Challenging Questions Mathematics – Compulsory Part Learning Unit: More about polynomials Question M0-04-07 Given \( f(x) = (x + 1)g(x) \), show that \( f(x – 3) \) is divisible by \( (x – 2) \). # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: More about polynomials Question M0-04-06 Consider \( f(x) = 6x^4 – 19ax^3 + 13a^2x^2 + 4a^3x – 4a^4 \). # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: More about polynomials Question M0-04-05 Consider \( f(x) = ax^2 + bx + c \) and \( g(x) = 4x^4 – 12x^3 + 13x^2 + hx + k \). # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: More about polynomials Question M0-04-04 When a polynomial \( f(x) \) is divided by \( (x – 1) \), \( (x – 2) \), and \( (x – 3) \), the remainders are \( 3, 1 \), and \( 3 \) respectively. Find the remainder when \(... » read more
Challenging Questions Mathematics – Compulsory Part Learning Unit: More about polynomials Question M0-04-03 Given \( f(x) = x^3 + 2x^2 + 3x + 4 \). Find the remainders when: # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: More about polynomials Question M0-04-02 Given \( f(x) = ax^3 + bx^2 + cx + d \). # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: More about polynomials Question M0-04-01 Divide \(a^2x^4+2abx^3+(2ac+b^2)x^2+2bcx+c^2\) by \(ax^2+bx+c\). # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: Equations of circles Question M0-13-10 The coordinates of \(A\) and \(B\) are \((1, 1)\) and \((7, 1)\) respectively. # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: Equations of circles Question M0-13-09 Two circles touch the y-axis at the point \((0, 4)\). The x-axis intersects the two circles, creating two chords with the same length of \(6\). Find the equations of the two circles. # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: Equations of circles Question M0-13-08 A point \(P \, (x_1, y_1)\) lies on a circle \(C: x^2 + y^2 + Dx + Ey + F = 0\). Show that the tangent to \(C\) at \(P\) is given by \( x_1x + y_1y + \frac{D}{2}(x_1 + x) +... » read more
Challenging Questions Mathematics – Compulsory Part Learning Unit: Equations of circles Question M0-13-07 The coordinates of \(A\) and \(B\) are \((x_1, y_1)\) and \((x_2, y_2)\) respectively. \(AB\) is the diameter of a circle. Using the following independent methods, show that the equation of this circle is given by: \( (x – x_1)(x – x_2) +... » read more
Challenging Questions Mathematics – Compulsory Part Learning Unit: Equations of circles Question M0-13-06 Given \(C_1: x^2 + y^2 + 4x – 6y + 9 = 0\) and \(C_2: x^2 + y^2 – 2x + 6y – 51 = 0\). # More challenging questions will be updated # Answer