HANS WOYDA MATHEMATICS QUIZ COMPETITION 2010/2011
ROUND 2
SECTION 1 - STARTERS (INDIVIDUAL)
Marks: 2 marks to either or both competitors for the correct answer
Time: 30 seconds.
Year
13 1) An arithmetic series has first term 6 and the sum of its
first 30 terms is 615. Find the second term.
12 2) Express the recurring decimal as a fraction in its lowest terms.
10-11 3) Express as a recurring decimal.
7-9 4) Express as a fraction in its lowest terms
13 5) Find a given that
12 6) A model of a building has scale factor 1:50. If the floor area
of the building is 1700m2 find, in m2, correct to one significant
figure, the floor area of the model.
10-11 7) Find the largest prime factor of 2010.
7-9 8) Find the area of a triangle with sides 6cm, 8cm and 10cm.
HANS WOYDA MATHEMATICS QUIZ COMPETITION 2010/2011
ROUND 2
SECTION 2 - GEOMETRY AND TRIGONOMETRY (PAIRS)
Marks: 2 marks to either or both pairs for the correct answer
Time: 90 seconds.
All the questions in this section refer to the cube ABCDEFGH of side 3cm.
Each of the points marked on the edges is 1 cm from a vertex.
Year
7-11 1) Find the area of rectangle LMNQ.
12-13 2) Find the area of rectangle LQTS.
7-11 3) Find the area of rectangle PQRS.
12-13 4) Find the area of trapezium PQFG.
HANS WOYDA MATHEMATICS QUIZ COMPETITION 2010/2011
ROUND 2
SECTION 3 - MENTAL ARITHMETIC AND PROBABILITY (INDIVIDUAL)
Marks: 2 or 1 to opponent
Time: 60 seconds
All questions are to be done mentally
Body Mass Index (BMI) =
Year
7-9 1) Find the BMI of Alf who is 2 m tall and has mass 80 kg.
2) Find the BMI of Bess who is 1.2 m tall and has mass 36 kg.
10-11 3) Find the mass of Ernie who is 1.5 m tall and has a BMI of 24.
4) Find, to the nearest kg, the mass of Flo who is 1.4 m tall
and has a BMI of 20.
12 5) Find, to the nearest 10cm, the height in centimetres of Chris who has mass 60 kg and has a BMI of 20.
6) Find, to the nearest 10cm, the height in centimetres of Doug who has mass 82 kg and has a BMI of 25.
13 7) Find, to the nearest kg, the mass of the tallest man.
He was 2.7m tall and had a BMI of 30.
8) Find, to the nearest kg, the mass of the tallest woman.
She was 2.2m tall and had a BMI of 30.
HANS WOYDA MATHEMATICS QUIZ COMPETITION 2010/2011
ROUND 2
SECTION 4 - TEAM QUESTION
Time: 5 minutes.
P(n) is defined as the product of the digits of the positive integer n.
For example: P(469) = 4 × 6 × 9 = 216
P(464) = 4 × 6 × 4 = 96 .
Find as many positive integers n as you can where n < 400 and
P(n) has a last (units) digit of 6.
You will be given 5 minutes for working. Then the Team Captain will be given some extra time to compile a single list of answers.
Marks:
1 point for each correct answer, -1 for each incorrect answer.
Each team receives their Total Points Score ÷ 10, rounded to the nearest integer (half rounds up), with minimum score zero.
Answers:
6, 16, 23, 28, 32, 44, 49, 61, 66, 78, 82, 87, 94,
116, 123, 128, 132, 144, 149, 161, 166, 178, 182, 187, 194,
213, 229, 231, 247, 268, 274, 279, 286, 292, 297,
312, 321, 326, 334, 343, 348, 362, 367, 376, 384, 389, 398
(47 solutions)
HANS WOYDA MATHEMATICS QUIZ COMPETITION 2010/2011
ROUND 2
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) Find, to the nearest 100, the sum of the first 7 terms of
the series
.
10-11 2) Find, correct to 2 significant figures, the sum of the first 12 terms
of the series
.
12 3) The sum of the infinite series is 1.
When the first 12 terms are added the sum is .
Find k correct to 2 significant figures.
13 4) The first three terms of a series for are given here: .
Use the first four terms to find an approximate value of .
Give your answer correct to 5 decimal places.
HANS WOYDA MATHEMATICS QUIZ COMPETITION 2010/2011
ROUND 2
SECTION 6 - ALGEBRA AND CALCULUS (INDIVIDUAL)
Marks: 2 or 1 for opponent
Time: 60 seconds.
Throughout this section the operation * is defined by
a * b = (a + b)(a2 – ab + b2) .
Example: 3 * 2 = (3 + 2)(32 – 3 × 2 + 22) = 5 × (9 – 6 + 4) = 35.
Year
7-9 1) Find the value of 4 * 2.
2) Find the value of 3 * 5 .
10-11 3) Find the value of (1 * 2) * 3 .
4) Find the value of (2 * (-1)) * ((-2) * 1) .
12 5) Given that (2x) * x = 1125, find the value of x .
6) Given that (4x) * (3x) + (2x) * 1 = 100, find the value of x.
13 ) Find [(2x)*)] .
8) Find .
HANS WOYDA MATHEMATICS QUIZ COMPETITION 2010/2011
ROUND 2
SECTION 7 - RACE (INDIVIDUAL)
Marks: 2 or 0
Time: 60 seconds.
Year
7-9 1) Find the two prime numbers with a sum of 100 and the largest difference.
10-11 2) Find the two prime numbers with a sum of 100 and the smallest difference.
12 3) Given that + 2 = a , find the value of a .
13 4) Solve
7-9 5) Find the number of degrees through which the hour hand
of a clock turns in 24 hours.
10-11 6) Find the number of triangular tiles shown below needed
to cover a square of side 48cm.
12 7) Find the area under the line between the lines
, and the x axis.
13 8) Find the value of sin 2010º .
HANS WOYDA MATHEMATICS QUIZ COMPETITION 2010/2011
ROUND 2
ANSWERS (allow equivalent answers except where stated)
SECTION 1
1. 7
2. 41/333 (must be in lowest terms)
3.
4. 1/81
5. 80
6. 0.7 (m2)
7. 67
8. 24 (cm2)
SECTION 2
1. 4 (cm2)
2. (cm2)
3. 3 (cm2)
4. 6 (cm2)
SECTION 3
1. 20
2. 25
3. 54 (kg)
4. 39 (kg)
5. 170 (cm)
6. 180 (cm)
7. 219 (kg)
8. 145 (kg)
SECTION 4
Please see separate answer sheet
SECTION 5
1. 779800
2. 9.0 (must be 2 S.F.)
3. 0.00024
4. 3.14085
SECTION 6
1. 72
2. 152
3. 756
4. 0
5. 5
6. 1
7. 24x2 + 6x5
8. (+ c)
SECTION 7
1. 3, 97
2. 47, 53
3. 3
4. 2
5. 720 (º)
6. 384
7. 25.5
8. -½