The angle between the secant and tangent from (i)–(ii) is arctan(1/4). Find m>0.

01 / Standard#Your turn

Official paper · jm02-2022 · 3(c)(iii) · PDF 5

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Their positive slopes are m and m/2.

Hint 2

Apply the tangent of the angle difference.

Worked solution

m=2±√2.

Checks and common pitfalls: Both positive slopes can produce the same angle difference.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Express the angle tangent.
$\frac{m-m/2}{1+m^2/2}=\frac m{2+m^2}=\frac14$
Solve the quadratic; both roots are positive.
$m^2-4m+2=0\implies m=2\pm\sqrt2$

Think first. Reveal a hint when the class is ready.

2022 JM02