Question The one-one function f is defined by for , where is a constant. a. i. State the greatest possible value of . ii. It is given that takes this greatest possible value. State the range of f and find an expression for . b. The function g is defined by […]
Question A curve has equation . The point A on the curve has coordinates . i. a. Find and simplify the equation of the normal through A. b. Find the x-coordinate of the point where this normal meets the curve again. […]
Question The diagram shows a triangle OAB in which angle ABO is a right angle, angle AOB = radians and AB = 5 cm. The arc BC is part of a circle with centre A and meets OA at C. The arc CD is part of a circle with centre O and meets OB at […]
Question The diagram shows a solid figure OABCDEF having a horizontal rectangular base OABC with OA = 6 units and AB = 3 units. The vertical edges OF, AD and BE have lengths 6 units, 4 units and 4 units respectively. Unit vectors , and are parallel to , and respectively. i. Find . […]
Question The diagram shows part of the curve with equation y = k(x3 − 7×2 + 12x) for some constant k. The curve intersects the line y = x at the origin O and at the point A(2, 2). i. Find the value of k. ii. Verify that the curve meets the line […]
Question A curve has a stationary point at and has an equation for which , where is a non-zero constant. i.Find the value of . ii.Find the equation of the curve. iii.Determine, showing all necessary working, the nature of the stationary point Solution i. We are given that; A stationary point on the curve is […]
Question i. Show that the equation may be expressed as ii. Hence solve the equation for . Solution i. We are given the equation; We have the trigonometric identity; From this we can substitute in above equation; ii. We are required to solve the equation for . From (i) we […]
Question The first term of a series is 6 and the second term is 2. i. For the case where the series is an arithmetic progression, find the sum of the first 80 terms. ii. For the case where the series is a geometric progression, find the sum to infinity. Solution i. […]
Question Two points A and B have coordinates (3a, -a) and (-a, 2a) respectively, where a is a positive constant. i. Find the equation of the line through the origin parallel to AB. ii. The length of the line AB is units. Find the value of a. Solution i. We are […]
Question A line has equation y = x + 1 and a curve has equation y = x2 + bx + 5. Find the set of values of the constant b for which the line meets the curve. Solution If two lines (or a line and a curve) intersect each other at a point then […]
Question Showing all necessary working, solve the equation . Solution We are required to solve the equation; Let , then taking square of both sides results in . Hence the given equation becomes; Now we have two options. Since ;