Number_2026-03-656

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

656

Question

Geordie was working on the following number pattern:
727^2 = 4 ×\times 10 + 9
828^2 = 5 ×\times 11 + 9
929^2 = 6 ×\times 12 + 9
10210^2 = 7 ×\times 13 + 9

Following this pattern, what is the value of 97297^2?

Worked Solution

Working with the pattern
727^2 = (7−3) × (7+3)+97 - 3)\ \times\ (7 + 3) + 9
828^2 = (8−3) × (8+3)+98 - 3)\ \times\ (8 + 3) + 9
929^2 = (9−3) × (9+3)+99 - 3)\ \times\ (9 + 3) + 9
10210^2 = (10−3) × (10+3)+910 - 3)\ \times\ (10 + 3) + 9

Therefore
97297^2 = (97−3) × (97+3)+9(97 - 3)\ \times\ (97 + 3) + 9
= 94 ×100+994\ \times 100 + 9
= 9409

Question Type

Answer Box

Variables

Variable nameVariable value
question
Geordie was working on the following number pattern:
>| | | | ------: | --------------------------- | | $7^2$ | \= 4 $\times$ 10 + 9 | | $8^2$ | \= 5 $\times$ 11 + 9 | | $9^2$ | \= 6 $\times$ 12 + 9 | | $10^2$ | \= 7 $\times$ 13 + 9 |

Following this pattern, what is the value of $97^2$?
workedSolution
Working with the pattern
>| | | | ------: | --------------------------- | | $7^2$ | \= ($7 - 3)\ \times\ (7 + 3) + 9$ | | $8^2$ | \= ($8 - 3)\ \times\ (8 + 3) + 9$ | | $9^2$ | \= ($9 - 3)\ \times\ (9 + 3) + 9$ | | $10^2$ | \= ($10 - 3)\ \times\ (10 + 3) + 9$ |

Therefore >| | | | ------: | --------------------------- | | $97^2$ | \= $(97 - 3)\ \times\ (97 + 3) + 9$ | | | \= $94\ \times 100 + 9$ | ||= {{{correctAnswer0}}}|
correctAnswer0
9409
prefix0
suffix0

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
correctAnswer09409

Variant 1

DifficultyLevel

655

Question

Tariq was working on the following number pattern:
11211^2 = 121
1112111^2 = 12 321
111121111^2 = 1 234 321
11111211111^2 = 123 454 321

Following this pattern, what is the value of 1111112111111^2?

Worked Solution

Working with the pattern
11211^2 = 121
1112111^2 = 12 321
111121111^2 = 1 234 321
11111211111^2 = 123 454 321

Therefore
1111112111111^2 = 12 345 654 321

Question Type

Answer Box

Variables

Variable nameVariable value
question
Tariq was working on the following number pattern:
>| | | | --------: | ---------------- | | $11^2$ | \= 121 | | $111^2$ | \= 12 321 | | $1111^2$ | \= 1 234 321 | | $11111^2$ | \= 123 454 321 |

Following this pattern, what is the value of $111111^2$?
workedSolution
Working with the pattern
>| | | | --------: | ---------------- | | $11^2$ | \= 121 | | $111^2$ | \= 12 321 | | $1111^2$ | \= 1 234 321 | | $11111^2$ | \= 123 454 321 |

Therefore >| | | | ---------: | ----------------------- | | $111111^2$ | \= {{{correctAnswer0}}}|
correctAnswer0
12 345 654 321
prefix0
suffix0

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
correctAnswer012 345 654 321

Variant 2

DifficultyLevel

657

Question

Bianca was working on the following number pattern:
626^2 = 4 ×\times 8 + 4
727^2 = 5 ×\times 9 + 4
828^2 = 6 ×\times 10 + 4
929^2 = 7 ×\times 11 + 4

Following this pattern, what is the value of 22222^2?

Worked Solution

Working with the pattern
626^2 = (6−2) × (6+2)+4(6 - 2)\ \times\ (6 + 2) + 4
727^2 = (7−2) × (7+2)+4(7 - 2)\ \times\ (7 + 2) + 4
828^2 = (8−2) × (8+2)+4(8 - 2)\ \times\ (8 + 2) + 4
929^2 = (9−2) × (9+2)+4(9 - 2)\ \times\ (9 + 2) + 4

Therefore
22222^2 = (22−2) × (22+2)+4(22 - 2)\ \times\ (22 + 2) + 4
= 20 × 24 + 420\ \times\ 24\ +\ 4
= 480+4480 + 4
= 484

Question Type

Answer Box

Variables

Variable nameVariable value
question
Bianca was working on the following number pattern:
>| | | | ----: | ---------------------------- | | $6^2$ | \= 4 $\times$ 8 + 4 | | $7^2$ | \= 5 $\times$ 9 + 4 | | $8^2$ | \= 6 $\times$ 10 + 4 | | $9^2$ | \= 7 $\times$ 11 + 4 |

Following this pattern, what is the value of $22^2$?
workedSolution
Working with the pattern
>| | | | ----: | ------------------------------------ | | $6^2$ | \= $(6 - 2)\ \times\ (6 + 2) + 4$ | | $7^2$ | \= $(7 - 2)\ \times\ (7 + 2) + 4$ | | $8^2$ | \= $(8 - 2)\ \times\ (8 + 2) + 4$ | | $9^2$ | \= $(9 - 2)\ \times\ (9 + 2) + 4$ |

