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 bonus cache contains questions from the Sixth Form caches.
1. From 1+1=21. When written in radians, the second positive solution to 2(Sin x)^2 +2 = 7Cos x is 5.A36 (to three decimal places). Find A.
2. From 1+1=22. A group of geocachers were asked about their caching habits. Two fifths of them liked puzzle caches. Two thirds of the group went to event caches. Of those who went to event caches, nine twenty-fifths also liked puzzle caches. Find the probability that a randomly chosen member of the group does not like puzzle caches and does not go to event caches. If you write your answer as a fraction in the simplest form possible, B= the numerator of the fraction.
3. From 1+1=23. A non-uniform rod PQ, of mass m and length 5H rests horizontally in equilibrium on two supports at R and T, where PR=TQ=H. The centre of mass of the rod is at K, where KT=5H/2. A particle of mass 5m/2 is placed at the midpoint of the rod. The magnitude of the normal reaction between the support at T and the rod is Cmg/12. Find C.
4. From 1+1=24. The gradient of y=(x^2)(Ln 3x) at x=5 is 32.0D to 2 decimal places. Find D.
5. From 1+1=25. The equation x^2+y*x+z=0, where y and z are different, has solutions x=y and x=z. E=5y+z.
6. From 1+1=26. F= the minimum value of x^2+y^2+2x*y+6x+6y+4, where * means multiply.
7. From 1+1=27. Becky and Adam are 51 miles apart and cycle towards each other. Starting at noon, Becky cycled at X mph. Starting at 2pm, Adam cycled at Y mph. They meet at 4pm. If they had both started at noon, they would have met at 2.50pm. G=2*Y.
8. From 1+1=28. dy/dx +2y*Tan x = Sin(2x) has a solution y=2 at x=pi/3. At x=pi/6, y=6-(3/4)LnH. Find H.
9. From 1+1=29. A gps manufacturer finds that the life expectancy of its units has a standard deviation of 5000 hours of use. On a random sample of 100 worn out units, it finds that the total hours of use for all units is 1740000 hours. If the 95% confidence interval for the mean lifetime of a unit is written as [p,q], J=(q-p)/140.
10. From 1+1=30. A light elastic string has natural length 10m and modulus of elasticity 130N. The ends of the string are attached to fixed points P and Q, which are at the same horizontal level and 12.6m apart. An object is attached to the midpoint of the string and hangs in equilibrium at a point 1.6m below PQ. Find K, the weight of the object, to 2 significant figures.
The cache can be found at N50 45.PQR E0 15.STU where P=B-A-9, Q=C-D-3E, R=F+G-5H-1, S=A+B+C-D-E+F-G-H-J+K+5, T=K-J+F, U=A+E-H+1
You can check your answers for this puzzle on GeoChecker.com.