Question i. Express in the form , where a and b are integers. ii. Hence express in the form where R > 0 and . iii. Using the result of part (ii), solve the equation for . Solution i. We are given the expression; provided that provided that […]
Question A curve has parametric equations i. Find an expression for in terms of t. ii. Find the exact value of at the stationary point. iii. Find the gradient of the curve at the point where it crosses the x-axis. Solution i. We are required to find for the parametric […]
Question The diagram shows the curve for 0 ≤ x ≤ 6. The region bounded by the curve and the lines x = 0, x = 6 and y = 0 is denoted by R. i. Use the trapezium rule with 2 strips to find an estimate of the area of R, giving your […]
Question The polynomial is defined by where is a constant. It is given that is a factor of i. Use the factor theorem to find the value of . ii. Factorise p(x) and hence show that the equation p(x) = 0 has only one real root. iii. Use logarithms to […]
Question i. Find ii. Without using a calculator, find the exact value of Solution i. We are required to find; We know that ; Therefore; Hence; Rule for integration of is: Rule for integration of is: Rule for integration of is: ii. We are required to find the exact […]
Question The variables x and y satisfy the equation y = Kxp, where K and p are constants. The graph of ln y against ln x is a straight line passing through the points (1.28, 3.69) and (2.11, 4.81), as shown in the diagram. Find the values of K and p correct to 2 decimal […]
Question The sequence of values given by the iterative formula With initial value , converges to . i. Determine the value of correct to 3 decimal places, giving the result of each iteration to 5 decimal places. ii. State an equation satisfied by and hence find the exact value of . Solution […]