Leaving Cert Higher Level Maths 2021 Question 7

Question 7 from leaving cert higher level maths 2021 paper 1 is a sequences and series question based on the swing of a pendulum grandfather clock. In part a we find the first few terms of the sequence and then the 25th term t25. We then use the Sn sum to n formula followed by finding the first term that is less than a given value. In part b we use the arc length formula to find the size of an angle and then use the sum to infinity formula to find the total distance the pendulum travelled.

[@SimpleScienceandMaths]

For question a(ii) the answer should be 3.6cm. Not sure what I put into my calculator! 45(0.9)^24 is correct.

[@MathsGrinds]

In part (iii) why not simply say (128.915/360) * 2 * pi * 100 = 225 cm? This could be done in one line! The accumulated angle and arc length differ only by a constant of proportionality.

[@lokkj1641]

for the last bit I got the same answer but did it by looking at the ratio of the angle : arc length. Will I be marked down for not using the formulas?

[@SimpleScienceandMaths]

No not at all, as long as what you did makes sense mathematically you will get the marks. It didn't specify that you had to use any specific method.

[@victoriaboyd5439]

why are parts aiii and biii not multiplied by 2 as the pendulum will go through these values twice on its path

[@SimpleScienceandMaths]

a swing is counted as moving one way only, so if it goes forward and back that is two swings

[@kd240889]

For part (iv) if I said 30 instead of 31, do you think I would lose many marks?

[@SimpleScienceandMaths]

A few but you'd probably get most marks

[@kd240889]

@@SimpleScienceandMaths alright thanks