Question The diagram shows a block of wood in the shape of a prism with triangular cross-section. The end faces are right-angled triangles with sides of lengths 3x cm, 4x cm and 5x cm, and the length of the prism is y cm, as shown in the diagram. The total surface area of the five faces is 144 […]
Question The curve with equation is sketched below. The point lies on the curve. a. i. Find ii. Hence find the area of the shaded region bounded by the curve and the line . b. The point lies on the curve with equation . i. Find the gradient of the curve at the point A. ii. Hence find an equation of the tangent to […]
Question The curve with equation is sketched below. a. i. Find the gradient of the curve with equation at the point A. ii. Hence find the equation of the normal to the curve at the point A, giving your answer in the form , where p and q are integers. b. i. Find the value of ii. Hence determine […]
Question a. Express in the form , where p and q are integers. b. i. Sketch the graph of , stating the coordinates of the minimum point and the point where the graph crosses the y-axis. ii. Write down an equation of the tangent to the graph of at its vertex. c. […]
Question The depth of water, y metres, in a tank after time t hours is given by , a. Find: i. ii. b. Verify that y has a stationary value when and determine whether it is a maximum value or a minimum value. c. i. Find the rate of change of the depth of water, in metres […]