Skip to content

Course home

1.5 B: Algebra and functions

1.5 B: Algebra and functions

EasyMediumHard
1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768697071727374
Question 28

The height of a laser beam trajectory relative to a datum is modeled by the function H(x)H(x)H(x), where

H(x)=2∣3x−9∣+4,x≥0 H(x) = 2|3x - 9| + 4, \quad x \ge 0 H(x)=2∣3x−9∣+4,x≥0

The minimum point on the beam's path is at the vertex VVV.

a.

Determine the coordinates of VVV.

[2]
b.

Find the values of x x\,x for which H(x)=x+7H(x) = x + 7H(x)=x+7.

[4]
c.

Consider the family of linear paths defined by G(x)=kx+1G(x) = kx + 1G(x)=kx+1, where k k\,k is a constant. Given that the equation H(x)=G(x)H(x) = G(x)H(x)=G(x) has exactly two distinct solutions,

find the range of possible values for kkk.

[4]
Markscheme

1.5 B: Algebra and functions Questions

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

532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, 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). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank