Q2 Indices in their simplest form 2

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TEAME CIT

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TEAME CIT 8 years, 5 months ago

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TEAME CIT 9 years, 2 months ago

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Name	Status	Author	Last Modified
Q2 Indices in their simplest form 2	draft	TEAME CIT	08/10/2016 22:21
Julie's copy of Q2 Indices in their simplest form 2	draft	Julie Crowley	15/11/2016 15:00

Question statement

Simplify the Indices

Give any introductory information the student needs.

			Name	Type	Generated Value

num11	list	[ 5, 2, 4, 3 ]
num111	integer	3
ans11	number	12
num12	list	[ 2, 5, 3, 4 ]
num121	integer	3
ans12a	number	3
ans12b	number	-3
num131	integer	2
num132	integer	4
ans13a	integer	2
num13	list	[ 9, 4, 5, 6, 3, 2 ]
ans13b	number	3
ans13c	number	-7
ans13d	number	7
num141	integer	4
num142	integer	8
ans14a1	integer	4
ans14b	number	6
num143	integer	3
num14	list	[ 4, 3, 5, 2, 8 ]
ans14c	number	-12
ans14d	number	-39
ans14aT	number	64
num21	list	List of 10 items
num211	list	[ 5, 7, 3 ]
ans21a	integer	15
ans21b	integer	7
ans21c	number	10
ans21d	number	-1
ans21e	number	-18
num22	list	List of 10 items
num221	list	[ 3, 7, 5 ]
ans22a	integer	15
ans22b	integer	7
ans22c	number	16
ans22d	number	-5
ans22e	number	12
num31	list	[ 3, 2, 6 ]
ans31	number	-1
num32	list	[ 8, 7, 3 ]
ans32	number	4
num321	list	[ 25, 49 ]
num33	list	[ 6, 8, 2, 4, 7 ]
ans33a	number	5
ans33b	number	7
ans33c	number	4
ans33d	number	-6
ans33e	number	-3
ans14a	rational	8
ans		Definition of variable `ans` is empty.
power		Definition of variable `power` is empty.

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
shuffle(2..5)[0..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: `list`

[ 5, 2, 4, 3 ]

→ Used by:

ans11

"Part a)" - prompt

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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4. Gap Gap 3. Number entry
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5. Gap Gap 4. Number entry
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6. Gap Gap 5. Number entry
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11. Gap Gap 10. Number entry
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12. Gap Gap 11. Number entry
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13. Gap Gap 12. Number entry
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14. Gap Gap 13. Number entry
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Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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4. Gap Gap 3. Number entry
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5. Gap Gap 4. Number entry
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6. Gap Gap 5. Number entry
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7. Gap Gap 6. Number entry
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8. Gap Gap 7. Number entry
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9. Gap Gap 8. Number entry
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10. Gap Gap 9. Number entry
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11. Gap Gap 10. Number entry
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12. Gap Gap 11. Number entry
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13. Gap Gap 12. Number entry
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14. Gap Gap 13. Number entry
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20. Gap Gap 19. Number entry
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21. Gap Gap 20. Number entry
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1. Step Information only

Gap-fill

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

Simplify each of the following, without using a calculator:

i) $[\frac{3^{\var{num11[0]}}.9^{\var{num11[1]}}}{3^{-\var{num11[2]}}.27^{\var{num11[3]}}}]^{\var{num111}}$

${ans}^{power} =$ {Gap 0.}^{Gap 1.}

ii) $[\frac{5^{\var{num12[0]}}.7^{\var{num12[1]}}}{5^{\var{num12[2]}}.7^{\var{num12[3]}}}]^{-\var{num121}}$

${ans}^{power} =$ {Gap 2.}^{Gap 3.} {Gap 4.}^{Gap 5.}

iii) $\frac{\var{num132}x^{\var{num13[0]}}.y^{-\var{num13[1]}}.z^{\var{num13[2]}}}{\var{num131}x^{\var{num13[3]}}.y^{\var{num13[4]}}.z^{-\var{num13[5]}}}$

${ans}^{power} =$ {Gap 6.} x^{Gap 7.} y^{Gap 8.} z^{Gap 9.}

iv) $(\frac{\var{num142}a^{\var{num14[0]}}.b^{-\var{num14[1]}}.c^{-\var{num14[2]}}}{\var{num141}a^{\var{num14[3]}}.b.c^{\var{num14[4]}}})^{\var{num143}}$

${ans}^{power} =$ {Gap 10.} a^{Gap 11.} b^{Gap 12.} c^{Gap 13.}

Advice

The following questions show the method to use to solve the above questions:

Part a)

i) $[\frac{3^2.2^4}{3^{-2}.2^5}]^2$

$[\frac{3^2}{3^{-2}}]^2.[\frac{2^4}{2^5}]^2$

$[3^4]^2.[2^{-1}]^2 = 3^6.2^{-2}$

ii) $[\frac{5^3.7^2}{5^{2}.7^4}]^{-1}$

$[5^1]^{-1}.[7^{-2}]^{-1} = 5^{-1}.7^2$

iii) $\frac{24x^2.y^{-4}.z^3}{8x^3.y^7.z^{-3}}$

$\frac{24}{8}.x^{2-3}.y^{-4-7}.z^{3+3} = 3.x^{-1}.y^{-11}.z^{6}$

iv) $[\frac{3a^2.b^{3}.c^{-2}}{2a^4.b.c^{2}}]^2$

$[\frac{3}{2}]^2.[a^{2-4}]^2.[b^{3-1}]^2.[c^{-2-2}]^2 = \frac{9}{4}.a^{-4}.b^{4}.c^{-8}$

Part b)

i) $\frac{5x^3.y^{4}.z}{2x^5.y^2.z^{3}} \times \frac{3x^7.y^{2}.z^{-5}}{x^{-8}.y^5.z}$

$\frac{5 \times 3}{2}.x^{3-5+7+8}.y^{4-2+2-5}.z^{1-3-5-1} = \frac{15}{2}.x^{13}.y^{-5}.z^{-8}$

ii) $\frac{3a^5.b^{-2}.c^{7}}{2a.b^{-3}.c^{5}} \div \frac{a^4.b^{3}.c}{a^{-2}.b^6.c^{-1}}$

$\frac{3}{2}.a^{5-1+4+2}.b^{-2+3+3-6}.c^{7-5+1+1} = \frac{3}{2}.a^{10}.b^{-2}.c^{4}$

iii) $4^{\frac{3}{2}}.8^{\frac{2}{3}}.16^{\frac{-3}{4}}$

$2^{\frac{3 \times2}{2}}.2^{\frac{2 \times3}{3}}.2^{\frac{-3 \times4}{4}}$

$2^{3+2-3} = 2^2$

iv) $[\frac{49a^4.b^{-3}.c}{25a^{-2}.b^{3}.c^{5}}]^{\frac{1}{2}}$

$[\frac{49}{25}]^{\frac{1}{2}}.[a^{4+2}]^{\frac{1}{2}}.[b^{-3-3}]^{\frac{1}{2}}.[c^{1-5}]^{\frac{1}{2}} = \frac{7}{5}.a^{3}.b^{-3}.c^{-2}$

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
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Information only

This question is used in the following exams:

Indices by Deirdre Casey in Deirdre's workspace.
Apprentices Year 1 Quiz 3 by Aoife O'Brien in Aoife's Exams.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

TEAME CIT 8 years, 5 months ago

TEAME CIT 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

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Q2 Indices in their simplest form 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

TEAME CIT 8 years, 5 months ago

TEAME CIT 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`