Question The curve C has equation . The point P, which lies on C, has coordinates (2, 1). a. Show that an equation of the tangent to C at the point P is y = 3x – 5. The point Q also lies on C. Given that the tangent to C at Q is parallel to […]
Question A curve with equation y=f(x) passes through the point (3,6). Given that a. use integration to find f(x). Give your answer as a polynomial in its simplest form. b. Show that , where p is a positive constant. State the value of p. c. Sketch the graph of y = f(x), showing the coordinates of […]
Question The equation 2×2 + 2kx + (k+2) = 0, where k is a constant, has two distinct real roots. a. Show that k satisfies k2 – 2k – 4 > 0 b. Find the set of possible values of k. Solution a. We are given that; For a quadratic equation , the expression for solution […]
Question Shelim starts his new job on a salary of £14 000. He will receive a rise of £1500 a year for each full year that he works, so that he will have a salary of £15 500 in year 2, a salary of £17 000 in year 3 and so on. When Shelim’s salary reaches £26 000, […]
Question The straight line has equation 2y = 3x + 7. The line crosses the y-axis at the point A as shown in Figure. a. i. State the gradient of . ii. Write down the coordinates of the point A. Another straight line intersects at the point B (1, 5) and crosses the x-axis at the point C, as shown in […]
Question Given that for all positive integers n, a) find the value of b) Find the value of Solution a. We are given that; We are required to find . Therefore, we substitute n=5; b. We are required to find . We can find as follows; Therefore ;
Question Figure 1 shows a sketch of a curve with equation y = f(x). The curve crosses the y-axis at (0, 3) and has a minimum at P (4, 2). On separate diagrams, sketch the curve with equation a. y = f(x + 4), b. y = 2f(x). On each diagram show the coordinates of minimum point and […]
Question Solve the simultaneous equations Solution We are given simultaneous equations; We rearrange the first equation to find x in terms of y. Substituting this from first equation in the second equation; We have the algebraic formula; Now we have two options. By substituting one-by-one these values of in first equation, we can find corresponding values of . For […]
Question , a. Find , giving each term in its simplest form. b. Find , giving each term in its simplest form. Solution a. We are given; We are required to find . Gradient (slope) of the curve is the derivative of equation of the curve. Hence gradient of curve with respect to is: Therefore; Rule for […]
Question Fully simplify a. b. Solution a. We are given; b. We are given; If we need a rational number in the denominator of a fraction, we need to follow procedure of “denominator rationalization” as given below. ü If the denominator is of the form then multiply both numerator and denominator by . ü If the denominator is of […]