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Hits: 116 Question The diagram shows part of the curve . i. Find the equation of the normal to the curve at the point where x=1 in the form , where m and c are constants. The shaded region is bounded by the curve, the coordinate axes and the line x=1. ii. Find, showing all necessary working, the volume obtained […]
Hits: 137 Question The function f is defined by for , . i. Find an expression for . The function g is defined by for , where a is a constant. ii. Find the value of a for which . iii. Find the possible values of a given that the equation has two equal roots. Solution i. […]
Hits: 312 Question In the diagram, OAXB is a sector of a circle with centre O and radius 10 cm. The length of the chord AB is 12 cm. The line OX passes through M, the mid-point of AB, and OX is perpendicular to AB. The shaded region is bounded by the chord AB and by the […]
Hits: 98 Question A curve for which passes through the point (3,-10). i. Find the equation of the curve. ii. Express in the form , where a and b are constants. iii. Find the set of values of x for which the gradient of the curve is positive. Solution i. We can find equation of the […]
Hits: 187 Question The horizontal base of a solid prism is an equilateral triangle of side x cm. The sides of the prism are vertical. The height of the prism is h cm and the volume of the prism is 2000 cm3. i. Express h in terms of x and show that the total surface area of the […]
Hits: 187 Question The equation of a curve is . i. Sketch the graph of for , stating the coordinates of the point of intersection with the y-axis. Points P and Q lie on the curve and have x-coordinates of and respectively. ii. Find the length of PQ correct to 1 decimal place. The line through […]
Hits: 135 Question a. An arithmetic progression has a first term of 32, a 5th term of 22 and a last term of −28. Find the sum of all the terms in the progression. b. Each year a school allocates a sum of money for the library. The amount allocated each year increases by 2.5%of the amount […]
Hits: 181 Question i. Prove the identity ii. Hence solve the equation for . Solution i. We have the trigonometric identity; We can write from this identity; Therefore; ii. We have the equation; From (i) we know that left hand side of given equation can be written as; Therefore; Using calculator […]
Hits: 135 Question Relative to an origin O, the position vectors of points A and B are given by and and angle AOB=90o. i. Find the value of . The point C is such that . ii. Find the unit vector in the direction of . Solution i. It is evident that angle AOB is between and . […]
Hits: 139 Question The coefficients of and in the expansion of are and respectively. Find the value of . . Solution We can find the coefficients of and in the expansion of given expression. Let us first find the coefficient of in the expansion of . We are given expression as; Expression for the general term in the Binomial expansion of is: […]
