Hits: 142
Hits: 142 Question i. Express in the form , where and , giving the exact value of R and the value of a correct to 2 decimal places. ii. Hence solve the equation Giving all solutions in the interval correct to 1 decimal place. iii. Determine the least value […]
Hits: 63 Question i. By sketching a suitable pair of graphs, show that the equation where x is in radians, has only one root for . ii. Verify by calculation that this root lies between x= 0.7 and x=0.9. iii. Show that this root also satisfies the equation iv. […]
Hits: 51 Question i. Show that . ii. Hence show that Solution i. We are given that; From this we can write; From this we can write; It can be formulated as; Hence; ii. We are required to show that; We have found in (i) that; Therefore; Rule for integration […]
Hits: 10 Question i. Express in the form , where and , giving the exact value of R and the value of a correct to 2 decimal places. ii. Hence solve the equation Giving all solutions in the interval correct to 1 decimal place. iii. Determine the least value of as […]
Hits: 19 Question i. By sketching a suitable pair of graphs, show that the equation where x is in radians, has only one root for . ii. Verify by calculation that this root lies between x= 0.7 and x=0.9. iii. Show that this root also satisfies the equation iv. […]
Hits: 15 Question i. Show that . ii. Hence show that Solution i. We are given that; From this we can write; From this we can write; It can be formulated as; Hence; ii. We are required to show that; We have found in (i) that; Therefore; Rule for integration […]
Hits: 60 Question i. Given that and find in terms of . ii. Solve the equation giving all solutions in the interval 0◦ ≤ x ≤ 360◦. Solution i. We are given; We are given that ; therefore; ii. We are required to solve giving all solutions […]
Hits: 32 Question The diagram shows the part of the curve for . i. Use the trapezium rule with 2 intervals to estimate the value of giving your answer correct to 2 decimal places. ii. The line y=x intersects the curve at point P. Use the iterative formula to determine the […]
Hits: 24 Question The curve with equation has one stationary point in the interval . Find the exact x-coordinate of this point. Solution We are required to find the x-coordinate of stationary point of the curve with equation; A stationary point on the curve is the point where gradient of the curve is […]
Hits: 45 Question The diagram shows the curve , for . A rectangle OABC is drawn, where B is the point on the curve with x-coordinate , and A and C are on the axes, as shown. The shaded region R is bounded by the curve and by the lines x = and […]
Hits: 23 Question Solve the equation , for . Solution We are required to solve; Therefore; We have the trigonometric identity; Let , then; Since , therefore; Using calculator we can find that; Properties of Domain Range Periodicity Odd/Even Translation/ Symmetry We utilize the periodicity/symmetry property of to find other solutions (roots): […]
Hits: 22 Question The diagram shows the curve , for . A rectangle OABC is drawn, where B is the point on the curve with x-coordinate , and A and C are on the axes, as shown. The shaded region R is bounded by the curve and by the lines x = and […]
Hits: 22 Question Solve the equation , for . Solution We are required to solve; Therefore; We have the trigonometric identity; Let , then; Since , therefore; Using calculator we can find that; Properties of Domain Range Periodicity Odd/Even Translation/ Symmetry We utilize the periodicity/symmetry property of to find other solutions (roots): […]
Hits: 55 Question (i) Show that (2 sin x + cos x)2 can be written in the form (ii) Hence find the exact value of Solution i. We are given that; We have formula; Therefore; Therefore; Therefore; ii. We are required to find the exact value of; From (i) we […]
Hits: 22 Question i. Given that , find the value of . ii. Hence, showing the use of an appropriate formula in each case, find the exact value of a. b. Solution i. We are given that; We have trigonometric identity; Let , then; Since , therefore; […]
Hits: 25 Question (i) Show that and hence find the exact value of; (ii) The region enclosed by the curve y = tan x + cos x and the lines x = 0, and y = 0 is shown in the diagram. Find the exact volume of the solid produced when this region […]
Hits: 33 Question The diagram shows the curve , for . The x-coordinate of the maximum point M is denoted by . i. Find and show that satisfies the equation tan 2x = 2x + 4. ii. Show by calculation that lies between 0.6 and 0.7. iii. Use the iterative formula to […]
Hits: 19 Question i. Express in the form , where and , Give the value of correct to 2 decimal places. ii.Hence solve the equation for . iii. State the largest value of k for which the equation has any solutions. Solution i. We are given the expression; We are […]
Hits: 43 Question (i) Show that (2 sin x + cos x)2 can be written in the form (ii) Hence find the exact value of Solution i. We are given that; We have formula; Therefore; Therefore; Therefore; ii. We are required to find the exact value of; From […]
Hits: 21 Question i. Given that , find the value of . ii. Hence, showing the use of an appropriate formula in each case, find the exact value of a. b. Solution i. We are given that; We have trigonometric identity; Let , then; Since , therefore; […]
