smc-1056-20-Cubic denom

Calculus, EXT2 C1 2024 HSC 12b

Use partial fractions to find (3 marks)

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Calculus, EXT2 C1 2022 SPEC1 4

Find . (4 marks)

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Mean mark 55%.

Calculus, EXT2 C1 2022 HSC 12d

Using partial fractions, evaluate , giving your answer in the form , where is a function of . (4 marks)

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Mean mark 85%.

Calculus, EXT2 C1 2021 HSC 11f

Express as a sum of partial fractions over . (3 marks)

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Calculus, EXT2 C1 2003 HSC 1d

Find the real numbers and such that

(2 marks)

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Hence find (2 marks)

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ii.

Calculus, EXT2 C1 2018 HSC 11c

By writing in the form ,

find . (4 marks)

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Calculus, EXT2 C1 2007 HSC 1e

It can be shown that

(Do NOT prove this.)

Use this result to evaluate (4 marks)

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$ $

Calculus, EXT2 C1 2006 HSC 1c

Given that can be written as

,

where and are real numbers, find (3 marks)

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Hence find (2 marks)

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ii.

Calculus, EXT2 C1 2010 HSC 1c

Find . (3 marks)

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Calculus, EXT2 C1 2011 HSC 1c

Find real numbers and such that

(2 marks)

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Hence, find (2 marks)

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ii.