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Hits: 29 Question The polynomial is defined by where and are constants. It is given that is a factor of . It is also given that the remainder is 18 when is divided by . i. Find the values of a and b. ii. When a and b have these values […]
Hits: 27 Question The equation of a curve is 3×2 + 4xy + y2 = 24. Find the equation of the normal to the curve at the point (1, 3), giving your answer in the form ax +by +c = 0 where a, b and c are integers. Solution i. We are given equation […]
Hits: 29 Question i. Show that ii. Hence find the exact value of; Solution i. We are required to show that; Since ; Therefore; ii. We are required to find the exact value of; As demonstrated in (i); Therefore; Rule for integration of is: Rule for integration of is: […]
Hits: 28 Question i. It is given that the positive constant a is such that ii. Show that iii. Use an iterative formula , to find a correct to 3 decimal places. Give the result of each iteration to 5 decimal places. Solution i. We are given that; Rule for […]
Hits: 37 Question A curve has equation y = 2 sin 2x − 5 cos 2x +6 and is defined for 0 ≤ x ≤ π. Find the x-coordinates of the stationary points of the curve, giving your answers correct to 3 significant figures. Solution We are required to find the x-coordinates of stationary points […]
Hits: 20 Question The variables x and y satisfy the equation y = Aepx, where A and p are constants. The graph of ln y against x is a straight line passing through the points (5, 3.17) and (10, 4.77), as shown in the diagram. Find the values of A and p correct to 2 decimal […]
Hits: 124 Question i. It is given that x satisfies the equation . Find the value of and, using logarithms, find the value of x correct to 3 significant figures. ii. Hence state the values of x satisfying the equation . Solution i. We are given; We can write it […]