Question The curve C has equation y=f(x), x>0, where Given that point P(4,5) lies on C, find a. f(x) b. an equation of the tangent to C at the point P, giving your answer in the form ax + by + c = 0, where a, b and c are integers. Solution a. We […]
Question a. On the axes below sketch the graphs of i. y = x (4 – x) ii. y = x2 (7 – x) showing clearly the coordinates of the points where the curves cross the coordinate axes. b. Show that the x-coordinates of the points of intersection of y = x (4 – x) and y = […]
Question a. Find an equation of the line joining A (7, 4) and B (2, 0), giving your answer in the form ax+by+c=0, where a, b and c are integers. b. Find the length of AB, leaving your answer in surd form. The point C has coordinates (2, t), where t > 0, and AC […]
Question a) Show that x2 + 6x + 11 can be written as (x + p)2 + q, where p and q are integers to be found. b) In the space at the top of page 7, sketch the curve with equation y = x2 + 6x +11, showing clearly any intersections with the coordinate axes. c) Find […]
Question f(x) = x2 + 4kx + (3+11k), where k is a constant. a) Express f(x) in the form (x + p)2 + q, where p and q are constants to be found in terms of k. Given that the equation f(x) = 0 has no real roots, b) find the set of possible values of […]
Question a) Factorise completely x3 – 4x b) Sketch the curve C with equation y = x3 – 4x showing the coordinates of the points at which the curve meets the x-axis. The point A with x-coordinates -1 and the point B with x-coordinate 3 lie on the curve C. c) Find an equation of the line which […]
Question The curve C has equation , x>0 a. Find in its simplest form. b. Find an equation of the tangent to C at the point where x=2. Solution a. We are given; We are required to find . Gradient (slope) of the curve is the derivative of equation of the curve. Hence gradient of curve with respect to […]
Question The line has equation 3x+5y-2=0. a. Find the gradient of line for . The line is perpendicular to and passes through the point (3,1). b. Find the equation of in the form y=mx+c, where m and c are constants.. Solution a. We are given equation of the line as; We are required to find the gradient of the line […]