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 The diagram shows the curve with parametric equations for . i. Show that . ii. Find the equation of the tangent to the curve at the point where the curve crosses the positive y-axis. Give the answer in the form y = mx +c. Solution i. We are required 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 The diagram shows part of the curve and its point of intersection P with the x-axis. i. Find the exact x-coordinate of P. ii. Show that the equation of the curve can be written and use integration to find the exact area of the shaded region enclosed by the curve and the […]
Question i. By sketching a suitable pair of graphs, show that the equation has two real root. ii. Use the iterative formula to find one of the real roots correct to 3 decimal places. Give the result of each iteration to 5 decimal places. iii. Hence find the coordinates of each of […]
Question The diagram shows part of the curve and its point of intersection P with the x-axis. i. Find the exact x-coordinate of P. ii. Show that the equation of the curve can be written and use integration to find the exact area of the shaded region enclosed by the curve and the […]
Question i. By sketching a suitable pair of graphs, show that the equation has two real root. ii. Use the iterative formula to find one of the real roots correct to 3 decimal places. Give the result of each iteration to 5 decimal places. iii. Hence find the coordinates of each […]
Question The equation of a curve is y3+4xy=16 i. Show that . ii. Show that the curve has no stationary points. iii. Find the coordinates of the point on the curve where the tangent is parallel to the y-axis. Solution i. We are required to find . Hence; To find […]
Question The equation of a curve is Find the equation of the tangent to the curve at the point . Give the answer in the form y = mx + c, where the values of m and c are correct to 3 significant figures. Solution We are required to find the equation of tangent to […]
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 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 A curve with equation y=f(x) passes through the point (4,9). Given that , x > 0 a. find f(x), giving each term in its simplest form. Point P lies on the curve. The normal to the curve at P is parallel to the line 2y + x = 0 b. Find x coordinate of […]
Question a. Factorise completely 9x – 4×3 b. Sketch the curve C with equation y = 9x – 4×3 Show on your sketch the coordinates at which the curve meets the x-axis. The points A and B lie on C and have x coordinates of –2 and 1 respectively. c. Show that the length of AB is […]
Question The curve C has equation , a. Find in its simplest form. b. Find an equation of the tangent to C at the point where x=-1. Give your answer in the form ax+by+c=0, where a, b and c are integers. Solution a. We are given; We are required to find . Gradient (slope) of the curve […]
Question A curve has equation and a line has equation , where k is a constant. a. Show that the x-coordinate of any point of intersection of the curve and the line satisfies the equation b. Given that the line and the curve do not intersect:. i. Show that . […]
Question A circle with center C has the equation . a. Express this equation in the form b. i. State the coordinates of C. ii. Find the radius of the circle, giving your answer in the form . c. i. The point P with coordinates (4,k) lies on the circle. Find the possible values of k. ii. The points […]
Question The diagram shows a sketch of a curve and a line. The curve has equation . The points A(-1,6) and B(2,30) lie on the curve. a. Find an equation of the tangent to the curve at the point A. b. i. Find ii. Calculate the area of the shaded region bounded by the curve and the line AB. […]
Question The line AB has equation . a. i. Find the gradient of AB. ii. Find an equation of the line that is perpendicular to the line AB and which passes through the point (-2,-3) . Express your answer in the form , where p, q and r are […]