Question (i) Show that (2 sin x + cos x)2 can be written in the form (ii) Hence find the exact value of Solution i. We are given that; We have formula; Therefore; Therefore; Therefore; ii. We are required to find the exact value of; From (i) we […]
Question The parametric equations of a curve are The point P on the curve has parameter p and it is given that the gradient of the curve at P is −1. i. Show that . ii. Use an iterative process based on the equation in part (i) to find the value of […]
Question The diagram shows the curve and its minimum point M. i. Show that the x-coordinate of M can be written in the form , where the value of a is to be stated. ii. Find the exact value of the area of the region enclosed by the curve and the […]
Question i. Given that , find the value of . ii. Hence, showing the use of an appropriate formula in each case, find the exact value of a. b. Solution i. We are given that; We have trigonometric identity; Let , then; Since , therefore; ii. […]
Question The polynomial is defined by where is a constant. i. Given that is a factor of , find the value of . ii. When has this value, a. Factorise p(x) completely, b. Find the remainder when p(x) is divided […]
Question The variables x and y satisfy the equation y = A(bx), where A and b are constants. The graph of ln y against x is a straight line passing through the points (0, 2.14) and (5, 4.49), as shown in the diagram. Find the values of A and b, correct to […]
Question Solve the equation . Solution SOLVING EQUATION: PIECEWISE Let, . We can write it as; We have to consider two separate cases; When When We have the equation; We have to consider two separate cases; When ; When ; Hence, the only solutions for the given equation are; SOLVING EQUATION: ALGEBRAICALLY Let, […]