Geomaths #2 Mystery Cache

To solve this second cache, you will need to solve maths problems similar to those found on a GCSE Higher Maths paper.  If you want, start at the first cache in the series (Geomaths #1) though there is no pre-requisite; you can do these in any order.

The cache can be found at N50 ab.cde W 000 fg.hjk.  The cache itself is a small black taped cylinder with room for small trackables and swaps.  To help you find it (as these caches are more about the maths than the find) it is hidden at the base of a tree (moved on 18/6/16).

Please do not include hints, spoilers etc in your logs about the questions or the cache location. This will be classed as cheating and may result in disqualification from the cache!

GEOCACHING EXAMINATIONS BOARD

General Certificate of Secondary Education

MATHEMATICS

HIGHER TIER

Time allowed: who can be first to find?

The number of answers in this paper is 10.

You do not need to show clearly how you work out your answer.

Use of a calculator is permitted.

Formula Sheet: Higher Tier

You may need to make use of some or all of the following formula.

Cosine Rule a² = b² + c² -2bc cos A

Sine Rule 

The quadratic equation

The solutions of ax² + bx + c = 0, where a ≠ 0, are given by

1. Rearrange the following, making g the subject.

Find g, if x = 13 and y = 5.

2. The equation x³ - x ² - 0.5 = 29 has a solution between x=3 and x=4.
Use trial and improvement to find x to 2 decimal places.

The second decimal place = j.

3. Olympic heptathlete Jessica Ennis wants to throw a world heptathlon record shotput throw of 17.32m.  Her trainer explains that if she can throw the shotput 10m into the air, the shotput will travel a further 13m before landing to achieve a world heptathlon record.  What angle would Jessica have to throw the shot put at to achieve this world heptathlon record?

Angle = .................................... The second digit (unit) =c.  i.e. #c.##

x + y = c

4. A geocacher is attempting a letterbox hybrid cache on Dartmoor.  The instructions tell the geocacher to walk on a bearing of 67˚ for a distance of 190m.  How many metres north is the destination from the start.

Distance north = ................................ The second digit (units) = f.  i.e. #f.

5. Solve the equation  to find x to 2 decimal places.  The second decimal place gives h.  i.e. #.#h

6. A baby clothes shop sells packs of baby clothes made up from vests and baby grows.  Sold separately, vests cost less than baby grows.

*         Pack A contains 4 vests and 2 baby grows, and costs £9.68.

*         Pack B contains 6 vests and 5 baby grows and costs £18.68.

Assuming that the shop has not applied any form of bulk discount, calculate the cost of (a) a vest and (b) a baby grow.

(a)   Vest: £........ Clue b is given by the first digit of the cost of the vest. i.e. £b.##

(b)  Baby grow: £........ Clue d is given by the third digit of the cost of the Baby grow i.e. £#.#d

7. This table shows the height of bean plants 2 weeks since germinating in a greenhouse.

a)    How many plants were planted overall? ...... = ae Clues a and e are given by this answer.

b)    Complete this table to show the cumulative frequency.

Second digit (units) of the 5^th row down is clue k.

 You can check your answers for this puzzle on Geocheck.org