Question The diagram shows the curve The curve crosses the y-axis at the point P and the gradient of the curve at P is m. The point Q on the curve has x-coordinate q and the gradient of the curve at Q is −m. i. Find the value of m and hence show that q […]
Question The parametric equations of a curve are , i. Find in terms of t and hence find the coordinates of the stationary point, giving each coordinate correct to 2 decimal places. ii. Find the gradient of the normal to the curve at the point where the curve crosses the x-axis. Solution […]
Question The polynomial is defined by where and are constants. It is given that is a factor of . It is also given that the remainder is 40 when is divided by . i. Find the values of a and b. ii. When a and b have these values, factorise p(x) completely. Solution […]
Question i. Find ii. Given that find the value of the positive constant a. Solution i. We are required to find; We have the trigonometric identity; It can be rearranged as; Therefore; provided that It can be rearranged as; Therefore; Rule for integration of is: Rule for integration of is: […]
Question Solve the equation for . Solution We are given the equation; Using calculator; Using calculator; To find the other solution of we utilize the odd/even property of . Properties of Domain Range Periodicity Odd/Even Translation/ Symmetry We use odd/even property; Therefore, we have two solutions (roots) of the equation; To find all the solutions […]
Question It is given that the variable x is such that and Find the set of possible values of x, giving your answer in the form a < x < b where the constants a and b are correct to 3 significant figures. Solution First we find the value of x for; Taking natural […]
Question Solve the equation ln(3x + 1) – ln(x + 2) = 1, giving your answer in terms of e. Solution We are given; Division Rule; We can write it as; Taking anti-logarithm of both sides; For any ;