Julie's copy of Q2 Indices in their simplest form 2

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Julie Crowley

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Julie Crowley commented 8 years, 4 months ago

Need to fix this question!

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Julie Crowley 8 years, 4 months ago

Created this as a copy of Q2 Indices in their simplest form 2.

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	[ 4, 5, 2, 3 ]
num111	integer	3
ans11	number	21
num12	list	[ 4, 2, 5, 3 ]
num121	integer	1
ans12a	number	1
ans12b	number	1
num131	integer	2
num132	integer	8
ans13a	integer	4
num13	list	[ 8, 7, 5, 6, 4, 3 ]
ans13b	number	2
ans13c	number	-11
ans13d	number	8
num141	integer	5
num142	integer	8
ans14a1	integer	4
ans14b	number	12
num143	integer	3
num14	list	[ 9, 2, 7, 5, 4 ]
ans14c	number	-9
ans14d	number	-33
ans14aT	number	64
num21	list	List of 10 items
num211	list	[ 3, 7, 5 ]
ans21a	integer	15
ans21b	integer	7
ans21c	number	19
ans21d	number	-1
ans21e	number	-15
num22	list	List of 10 items
num221	list	[ 3, 5, 7 ]
ans22a	integer	21
ans22b	integer	5
ans22c	number	19
ans22d	number	-5
ans22e	number	-1
num31	list	[ 7, 3, 2 ]
ans31	number	8
num32	list	[ 5, 4, 6 ]
ans32	number	-1
num321	list	[ 81, 49 ]
num33	list	[ 8, 6, 4, 2, 3 ]
ans33a	number	9
ans33b	number	7
ans33c	number	6
ans33d	number	-4
ans33e	number	-1
ans14a	rational	512/125
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`

[ 4, 5, 2, 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
  Add
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
  Add
Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Number entry
  Add
5. Gap Gap 4. Number entry
  Add
6. Gap Gap 5. Number entry
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7. Gap Gap 6. Number entry
  Add
8. Gap Gap 7. Number entry
  Add
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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15. Gap Gap 14. Number entry
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16. Gap Gap 15. Number entry
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17. Gap Gap 16. Number entry
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18. Gap Gap 17. Number entry
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19. Gap Gap 18. 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?
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Information only

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Julie's copy of Q2 Indices in their simplest form 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Julie Crowley commented 8 years, 4 months ago

Julie Crowley 8 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

Loading...

Error

Julie's copy of Q2 Indices in their simplest form 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Julie Crowley commented 8 years, 4 months ago

Julie Crowley 8 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`