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1.2 Algebra and Functions

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Question 32

The operating efficiency of a specialized geothermal heat pump is modeled by the function E(T)=T3+(k−3)T2+10T+cE(T) = T^3 + (k - 3)T^2 + 10T + cE(T)=T3+(k−3)T2+10T+c, where T T\,T is the temperature difference across the system in degrees Celsius, and k k\,k and c c\,c are constants with k>0k > 0k>0.

Given that (T−1)(T - 1)(T−1) is a factor of E(T)E(T)E(T):

a.

Show that k+c=−8k + c = -8k+c=−8.

[2]
b.

Given also that when E(T)E(T)E(T) is divided by (T+k)(T + k)(T+k), the remainder is -42:

Show that 3k2+10k−c−42=03k^2 + 10k - c - 42 = 03k2+10k−c−42=0.

[3]
c.

Hence find the value of k k\,k and the value of ccc.

[3]
d.

Find a quadratic expression g(T)g(T)g(T) such that E(T)=(T−1)g(T)E(T) = (T - 1)g(T)E(T)=(T−1)g(T).

[2]
Markscheme

1.2 Algebra and Functions Questions

  1. A Level
  2. /Maths
  3. /1.2 Algebra and Functions

302 exam-style questions on WJEC A Level Maths 1.2 Algebra and Functions, covering 1.2.1 Algebra and Functions, 1.2.2 Algebra and Functions, 1.2.3 Algebra and Functions, 1.2.4 Algebra and Functions, 1.2.5 Algebra and Functions, 1.2.6 Algebra and Functions, 1.2.7 Algebra and Functions, 1.2.8 Algebra and Functions, 1.2.9 Algebra and Functions, 1.2.10 Algebra and Functions, 1.2.11 Algebra and Functions, and 1.2.12 Algebra and Functions. Each one has a worked solution and a mark scheme showing where the marks go.

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