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Hits: 166 Question Figure shows a sketch of part of the curve y = f(x), , where f(x) = (2x – 5)2(x + 3) a. Given that i. the curve with equation y = f(x) – k, , passes through the origin, find the value of the constant k, ii. the curve with equation y = f(x + c), […]
Hits: 371 Question a. On separate axes sketch the graphs of i. y = –3x + c, where c is a positive constant, ii. On each sketch show the coordinates of any point at which the graph crosses the y-axis and the equation of any horizontal asymptote. Given that y = –3x + c, where c is a positive […]
Hits: 145 Question The straight line , shown in Figure, has equation 5y = 4x + 10. The point P with x coordinate 5 lies on . The straight line is perpendicular to and passes through P. a. Find an equation for , writing your answer in the form ax + by + c = […]
Hits: 438 Question The curve C has equation y=f(x), x>0, where Given tht the point P(4,-8) lies on the curve C; a. find the equation of the tangent to C at P, giving your answer in the form y = mx + c, where m and c are constants. a. find f(x), giving each term in […]
Hits: 57 Question a. Given y = 2x, show that can be written in the form b. Hence solve Solution a) We have the equation; We are given that y = 2x; b) We are required to solve; As demonstrated in (a) this can be written as; Now we have two options. For these values of y, we can find […]
Hits: 53 Question f(x) = x2 – 8x + 19 a. (a) Express f(x) in the form (x + a)2 + b, where a and b are constants. The curve C with equation y = f(x) crosses the y-axis at the point P and has a minimum point at the point Q. b. Sketch the graph of C […]
Hits: 444 Question A company, which is making 140 bicycles each week, plans to increase its production. The number of bicycles produced is to be increased by d each week, starting from 140 in week 1, to 140 + d in week 2, to 140 + 2d in week 3 and so on, until the company is producing 206 […]
Hits: 74 Question A sequence is defined by , , Where k is a positive constant. a) Write down expressions for and in terms of k, giving your answers in their simplest form. Given that , b) Find an exact value for k. Solution a. We are given that sequence is defined by We are required to find […]
Hits: 70 Question Given , find the value of when x=8, writing your answer in the form where a is a rational number. Solution 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 differentiation […]
Hits: 100 Question Find giving each term in its simplest form. Solution We are given; Rule for integration of is: Rule for integration of is: Rule for integration of is:
Hits: 40 Question Express in the form , giving y in the form ax + b, where a and b are constants. Solution We are given; Hence; Therefore;