Mathematics Past Questions and Answers

If \(f(x) = 3x^{3} + 8x^{2} + 6x + k\) and \(f(2) = 1\), find the value of k.

A binary operation \(\otimes\) is defined by \(m \otimes n = mn + m - n\) on the set of real numbers, for all m, n \(\in\) R. Find the value of 3 \(\otimes\) (2 \(\otimes\) 4).

<table class='tbn'><tbody><tr><td> Age in years </td><td> 7 </td><td> 8 </td><td> 9 </td><td> 10 </td><td> 11 </td></tr><tr><td> No of pupils </td><td> 4 </td><td> 13 </td><td> 30 </td><td> 44 </td><td> 9 </td></tr></tbody></table><br/><br/><br/>The table above shows the number of pupils in a class with respect to their ages. If a pie chart is constructed to represent the age, the angle corresponding to 8 years old is

<table class='tbn'><tbody><tr><td> Score (x) </td><td> 0 </td><td> 1 </td><td> 2 </td><td> 3 </td><td> 4 </td><td> 5 </td><td> 6 </td></tr><tr><td> Freq (f) </td><td> 5 </td><td> 7 </td><td> 3 </td><td> 7 </td><td> 11 </td><td> 6 </td><td> 7 </td></tr></tbody></table><br/><br/><br/>Find the mean of the data.<br/>

<table class='tbn'><tbody><tr><td> Score (x) </td><td> 0 </td><td> 1 </td><td> 2 </td><td> 3 </td><td> 4 </td><td> 5 </td><td> 6 </td></tr><tr><td> Freq (f) </td><td> 5 </td><td> 7 </td><td> 3 </td><td> 7 </td><td> 11 </td><td> 6 </td><td> 7 </td></tr></tbody></table><br/><br/><br/>Find the variance<br/>