Hits: 86
Hits: 86 Question The diagram shows the curve , for and its maximum point M. i. Show that ii. Hence find the x-coordinate of M, giving your answer correct to 2 decimal places.. Solution i. We are given that; Therefore; We apply product rule to find the derivative. If and are […]
Hits: 70 Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases; OR We have the equation; We have to consider both moduli separately and it leads to following cases; It cannot be solved for x. Hence, the only solution […]
Hits: 116 Question The diagram shows the curve , for and its maximum point M. i. Show that ii. Hence find the x-coordinate of M, giving your answer correct to 2 decimal places.. Solution i. We are given that; Therefore; We apply product rule to find the derivative. If and are […]
Hits: 77 Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases; OR We have the equation; We have to consider both moduli separately and it leads to following cases; It cannot be solved for x. Hence, the only […]
Hits: 76 Question Solve the equation. Solution SOLVING EQUATION: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases; OR We have the equation; We have to consider both moduli separately and it leads to following cases; Hence, the only solution for the given equation is; SOLVING […]
Hits: 180 Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following with their corresponding inequality; When When When If then above four intervals translate […]
Hits: 44 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. […]
Hits: 334 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 […]
Hits: 47 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 […]
Hits: 14 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 […]
Hits: 134 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 […]
Hits: 15 Question Solve each of the following inequalities: a. b. . Solution a. b. 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 & . Standard form of quadratic equation is; The graph of quadratic […]
Hits: 43 Question a. i. Express in the form where p and q are integers. ii. Hence write down the maximum value of . b. i. Factorise . ii. Sketch the curve with equation , stating the values of x where the curve crosses the x-axis and the […]
Hits: 734 Question i. Express in the form . ii. Hence, or otherwise, find the set of values of satisfying . Solution i. We have the expression; We use method of “completing square” to obtain the desired form. We complete the square for the terms which involve . We have the algebraic formula; For the given case we can compare […]