Go For Gold

1
Go For Gold

• Preparing for UKMT Senior Maths Challenge

Dr Neill Cooper, Wilsons School
2
About SMC

• Run by the UK Maths Trust
• You can put good results on your UCAS personal
  statement/reference
• About 90,000 students take the test
• Of these 7 get Gold, 13 Silver
• NO CALCULATORS

3
SMC scoring

• You start with 25 marks
• Every question from the easiest to the most
  difficult is worth 4 marks
• Every wrong answer loses 1 mark
• In the 2005 paper you needed 71 for a silver, 83
  for a gold and 96 to qualify for the BMO
• So 12 correct answer for a silver, and 15 for a
  gold.

4
SMC scoring

• In the 2007 paper you needed 61 for a silver, 75
  for a gold and 88 to qualify for the BMO
• So 9 correct answer for a silver, and 13 for a
  gold.

5
SMC scoring

• 12 (or 9) correct answer for a silver, and 15 (or
  13) for a gold.
• Allowing for a few wrong answers this means that
  questions 11 to 20 are very important

6
Question types
7
Question types

• Geometry and spatial awareness
• Logic and reasoning
• Number and arithmetic

8
Question types

• Geometry and spatial awareness
• Logic and reasoning
• Number and arithmetic

Questions 1 to 10
9
Question types

• Geometry and spatial awareness
• Logic and reasoning
• Number and arithmetic

10
Q11

• Radii go from 1 to 12
• Area of edges is 2prh
• So total is 2px2x1 2px2x1 ... 2px2x12.
• Changing term is a triangular number, so sum 1 to
  12 is 13x678
• Area of edges is 78x4p312p
• Area top is same as base area px122 144p
• Total area 456 p

11
Q13
abcde2v2w2x2y2z5180900
a
e
z
z
y
180-z
v
180-y
y
180-v
v
180-w
180-x
b
w
x
d
w
x
c
5180-(vwxyz) 540
vwxyz 360
abcde180
12
Q13
a
e
180-(bd)
180-(ac)
180-(ce)
180-(ad)
180-(be)
b
d
c
180-(be)180-(ac) ... 540
900 -2(abcde) 540
abcde 180
13
Q17
Area of square (2v2)2 (4 2 2v2) 6
2v2
1
1
1
1
v2
Area of triangle 1/2
Area 4 triangles 2
Total Area 8 2v2
14
Q18
v3
1
If linear scale factor is x Then volume scale
factor is x3
(v3)3 3 v3
15
Question types

• Geometry and spatial awareness
• Logic and reasoning
• Number and arithmetic

16
Q12

• Simpler to solve if we square
• x is between 152 225 and 162 256
• Multiples of 7 21 10 210
• 210 21 231 then 238, 245, 252
• So 4 values of x

17
Q15

• If 1st statement is true then 2nd is also true,
  so first must be false Alice is not the mother.
• Similarly the 3rd cannot be true so Beth is not
  the mother.
• If 2nd true then Diane must be the mother, so 4th
  also true. So 2nd statement is false.
• So only 4th statement is true. Hence Diane or
  Ella is themother.
• But if Diane mother then 2nd statement is true.
  So Ella must be the mother.

18
Q19

• y x x has only one y value for each x value,
  so B is false.
• When x is negative y is negative, so only A and B
  correct.
• When x is positive y x2 so only A and D
  correct.
• Hence A is correct.

19
Question types

• Geometry and spatial awareness
• Logic and reasoning
• Number and arithmetic

20
Q14

• Use trial and error
• 12 1 leaves remainder 1
• 22 4 leaves remainder 4
• 32 9 leaves remainder 3
• 42 16 leaves remainder 4 again
• 52 25 leaves remainder 1 again
• 62 36 leaves remainder 0
• So 2 cannot occur

21
Q14

• Use algebra to show that all square numbers are
  of the form 3m or 3m1, and can ever be 3m2.
• So 2 cannot occur
• Think of a square number whose last digit is 2.
• You cant find any square number ending in 2, 3,
  7 or 8!

22
Q16

• Total arrangements 2 x 5 x 5 x 3 150
• Think of who is on the sub bench.
• Cannot have subbed all 4so 1 x 4 x 4 x 2 32
  not allowed
• Total 150 32 118

23
Q20
2
v3
2
Area v3
24
(No Transcript)
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Future Twilight EventsAll 4pm on Mondays

• 13th October Oxford Entrance paper
• 17th November Oxbridge Maths interview practice
• 1st December BMO preparation
• Spring 2009 Cambridge STEP paper preparation
• March 2009 Maths Circle Lectures