Question It is given that i. Show that ii. Use an iterative formula based on the equation in part (i) to find the value of a correct to 3 decimal places. Give the result of each iteration to 5 decimal places. Solution i. We are given that; Rule for integration of […]
Question The parametric equations of a curve are Find the equation of the tangent to the curve when t = 0 giving your answer in the form ax + by + c = 0, where a, b and c are integers. Solution We are required to find the equation of tangent to the curve at […]
Question Find the exact value of giving the answer in the form ln k. Solution We are required to find the exact value of Rule for integration of is: This integral is valid only when . Division Rule; Power Rule;
Question Find the x-coordinates of the stationary points of the following curves: i. ii. Solution i. First we are required to find the x-coordinate of the stationary points of the following curve. A stationary point on the curve is the point where gradient of the curve is equal to […]
Question The variables x and y satisfy the equation y = Kxm, where K and m are constants. The graph of ln y against ln x is a straight line passing through the points (0.22, 3.96) and (1.32, 2.43), as shown in the diagram. Find the values of K and m, correct to 2 significant […]
Question i. Find ii. Find the exact value of Solution i. We are required find; We know that; Therefore; Hence; Rule for integration of is: Rule for integration of is: Rule for integration of is: Rule for integration of is: ii. We are required to find […]
Question i. By sketching a suitable pair of graphs, show that the equation has exactly one real root . ii. Verify by calculation that 4.5 < < 5.0. iii. Use the iterative formula to find correct to 2 decimal places. Give the result of each iteration to 4 decimal places. Solution […]
Question A. Find the gradient of the curve At the point (1,1). B. The parametric equations of a curve are Find the gradient of the curve at the point (−3, 3). Solution A. We are given equation of the curve as; We are required to find expression for gradient of the curve. Gradient (slope) […]
Question The diagram shows the curve and its minimum point M. i. Show that the x-coordinate of M is . ii. The region shaded in the diagram is enclosed by the curve and the lines , and . Use integration to show that the area of the shaded region is . Solution […]
Question A. Find the gradient of the curve At the point (1,1). B. The parametric equations of a curve are Find the gradient of the curve at the point (−3, 3). Solution A. We are given equation of the curve as; We are required to find expression for gradient of the curve. Gradient (slope) […]
Question The diagram shows the curve and its minimum point M. i. Show that the x-coordinate of M is . ii. The region shaded in the diagram is enclosed by the curve and the lines , and . Use integration to show that the area of the shaded region is . […]
Question i. Given that show that the positive constant a satisfies the equation ii. Use an iterative formula, , with to find the value of correct to 3 decimal places. Give the result of each iteration to 5 decimal places. Solution i. We are given that; Rule for integration of is: Rule for […]
Question The variables x and y satisfy the equation where A and p are constants. The graph of against x is a straight line passing through the points (2,1.60) and (5, 2.92) as shown in the diagram. Find the values of A and p correct to 2 significant figures. Solution We are given; Taking natural […]
Question i. Solve the equation . ii. Hence, using logarithms, solve the equation , giving the answer correct to 3 significant figures. Solution i. SOLVING EQUATION: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases; OR We have the equation; We have […]
Question i. Solve the equation . ii. Hence, using logarithms, solve the equation , giving the answer correct to 3 significant figures. Solution SOLVING EQUATION: ALGEBRAICALLY i. Let, . We can write it as; We have to consider two separate cases; When When We have the equation; It […]
Question Use logarithms to solve the equation 5x+3 = 7x−1 giving the answer correct to 3 significant figures. Solution We are given; Taking natural logarithm of both sides; Power Rule;
Question i. Use logarithms to solve the equation 2x = 205, giving the answer correct to 3 significant figures. ii. Hence determine the number of integers n satisfying Solution i. We are required to solve the equation; Taking natural logarithm of both sides; Power Rule; ii. We are […]
Question i. Use logarithms to solve the equation 2x = 205, giving the answer correct to 3 significant figures. ii. Hence determine the number of integers n satisfying Solution i. We are required to solve the equation; Taking natural logarithm of both sides; Power Rule; ii. We are […]
Question i. Solve the equation . ii. Hence, using logarithms, solve the equation , giving the answer correct to 3 significant figures. Solution i. SOLVING EQUATION: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases; OR We have the equation; We have […]