Question A curve has equation Find the equation of the normal to the curve at the point (1, 2). Give your answer in the form ax + by + c = 0, where a, b and c are integers. Solution We are given equation of the curve as; We are required to find the equation […]
Question The parametric equations of a curve are Find the equation of the tangent to the curve at the point for which t = 0. Give 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 […]
Question The diagram shows the curve , for and its maximum point M. i. Show that ii. Hence find the x-coordinate of M, giving your answer correct to 2 decimal places.. Solution i. We are given that; Therefore; We apply product rule to find the derivative. If and are functions of […]
Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases; OR We have the equation; We have to consider both moduli separately and it leads to following cases; It cannot be solved for x. Hence, the only solution for the […]
Question The diagram shows the curve , for and its maximum point M. i. Show that ii. Hence find the x-coordinate of M, giving your answer correct to 2 decimal places.. Solution i. We are given that; Therefore; We apply product rule to find the derivative. If and are functions of […]
Question The parametric equations of a curve are Find the equation of the tangent to the curve at the point for which t = 0. Give 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 […]
Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases; OR We have the equation; We have to consider both moduli separately and it leads to following cases; It cannot be solved for x. Hence, the only solution for […]
Question The equation of a curve is 3×2+3xy+y2=3 i. Find the equation of the tangent to the curve at the point (2, −1), giving your answer in the form ax +by +c = 0, where a, b and c are integers. ii. Show that the curve has no stationary points. Solution […]
Question Solve the equation. Solution SOLVING EQUATION: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases; OR We have the equation; We have to consider both moduli separately and it leads to following cases; Hence, the only solution for the given equation is; SOLVING EQUATION: ALGEBRAICALLY […]
Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following with their corresponding inequality; When When When If then above four intervals translate to following […]
Question A sketch of part of the curve C with equation , x>0 is shown in Figure. Point A lies on C and has an x coordinate equal to 2 a. Show that the equation of the normal to C at A is y = –2x + 7. The normal to C at A meets C […]
Question The curve C has equation . The line L has equation y = 3x + k, where k is a positive constant. a. Sketch C and L on separate diagrams, showing the coordinates of the points at which C and L cut the axes. Given that line L is a tangent to C, b. find the […]
Question Figure 2 shows a right angled triangle LMN. The points L and M have coordinates (–1, 2) and (7, –4) respectively. a. Find an equation for the straight line passing through the points L and M. Give your answer in the form ax + by + c = 0, where a, b and c are integers. Given […]
Question Given that f(x) = 2×2 + 8x + 3 a. find the value of the discriminant of f(x). b. Express f(x) in the form p(x + q)2 + r where p, q and r are integers to be found. The line y = 4x + c, where c is a constant, is a tangent […]
Question A curve with equation y=f(x) passes through the point (4,25). Given that a. find f(x) simplifying each term. b. Find an equation of the normal to the curve at the point (4, 25). Give your answer in the form ax + by + c = 0, where a, b and c are integers to […]
Question The line , shown in figure has equation 2x+3y = 26. The line passes through the origin O and is perpendicular to . a. Find an equation for the line . The line intersects the line at the point C. Line crosses the y-axis at the point B as shown in Figure. b. Find the area of triangle OBC. […]
Question Figure 1 shows a sketch of the curve C with equation , x ≠ 0. The curve C crosses the x-axis at the point A. a. State the x coordinate of the point A. The curve D has equation y = x2(x – 2), for all real values of x. b. A copy of Figure 1 […]
Question The curve C has equation . The point P, which lies on C, has coordinates (2, 1). a. Show that an equation of the tangent to C at the point P is y = 3x – 5. The point Q also lies on C. Given that the tangent to C at Q is parallel to […]
Question A curve with equation y=f(x) passes through the point (3,6). Given that a. use integration to find f(x). Give your answer as a polynomial in its simplest form. b. Show that , where p is a positive constant. State the value of p. c. Sketch the graph of y = f(x), showing the coordinates of […]
Question The straight line has equation 2y = 3x + 7. The line crosses the y-axis at the point A as shown in Figure. a. i. State the gradient of . ii. Write down the coordinates of the point A. Another straight line intersects at the point B (1, 5) and crosses the x-axis at the point C, as shown in […]