1. Mathematical Treasure-hunt:
Cut out each of the question slides and place them around the room, stick them on the walls if you wish.
Print out and distribute the answer sheet, one per pupil, or team, and set them off to find the answers.
The correct answer is:
14, 5, 18, 2, 16, 15, -2/3, 9, 17, 6, 25, -1/2, 1/3, -23, 19, 1/4

2. Name: Name: Answer Sheet Answer Sheet Mathematical Treasure-hunt:

3. 14 ? 5 ? Mathematical Treasure-hunt: Mathematical Treasure-hunt:
Two submarines are travelling in straight lines through the ocean. Relative to a fixed origin, the vector equations of the two lines, l1 and l2, along which they travel are
r = 3i + 4j – 5k + (i – 2j + 2k)
and
r = 9i + j – 2k +  (4i + j – k),
where  and  are scalars.
Given that l1 and l2 intersect at the point A, find the i coefficient of the position vector of A.
Mathematical Treasure-hunt: 14
Previous Answer ?
To the next clue
Mathematical Treasure-hunt: 5
Previous Answer ?
To the next clue
Find the value of this integral.

4. 18 ? 2 ? Mathematical Treasure-hunt: Mathematical Treasure-hunt:
Previous Answer ?
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Mathematical Treasure-hunt: 2
Previous Answer ?
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Given that
Given that
Find the value of the constant A.
Find the value of the constant B.

5. 16 ? 15 ? Mathematical Treasure-hunt: Mathematical Treasure-hunt:
Previous Answer ?
To the next clue
Mathematical Treasure-hunt: 15
Previous Answer ?
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Relative to a fixed origin O, the point A has position vector 4i + 8j – k,
and the point B has position vector
7i + 14j + 5k.
Calculate the cosine of OAB.
Using your answers to the previous two questions, find the coefficient of x3 in the series expansion in ascending powers of x of:

6. ? 9 ? -2/3 Mathematical Treasure-hunt: Mathematical Treasure-hunt:
Previous Answer ?
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Mathematical Treasure-hunt: 9
Previous Answer ?
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The circle C has equation
x2 + y2 – 8x – 16y – 209 = 0.
Find the radius of C.
Given that the exact value of this integral is
aln /9,
find the value of a.

7. 17 ? 6 ? Mathematical Treasure-hunt: Mathematical Treasure-hunt:
Previous Answer ?
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Mathematical Treasure-hunt: 6
Previous Answer ?
To the next clue R
Referred to an origin O, the points A, B and C have position vectors (9i – 2j + k), (6i + 2j + 6k) and
(3i + pj + qk) respectively, where p and q are constants.
The line l passes through A and B.
Given that C lies on l, find the value of p.
The diagram shows part of the curve with equation y = x The finite region R is bounded by the curve, the x-axis and the lines x = 0 and x = 2. Using integration, find the volume of the solid generated when R is rotated through 360 about the x-axis, giving your answer in terms of .
Now divide your answer by . Then round to the nearest integer. This leads you to the next question.

8. 25 ? -½ ? Mathematical Treasure-hunt: Mathematical Treasure-hunt:
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Mathematical Treasure-hunt: -½
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An expansion of (1 + 3x)2 is valid when x < a.
What is a?
For which values of x is this function undefined?
Find the average of these numbers.

9. 1/3 ? -23 ? Mathematical Treasure-hunt: Mathematical Treasure-hunt:
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Mathematical Treasure-hunt:
-23
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Find the coefficient of x in the expansion of
as a series in ascending powers of x.
The line l1 has equation
r= (i + 2j - 3k) + λ (4i – 5j + 3k), where λ is a scalar parameter.
The line l2 has equation
r= (4i – 4j + 3k) +  (i – 2j + 2k), where  is a scalar parameter.
Find, to the nearest degree, the acute angle between the lines l1 and l2.

10. 19 ? ¼ ? Mathematical Treasure-hunt: Mathematical Treasure-hunt:
Previous Answer ?
To the next clue
Mathematical Treasure-hunt:
Previous Answer ?
To the next clue R
The curve C with equation y = 2ex + 5 meets the y-axis at the point M.
The normal to C at M crosses the x-axis at the point N(n, 0).
Find n.
The graph shows the curve with equation y = x½ e2x.
Find the x-coordinate of M, the maximum point of the curve.