Query [from KN]: A variable X has a Binomial Distribution, where n=25 and p=0.8. I'm meant to work out P(X>15), but my Binomial Table doesn't list p-values above 0.5?
Response: As this is a Binomial Distribution, while you are counting 'success' you are counting 'failure' also at the same time.
So, think of Y~B(25,0.2) instead and look up your tables for P(Y<10).
Query [from KW]: A circle has a radius of 2X cm and a triangle has sides of [2X+1], 3X and [3X+4] cm. The perimeters are equal. Write an equation in terms of X to represent this fact and hence find the value of X correct to 2 decimal places?
Response: Click on the image graphic to view the solution (opens in new window):
Here is a recent news extract from the TES website ...
"... World Maths Day is one of the world’s largest global educational events. Students from across the globe unite in a celebration of numbers over the internet. The event aims to lift numeracy standards in a fun and meaningful way.
In the inaugural World Maths Day event more than 287,000 students from 98 countries combined to correctly answer 38,904,275 mathematics questions.
World Maths Day takes place on the first Wednesday in March - in 2008 the event will occur on the 5th of March....."
Query: How do I find out the range of x-values for which 2x2<7x+4?
Response: The first step here is to try and solve the inequality by factorisation!
Rearranging to... 2x2-7x-4<0 gives (2x+1)(x-4)<0.
Hence,
This leads to the solution of -0.5 < x < 4
You should check the solution by trying a suitable value of x (e.g. x=0) back in the original inequality.
Query [from Mr. Howells]: If I borrow money at 6.8% APR on an interest-only basis, how long will it take for the debt to double?
Response: If this rate of annual interest is fixed for the duration of the loan, then each year the debt owing increases by a factor of x1.068.
Hence, you will have doubled the debt after t years, where (1.068)t>2. This means that after 11 years your debt will have increased to beyond double the sum raised.
NOTE: This timing will not vary, irrespective of how much you originally borrow.
Query [from Jon]: Why can't I use 2x108 as an approximation for 1.98x108?
Response: I know it's tempting to do this. However, you should consider the true values of the standard form numbers you're meant to be comparing.
First, 1.98 x 108 = 198,000,000 (198 million)
Secondly, 2 x 108 = 200,000,000 (200 million)
These numbers are 2,000,000 (2 million) away from each other in value!
Query [from KK]: How do I find out two and a quarter raised to the power of two and a half, expressing it as a ratio p/q, without using a calculator?
Response: Do the following...
Query [from LauraP]: How do I factorise 3x3-x2-20x-12 completely?
Response: Do the following steps...
Click on the image graphic to view the solution (opens in new window):
Tom Raftery posed an interesting question to accompany the photograph he placed onto his personal space on the photo-sharing website, Flickr.
See if can you spot the numerical error made in one of their European stores by the U.K. Supermarket giant, Tesco...
Query [from Tripod]: I can't work out the last part of this question. Can you help?
Response: This is an example of a velocity-time graph. The total distance travelled is found by calculating the area 'under' the graph.
Please look at the solution provided (opens in new window):
