Hits: 472
Hits: 472 Question i. Prove the identity ii. Hence solve the equation for Solution i. First, we are required to show that; Since ; We have the trigonometric identity; From this we can write; Therefore; We have the algebraic formula; ii. We are required to solve the equation; […]
Hits: 419 Question The function f is defined by for . i. Express in the form of where and are constants. ii. State the greatest value of . The function g is defined by for . iii. Find the value of for which . Solution i. We have the expression; […]
Hits: 426 Question The diagram shows a trapezium ABCD in which the coordinates of A, B and C are (4, 0), (0, 2) and (h, 3h) respectively. The lines BC and AD are parallel, angle ABC = 90o and CD is parallel to the x- axis. i. Find, by calculation, the value of h. […]
Hits: 444 Question A sector of a circle of radius cm has an area of cm2. Express the perimeter of the sector in terms of and . Solution We are given that for the circular sector; We are required to find expression for perimeter of the circular sector. Expression for perimeter of a circular sector […]
Hits: 391 Question The line , where is a constant, is a tangent to the curve at the point on the curve. i.Find the value of . ii.Find the coordinates of . Solution i. We are given equation of the line as; We are given equation of the curve as; It is given that line […]
Hits: 734 Question The term independent of x in the expansion of , where k is a constant, is 540. (i) Find the value of k. (ii) For this value of k, find the coefficient of x2 in the expansion. Solution (i) Expression for the general term in the Binomial expansion of is: In […]
Hits: 142 Question The diagram shows the curve with equation . i.The straight line with equation y = x + 3 intersects the curve at points A and B. Find the length of AB. ii.The tangent to the curve at a point T is parallel to AB. Find the coordinates of T. iii.Find the coordinates […]
Hits: 220 Question The diagram shows part of the curve with equation . The shaded region is bounded by the curve, the x-axis and the line x = 3. i. Find, showing all necessary working, the volume obtained when the shaded region is rotated through 360O about the x-axis. ii. P is the […]
Hits: 276 Question i. Express in the form of . The function f is defined by for , where is constant. ii. State the largest value of for which is a decreasing function. The value of is now given to be 1. iii. Find an expression for and state the domain of . […]
Hits: 181 Question a) Solve the equation for . b) The diagram shows part of the graph of , where is measured in radians and and are constants. The curve intersects the x-axis at and the y-axis at . Find the values of and . Solution a) We are required to solve the […]
Hits: 284 Question i. The first and second terms of a geometric progression are p and 2p respectively, where p is a positive constant. The sum of the first n terms is greater than 1000p. Show that 2n > 1001. ii. In another case, p and 2p are the first and second terms […]
Hits: 233 Question Two vectors, and , are such that and Where is a constant. i. Find the values of for which is perpendicular to . ii. Find the angle between and when q = 0. Solution i. We are given that; If and & , then and are perpendicular. Therefore, if […]
Hits: 182 Question A curve has equation . i. Find and . ii. Find the x-coordinates of the stationary points and, showing all necessary working, determine the nature of each stationary point. Solution i. We are required to find and . Therefore, we find the derivative of equation of the curve. […]
Hits: 390 Question In the diagram, CXD is a semicircle of radius 7 cm with centre A and diameter CD. The straight line YABX is perpendicular to CD, and the arc CYD is part of a circle with centre B and radius 8 cm. Find the total area of the region enclosed by the two […]
Hits: 182 Question A curve with equation y = f(x) passes through the points (0, 2) and (3, −1). It is given that , where is a constant. Find the value of . Solution i. We can find equation of the curve from its derivative through integration; For the given case; Therefore; Rule for […]
Hits: 314 Question The coefficient of in the expansion of is -2160. Find the value of the constant . Solution We are given expression as; Expression for the general term in the Binomial expansion of is: First rewrite the given expression in standard form. In the given case: Hence; Since we are looking for the […]
Hits: 481 Question i. Find the quotient when is divided by , and show that the remainder is 5. ii. Show that the equation has exactly one real root. Solution i. Hence quotient is and remainder is . ii. We are required to show that following equation has exactly […]