Download Year 10 Maths Feast 2017 Practice

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Year 10 Maths Feast 2017
Practice - 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:
Use  =3. Circumference of a circle =2 r. Volume of a cylinder =  r 2h.
Ryan, Sarah and Tara are each given a piece of rectangular paper with an area of 324 cm 2.
Ryan made a cylinder with a radius of 2 cm.
r
Sarah made a cylinder with a radius of 3 cm.
Tara made a cylinder with a radius of 4 cm.
Circumference
Who made the cylinder with the largest volume?
Height (h)
Rough working space (will not be marked)
Problem A: Answer (explain your solution fully)
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Problem B:
Eight drivers took part in a charity motor race (Alonso, Button, Chilton, Davidson, Ericsson,
Fango, Grosjean and Hamilton). Each driver has a qualifying position and a race finishing
position. From the information given below, you must determine the qualifying order and race
finishing order.








The 8th qualifier finished in 3rd position.
Davidson qualified one position above Grosjean, but finished one position behind him.
Alonso qualified and finished in 2nd position.
The 3rd qualifier won the race.
Ericsson finished the race last.
Button finished below his qualifying position of 6th.
Hamilton finished 5 places below his qualifying position.
Chilton finished 2 places behind Fango.
Rough working space (will not be marked)
Problem B: Answer (complete the table below)
Qualifying
1st
2nd
3rd
4th
5th
6th
7th
8th
Race Finish
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Problem C:
In a sequence:
u1  2, u2  3, u3  4, u4  5.
1
Each following term is
.
product of the previous four terms
For example:
1
1
u5 

2  3  4  5 120
Find u6 , u 7 , u8 , u 9 , u10 .
Explain what is happening?
What is u94 ?
Rough working space (will not be marked)
Problem C: Answer (explain your solution fully)
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Problem D:
Moses completed an 8 km training run.
He recorded his time at the end of each kilometre that he ran (see the table below).
Kilometre
1st
2nd
3rd
4th
5th
6th
7th
8th
Time (Minutes:Seconds)
7:15
13:39
20:11
26:08
32:04
38:13
44:01
49:31
What was his best time for five consecutive kilometres?
Which kilometre did Moses run the fastest?
Moses is going to run in a 5 kilometre race and sets himself a target race time.
What time should he set himself?
Problem D: Answer (explain your solution fully)
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Problem E:
x2
5
x3
Examples of Quadratic Equations: x 2  16, ( x  8)2  4, 2 x 2  x  3  5
Examples of Inequalities: 2 x  4  12, 3x -1  x  2, 10  2 x  14
Examples of Linear Equations: 2 x  1  7, 3x  1  2 x  4,
Below is a table. Your task is to complete the table, by entering an appropriate
equation or inequality that will satisfy the conditions given in the row and column
of each entry.
Rough working space (will not be marked)
Linear Equation
Solution is x = 2
Solutions lie
between 3 and 7
No solutions
Quadratic Equation
Inequality
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Problem F:
A coach tour takes a group of 30 people to a museum.
The entry fee for the museum is £4 for adults, £3 for over 65's and £1.50 for children.
If the museum collects £60 in entry fees, how many adults, over 65's and children are there in
the group?
Hint: there are three possible solutions to this and you will need all three to get all of the marks,
but you will get some marks for one solution.
Rough working space (will not be marked)
Problem F: Answer (explain your solution fully)