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1.1 Algebra and functions

1.1 Algebra and functions

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Question 122

An engineer determines that the volume V(t)V(t)V(t) of a specialized industrial component is modeled by the polynomial:

V(t)=125t3+150t2+55t+6 V(t) = 125t^3 + 150t^2 + 55t + 6 V(t)=125t3+150t2+55t+6

where t t\,t is a dimension-scaling factor.

a.

Use the factor theorem to prove that (5t+1)(5t + 1)(5t+1) is a factor of V(t)V(t)V(t).

[2]
b.

Factorise V(t)V(t)V(t) completely.

[3]
c.

Hence, prove that 375m3+450m2+165m+18375m^3 + 450m^2 + 165m + 18375m3+450m2+165m+18 is a multiple of 18 when m m\,m is a positive whole number.

[3]
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1.1 Algebra and functions Questions

  1. A Level
  2. /Maths
  3. /1.1 Algebra and functions

306 exam-style questions on CCEA A Level Maths 1.1 Algebra and functions, covering 1.1.1 Algebra and functions, 1.1.2 Algebra and functions, 1.1.3 Algebra and functions, 1.1.4 Algebra and functions, 1.1.5 Algebra and functions, 1.1.6 Algebra and functions, 1.1.7 Algebra and functions, 1.1.8 Algebra and functions, 1.1.9 Algebra and functions, 1.1.10 Algebra and functions, 1.1.11 Algebra and functions, 1.1.12 Algebra and functions, 1.1.13 Algebra and functions, and 1.1.14 Algebra and functions. Each one has a worked solution and a mark scheme showing where the marks go.

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