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Further Mathematics Past Questions


Question 106:


Given n = 3, evaluate \(\frac{1}{(n-1)!} - \frac{1}{(n+1)!}\)

A. \(12\)
B. \(2\frac{1}{2}\)
C. \(2\)
D. \(\frac{11}{24}\)


Question 107:


Find the coefficient of \(x^{3}\) in the expansion of \([\frac{1}{3}(2 + x)]^{6}\).

A. \(\frac{135}{729}\)
B. \(\frac{149}{729}\)
C. \(\frac{152}{729}\)
D. \(\frac{160}{729}\)


Question 108:


If \(y = 4x - 1\), list the range of the domain \({-2 \leq x \leq 2}\), where x is an integer.

A. {-9, -1, 2,3, 4}
B. {-9, -2, 0, 1, 7}
C. {-5, -4, -3, -2}
D. {-9, -5, -1, 3, 7}


Question 109:


Factorize completely: \(x^{2} + x^{2}y + 3x - 10y + 3xy - 10\).

A. (x + 2)(x + 5)(y + 1)
B. (x + 2)(x - 5)(y + 1)
C. (x - 2)(x + 5)(y + 1)
D. (x - 2)(x - 5)(y + 1)


Question 110:


If the solution set of \(x^{2} + kx - 5 = 0\) is (-1, 5), find the value of k.

A. -6
B. -4
C. 4
D. 5






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