Question i. Express in the form , where and , stating the exact value of R and and the value of correct to 2 decimal places. ii. Hence solve the equation Giving all solutions in the interval . Solution i. We are given the expression; We are required to write it in […]
Question A. Find i. ii. B. Use the trapezium rule with 2 intervals to estimate the value of giving your answer correct to 2 decimal places. Solution A. i. We are required to find; Rule for integration of is: Rule for integration of is: Rule for integration of […]
Question The parametric equations of a curve are , , for . i. Show that . ii. Find the coordinates of the point on the curve at which the gradient is -4. Solution i. We are required to show that for the parametric equations given below; If a curve is given parametrically […]
Question i. The polynomial , where a is a and b are constants, is denoted by . It is given that when p(x) is divided by (x – 3) the remainder is 14, and that when p(x) is divided by (x + 2) the remainder is 24. Find the values of a and b. […]
Question The equation of a curve is . Find the exact x-coordinate of each of the stationary points of the curve and determine the nature of each stationary point. Solution First we are required to find the exact x-coordinate of each of the stationary points of the curve. A stationary point on the curve is […]
Question The diagram shows the curve y = x4 +2x −9. The curve cuts the positive x-axis at the point P. i. Verify by calculation that the x-coordinate of P lies between 1.5 and 1.6. ii. Show that the x-coordinate of P satisfies the equation iii. Use the iterative formula to determine the x-coordinate […]
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 to following […]