Algebra, NAPX-G4-NC25 SA

Question

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Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

684

Question

The table below shows the relationship between the width of a tree's trunk in centimetres and how old it is in months.


Age in months 6 9 12 15 18
Width of trunk (cm) 618\frac{1}{8} 614\frac{1}{4} 638\frac{3}{8} 612\frac{1}{2} 658\frac{5}{8}


If this pattern continues, how old would you expect a tree with a 7 cm wide trunk to be?

Worked Solution

Continuing the pattern adding 18\frac{1}{8}:

Age in months 18 21 24 27
Width of trunk (cm) 658\frac{5}{8} 634\frac{3}{4} 678\frac{7}{8} 7


∴\therefore Expected age = 27 months

Question Type

Answer Box

Variables

Variable nameVariable value
question
The table below shows the relationship between the width of a tree's trunk in centimetres and how old it is in months.
>>| Age in months | 6|9|12|15|18| |:-:|:-:|:-:|:-:|:-:|:-:| | Width of trunk (cm) | 6$\frac{1}{8}$|6$\frac{1}{4}$|6$\frac{3}{8}$|6$\frac{1}{2}$|6$\frac{5}{8}$|

If this pattern continues, how old would you expect a tree with a 7 cm wide trunk to be?
workedSolution
Continuing the pattern adding $\frac{1}{8}$:
>>| Age in months | 18|21|24|27| |:-:|:-:|:-:|:-:|:-:| | Width of trunk (cm) | 6$\frac{5}{8}$|6$\frac{3}{4}$|6$\frac{7}{8}$|7|

$\therefore$ Expected age = {{{correctAnswer0}}} {{{suffix0}}}
correctAnswer0
27
prefix0
suffix0
months

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer027

months

Variant 1

DifficultyLevel

681

Question

The table below shows the relationship between the length of a gecko in centimetres and how old it is in months.


Age in months 4 6 8 10 12
Length (cm) 838\frac{3}{8} 812\frac{1}{2} 858\frac{5}{8} 834\frac{3}{4} 878\frac{7}{8}


If this pattern continues, how old would you expect a 9.5 cm gecko to be?

Worked Solution

Continuing the pattern adding 18\frac{1}{8}:

Age in months 12 14 16 18 20 22
Length (cm) 878\frac{7}{8} 9 918\frac{1}{8} 914\frac{1}{4} 938\frac{3}{8} 912\frac{1}{2}


∴\therefore Expected age = 22 months

Question Type

Answer Box

Variables

Variable nameVariable value
question
The table below shows the relationship between the length of a gecko in centimetres and how old it is in months.
>>| Age in months | 4|6|8|10|12| |:-:|:-:|:-:|:-:|:-:|:-:| | Length (cm) | 8$\frac{3}{8}$|8$\frac{1}{2}$|8$\frac{5}{8}$|8$\frac{3}{4}$|8$\frac{7}{8}$|

If this pattern continues, how old would you expect a 9.5 cm gecko to be?
workedSolution
Continuing the pattern adding $\frac{1}{8}$:
>>| Age in months | 12|14|16|18|20|22| |:-:|:-:|:-:|:-:|:-:|:-:|:-:| | Length (cm) | 8$\frac{7}{8}$|9|9$\frac{1}{8}$|9$\frac{1}{4}$|9$\frac{3}{8}$|9$\frac{1}{2}$|

$\therefore$ Expected age = {{{correctAnswer0}}} {{{suffix0}}}
correctAnswer0
22
prefix0
suffix0
months

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer022

months

Variant 2

DifficultyLevel

670

Question

The table below shows the relationship between the length of a garden worm in centimetres and how old it is in months.


Age in months 7 10 13 16 19
Length (cm) 235\frac{3}{5} 245\frac{4}{5} 3 315\frac{1}{5} 325\frac{2}{5}


If this pattern continues, how old would you expect a 4.4 cm worm to be?

