This mathematical series of puzzle caches has questions from all levels of school education, from Key Stage 1 (age 5-7) in the first few caches, all the way up to Further Maths A-Level in the last few caches. Everybody should be able to get the solutions to the first few caches, but how far through the series will you be able to get? For a full description of the series, please see the first cache “1+1=1”. If you can’t solve a particular set of questions, try asking somebody of the appropriate age, or your friendly neighbourhood Maths teacher!
Please note that many of the caches are hidden near busy roads, so please take care when finding them, especially if you have children with you. It is worth noting that there is parking possible within a few hundred metres of all caches and a quick look on a satellite view map should show suitable places.
This cache contains questions from the A-Level Further Maths course, from the Further Pure modules.
1. Z=-13+5i. A= the digit in the third decimal place of arg Z in radians (positive solution).
2. The matrix M has 4 in the top left position, -4 in the top right position, -1 in the bottom left position and 2 in the bottom right position. B= the number in the bottom right position of the inverse of M.
3. dy/dx +2y*Tan x = Sin(2x) has a solution y=2 at x=pi/3. At x=pi/6, y=6-(3/4)LnC. Find C.
4. r=1+2CosG, (where G is usually represented as ‘theta’), and takes values from zero to pi/2. At the point P, the tangent to the curve is parallel to the initial line. Given that O is the pole, the length OP=(U + sqrt(W))/V, where sqrt(W) means the square root of W. D=W/U-V.
5. Cosh (2x) – 5 Sinh (x) = 4 has two solutions. The larger of the two is Ln (3 + sqrt(F)). Find F.
The cache can be found at N50 45.PQR E0 14.STU where P=A+B, Q=D-A, R=B+C, S=F-B, T=D/(A+C), U=F-D-B
You can check your answers for this puzzle on GeoChecker.com.