Skip to content
MathsGenie logo
Open app

Course home

  1. A Level
  3. Maths AQA
  5. Question bank

1.5 B: Algebra and functions

EasyMediumHard
123456789101112131415
Question 12
a.

Sketch the curve with equation

y=x2(2x−a) y = x^2(2x - a) y=x2(2x−a)

where a>0a > 0a>0.

[3]
bi.

The polynomial p(x)p(x)p(x) is given by

p(x)=x2(2x−a)−64 p(x) = x^2(2x - a) - 64 p(x)=x2(2x−a)−64

It is given that x−8x - 8x−8 is a factor of p(x)p(x)p(x). Use the factor theorem to show that a=15a = 15a=15.

[3]
bii.

State the transformation which maps the curve with equation y=x2(2x−15)y = x^2(2x - 15)y=x2(2x−15) onto the curve with equation y=x2(2x−15)−64y = x^2(2x - 15) - 64y=x2(2x−15)−64.

[1]
biii.

The polynomial x2(2x−15)−64x^2(2x - 15) - 64x2(2x−15)−64 can be written as (x−8)(2x2+bx+c)(x - 8)(2x^2 + bx + c)(x−8)(2x2+bx+c). Without finding the values of bbb and ccc, use your knowledge of the transformation in part (b)(ii) and the sketch in part (a) to explain why

b2<8c b^2 < 8c b2<8c
[4]

1.5 B: Algebra and functions Questions

  1. A Level
  2. /Maths
  3. /1.5 B: Algebra and functions

Practise AQA A Level Maths 1.5 B: Algebra and functions with exam-style questions for A Level Maths. 358 questions covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

Question bank