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Hits: 183 Question The function is defined for . It is given that has a minimum value when and that . (i) Find . It is now given that , and are the first three terms respectively of an arithmetic progression. (ii) Find the value of . (iii) Find , and hence find the minimum value of […]
Hits: 183 Question a. Fig. 1 shows part of the curve and the line y = h, where h is a constant. (i) The shaded region is rotated through 360o about the y-axis. Show that the volume of revolution, V, is given by […]
Hits: 224 Question A(-1,1) and P(a,b) are two points, where a and b are constants. The gradient of AP is 2. (i) Find an expression for b in terms of a. (ii) B(10,-1) is a third point such that AP = AB. Calculate the coordinates of the possible positions […]
Hits: 443 Question The diagram shows two circles with centres A and B having radii 8 cm and 10 cm respectively. The two circles intersect at C and D where CAD is a straight line and AB is perpendicular to CD. (i) Find angle ABC in radians. (ii) Find the area of the shaded region. Solution (i) It is evident from […]
Hits: 188 Question The line 3y+x=25 is a normal to the curve y= x2 – 5x + k. Find the value of the constant k. Solution If a line is normal to the curve , then product of their slopes and at that point (where line is normal to the curve) is; Therefore, by finding slopes of both the […]
Hits: 147 Question (i) Show that the equation may be expressed as . (ii) Hence solve the equation for 0o < < 180o. Solution (i) We are given that; Utilizing ; (ii) We are required to solve the equation for 0o < < 180o. From (i) we know that given equation can be written as; Now we have two options. Using […]
Hits: 207 Question Relative to an origin O, the position vectors of points A, B and C are given by and The point P lies on AB and is such that . i. Find the position vector of P. ii. Find the distance OP. iii. Determine whether OP is perpendicular to AB. Justify your answer. Solution i. We are […]
Hits: 174 Question Find the coordinates of the points of intersection of the curve with the curve . Solution If two lines (or a line and a curve) intersect each other at a point then that point lies on both lines i.e. coordinates of that point have same values on both lines (or on the line and the […]
Hits: 291 Question The common ratio of a geometric progression is r. The first term of the progression is and the sum to infinity is S. i. Show that S = 2 − r. ii. Find the set of possible values that S can take. Solution i. From the given information, we can compile following data about […]
Hits: 149 Question The coefficients of and in the expansion of are equal. Find the value of the non-zero constant a. Solution We need to equate the coefficients of and in the expansion of given expression. We are given expression as; Expression for the general term in the Binomial expansion of is: In the given case: Hence; Since we are looking for […]
Hits: 364 Question i. Express in the form , where a, b and c are constants. The function is defined by for , where p is a constant. ii. State the smallest value of for which is a one-one function. iii. For this value of , obtain an expression for , and state the domain of . iv. State the set of values […]
