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1.1.10 Algebra and functions

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Question 58

Let $f(x) = 36x^3 - 27x^2 - 4x + 3$ .

Use the factor theorem to show that $(3 x - 1)$ is a factor of $f (x)$ .

[2]

Express $f (x)$ as a product of three linear factors.

[3]

A mechanical engineer modeling the resonance of a suspension bridge determines that the equilibrium angles $θ\theta$ are given by the equation:

\frac{12\sec^2 \theta + \cos \theta}{4} = 2.25\sec \theta + \frac{1}{3}

Prove that there are no real values of $θ\theta$ that satisfy this stability condition.

[4]

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 58

Let $f(x) = 36x^3 - 27x^2 - 4x + 3$ .

Use the factor theorem to show that $(3 x - 1)$ is a factor of $f (x)$ .

[2]

Express $f (x)$ as a product of three linear factors.

[3]

A mechanical engineer modeling the resonance of a suspension bridge determines that the equilibrium angles $θ\theta$ are given by the equation:

\frac{12\sec^2 \theta + \cos \theta}{4} = 2.25\sec \theta + \frac{1}{3}

Prove that there are no real values of $θ\theta$ that satisfy this stability condition.

[4]

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.