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1.1.10 Algebra and functions

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Question 43

A theoretical model for the potential energy $E$ in a micro-system is given by the function

E(t) = 27t^3 + 54t^2 + 33t + 6

where $t$ is a dimensionless time parameter.

Use the factor theorem to prove that $(3 t + 1)$ is a factor of $E (t)$ .

[2]

Factorise $E (t)$ completely.

[3]

Hence, prove that $108n^3 + 216n^2 + 132n + 24$ is a multiple of 24 when $n$ is a positive integer.

[3]

Markscheme

1.1.10 Algebra and functions Questions

A Level
Maths
1.1.10 Algebra and functions

64 exam-style questions on CCEA A Level Maths 1.1.10 Algebra and functions. Each one has a worked solution and a mark scheme showing where the marks go.

1.1.10 Algebra and functions

Question bank

1.1.10 Algebra and functions

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

Question 43

A theoretical model for the potential energy $E$ in a micro-system is given by the function

E(t) = 27t^3 + 54t^2 + 33t + 6

where $t$ is a dimensionless time parameter.

Use the factor theorem to prove that $(3 t + 1)$ is a factor of $E (t)$ .

[2]

Factorise $E (t)$ completely.

[3]

Hence, prove that $108n^3 + 216n^2 + 132n + 24$ is a multiple of 24 when $n$ is a positive integer.

[3]

Markscheme

1.1.10 Algebra and functions Questions

A Level
Maths
1.1.10 Algebra and functions

64 exam-style questions on CCEA A Level Maths 1.1.10 Algebra and functions. Each one has a worked solution and a mark scheme showing where the marks go.