Surds 2

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9 years, 8 months ago

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joshua boddy 9 years, 8 months ago

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Name	Status	Author	Last Modified
Surds 2	Ready to use	joshua boddy	01/06/2016 09:47
Numerical Skills Surds 2 - Formative assessment	Ready to use	Jinhua Mathias	28/08/2024 12:15
Numerical Skills Surds 2 - Summative assessment	Ready to use	Jinhua Mathias	28/08/2024 12:15
Numbers VI: surds (rationalising the denominator - simple)	Ready to use	Luke Park	18/08/2016 12:16
Katherine's copy of Surds 2	draft	Katherine Tomlinson	31/07/2017 11:57

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Question statement

Express each of the following in the form $\frac{a\sqrt{b}}{c}$ where a, b and c are integers, where a and c have no common factors

Give any introductory information the student needs.

			Name	Type	Generated Value

a1	integer	18
a2	integer	10
a3	number	2
b1	integer	16
b2	integer	6
b3	number	2
c1	integer	17
c2	integer	3
d1	integer	7
d2	rational	6
d3	number	6
d4	integer	12
e1	integer	7
e2	integer	3
e3	integer	3
e4	integer	5
e5	number	1
f1	integer	2
f2	integer	5
f3	integer	11
f4	integer	3
f5	integer	44
f6	integer	675
f7	integer	9
f8	integer	27

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random(2..19)

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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:

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Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
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Gap-fill

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

$\frac{\var{a1}}{\sqrt{\var{a2}}}=$ Gap 0. $\sqrt{}$ Gap 1.Gap 2.

Advice

The best approach here is to first rationalise the denominator. We do this by multiplying both top and bottom by an approriate value.

For example to rationalise the denominator for an expression like $\frac{a}{\sqrt{b}}$ , we multiply numerator and denominator by $\sqrt{b}$ to get $\frac{a\sqrt{b}}{b}$

Similarly to rationalise the denominator for an expression like $\frac{a+\sqrt{b}}{c+\sqrt{d}}$ , we multiply numerator and denominator by $c-\sqrt{d}$ to get $\frac{(a+\sqrt{b})(c-\sqrt{d})}{c^2-d}$

Dont forget that:

$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

$(a+\sqrt{b})(a-\sqrt{b})=a^2-b$

Remember to check that your answer is in its simplest form.

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

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This question is used in the following exam:

mas0001 Surds by Bill Foster in Bill's workspace.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

joshua boddy 9 years, 8 months ago

joshua boddy 9 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Surds 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

joshua boddy 9 years, 8 months ago

joshua boddy 9 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`