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Hits: 29 Question a. i. Express in the form , where and are constants to be found. ii. Hence, or otherwise, and showing all necessary working, solve the equation For . b. The diagram shows the graphs of and for . The graphs intersect at the points A […]
Hits: 60 Question The diagram shows a triangle OAB in which angle OAB = 90o and OA = 5 cm. The arc AC is part of a circle with centre O. The arc has length 6 cm and it meets OB at C. Find the area of the shaded region. Solution It is evident from […]
Hits: 342 Question i. Solve the equation for . ii. Sketch, on the same diagram, the graphs of and for . iii. Use your answers to parts (i) and (ii) to find the set of values of x for for which . Solution i. We have the equation; We know that […]
Hits: 540 Question The diagram shows points A and B on a circle with centre O and radius r. The tangents to the circle at A and B meet at T. The shaded region is bounded by the minor arc AB and the lines AT and BT. Angle AOB is radians. i. In the […]
Hits: 204 Question The function f, is such that for . It is given that and . i. Find the values of the constants a and b. ii. Find the set of values of k for which the equation f(x) = k has no solution. Solution i. We are given the function […]
Hits: 539 Question The diagram shows a circle with centre O and radius r cm. The points A and B lie on the circle and AT is a tangent to the circle. Angle radians and OBT is a straight line. i. Express the area of the shaded region in terms of r and . […]
Hits: 168 Question i.Prove the identity ii.Hence solve the equation for . Solution i. We have the trigonometric identity; ii. We have the equation; From (i) we know that left hand side of given equation can be written as; Therefore; […]
Hits: 101 Question i. Express in the form , where and , giving the value of correct to 2 decimal places. ii. Hence solve the equation for . Solution i. We are given the expression; We are required to write it in the form; If and are positive, then; can be written […]
Hits: 80 Question A curve is defined by the parametric equations for . i. Find the exact gradient of the curve at the point for which . ii. Find the value of at the point where the gradient of the curve is 2, giving the value correct to 3 significant figures. Solution […]
Hits: 66 Question a. Show that b. Find the exact value of Show all necessary working. Solution a. We are required to show; Rule for integration of is: Division Rule; Power Rule; b. We are required to find; Since , we can rearrange to write; Rule for integration of is: Rule for integration […]
Hits: 50 Question i. Show that ii. Hence, show that iii. Solve the equation For . Show all the necessary working. Solution i. First we are required to show that; provided that provided that provided that ii. We are required to show that; As shown in […]
Hits: 39 Question a. Find b. Find the exact value of Show all necessary working. Solution a. We are given that; Rule for integration of is: Rule for integration of is: Rule for integration of is: b. We are required to find the exact value of; Rule for integration of is: Rule for […]
Hits: 53 Question a. Showing all necessary working, solve the equation for . b. Showing all necessary working, solve the equation for . Solution a. We are given; provided that provided that Let , then; We are given that ; interval for can be found as follows. Multiplying entire inequality with […]
Hits: 47 Question It is given that Where is a constant. i. Show that ii. Using the equation in part (i), show by calculation that 0.5 < a < 0.75. iii. Use an iterative formula, based on the equation in part (i), to find the value of a correct to 3 significant […]
Hits: 39 Question a. Showing all necessary working, solve the equation for . b. Showing all necessary working, solve the equation for . Solution a. We are given; provided that provided that Let , then; We are given that ; interval for can be found as follows. Multiplying entire inequality with […]
Hits: 44 Question It is given that Where is a constant. i. Show that ii. Using the equation in part (i), show by calculation that 0.5 < a < 0.75. iii. Use an iterative formula, based on the equation in part (i), to find the value of a correct to 3 significant […]
Hits: 42 Question a. i. Express in the form , where and . ii. Hence find the smallest positive value of satisfying the equation b. Solve the equation for , showing all necessary working and giving the answers correct to 2 decimal places. Solution i. We are given the expression; We […]
Hits: 59 Question a. Find the exact value of Show all necessary working. b. Use the trapezium rule with two intervals to find an approximation to Solution a. We are required to show; We know that , therefore; Rule for integration of is: Rule for integration of is: Rule for integration of is: Rule […]
Hits: 30 Question a. i. Express in the form , where and . ii. Hence find the smallest positive value of satisfying the equation b. Solve the equation for , showing all necessary working and giving the answers correct to 2 decimal places. Solution i. We are given the expression; We […]
Hits: 43 Question a. Find the exact value of Show all necessary working. b. Use the trapezium rule with two intervals to find an approximation to Solution a. We are required to show; We know that , therefore; Rule for integration of is: Rule for integration of is: Rule for integration of is: Rule […]