I/GCSE Mathematics Question Analysis Topic: Mathematics - Short Questions
Exam Question:
1) Find the distance between the planes 2x−y+2z=5 and 5x−2.5y+5z=20.
2) A die, whose faces are marked 1,2,3 in red and 4,5,6 in green, is tossed. Let A be the event "number obtained is even" and B be the event "number obtained is red". Find if A and B are independent events.
Answer:
For I/GCSE Mathematics, you should know:
1) With two parallel planes of forms:
ax + by + cz = d1, and
ax + by + cz = d2, the distance between them is
|d1 - d2| / sqrt(a2 + b2 + c2)
5x - 2.5y + 5z = 20
Factorize --> 2.5(2x - y + 2z) = 2.5 x 8
--> Second equation written as: 2x - y + 2z = 8
As such, the distance between the two planes is
|8 - 5| / sqrt(22 + 12 + 22) = 1 unit.
2) With regards to the information given,
A = {2, 4, 6}
B = {1, 2, 3}
Therefore A∩B = {2}
P(A∩B) = 1/6
P(A) = 1/2
and P(B) = 1/2
Multiplying these together, we have:
P(A) * P(B) = 1/4 =/= P(A∩B)
As such, we know that A and B are independent events.
Work hard for your I/GCSE Mathematics examination!
End of analysis. Great!