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Hits: 230 Question Figure 1 shows a sketch of the curve C with equation y = f(x) where f (x) = x2(9 –2x) There is a minimum at the origin, a maximum at the point (3, 27) and C cuts the x-axis at the point A. a. Write down the coordinates of the point A. b. […]
Hits: 35 Question The line L1 has equation 4y + 3 = 2x. The point A (p, 4) lies on L1. a. Find the value of the constant p. The line L2 passes through the point C (2, 4) and is perpendicular to L1. b. Find an equation for L2 giving your answer in the form ax […]
Hits: 23 Question Where p and q are integers. a. Find the value of p and the value of q. b. Calculate the discriminant of . c. On the axes on page 17, sketch the curve with equation showing clearly the coordinates of any points where the curve crosses the coordinate axes. Solution a. We have the […]
Hits: 34 Question The point P(4,–1) lies on the curve C with equation y = f(x), x > 0, and a. Find the equation of the tangent to C at the point P, giving your answer in the form y = mx + c, where m and c are integers. b. Find f(x). Solution a. We are […]
Hits: 46 Question A boy saves some money over a period of 60 weeks. He saves 10p in week 1, 15p in week 2, 20p in week 3 and so on until week 60. His weekly savings form an arithmetic sequence. a. Find how much he saves in week 15 b. Calculate the total amount he […]
Hits: 12 Question A sequence of numbers is defined by , Where is a constant. a) Write down an expression, in terms of c, for . b) Show that Given that c) Find a range of values of c. Solution a) We are given that sequence is defined by We are required to find . We […]
Hits: 11 Question a. Find , giving each term in its simplest form. b. Find . 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 differentiation is of is: Rule […]
Hits: 12 Question Show that can be written 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 […]
Hits: 9 Question a. Evaluate , giving your answer as an integer. b. Simplify fully . Solution a. b.
Hits: 34 Question Find Giving each term in its simplest form. Solution a. We are required to find; Rule for integration of is: Rule for integration of is: