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(a) The clock shows the time 1.00 am.
(i) Write down the mathematical name for the type of angle shown. .............................................. [1]
(ii) Explain why hand $H$ rotates through $360^{\circ}$ in 12 hours. ........................................................................................................................... [1]
(iii) Write down the calculation to show that the clockwise angle from hand $M$ to hand $H$ is $30^{\circ}$. [1]
(iv) Write down a calculation to show that the anticlockwise angle from hand $M$ to hand $H$ is $330^{\circ}$. [1]
(b) This clock shows the time 4.00 am.
(i) Work out the clockwise angle from hand $M$ to hand $H$. .............................................. [2]
(ii) Work out the anticlockwise angle from hand $M$ to hand $H$. .............................................. [2]
(c) Write down the clockwise angle from hand $M$ to hand $H$ at 6.00 am. .............................................. [1]
(d) Complete the table using part (b) and part (c).
You may use the clock diagrams and patterns to help you.
[Table_1]
[4]
(e) Find an expression for the clockwise angle at hour $x$. .............................................. [1]
(f) Write down the rule for continuing the sequence in the anticlockwise angle column. ........................................................................................................................... [1]
(g) Find an expression for the anticlockwise angle at hour $x$. .............................................. [1]
526
574
518
(a) In one hour, hand $H$ rotates clockwise from one number to the next number. For example, from 1.00 am to 2.00 am hand $H$ rotates from 1 to 2.
Show that hand $H$ rotates $0.5^\circ$ in one minute.
[1]
(b) In one hour, hand $M$ rotates through a full circle.
Show that hand $M$ rotates $6^\circ$ in one minute.
[1]
524
549
514
(a) This clock shows the time 1.10 am.
(i) Use Question 2(a) to find the angle that hand $H$ has rotated in the 10 minutes since 1.00 am.
......................................................... [2]
(ii) Use Question 2(b) to find the angle that hand $M$ has rotated in the 10 minutes since 1.00 am.
......................................................... [2]
(iii) Show that the clockwise angle from hand $H$ to hand $M$ at 1.10 am is $25^\circ$. [1]
(b) Complete the table using your results from part (a)(i) and part (a)(ii).
You may use the clock diagrams and patterns to help you.
[Table_1]
......................................................... [6]
(c) Find an expression, in terms of $m$, for the clockwise angle between the hands.
......................................................... [2]
(d) Find how many minutes and seconds after 1.00 am the clockwise angle is $270^\circ$.
Give your answer correct to the nearest second.
..................... minutes .................... seconds [5]
575
574
600
