IGCSE Mathematics - International (0607) — October–November 2023, Paper 62

In one hour, hand H rotates clockwise from one number to the next (e.g. from 1.00 am to 2.00 am hand H rotates from 1 to 2, i.e. 30° in 60 minutes). Show that hand H rotates 0.5°…

This clock shows the time 1.10 am. Show that the clockwise angle from hand H to hand M at 1.10 am is 25°. (At 1.00 am the angle from M to H clockwise is 30°; H moves 0.5° per…

This clock shows the time 2.15 am. Show that the clockwise angle between the hands is 22.5°.

Complete the table using expressions of the form am + b for the clockwise angle (m minutes after h), for h = 1, 2, 3, 4. Use your expressions from Question 2(c) (h=1: 5.5m − 30)…

Semicircular arch model: this arch is a semicircle. The width is 8 m. Write down the height of the arch.

The formula for the radius is r = (4h² + w²)/(8h). Show that, when w = 8, r = h/2 + 8/h.

Use Pythagoras' Theorem to show that the model for r in terms of h and w is r = h²/w + w/4.