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Hits: 18 Question The diagram shows a sector OAC of a circle with centre O. Tangents AB and CB to the circle meet at B. The arc AC is of length 6 cm and angle radians. i. Find the length of OA correct to 4 significant figures. ii. Find the perimeter of the shaded […]
Hits: 5 Question i. Given that , show, without using a calculator, that . ii. Hence, showing all necessary working, solve the equation for Solution i. We are given that; Since ; We have the trigonometric identity; From this we can write; Therefore; Let ; Now we have two options. Since […]
Hits: 14 Question The functions is defined for , where and are positive constants. The diagram shows the graph of y = f(x). i. In terms of and state the range of . ii. State the number of solutions of the following equations. a) […]
Hits: 840 Question The diagram shows triangle ABC which is right-angled at A. Angle radians and AC = 8 cm. The points D and E lie on BC and BA respectively. The sector ADE is part of a circle with centre A and is such that BDC is the tangent to the arc DE at […]
Hits: 212 Question The equation of a curve is and the equation of a line is . i.State the smallest and largest values of y for both the curve and the line for . ii.Sketch, on the same diagram, the graphs of and for . iii.State the number of solutions of the equation for . […]
Hits: 257 Question Angle x is such that sin x = a + b and cos x = a − b, where a and b are constants. A curve is such that . The point P (2,9) lies on the curve. i. Show that a2 +b2 has a constant value for all values of […]
Hits: 225 Question The functions f is defined by for , i. State the range of . ii. Sketch the graph of . The functions g is defined by for , where is a constant. iii. State the largest value of for which g has an inverse. iv. For this value of , […]
Hits: 387 Question i. Prove the identity ii. Hence solve the equation for Solution i. First, we are required to show that; Since ; We have the trigonometric identity; From this we can write; Therefore; We have the algebraic formula; ii. We are required to solve the equation; […]
Hits: 138 Question a) Solve the equation for . b) The diagram shows part of the graph of , where is measured in radians and and are constants. The curve intersects the x-axis at and the y-axis at . Find the values of and . Solution a) We are required to solve the […]
Hits: 172 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: 170 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: 181 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: 154 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: 149 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: 87 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: 89 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: 90 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: 84 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: 63 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: 200 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 […]