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Hits: 24 Question Figure shows a sketch of the curve H with equation; , a. Give the coordinates of the point where H crosses the x-axis. b. Give the equations of the asymptotes to H. c. Find an equation for the normal to H at the point P(–3, 3). This normal crosses the x-axis […]
Hits: 36 Question Given the simultaneous equation; Where k is a non zerp constant. a. Show that Given that has equal roots, b. find the value of K. Solution a. We are given that; To write a single equation in terms of x and k, we find expression for y from first equation; We substitute this expression […]
Hits: 18 Question , a. Show that Where A and B are constants to be found. b. Find Given that the point (-3,10) lies on the curve with equation y=f(x), c. Find f(x). Solution a. We are given; Therefore; b. We are given; We are required to find . Second derivative is the derivative of […]
Hits: 93 Question Figure 1 shows a sketch of the curve with equation y = f(x) where , The curve crosses the x-axis at (1, 0), touches it at (–3, 0) and crosses the y-axis at (0, –9). a. In the space below, sketch the curve C with equation y=f(x+2) and state the coordinates of the points […]
Hits: 150 Question A company, which is making 200 mobile phones each week, plans to increase its production. The number of mobile phones produced is to be increased by 20 each week from 200 in week 1 to 220 in week 2, to 240 in week 3 and so on, until it is producing 600 in week N. […]
Hits: 22 Question The straight line L1 passes through the points (–1, 3) and (11, 12). a. Find an equation for L1 in the form ax + by + c = 0, where a, b and c are integers. The line L2 has equation 3y + 4x – 30 = 0. b. Find the coordinates of the point […]
Hits: 10 Question Find the set of values of x for which a. b. Solution a. We are given; b. We are required to solve the inequality; We solve the following equation to find critical values of ; Now we have two options; Hence the critical points on the curve for the given condition are & -3. […]
Hits: 15 Question A sequence is defined by , for Where is a constant. a) Find an expression for in terms of k. Given that , b) Find the two possible values of k. Solution a) We are given that sequence is defined by We are required to find . We can utilize the given expression for general terms […]
Hits: 5 Question a. Find the value of . b. Simplify fully . Solution a. b.
Hits: 11 Question Find giving each term in its simplest form. Solution We are given; Rule for integration of is: Rule for integration of is:
Hits: 7 Question Simplify giving your answer in the form , where a and b are integers. Solution 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 […]