Toowoomba Education Centre

MATHEMATICS TEAM CHALLENGE 2014

TEAM EVENT: Year 8 Time: 45 minutes ( Calculators are allowed) Total: 150 points_ Please write answers on the answer sheet.

T1. (10 points) How many times does the digit “1” appear if all of the counting numbers from 1 to 100 are written down?

T2. (20 points) How many triangles are in this figure?

T3. (20 points) The hours 2, 4, 7 and 11 are connected to form a quadrilateral on a clockface. What is the measure of the largest interior angle?

T4. (10 points) Find the largest two-digit integer that is increased by 20% of its value if its digits are reversed. T5. (15 points) Every 13th day, Mary visits the park, hoping to find Fred there; every 17th day, Fred does the same, hoping to find Mary. They just missed each other when Mary visited the park on Christmas Eve and Fred went on Christmas Day. On what date will they eventually meet?

T6. (20 points) How many three-digit numbers can be written using no 0’s and at least one 6?

T7. (10 points) The ratio of the lengths of a right-rectangular prism is 1: 2 : 4 and the total surface area is 252 m2. What is the volume?

T8. (15 points) A certain number has exactly eight factors, of which 35 and 77 are two. What is the number?

T9. (15 points) A farmer bought 100 head of livestock with exactly $100. Pigs were $10 each, sheep were $3 each and chickens were $0.50 each. If he bought at least one of each, how many chickens did he buy?

T10. (15 points) A prime-prime is a prime number that remains prime when its unit digit is truncated. (e.g., 131 is a prime- prime because 13 is prime). How many two-digit prime-primes are there?

School Name:______Team 1:

Team 2:

2014 MATHS TEAM CHALLENGE YEAR EIGHT TEAM EVENT

ANSWER SHEET

Question Answers Points T1. (10 points)

T2. (20 points)

T3. (20 points)

T4. (10 points)

T5. (15 points)

T6. (20 points)

T7. (10 points)

T8. (15 points)

T9. (15 points)

T10. (15 points)

Total /150 2014 MATHS TEAM CHALLENGE YEAR EIGHT TEAM EVENT

ANSWER SHEET

Question Answers Points T1. (10 points) 21 times

T2. (20 points) 20

T3. (20 points) 105º

T4. (10 points) 45

T5. (15 points) 14th February

T6. (20 points) 217

T7. (10 points) 216 m3

T8. (15 points) 385

T9. (15 points) 94 chickens

T10. (15 points) 9