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Hits: 56 Question The gradient of a curve C is given by , x≠0. a. Show that . The point (3, 20) lies on C. b. Find an equation for the curve C in the form y = f(x). Solution a. We are given that; b. We are given that point (3,20) lies […]
Hits: 834 Question The points Q (1, 3) and R (7, 0) lie on the line , as shown in Figure. The length of QR is . a. Find the value of a. The line l2 is perpendicular to , passes through Q and crosses the y-axis at the point P, as shown in Figure. Find […]
Hits: 55 Question The curve C has equation , where k is a constant. a. Find . Point A with x-coordinate lies on C. The tangent to C at A is parallel to the line with equation . Find b. The value of k. c. The value of y-coordinate of A. Solution a. Gradient (slope) of […]
Hits: 533 Question Given that the equation 2qx2 + qx – 1 = 0, where q is a constant, has no real roots, a. show that q2 + 8q < 0. b. Hence find the set of possible values of q. Solution a. We are given; We are given that given equation has no real roots. […]
Hits: 231 Question Sue is training for a marathon. Her training includes a run every Saturday starting with a run of 5 km on the first Saturday. Each Saturday she increases the length of her run from the previous Saturday by 2 km. a. Show that on the 4th Saturday of training she runs 11 km. b. […]
Hits: 35 Question The curve C has equation and the line has equation y = 2x + 5. a. On the axes below, sketch the graphs of C and , indicating clearly the coordinates of any intersections with the axes. b. Find the coordinates of the points of intersection of C and . Solution a. […]
Hits: 52 Question A sequence x1, x2, x3, …. ……. is given by: x1=1, xn+1=axn – 3, n≥1, where a is a constant. a. Find an expression for x2 in terms of a. b. Show that x3=a2 – 3a – 3. Given that x3=7, c. find the possible values of a. Solution a. We are given […]
Hits: 13 Question , a. Differentiate to find . Given that , b. Find the value of x. Solution a. We are required to differentiate; Rule for differentiation of is: Rule for differentiation of is: Rule for differentiation is of is: b. We are given that; We have found in (a) that; We are given that […]
Hits: 65 Question Figure 1 shows a sketch of the curve with equation y = f(x). The curve passes through the point (0,7) and has a minimum point at (7, 0). On separate diagrams, sketch the curve with equation a. y = f(x) + 3, b. y = f(2x). On each diagram, show clearly the coordinates […]
Hits: 11 Question Factorise completely x3 – 9x Solution
Hits: 14 Question Find Solution We are required to find; Rule for integration of is: Rule for integration of is: Rule for integration of is: