Question The curve C has equation . The line L has equation y = 3x + k, where k is a positive constant. a. Sketch C and L on separate diagrams, showing the coordinates of the points at which C and L cut the axes. Given that line L is a tangent to C, b. find the […]
Question Figure 1 shows the plan of a garden. The marked angles are right angles. The six edges are straight lines. The lengths shown in the diagram are given in metres. Given that the perimeter of the garden is greater than 40 m, a. show that x > 1.7 Given that the area of the garden is less […]
Question Given that f(x) = 2×2 + 8x + 3 a. find the value of the discriminant of f(x). b. Express f(x) in the form p(x + q)2 + r where p, q and r are integers to be found. The line y = 4x + c, where c is a constant, is a tangent […]
Question Find the set of values of x for which a. b. c. both and . Solution a. We are given; b. We are required to solve the inequality; We solve the following equation to find critical values of ; Now we have two options; Hence the critical points on the curve for the given condition are -3 & […]
Question The equation 2×2 + 2kx + (k+2) = 0, where k is a constant, has two distinct real roots. a. Show that k satisfies k2 – 2k – 4 > 0 b. Find the set of possible values of k. Solution a. We are given that; For a quadratic equation , the expression for solution […]