Question The line has equation y=3x+2 and the line has equation 3x+2y-8=0. a. Find the gradient of line for . The point of intersection of and is P. b. Find the coordinates of P. The lines and cross the line y=1 at the points A and B respectively. c. Find the area of triangle ABP. Solution a. […]
Question The curve C has equation , . The points P and Q lie on C and have x-coordinates 1 and 2 respectively. a. Show that the length of PQ is . b. Show that the tangents to C at P and Q are parallel. c. Find an equation for the normal to C at […]
Question The curve C has equation y= f(x) passes through the point (5,65). Given that; a. Use integration to find f(x). b. Hence show that c. In the space provided on page 17, sketch C, showing the coordinates of the points where C crosses the x-axis. Solution a. We are required to find f(x), when; […]
Question Figure 1 shows a sketch of the curve with equation , x ≠0. a. On a separate diagram, sketch the curve with equation , x≠−2, showing the coordinates of any point at which the curve crosses a coordinate axis. b. Write down the equations of the asymptotes of the curve in part (a). Solution a. […]
Question a. On the same axes sketch the graphs of the curves with equations i. y=x2(x –2), ii. y=x(6 –x), and indicate on your sketches the coordinates of all the points where the curves cross the x-axis. b. Use algebra to find the coordinates of the points where the graphs intersect. Solution a. […]
Question The curve C has equation , x > 0. a. Find an expression for . b. Show that the point P (4, 8) lies on C. c. Show that an equation of the normal to C at the point P is 3y=x + 20. The normal to C at P cuts the x-axis at […]
Question The curve C has equation y= f(x), x ≠ 0, and the point P(2,1) lies on C. Given that; a. find f(x). b. Find an equation for the tangent to C at the point P, giving your answer in the form y =mx + c, where m and c are integers. Solution a. We are required […]
Question a. i. Express in the form , where p and q are integers. ii. Write down the coordinates of the vertex (minimum point) of the curve with equation iii. […]
Question The point and have coordinates and respectively. a. i. Show that the gradient of AB is . ii. Hence find an equation of the line AB, giving your answer in the form , where a, b and c are integers. b. i. Find an equation of the line which passes through […]
Question The curve with equation is sketched below. The curve cuts the x-axis at the point A (-1, 0) and cuts the y-axis at the point B. a. i. State the coordinates of the point B and hence find the area of the triangle AOB, where O is the origin. […]
Question The line AB has equation and the point A has coordinates . a. i. Find the gradient of AB. ii. Hence find an equation of the straight line which is perpendicular to AB and which passes through A. b. The line AB intersects the line with equation at the point B. Find the coordinates of B. c. The point C […]