Worked Solution

Continuing the pattern adding 15\frac{1}{5}:

Age in months 19 22 25 28 31 34
Length (cm) 325\frac{2}{5} 335\frac{3}{5} 345\frac{4}{5} 4 415\frac{1}{5} 425\frac{2}{5}


∴\therefore Expected age = 34 months

Question Type

Answer Box

Variables

Variable nameVariable value
question
The table below shows the relationship between the length of a garden worm in centimetres and how old it is in months.
>>| Age in months | 7|10|13|16|19| |:-:|:-:|:-:|:-:|:-:|:-:| | Length (cm) | 2$\frac{3}{5}$|2$\frac{4}{5}$|3|3$\frac{1}{5}$|3$\frac{2}{5}$|

If this pattern continues, how old would you expect a 4.4 cm worm to be?
workedSolution
Continuing the pattern adding $\frac{1}{5}$:
>>| Age in months | 19|22|25|28|31|34| |:-:|:-:|:-:|:-:|:-:|:-:|:-:| | Length (cm) | 3$\frac{2}{5}$|3$\frac{3}{5}$|3$\frac{4}{5}$|4|4$\frac{1}{5}$|4$\frac{2}{5}$|

$\therefore$ Expected age = {{{correctAnswer0}}} {{{suffix0}}}
correctAnswer0
34
prefix0
suffix0
months

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer034

months

Variant 3

DifficultyLevel

691

Question

The table below shows the relationship between the weight of a sea slug in grams and how old it is in days.


Age in days 4 8 12 16 20
Weight in grams (g) 1945\frac{4}{5} 20110\frac{1}{10} 2025\frac{2}{5} 20710\frac{7}{10} 21


If this pattern continues, how old would you expect a sea slug with a weight of 22.2 g to be?

Worked Solution

Continuing the pattern adding 310\frac{3}{10}:

Age in days 20 24 28 32 36
Weight in grams (g) 21 21310\frac{3}{10} 2135\frac{3}{5} 21910\frac{9}{10} 2215\frac{1}{5}


∴\therefore Expected age = 36 days

Question Type

Answer Box

Variables

Variable nameVariable value
question
The table below shows the relationship between the weight of a sea slug in grams and how old it is in days.
>>| Age in days| 4|8|12|16|20| |:-:|:-:|:-:|:-:|:-:|:-:| | Weight in grams (g) | 19$\frac{4}{5}$|20$\frac{1}{10}$|20$\frac{2}{5}$|20$\frac{7}{10}$|21|

If this pattern continues, how old would you expect a sea slug with a weight of 22.2 g to be?
workedSolution
Continuing the pattern adding $\frac{3}{10}$:
>>| Age in days| 20|24|28|32|36| |:-:|:-:|:-:|:-:|:-:|:-:| | Weight in grams (g) | 21|21$\frac{3}{10}$|21$\frac{3}{5}$|21$\frac{9}{10}$|22$\frac{1}{5}$|

$\therefore$ Expected age = {{{correctAnswer0}}} {{{suffix0}}}
correctAnswer0
36
prefix0
suffix0
days

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer036

days

Variant 4

DifficultyLevel

689

Question

The table below shows the relationship between the height of a seedling in millimetres and how old it is in days.


Age in days 20 24 28 32 36
Height of seedling (mm) 4078\frac{7}{8} 4114\frac{1}{4} 4158\frac{5}{8} 42 4238\frac{3}{8}


If this pattern continues, how old would you expect a seedling with a height of 43.5 mm to be?

Worked Solution

Continuing the pattern adding 38\frac{3}{8}:

Age in days 36 40 44 48
Height of seedling (mm) 4238\frac{3}{8} 4234\frac{3}{4} 4318\frac{1}{8} 4312\frac{1}{2}


∴\therefore Expected age = 48 days

Question Type

Answer Box

Variables

Variable nameVariable value
question
The table below shows the relationship between the height of a seedling in millimetres and how old it is in days.
>>| Age in days| 20|24|28|32|36| |:-:|:-:|:-:|:-:|:-:|:-:| | Height of seedling (mm) | 40$\frac{7}{8}$|41$\frac{1}{4}$|41$\frac{5}{8}$|42|42$\frac{3}{8}$|

If this pattern continues, how old would you expect a seedling with a height of 43.5 mm to be?
workedSolution
Continuing the pattern adding $\frac{3}{8}$:
>>| Age in days| 36|40|44|48| |:-:|:-:|:-:|:-:|:-:| | Height of seedling (mm) | 42$\frac{3}{8}$|42$\frac{3}{4}$|43$\frac{1}{8}$|43$\frac{1}{2}$|

$\therefore$ Expected age = {{{correctAnswer0}}} {{{suffix0}}}
correctAnswer0
48
prefix0
suffix0
days

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer048

days

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