HANS WOYDA MATHEMATICS QUIZ COMPETITION 2011/2012
ROUND 3
SECTION 1 - STARTERS (INDIVIDUAL)
Marks: 2 marks to either or both competitors for the correct answer
Time: 30 seconds.
Year
13 1) Given that x
2 
8 x
 n

0 , find how many values of n > 0 will give integer solutions.
12 2) The interior angle of a regular polygon is three times the exterior angle. Find the number of sides of the polygon.
10-11 3)
4
5
3
of
8
of a number is 6. Find the number.
7-9 4) Find
4
9
of
3
4
of 24.
Questions 5 and 6 refer to the diagram where
A
P = a , = b and P lies on AB.
O
13 5) Given that Q lies on OP, OQ =
2
3
OP, and find the ratio AP:AB .
 a
12 6) Given that
Q
A b
A
, find the ratio AP:AB b ,
B
A
10-11 7) A 12 hour clock shows 6 o’clock. Find the time on the clock after the minute hand has turned through 900 o .
7-9 8) A rhombus has sides of 13cm and a diagonal of 10cm.

Find the area of the rhombus.

HANS WOYDA MATHEMATICS QUIZ COMPETITION 2011/2012
ROUND 3
SECTION 2 - GEOMETRY AND TRIGONOMETRY (PAIRS)
Marks: 2 marks to either or both pairs for the correct answer
Time: 90 seconds.
Year
U
7-11 1) PQTU is a rectangle.
PQ = QR = RS.
Angle PQR = 110º.
Find the size of angle PRS.
T S
R
12-13 2) A, B and C are three vertices of a regular 15-sided polygon.
Find the size of angle ABC.
12-13 4) E and F are the midpoints of sides
BC and AB of the square ABCD.
AE and DF intersect at G.
Find the ratio GE : GD.
B
7-11 3) Each of the small circles has radius a .
Find the radius of the large circle in terms of a .
B
F
C
G
E
A
C
110º
P
Q
A D


HANS WOYDA MATHEMATICS QUIZ COMPETITION 2011/2012
ROUND 3
SECTION 3 - MENTAL ARITHMETIC AND PROBABILITY
(INDIVIDUAL)
Marks: 2 or 1 to opponent
Time: 60 seconds
All questions are to be done mentally
A set of jigsaw puzzles are all rectangular. The pieces are in rows and columns. Note that corner pieces have two straight edges, side pieces have one straight edge and interior pieces have no straight edge.
An m  n jigsaw has m rows and n columns, where n > m > 2 (so that the puzzle has “landscape” orientation). n columns m rows
Year
7-9 1) A jigsaw has 35 pieces.
Find how many pieces have exactly one straight edge.
2) A jigsaw has 77 pieces.
Find how many pieces have at least one straight edge.

HANS WOYDA MATHEMATICS QUIZ COMPETITION 2011/2012
ROUND 3
SECTION 3 - MENTAL ARITHMETIC AND PROBABILITY
(INDIVIDUAL) ( continued )
10-11 3) A jigsaw has 15 pieces with no straight edge.
Find how many pieces the jigsaw has.
4) Find how many jigsaws, of different shapes, could have 80 pieces.
12 5) A jigsaw has 63 pieces.
Find the minimum number of pieces with no straight edge.
6) A jigsaw has 56 pieces.
Find the maximum number of pieces with one straight edge
13 7) One piece is chosen at random from a 35 piece jigsaw.
Find the probability, as a fraction in its lowest form, that the piece has at least one straight edge.
8) Two pieces are chosen at random from a 35 piece jigsaw.
Find the probability, as a fraction in its lowest form, that neither piece has a straight edge.

HANS WOYDA MATHEMATICS QUIZ COMPETITION 2011/2012
ROUND 3
SECTION 4 - TEAM QUESTION
Time: 5 minutes.
The number 7 777 777 can be expressed as the product of prime factors:
7 777 777 = 7 × 239 × 4649.
Express each of the following as the product of prime factors:
22 = (½ mark)
333 =
4 444 =
55 555 =
666 666 =
88 888 888 =
(½ mark)
(½ mark)
(1 mark)
(1 mark)
(1½ marks)
Marks:
Give the marks indicated for the complete prime factorisation, with no mark for an incomplete factorization and no penalty for incorrect answers or omissions.
Maximum mark 5, minimum mark 0, ½ rounds up.
Answers:
22 = 2  11
333 =
4444 =
55555 =
3 2
 37
2 2
 11  101
5  41  271
666666 =
88888888 =



