You're viewing 1 free preview question for Maths AI SL — subscribe to unlock 74 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Geometric Sequences and Series · Paper 2 — Free Maths AI SL Practice Questions

1MasterySAQ-SDefinition and general term of geometric sequences10 marksPaper 2~15 min

A ball is dropped from a height of

2\,\text{m}

. On each bounce, it rebounds to

60\%

of its previous height. The height of the ball on the

n

th bounce is

h_n

metres, modelled by a geometric sequence where

n = 1

is the first bounce.

(a)

Write down the values of

u_1

and

r

for this geometric sequence, and hence write down an expression for

h_n

. [2 marks]

(b)

Calculate the height of the ball on the 5th bounce. [2 marks]

(c)

Determine the smallest value of

n

for which

h_n < 0.1\,\text{m}

. [2 marks]

(d)

The ball is considered to have "effectively stopped bouncing" once the total vertical distance it has travelled (both falling and rising) from the moment is dropped exceeds

9.5\,\text{m}

. Determine whether this occurs before or after the 10th bounce, justifying your answer. [4 marks]

Solutions

Questions 2-75

Unlock these questions with Premium

That's every free question here — 1 of 75.

+74 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade