Mathematics AI: ALGEBRA-FUNCTIONS - ROOTS Topical Past Paper Questions

[Maximum mark: 6] A function is defined by $ f(x)=\frac{4}{x}-3 $, for $ -6 \leq x \leq 10 $, $ x \neq 0 $. (a) Find $ f(10) $. (b) Find the range of $ f $. (c) Find $ f^{-1}(-2) $.

[Maximum mark: 12] A hygiene inspector lives in Town A and must visit restaurants in five towns (B–F), before returning to A. The inspector must not repeat any of the towns. The distances, in km, between the six towns are shown in the table. (a) Starting at A, use the nearest nei…

[Maximum mark: 12] A plane takes off from a horizontal runway. Let point O be the point where the plane begins to leave the runway and x be the horizontal distance, in km, of the plane from O. The function h models the vertical height, in km, of the nose of the plane from the hor…