Question The length, metres, of a Green Anaconda snake which is t years old is given approximately by the formula where 1 t 10. Using this formula, find i. ii. the rate of growth of a Green Anaconda snake which is 5 years old. Solution i. We are given; We are required to find . […]
Question A curve has equation and a line has equation , where is a non-zero constant. i. Find the set of values of for which the curve and the line have no common points. ii. State the value of for which the line is a tangent to the curve and, for this case, find the coordinates of the […]
Question The diagram shows part of the curve . The curve cuts the y-axis at A and the line at B. i. Show that the equation of the line AB is . ii. Find the volume obtained when the shaded region is rotated through 360o about the x-axis. Solution i. To find the equation of the line either we […]
Question The diagram shows an open rectangular tank of height meters covered with a lid. The base of the tank has sides of length meters and meters and the lid is a rectangle with sides of length meters meters. When full the tank holds 4m3 of water. The material from which the tank is made is of negligible thickness. The […]
Question The diagram shows a pyramid OABCP in which the horizontal base OABC is a square of side 10 cm and the vertex P is 10 cm vertically above O. The points D, E, F, G lie on OP, AP, BP, CP respectively and DEFG is a horizontal square of side 6 cm. The height of DEFG above […]
Question The diagram shows part of the curve and the line . The curve and the line meet at points A and B. i. Find the coordinates of A and B. ii. Find the length of the line AB and the coordinates of the mid-point of AB. Solution i. If two lines (or a line and a curve) […]
Question The diagram shows points A, C, B, P on the circumference of a circle with centre O and radius 3 cm. Angle AOC = angle BOC = 2.3 radians. i. Find angle AOB in radians, correct to 4 significant figures. ii. Find the area of the shaded region ACBP, correct to 3 significant figures. Solution i. We know that […]
Question Prove the identity Solution We have the equation; We have the relation , therefore, We have the trigonometric identity; We can write it as; Therefore; We have the relation , therefore,
Question The function f is defined by for . i. Express in the form of and hence state the range of . ii. Obtain an expression for and state the domain of . The function g is defined by for . The function is such that and the domain of is . iii. Obtain an expression for . Solution i. […]
Question i. Find the first three terms in the expansion, in ascending powers of . ii. Find the coefficient in the expansion of . Solution i. Expression for the Binomial expansion of is: First rewrite the given expression in standard form. In the given case: Hence; ii. To find the coefficient of in the expansion of […]
Question a) The first and second terms of an arithmetic progression are 161 and 154 respectively. The sum of the first terms is zero. Find the value of . b) A geometric progression, in which all the terms are positive, has common ratio r. The sum of the first terms is less than 90% of the sum […]