The Answers Quiz 1 Sports day In a

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The Answers Quiz

The Answers Quiz

1. Sports day In a 100 m race athletes A, B and C each

1. Sports day In a 100 m race athletes A, B and C each run at a uniform pace throughout. If A beats B by 10 m, and B beats C by 10 m, by how many metres does A beat C? A. B. C. D. E. 20 m 19 m 21 m 30 m None of the above

1. Sports day In a 100 m race athletes A, B and C each

1. Sports day In a 100 m race athletes A, B and C each run at a uniform pace throughout. If A beats B by 10 m, and B beats C by 10 m, by how many metres does A beat C? A. B. C. D. E. 20 m 19 m 21 m 30 m None of the above A runs 100 m while B runs 90 m so B’s speed is 9/10 of A’s speed. B runs 100 m while C runs 90 m so C’s speed is 9/10 of B’s speed. Therefore C’s speed is (9/10)×(9/10) =(81/100) that of A’s speed. So while A runs 100 m, C runs 81 m.

2. Snack time Break a breadstick in two places, what is the probability that

2. Snack time Break a breadstick in two places, what is the probability that you can make a triangle with the remaining pieces? A. 1/4 B. 1/3 C. 1/6 D. 1 E. None of the above

2. Snack time Break a breadstick in two places, what is the probability that

2. Snack time Break a breadstick in two places, what is the probability that you can make a triangle with the remaining pieces? A. 1/4 B. 1/3 C. 1/6 D. 1 E. None of the above A triangle is only possible if no section is larger than ½. Both breaks are on the same side of the midpoint with probability ½. If the breaks a and b are on different sides of the midpoint then the probability that a is further left in the left half than b is right in the right half is ½. Put these together to get the answer ¼. a b

3. Old Ghizas Pharaoh Matheses built a square based pyramid filled with gold. Four

3. Old Ghizas Pharaoh Matheses built a square based pyramid filled with gold. Four sides were equilateral triangles. Pharaoh Matheses’ son, Bob, squandered a lot of gold. He took the four equilateral triangles from Matheses’ pyramid and built a triangle based pyramid filled with gold. How much gold does Bob’s pyramid contain as a fraction of the volume of the original pyramid? A. 1/2 B. 1/3 HINT: The volume of pyramid is 1/3 × Height × Area of the base C. 3/4 D. 1/6 E. None of the above

3. Old Ghizas A. 1/2 B. 1/3 C. 3/4 D. 2/3 E. None of

3. Old Ghizas A. 1/2 B. 1/3 C. 3/4 D. 2/3 E. None of the above

4. Island A circular island is empty apart from 6 trees. A tree is

4. Island A circular island is empty apart from 6 trees. A tree is hidden only when it lies directly behind another tree from the perspective of the observer. What is the highest possible number of people that can stand on the island, with each person seeing a different number of trees? A. 3 B. 4 C. 5 D. 6 You may arrange the trees however you like.

4. Island A circular island is empty apart from 6 trees. A tree is

4. Island A circular island is empty apart from 6 trees. A tree is hidden only when it lies directly behind another tree from the perspective of the observer. What is the highest possible number of people that can stand on the island, with each person seeing a different number of trees? A. 3 B. 4 C. 5 D. 6