HANS WOYDA MATHEMATICS QUIZ COMPETITION 2011/2012
FINAL
SECTION 1 - STARTERS (INDIVIDUAL)
Marks: 2 marks to either or both competitors for the correct answer
Time: 30 seconds.
7-9 1) Next year Tom will be twice as old as he was five years ago. Find how old he will be in ten years’ time.
10-11 2) The density of a form of rock is 2.5 g/cm3. The mass of 1 km3 of this rock is 2.5 × 10 n tonne. Find the value of n.
12 3) Find the lowest positive integer which leaves a remainder 6 when divided by 7 and leaves a remainder 12 when divided by 13.
13 4) Give the equation of this quadratic graph in the form y = a(x – b)2 + c.
7-9 5) Find the value of 8.71 × 14.3 + 14.3 × 1.29 .
10-11 6) When I slow down from a jog to a walk my speed decreases by 20 %. Find the percentage by which the time I take to cover a mile then increases.
12 7) Find the perimeter of triangle ABC.
13 8) Ten cards are numbered 1 to 10 and put in a hat. Three cards are drawn one at a time, without replacement. Find the probability that they are drawn in increasing order.
HANS WOYDA MATHEMATICS QUIZ COMPETITION 2011/2012
FINAL
SECTION 2 - GEOMETRY AND TRIGONOMETRY (PAIRS)
Marks: 2 marks to either or both pairs for the correct answer
Time: 90 seconds.
Year
7-11 1) The diagram shows the dimensions of a flag. Given that each section of the flag has the same area, find the value of x.
12-13 2) This flag has dimensions 3 by 2y. Given that each section of the flag has the same area and that each section has the same perimeter, find x and y.
7-11 3) The Congo flag is divided into three sections by two parallel lines through opposite corners. Given each section of the flag has the same area, find an exact expression for the width d of the central stripe.
12-13 4) This square flag of side 2 has a white cross symmetrically placed on a coloured background. Given that the white area is the same as the total area of the coloured regions, find an exact expression for the width of the cross, y .
HANS WOYDA MATHEMATICS QUIZ COMPETITION 2011/2012
FINAL
SECTION 3 - MENTAL ARITHMETIC AND PROBABILITY (INDIVIDUAL)
Marks: 2 or 1 to opponent
Time: 60 seconds
All questions are to be done mentally
A PIN number is a four digit number which may start with one or more zeros and may include repeated digits.
Year
7-9 1) Find how many possible PIN numbers there are.
2) Find how many PIN numbers are multiples of 4.
10-11 3) Find how many PIN numbers there are in which each digit is prime.
4) Find how many PIN numbers there are in which each digit is odd.
12 5) Find how many PIN numbers there are of the form abba, where a and b are different digits
6) Find how many PIN numbers there are of the form abbc, where a, b and c are different digits.
13 7) Find how many PIN numbers there are with four different digits.
8) Find how many PIN numbers there are with four different digits arranged in ascending order.
HANS WOYDA MATHEMATICS QUIZ COMPETITION 2011/2012
FINAL
SECTION 4 - TEAM QUESTION
Time: 5 minutes.
Using only prime numbers, find sets of at least two prime numbers with the given sums and products, entering your answers on the sheet provided.
Each answer should be given as an ordered list of primes, starting with the smallest prime. A prime may appear more than once in an answer.
Remember that 1 is not a prime number.
Examples:
Sum / Product / Ordered list of primes8 / 15 / 3, 5
11 / 28 / 2, 2, 7
51 / 4301 / 11, 17, 23
Marks:
Each correct set of primes is worth one point, with no penalty for errors or omissions.
Each team’s score is (total points)/3 , rounded to the nearest whole number.
