4PM1/01R June 2024 Question 4: Quadratic Inequalities

Question 1

Show that the sector area A equals (r/2)(21 − r), using the arc length and angle.

Accepted Answer

Arc length: rθ = 21 − r, so θ = (21 − r)/r A = ½r²θ = (r²/2) × (21 − r)/r A = (r/2)(21 − r) Answer: A = (r/2)(21 − r) shown

Question 2

Find all values of r for which the sector area is greater than or equal to 27 cm².

Accepted Answer

(r/2)(21 − r) ≥ 27 r² − 21r + 54 ≤ 0 (r − 18)(r − 3) = 0 gives r = 3, 18 3 ≤ r ≤ 18 Answer: 3 ≤ r ≤ 18

Question 3

Using your values of r, write down the corresponding set of possible values of θ.

Accepted Answer

θ = (21 − r)/r r = 18 gives θ = 1/6; r = 3 gives θ = 6 1/6 ≤ θ ≤ 6 Answer: 1/6 ≤ θ ≤ 6

4PM1/01R Jun 2024, Question 4: Quadratic Inequalities