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1.2 Algebra and Functions

1.2 Algebra and Functions

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Question 1

f(x)=2x3−5x2−4x+12f(x) = 2x^3 - 5x^2 - 4x + 12f(x)=2x3−5x2−4x+12

a.

Use the factor theorem to show that (x−2)(x - 2)(x−2) is a factor of f(x)f(x)f(x).

[2]
b.

Hence, show that f(x)=0f(x) = 0f(x)=0 only has two distinct real roots

[4]
c.

Sketch the graph of y=f(x)y = f(x)y=f(x)

[3]
d.

Deduce, giving a reason for your answer, the number of real roots of the equation:

2x3−5x2−4x+10=0 2x^3 - 5x^2 - 4x + 10 = 0 2x3−5x2−4x+10=0
[2]
e.

Given that k k\,k is a constant and the curve with equation y=f(x+k)y = f(x + k)y=f(x+k) passes through the origin, find the two possible values of kkk

[3]
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.

Question bank