Toowoomba Education Centre

MATHEMATICS TEAM

CHALLENGE 2013

TEAM EVENT: Year 8 Time: 45 mins

(Calculators are allowed) Total: 150 points_

Please write answers on the answer sheet.

T1. (10 points)

What is the largest product that one can obtain by multiplying a two-digit number by a three-digit number using each of the digits 2, 3, 4, 5 and 6 once to generate the two numbers?

T2. (20 points)

Determine the missing term; then express the resulting sum as a fraction xy.

0.01 + 0.001 + 0.0002 + 0.00003 + 0.000005 + 0.0000008 + 0.00000013 + 0.000000021 + __ = xy

T3. (20 points)

A game involves scoring either 3 points and/or 7 points at a time. What scores cannot be attained.

T4. (10 points)

What positive integer values of a and b satisfy the equation below?

ab = ba

T5. (15 points)

A dartboard has four concentric circles, and the radius of the inner circle is 10 cm. If the probability of landing in each of the four regions is the same, what is the radius of the outer most circle?

T6. (20 points)

How many different three-digit numbers can be made from the digits 3, 6, 6, 7 and 9?

T7. (10 points)

The equation 91 = 12 + 22 + 32 + 42 + 52 + 62 shows that 91 is the sum of the first six squares, so 91 is a square pyramidal number. It is also a triangular number since.

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 = 91

There is another two-digit number that is both a square pyramidal number and a triangular number. What is the number?

T8. (15 points)

What is the unit digit when 22013 is written in expanded form?

T9. (15 points)

The Sun rotates once every 25 days. If its radius were suddenly halved, it would rotate four times quicker and take only 6.25 days. How long would it take the Sun to rotate if its original axis were suddenly decreased by a factor of 10?

T10. (15 points)

Computers store data and manipulate information by using binary digits or bits. These bits represent switches and can be in one of two positions- on or off. On and off can be represented by the numbers 1 and 0, and all of the activity and storage of the computer involves changes in the positions of these switches.

Eight bits make one byte and 210 = 1024 bytes which makes one kilobyte. Suppose information was printed as a single line of text, then one byte or 8 digits (eg 01110011) in 12 point font is approximately 1.5 centimetres in length.

The computer on board Apollo 11 had a memory capacity of 64 kilobytes. What is the length of the memory capacity in metres?

School Name:______Team 1:

Team 2:

2013 MATHS TEAM CHALLENGE

YEAR EIGHT

TEAM EVENT

ANSWER SHEET

Question /

Answers

Points

T1. (10 points)
T2. (20 points) / x = ______, y = ______
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