WMA11 Jan 2019

4. WMA11/01 Edexcel IAL P1 January 2019, Q4 (Equations and Inequalities)

Figure 1 shows a line l1​​ with equation 2y = x and a curve C with equation​​ y = 2x -18x2​​ 

The region R, shown unshaded in​​ Figure 1, is bounded by the line l1, the curve C and a line l2​​ 

Given that l2​​ is parallel to the y-axis and passes through the intercept of C with the positive x-axis, identify the inequalities that define R.​​ 

(3)

SOLUTION​​ 

Since the region is enclosed between the solid lines, the inequalities must be either​​ ≤​​ or​​ ≥.​​ 

Keeping in view the above flash card.​​ 

Region is​​ 

• below/outside the quadratic curve; therefore,

y≤12x2-4x+3

• above the straight line PQ; therefore,​​ 

y≥-3x+7

• left to the line​​ x=2, so​​ 

x≤-2

y=2x-18x2

y=0

2x-18x2=0

16x-x2=0

x16-x=0

x=0,   x=16