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Hits: 50 Question The diagram shows the curve . The shaded region R is bounded by the curve and by the lines x = 0, y = 0 and x = a, where a is positive. The area of R is equal to . i. Find an equation satisfied by a, and show […]
Hits: 45 Question A. Find B. i. Use the trapezium rule with 2 intervals to estimate the value of giving your answer correct to 3 decimal places. ii. Using a sketch of the graph of for , explain whether the trapezium rule gives an under-estimate or an over-estimate of the true value of […]
Hits: 62 Question The parametric equations of a curve are i. Find the exact value of the gradient of the curve at the point P where y = 6. ii. Show that the tangent to the curve at P passes through the point . Solution i. We are need for […]
Hits: 32 Question i. The polynomial , where a is a and b are constants, is denoted by . It is given that and (x + 2) are factors of p(x). Find the values of a and b. ii. When a and b have these values, factorise p(x) completely. Solution i. We are […]
Hits: 28 Question Solve the equation , giving all solutions in the interval . Solution We are required to solve the equation; We know that; provided that provided that Hence; We have the trigonometric identity; From this we can get; Therefore; Let ; Now we have two options. Since Using calculator we can […]
Hits: 13 Question The curve has one stationary point. Find the coordinates of this stationary point. Solution We are required to find the coordinates of point M which is minimum point of the curve; A stationary point on the curve is the point where gradient of the curve is equal to zero; Since point […]
Hits: 9 Question i. Find ii. Hence find , expressing your answer in the form ln a, where a is an integer. Solution i. We are required to find; Rule for integration of is: This integral is valid only when . ii. We are required to find; Rule for integration of is: This […]