Hits: 506
Hits: 506 Question The diagram shows part of the curve and a point and which lie on the curve. The tangent to the curve at B intersects the line at the point C. i. Find the coordinates of C. ii. Find the area of the shaded region. Solution i. We are required to find the coordinates of point C. […]
Hits: 1166 Question The diagram shows three points , and . The point X lies on AB, and CX is perpendicular to AB. Find, by calculation, i. the coordinates of X, ii. the ratio AX : XB. Solution i. We are required to find the coordinates of point X. It is evident from the diagram that point […]
Hits: 481 Question The non-zero variables x, y and u are such that . Given that , find the stationary value of u and determine whether this is a maximum or a minimum value. Solution We are given that; We are also given; Substituting this value of in the equation of . A stationary point on the curve is the point where gradient of the […]
Hits: 425 Question i. Express the equation as a quadratic equation in . ii. Solve the equation for , giving solutions in terms of . Solution i. We are given that; We know that; Therefore; We have the trigonometric identity; It can be rearranged as follows; Substituting this expression of in the above equation; It can be rewritten as; This […]
Hits: 2552 Question The diagram shows a circle C with centre O and radius 3 cm. The radii OP and OQ are extended to S and R respectively so that ORS is a sector of a circle with centre O. Given that PS = 6 cm and that the area of the shaded region is equal to […]
Hits: 289 Question A curve is such that and is a point on the curve. Find the equation of the curve. Solution We are given that curve passes through the point and we are required to find the equation of the curve. We can find equation of the curve from its derivative through integration; For the given case; Therefore; Rule […]
Hits: 653 Question The diagram shows a parallelogram OABC in which relative to an origin , the position vectors of three points A, B and C are given by and i. Use a scalar product to find angle BOC. ii. Find a vector which has magnitude 35 and is parallel to the vector . Solution i. We recognize that […]
Hits: 365 Question A function is defined by , for , where is a constant. i. In the case where , solve the equation . The function is defined by , . ii. Find the set of values of for which the equation has no real solutions. The function h is defined by , . iii. Find an expression for . Solution i. […]
Hits: 432 Question i. Find the first three terms in the expansion of in ascending powers of . ii. Given that coefficient of in the expansion of is 240, find the possible values of . Solution i. Expression for the Binomial expansion of is: In the given case: Hence; ii. To find the value of in the expansion of […]
Hits: 1237 Question a) In an arithmetic progression, the sum, , of the first terms is given by . Find the first term and the common difference of the progression. b) The first 2 terms of a geometric progression are 64 and 48 respectively. The first 3 terms of the geometric progression are also the 1st term, […]