QUESTION 06 Let \(O(0,0)\), \(A(1,1)\) and \(B(x,-1)\). The positive value of \(x\) such that \(\angle AOB = \dfrac{\pi}{3}\) can...

QUESTION 07 Find the radius of the sphere \(x^2 + y^2 + z^2 = 2x + 6y - 1\)....

QUESTION 08 The tangent line to the curve \(y = \dfrac{1}{2}x^2 + 3\) \((x \ge 0)\) which passes through...

QUESTION 09 Calculate the sum: \ Determine the value of \(b - a\). 🔍 Solution \begin{equation*}...

QUESTION 10 Calculate the limit: \ 🔍 Solution \begin{equation*} \begin{split} & \text{1. Method 1: Algebraic Factorization} \\\\ & \text{Factorize...

QUESTION 11 Let \(f(x) = \cos^3 x\). The value of \(f'\left(\dfrac{\pi}{6}\right)\) can be written as a simplified fraction \(\dfrac{a}{b}\)....

QUESTION 12 Evaluate the definite integral: \ The result can be expressed in the...

QUESTION 13 Let \(A = \begin{pmatrix} 1 & 2 \\ a & b \end{pmatrix}\) and \(I = \begin{pmatrix} 1...

QUESTION 14 Given the function \(f(x) = x e^{-x^2}\). (A) The derivative \(f'(x)\) can be expressed in the form...

QUESTION 02 The sum of all solutions of the equation \(\sin 2x = \sqrt{3} \cos x\) for \(0 \le...