a}) + sqrt({v^2*a})-sqrt({b^2*a})}$

Look for factors of the surds which are square numbers ( $4, 9, 16, 25, 36, 49, 64, 81, 100, ...$ ).

In this question the second term has a square factor $\var{v^2}$ and the third term has a square factor $\var{b^2}$ .

$\begin{align} \simplify[!cancelTerms]{{d}sqrt({a}) + sqrt({v^2*a})-sqrt({b^2*a})} &= \var{d}\sqrt{\var{a}} + (\sqrt{\simplify{{v}^2}} \times \sqrt{\var{a}})-(\sqrt{\simplify{{b}^2}} \times \sqrt{\var{a}}) \\ &= \var{d}\sqrt{\var{a}} +\var{v}\sqrt{\var{a}}-\var{b}\sqrt{\var{a}} \\ &= \simplify{({d}+{v}-{b})sqrt({a})} \text{.} \end{align}$

$\begin{align} \simplify{{d}sqrt({a}) - {b}sqrt({v}^2{a})+{n}sqrt({b}^2*{a})} &= \var{d}\sqrt{\var{a}} - \var{b}(\sqrt{\simplify{{v}^2}} \times \sqrt{\var{a}})+\var{n}(\sqrt{\simplify{{b}^2}} \times \sqrt{\var{a}}) \\ &= \var{d}\sqrt{\var{a}} -\var{b}(\simplify{{v}*sqrt({a})})+\var{n}(\simplify{{b}*sqrt({a})}) \\ &= \simplify{{d}sqrt({a})}-\simplify{{b}*{v}sqrt({a})}+\simplify{{n}*{b}sqrt({a})} \\ &= \simplify{({d}-{b}*{v}+{n}*{b})sqrt({a})} \text{.} \end{align}$

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Mathematical expression
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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

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Comment

Checkpoint description

Don Shearman 3 years, 9 months ago

Jim Pettigrew 4 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Copy of Q2 Adding and subtracting surds

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Don Shearman 3 years, 9 months ago

Jim Pettigrew 4 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`