Therefore >| | | | -----: | ------------------------------------- | | $22^2$ | \= $(22 - 2)\ \times\ (22 + 2) + 4$ | | | \= $20\ \times\ 24\ +\ 4$ | | | \= $480 + 4$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
484
prefix0
suffix0

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
correctAnswer0484

Variant 3

DifficultyLevel

658

Question

Kofi was working on the following number pattern:
626^2 = 4 ×\times 7 + 8
727^2 = 5 ×\times 8 + 9
828^2 = 6 ×\times 9 + 10
929^2 = 7 ×\times 10 + 11

Following this pattern, what is the value of 99299^2?

Worked Solution

Working with the pattern
626^2 = (6−2) × (6+1)+(6+2)(6 - 2)\ \times\ (6 + 1) + (6 + 2)
727^2 = (7−2) × (7+1)+(7+2)(7 - 2)\ \times\ (7 + 1) + (7 + 2)
828^2 = (8−2) × (8+1)+(8+2)(8 - 2)\ \times\ (8 + 1) + (8 + 2)
929^2 = (9−2) × (9+1)+(9+2)(9 - 2)\ \times\ (9 + 1) + (9 + 2)

Therefore
99299^2 = (99−2) × (99+1)+(99+2)(99 - 2)\ \times\ (99 + 1) + (99 + 2)
= 97 × 100+10197\ \times\ 100 + 101
= 9700+1019700 + 101
= 9801

Question Type

Answer Box

Variables

Variable nameVariable value
question
Kofi was working on the following number pattern:
>| | | | ----: | ---------------------------- | | $6^2$ | \= 4 $\times$ 7 + 8 | | $7^2$ | \= 5 $\times$ 8 + 9 | | $8^2$ | \= 6 $\times$ 9 + 10 | | $9^2$ | \= 7 $\times$ 10 + 11 |

Following this pattern, what is the value of $99^2$?
workedSolution
Working with the pattern
>| | | | ----: | ---------------------------------------- | | $6^2$ | \= $(6 - 2)\ \times\ (6 + 1) + (6 + 2)$ | | $7^2$ | \= $(7 - 2)\ \times\ (7 + 1) + (7 + 2)$ | | $8^2$ | \= $(8 - 2)\ \times\ (8 + 1) + (8 + 2)$ | | $9^2$ | \= $(9 - 2)\ \times\ (9 + 1) + (9 + 2)$ |

Therefore >| | | | -----: | ------------------------------------------- | | $99^2$ | \= $(99 - 2)\ \times\ (99 + 1) + (99 + 2)$ | | | \= $97\ \times\ 100 + 101$ | | | \= $9700 + 101$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
9801
prefix0
suffix0

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
correctAnswer09801

Variant 4

DifficultyLevel

659

Question

Yara was working on the following number pattern:
5 × 75\ \times\ 7 = 62−16^2 - 1
6 × 86\ \times\ 8 = 72−17^2 - 1
7 × 97\ \times\ 9 = 82−18^2 - 1
8 × 108\ \times\ 10 = 92−19^2 - 1

Following this pattern, what is the value of  49×51\ 49 \times 51?

Worked Solution

Working with the pattern
5 × 75\ \times\ 7 = (5+1)2−1(5 + 1)^2 - 1
6 × 86\ \times\ 8 = (6+1)2−1(6 + 1)^2 - 1
7 × 97\ \times\ 9 = (7+1)2−1(7 + 1)^2 - 1
8 × 108\ \times\ 10 = (8+1)2−1(8 + 1)^2 - 1

Therefore
49 × 5149\ \times\ 51 = (49+1)2−1(49 + 1)^2 - 1
= 502−150^2 - 1
= 2500−12500 - 1
= 2499

Question Type

Answer Box

Variables

Variable nameVariable value
question
Yara was working on the following number pattern:
>| | | | ---------------: | ----------------------- | | $5\ \times\ 7$ | \= $6^2 - 1$ | | $6\ \times\ 8$ | \= $7^2 - 1$ | | $7\ \times\ 9$ | \= $8^2 - 1$ | | $8\ \times\ 10$ | \= $9^2 - 1$ |

Following this pattern, what is the value of $\ 49 \times 51$?
workedSolution
Working with the pattern
>| | | | ---------------: | ----------------------- | | $5\ \times\ 7$ | \= $(5 + 1)^2 - 1$ | | $6\ \times\ 8$ | \= $(6 + 1)^2 - 1$ | | $7\ \times\ 9$ | \= $(7 + 1)^2 - 1$ | | $8\ \times\ 10$ | \= $(8 + 1)^2 - 1$ |

Therefore >| | | | ----------------: | ----------------------- | | $49\ \times\ 51$ | \= $(49 + 1)^2 - 1$ | | | \= $50^2 - 1$ | | | \= $2500 - 1$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
2499
prefix0
suffix0

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
correctAnswer02499

Tags

  • nap_nc
  • staging_suejones