Question The diagram shows the curve with parametric equations for . i. Show that can be expressed in the form ii. Find the equation of the normal to the curve at the point where the curve crosses the positive y-axis. Give your answer in the form y = mx +c, where the constants […]
Question i. Show that ii. Solve the equation for . iii. Find the exact value of Solution i. We are required to show that; Since ; Therefore; provided that ii. We are required to solve the equation for . We are given that; As demonstrated in (i); Since ; […]
Question The diagram shows the curve and its stationary point M. The x-coordinate of M is m. i. Find an expression for and hence show that . ii. Use an iterative formula based on the equation in part (i) to find the value of m correct to 4 significant figures. Give the result […]
Question The polynomial is defined by where is a constant. i. Use the factor theorem to show that (x +1) is a factor of p(x) for all values of a. ii. Given that the remainder is −42 when p(x) is divided by (x −2), find the value of a. iii. When a […]
Question The definite integral is defined by i. Show that . ii. Sketch the curve for . iii. State whether an estimate of obtained by using the trapezium rule will be more than or less than 8e −2. Justify your answer. Solution i. We are given that; Rule for integration […]
Question i. Given that , find the value of 2y. ii. Use logarithms to find the value of y correct to 3 significant figures. Solution i. We are given; We can write it as; Let , then; Now we have two options. Since ; Taking natural logarithm of both […]
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; It can be written as; We have to consider two separate cases; When ; When ; Hence, the only solutions for the given equation are; […]