Mathematics

The positive integers and satisfy What is the value of ?

This question was sent in by a student, which I think is rather interesting given 2015 A’levels P1 Q3 had something similar. Use a definite integral to evaluate , given your answer correct [...]

All possible straight lines joining the vertices of a cube with mid-points of its edges are drawn. At how many points inside the cube do two or more of these lines meet?

Most JCs by now should be embarking on their Statistics Journey. I know a school that is finishing up really fast, and I think they will easily finish the syllabus by May. So I notice many [...]

So I posted up a question titled “AHOY! The Pirate Story Problem” which can be found here. Here is the solution! We begin with a more intuitive idea. Consider only 2 pirates. Pirate 2 [...]

A student asked me this question recently. I think this is from AMC. There are 42 points placed on a straight line so that each distance from to is where . What is the sum of the distances [...]

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (a) (i) Alternatively, (ii) When , required probability (b) Key GC with [...]

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) (ii) (iii) P(B’|A) (iv) since A and C are independent (v)

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Let X and Y denote the mass of a apple and pear in grams [...]

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions. (i) Number of ways ways (ii) Number of ways ways (iii) Number of ways [...]