2  3 2  11  13  259
2 3  11  73  101  137


HANS WOYDA MATHEMATICS QUIZ COMPETITION 2011/2012
ROUND 3
SECTION 5 - CALCULATORS (INDIVIDUAL)
Marks: 2 to either or both competitors for the correct answer
Time: 90 seconds
You are reminded that the written questions are to be given simultaneously to the respective pupils at the beginning of this section.
The same formula is to be used for all questions.
W

( p  q )
( a  n bc )
Year
7-9 1)

W

( p  q ) n
( a  bc )
.
Evaluate W when p = 2.3, q = 0.75, n = 2, a = 12, b =3, c = 2 .
Give your answer correct to 3 significant figures.
10-11 2) W

( p  q ) n
( a  bc )
.

Evaluate W when p = sin 20 o , q = cos 65 o , n = 4, a = 12.75, b =3, c =

.
Give your answer correct to 3 significant figures.

12 3) W

( p  q ) n
( a  bc )

.


Evaluate W when p = 6.2
2 , q = (-0.31)
3
, n = c = 0.2 .
1
4
, a = 2cos 40 o , b =3sin85 o ,
Give your answer correct to 3 significant figures.

 
13 4) W


( p  q ) n
( a  bc )
.
Evaluate W when p = e 2 , q = ln 3, n = 6, a = sin 2 17.1
o , b = cos 4 25.2
o , c =
 
.
Give your answer correct to 3 significant figures.
  

HANS WOYDA MATHEMATICS QUIZ COMPETITION 2011/2012
ROUND 3
SECTION 6 - ALGEBRA AND CALCULUS (INDIVIDUAL)
Marks: 2 or 1 for opponent
Time: 60 seconds.
For all the questions in this section
[ a, b ] = a  b a  b
 ab , where a  b .
For example: .
Year

7-9 1) Find [ a, b ] when a = 3 and b   2
2) Find [ a, b ] when a = 7 and b  9 .
10-11 3) Find x , given that [(
 3 x
), 5 x ] 
7
2
4) Find x , given that [
2 x
, x ]   6
12 5) Find x , given that [ x , 4]   11
6) Find x , given that [1, 2 x ]   5
13 7) Find x ( x ≠ 0), given that [ x , 0] = [4, x ]
8) Find x , given that [2 x , x ] = [ x , (
 2 x
)]


HANS WOYDA MATHEMATICS QUIZ COMPETITION 2011/2012
ROUND 3
SECTION 7 - RACE (INDIVIDUAL)
Marks: 2 or 0
Time: 60 seconds.
Year
7-9 1) Find the largest factor, less than 3737, of 3737.
10-11 2) Find the largest factor, less than 129129, of 129129.
12 3) In 5 minutes Jack swims 3 lengths of a pool while Jill swims
5 lengths.
If they both start together at the shallow end find how many minutes later they will next be at the shallow end at the same time.
13 4) A geometric series has first term 6 and its sum to infinity
is 4. Find the second term.
7-9 5) If x and y are positive integers find how many points ( x , y ) lies on the straight line with equation x + y = 59 .
10-11 6) The square of the cube root of a positive number is 100.
Find the number.
12 7) Find the third side of a right angled triangle whose two longest sides are 40 cm and 41 cm.
13 8) Given that ( 2
 x ) 3
 a
 bx
 cx 2
 dx 3 find a  b  c  d .


HANS WOYDA MATHEMATICS QUIZ COMPETITION 2011/2012
ROUND 3
ANSWERS ( allow equivalent answers )
SECTION 1
1. 4
2. 8
SECTION 5
1. 3.80
[must be 3 s.f.]
3. 20
4. 8
5. 1 : 5
6. 2 : 7
7. 8.30
8. 120 (cm 2 )
SECTION 2
1.
105 (º)
2. 60 (º)
3. 3 a
4. 3 : 4
SECTION 3
1.
2.
3.
4.
16
32
35
3
5. 19
6. 28
7. 4/7
8. 3/17
SECTION 4
Please see question sheet
2. 0.187
3. 2.58
4. 253 000
SECTION 6


1.
2.
3.
4.
6

1
5
 71

1
2
3
2


5.
6. 1,
7.
2, 5
7
2
3
2

5
6

SECTION 7

1. 101
2. 43043
3. 10 (min)
4. -3
5. 58
6. 1000
7. 9
8. 1