3. WMA11/01 Edexcel IAL P1 Oct 2021 Q3 (Quadratic & Equations and Inequalities)
(i) Solve
(3)
(ii)
Figure 1 shows a sketch of the curve C and the straight line l.
The infinite region R, shown shaded in Figure 1, lies in quadrants 2 and 3 and is bounded by C and l only.
Given that
l has a gradient of 3
C has equation
C and l intersect on the negative x‑axis use inequalities to define the region R.
(3)
SOLUTION
i-
Most of the students get confused in this question. They would simply divide 3 by 4 and believes that the solution of x is x<3/4 which is incorrect. This issue results when students fail to understand that they have inequality nor the equation. When solving inequalities, always remember that dividing or mutiplying any term by a negative number results in change of the inequality sign. Righnow, in our case, we aren’t told whether x is greater than 0 or not. Therefore, to avoid any possibility of dividing or multiplying by negative value of x, let us multiply both sides of inequality by x2. In this way, we may would have a positive number multiplying the inequality and there will be no worries of swaping the sign of inequality.
Cinsidering inequality as equation to find the critical points.
Since the inequality sign is >, so the region in the graph would be as shown below (yellow shaded portion of curve).
ii-
First, we need to find the equation of line by using point-slope formula. The line passes through one of the solution of curve and has the gradient 3.
For the curve, when
Therefore, the line and curve intersect at point (-5, 0)
Using this point and the gradient of line provided in question to find the equation of line.
Since the region is enclosed between the solid lines, the inequalities must be either
Keeping in view the above flash card.
Region is
below/outside the quadratic curve; therefore,
above the straight line; therefore,
leftside of point x= -5
