SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

  • Login
  • Get Help
  • About

PATTERNS, FUR1 2010 VCAA 9 MC

Before he began training, Jethro’s longest jump was 5.80 metres.
After the first month of training, his longest jump had increased by 0.32 metres.
After the second month of training, his longest jump had increased by another 0.24 metres.
After the third month of training, his longest jump had increased by another 0.18 metres.

If this pattern of improvement continues, Jethro’s longest jump, correct to two decimal places, will be closest to

A.    `6.54\ text(metres.)`

B.    `6.68\ text(metres.)`

C.    `7.00\ text(metres.)`

D.    `7.08\ text(metres.)`

E.    `7.25\ text(metres.)`

Show Answers Only

`D`

Show Worked Solution

`text(Sequence of “increases” is)`

♦ Mean mark 38%.

`0.32, 0.24, 0.18,\ …`

`text(GP where)\ \ \ a` `= 0.32, and`
`r` `=t_(2)/t_(1)=0.24/0.32=0.75`

`text(S)text(ince)\ \ \|\ r\ |< 1,`

`S_oo` `=a/(1 – r)`
  `=0.32/(1 – 0.75)`
  `=1.28`

 

`:.\ text(Jethro’s longest jump will be  5.8 + 1.28 = 7.08 m.)`

`=> D`

 

Filed Under: APs and GPs - MC

Copyright © 2014–2025 SmarterEd.com.au · Log in