Year 10 Maths Feast 2015 Mains: Problems, Problems, ...... (20

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Year 10 Maths Feast 2015
Mains: Problems, Problems, ...... (20 marks)
There are six problems below – as a team you will score
maximum marks for correct solutions to FOUR of them.
You can attempt all six if you wish, but only hand in a maximum
of FOUR.
You can answer each question as a group or as individuals –
it’s up to you!
There is space on each sheet for rough working.
Write the solution to a problem in the answer box below the
question. Draw a diagram if that helps to explain your answer.
Set out your answers clearly so that the working can easily be
followed to score maximum marks.
Each question will score up to maximum of 5 marks.
The answer on its own will only score 1 mark.
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Problem A:
Sam wants to paper the wall in her bedroom with vertically striped paper. The wall is 2 metres
high and 6 metres wide and has no windows or doors.
Each roll of paper is 56cm wide and 10m long and costs £4.99.
How much will it cost to paper the wall?
Rough working space (will not be marked)
Problem A: Answer (explain your solution fully)
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Problem B:
The loading bay of a van is approximately a cuboid of internal dimensions 1.5m wide, 1.5m high
and 3m long.
What is the maximum number of boxes of dimensions 40cm by 50cm by 30cm that can be fitted
in the loading bay?
Rough working space (will not be marked)
Problem B: Answer (explain your solution fully)
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Problem C:
The doctor has told Graham that he needs to take 5ml of medicine every 6 hours and has given
him a bottle containing 25cl.
If Graham takes his first dose at noon on 9 th September, when will he take his last dose?
Rough working space (will not be marked)
Problem C: Answer (explain your solution fully)
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Problem D:
Hayley wants to store her photos on a 1GB SD memory card.
Each image is between 2MB and 5MB in size.
How many images can Hayley store?
Rough working space (will not be marked)
Problem D: Answer (explain your solution fully)
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Problem E:
In a field there is a shed on a rectangular base, 10 metres long and 6 metres wide. A goat is
tethered to a rope 12 metres long, attached to a corner of the shed.
The goat cannot get into the shed, there is grass growing in every part of the field outside the
shed and the goat cannot reach the edge of the field.
Find the area of grass the goat can graze, in terms of π.
Rough working space (will not be marked)
Problem E: Answer (explain your solution fully)
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Problem F:
The school Sports Day has separate 100m races, 200m races and 400m races for girls and
boys, and for each year group from 7 to 10 inclusive.
Each 100m race takes about 30 seconds, each 200m race takes about 1 minute and each
400m race takes about 2 minutes.
If it takes 5 minutes to set up each race, how long will Sports Day last?
Rough working space (will not be marked)
Problem F: Answer (explain your solution fully)