Hits: 179
Hits: 179 Question i. Express in the form of where a, b and c are constants. The function f is defined by for . ii. State the largest value of the constant k for which f is a one-one function. iii. For this value of k find an expression for and state the […]
Hits: 65 Question A curve has equation and a line has equation , where is a constant. i.Show that, for all values of k, the curve and the line meet. ii.State the value of k for which the line is a tangent to the curve and find the coordinates of the point where the line […]
Hits: 31 Question The function f is defined by for . Determine, showing all necessary working, whether f is an increasing function, a decreasing function or neither. Solution We are given function; We are required to find whether is an increasing function, decreasing function or neither. To test whether a function is increasing or […]
Hits: 164 Question The equation of a curve is and the equation of a line is , where k is a constant. i. Find the set of values of k for which the line does not meet the curve. In the case where k = 15, the curve intersects the line at points A and […]
Hits: 153 Question The function f is defined by for . i. Express in the form of where a and b are constants. ii. State the range of . The function g is defined by for . iii. State the largest value of k for which g has an inverse. iv. Given that […]
Hits: 134 Question The diagram shows a triangle ABC in which BC = 20 cm and angle ABC = 90o. The perpendicular from B to AC meets AC at D and AD = 9 cm. Angle BCA = . i. By expressing the length of BD in terms of in each of the triangles […]
Hits: 420 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 […]
Hits: 168 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 […]
Hits: 63 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 ;
Hits: 263 Question The functions f and g are defined by for for . i. a. State the range of the function f. b. State the range of the function g. c. State the range of the function fg. ii. Explain why the function gf cannot be formed. iii. Find the set […]
Hits: 247 Question A curve has equation and a line has equation , where is a constant. i.Find the set of values of for which the curve and the line meet. ii.The line is a tangent to the curve for two particular values of . For each of these values find the x-coordinate of the […]
Hits: 559 Question The one-one function f is defined by for , where c is a constant. i. State the smallest possible value of c. In parts (ii) and (iii) the value of c is 4. ii. Find an expression for and state the domain of . iii. Solve the equation , […]
Hits: 732 Question i. The tangent to the curve y = x3 − 9×2 + 24x − 12 at a point A is parallel to the line y = 2 − 3x. Find the equation of the tangent at A. ii. The function f is defined by f(x) = x3 − 9×2 + 24x […]
Hits: 105 Question Express 3×2 − 12x + 7 in the form a(x + b)2 + c, where a, b and c are constants. Solution We have the expression; We use method of “completing square” to obtain the desired form. Next we complete the square for the terms which involve . We have the algebraic […]
Hits: 849 Question The function is defined by for . i. Express in the form , where a and b are constants. ii. State the coordinates of the stationary point on the curve y = f(x). The function is defined by for . iii. State the smallest value of k for […]
Hits: 557 Question The equation of a curve is , where is a constant. i. Find the set of values of for which the whole of the curve lies above the x-axis. ii. Find the value of for which the line y + 2x = 7 is a tangent to the curve. Solution […]
Hits: 764 Question The curve with equation passes through the origin. i. Show that the curve has no stationary points. ii. Denoting the gradient of the curve by m, find the stationary value of m and determine its nature. Solution i. We are required to show that curve has no stationary points. […]
Hits: 777 Question Functions f and g are defined for by; i.Find the points of intersection of the graphs of y = f(x) and y = g(x). ii.Find the set of values of x for which f(x) > g(x). iii.Find an expression for fg(x) and deduce the range of fg. The function h […]