Topical Revision Paper 6 Unit 6 Modulus Functions

Topical Revision Paper 6 Term 2 Unit 6: Modulus Functions Question 1: Sketch the graph 3y x a   where 03 a , showing clearly the intercepts with the axes. [3] Solution: G1 – correct V-shaped G1 – V-shape shifted to be right by 3 units. G1 – V-shape shifted downwards by a units. Question 2: Sketch the graphs of 2yx and 2 34y x x   for the domain 25 x   on the same axes and hence state the number of solutions of the equation 22 3 4x x x    . [5] Solution:

No of solutions = 4 Question 3: The diagram shows part of the graph of 𝑦 = 4 − |2𝑥 − 3|. (i) Find the coordinates of the points A, B and C. [4] (ii) Solve the inequality 4 − |2𝑥 − 3| < 𝑥 − 2. [3] (i) B ( , 4)

A ( , 0) C ( , 0) (ii) When 32 3 0, . . 2x i e x   2 3 6xx   33 (after combining with ) 2xx   When 32 3 0, . . 2x i e x   2 3 6xx   33 (after combining with ) 2xx   x < ̶ 3 or x > 3 Question 5: Sketch the graphs of 2y = |x – 2| and y = x + 2 for –3 ≤ x ≤ 3. Hence, or otherwise, solve the equation 2 2.2 x x  [5] Solution: 2y = |x – 2| 2 2 xy 

2 3x 2 22 12 2 3 12 2 3 x x x x x x       