Mathematics Past Questions and Answers

Each of the 90 students in a class speak at least Igbo or Hausa. If 56 students speak Igbo and 50 speak Hausa, find the probability that a student selected at random from the class speaks Igbo only.

If \(x = i - 3j\) and \(y = 6i + j\), calculate the angle between x and y.

The gradient of a curve at the point (-2, 0) is \(3x^{2} - 4x\). Find the equation of the curve.

If \(\alpha\) and \(\beta\) are the roots of \(x^{2} + x - 2 = 0\), find the value of \(\frac{1}{\alpha^{2}} + \frac{1}{\beta^{2}}\).

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