HANS WOYDA MATHEMATICS QUIZ COMPETITION 2011/2012
FINAL
SECTION 4 - TEAM QUESTION
Answer sheet
Sum / Product / Ordered list of primes10 / 36
12 / 60
12 / Smallest possible
12 / Largest possible
14 / 100
14 / 120
30 / 221
30 / Largest possible
26 / 169
17 / 210
8 / 16
2n / 2n
31 / 1001
36 / 323
k / k
HANS WOYDA MATHEMATICS QUIZ COMPETITION 2011/2012
FINAL
SECTION 4 - TEAM QUESTION
Solutions
Sum / Product / Ordered list of primes10 / 36 / 2, 2, 3, 3
12 / 60 / 2, 2, 3, 5
12 / Smallest possible / 5, 7
12 / Largest possible / 3, 3, 3, 3
14 / 100 / 2, 2, 5, 5
14 / 120 / 2, 2, 2, 3, 5
30 / 221 / 13, 17
30 / Largest possible / 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
26 / 169 / 13, 13
17 / 210 / 2, 3, 5, 7
8 / 16 / 2, 2, 2, 2
2n / 2n / 2, 2, 2, …, 2 (n of them)
31 / 1001 / 7, 11, 13
36 / 323 / 17, 19
k / k / 2, 2
HANS WOYDA MATHEMATICS QUIZ COMPETITION 2011/2012
FINAL
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.
Year
7-9 1) Evaluate , giving your answer correct to 3 significant figures.
10-11 2) Find the area of this trapezium, giving your answer correct to 3 significant figures.
12 3) Find the value of , giving your answer in standard form correct to 3 significant figures.
13 4) The real root of the equation lies between 1 and 2.
Use the iterative formula
to find this root correct to two decimal places.
HANS WOYDA MATHEMATICS QUIZ COMPETITION 2011/2012
FINAL
SECTION 6 - ALGEBRA AND CALCULUS (INDIVIDUAL)
Marks: 2 or 1 for opponent
Time: 60 seconds.
Year
7-9 1) Find the value of x which makes the value of as small as possible.
2) Find the value of x which makes the value of
as large as possible.
10-11 3) Find the shortest distance between the curves and when they are drawn on the same axes.
4) Find the shortest distance between the curves and when they are drawn on the same axes.
12 5) Find the equation of the line of symmetry of the graph of .
6) Find the equation of the line of symmetry of the graph of .
13 7) Sketch the graph of
8) Sketch the graph of
HANS WOYDA MATHEMATICS QUIZ COMPETITION 2011/2012
FINAL
SECTION 7 - RACE (INDIVIDUAL)
Marks: 2 or 0
Time: 60 seconds.
Year
7-9 1) In an election with five candidates 119 votes are cast. One candidate is the clear winner, having more votes than any of the other four candidates. Find the lowest number of votes that the winner could have received.
10-11 2) Evaluate , giving your answer as a fraction in its lowest terms.
12 3) Solve the equation .
13 4) Evaluate when .
7-9 5) In a very simple code the letter A is replaced with the number 1, B with 2, and so on. Decode the message 8 1 14 19 23 15 25 4 1
10-11 6) Find the obtuse angle between the two hands of a clock at the time 6.06 .
12 7) Given that x and y are both positive, and that
, find the value of .
13 8) Find the values of the digits a and b if the number 4a11b3 is a multiple of 99 .
HANS WOYDA MATHEMATICS QUIZ COMPETITION 2011/2012
FINAL
ANSWERS (allow equivalent answers)
SECTION 1
1. 21
2. 9
3. 90
4.
5. 143
6. 25 (%)
7. 120
8. 1/6
SECTION 2
1. 1
2. x = 1, y = 3/2
3. 1/√2
4. √2 – 1
SECTION 3
1. 10 000
2. 2500
3. 256
4. 625
5. 90
6. 720
7. 5040
8. 210
SECTION 4
Please see solution sheet
SECTION 5
1. 0.962
2. 29.7 (cm2)
3. 7.93 × 106646
4. 1.41
SECTION 6
1. 7
2. -2.5
3. 4
4. 0
5. x = -4
6. x = 0
7.
8.
SECTION 7
1. 25
2. 63/80
3. 1/2
4. 1
5. HANS WOYDA
6. 147 (º)
7. 12
8. a = 5, b = 4