CAIE A-Level Mathematics A2 3.1.1 Modulus Equations Questions

Practise sketching and solving equations involving transformed and modulus functions.

Exam points

sketch transformed and modulus function graphs
solve equations and inequalities using graph intersections
interpret parameter effects on transformed functions

[Maximum number: 4]

Solve the inequality |2 x+3|>3|x+2|.

Square both sides:
$(2x+3)^2>9(x+2)^2.$
Then
$4x^2+12x+9>9x^2+36x+36,$
so
$5x^2+24x+27<0.$
Factorising,
(5x+9)(x+3)<0.
The critical values are x=-3 and $x=-\frac95$ . The product is negative between them, hence
$-3<x<-\frac95.$

B1 for the non-modular squared inequality or equivalent linear equations. M1 for solving the quadratic/equations. A1 for critical values -3 and $-\frac95$ . A1 for $-3<x<-\frac95$ , with strict inequalities.

Figure for Answer to Question CAIE A-Level Mathematics A2 3.1.1 Modulus Equations Questions question 1 — CAIE A-Level Mathematics A2

All question bank results loaded

CAIE A-Level Mathematics A2 3.1.1 Modulus Equations Questions question 1