Further Mathematics Past Questions and Answers

Given that \(x^{2} + 4x + k = (x + r)^{2} + 1\), find the value of k and r.

A K = 5, r = -1
B K = 5, r = 2
C K = 2, r = -5
D K = -1, r = 5

Question 142:

Given the statements:
p : the subject is difficult
q : I will do my best
Which of the following is equivalent to 'Although the subject is difficult, I will do my best'?

A \(p \vee q\)
B \(\sim p \vee q\)
C \(p \wedge (\sim q)\)
D \( p \wedge q\)

Question 143:

If \(36, p, \frac{9}{4}, q\) are consecutive terms of an exponential sequence (G.P.). Find the sum of p and q.

A \(\frac{9}{16}\)
B \(\frac{81}{16}\)
C \(9\)
D \(9\frac{9}{16}\)

Question 144:

Find the minimum value of \(y = x^{2} + 6x - 12\).

A -21
B -12
C -6
D -3

Question 145:

A line passes through the origin and the point \((1\frac{1}{4}, 2\frac{1}{2})\), what is the gradient of the line?