Hits: 63
Hits: 63 Question Solve the equation , giving all solutions in the interval . Solution We are required to solve; We have trigonometric identity; To solve this equation for , we can substitute . Hence, Since given interval is , for interval can be found as follows; Multiplying the entire inequality with 2; […]
Hits: 59 Question i. Express in terms of . ii. Hence show that Solution i. We are given that; From this we can write; We have the trigonometric identity; From this we can write; Hence; ii. We are required to show that; We have found in (i) that; Therefore; […]
Hits: 97 Question i. Express in the form , where and , stating the exact value of R and and giving the value of correct to 2 decimal places. ii. Hence solve the equation Giving all solutions in the interval . iii. Write down the least value of as varies. Solution […]
Hits: 134 Question The parametric equations of a curve are x = 1 + 2 sin2θ , y = 4 tanθ , i. Show that ii. Find the equation of the tangent to the curve at the point where , giving your answer in the form y = mx + c. Solution […]
Hits: 105 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=1.1 and x=1.2. iii. Use the iterative formula to determine this root correct to […]
Hits: 74 Question The diagram shows the part of the curve for . Find the x-coordinates of the points on this part of the curve at which the gradient is 4. Solution We are required to find the x-coordinate of the points on the curve where gradient is 4. Therefore first we need […]
Hits: 61 Question i. Prove that ii. Hence a. Solve for the equation b. find the exact value of . Solution i. We are given that; We utilize following relations; provided that provided that Therefore; We utilize following relation; Therefore; ii. We are required to solve; As […]
Hits: 123 Question i. Prove that ii. Hence a. Solve for the equation b. find the exact value of . Solution i. We are given that; We utilize following relations; provided that provided that Therefore; We utilize following relation; Therefore; ii. We are required to solve; As […]
Hits: 145 Question i. Express in the form , where and , Give the exact value of R and the value of correct to 2 decimal places. ii. Hence solve the equation for . iii. Find the greatest and least possible values of as varies. Solution i. We are given […]
Hits: 148 Question A curve has parametric equations Find the exact gradient of the curve at the point for which . Solution i. Gradient (slope) of the curve at the particular point is the derivative of equation of the curve at that particular point. Gradient (slope) of the curve at a particular […]
Hits: 612 Question i. Sketch, on the same diagram, the graphs of and for . ii. Verify that is a root of the equation , and state the other root of this equation for which . iii. Hence state the set of values of , for , for which Solution i. We are required to sketch and for . First we sketch for […]
Hits: 1031 Question The diagram represents a metal plate , consisting of a sector of a circle with centre and radius , together with a triangle which is right-angled at C. Angle radians and is perpendicular to . i. Find an expression in terms of and for the perimeter of the plate. ii. For the case where and […]
Hits: 1107 Question The function f is such that , for , where is a constant. i. In the case where , a. Find the range of , b. Find the exact solutions of the equation . ii. In the case where , a. Sketch the graph of , […]
Hits: 918 Question A curve has equation and P(2, 2) is a point on the curve. i. Find the equation of the tangent to the curve at P. ii. Find the angle that this tangent makes with the x-axis. Solution i. To find the equation of the line either we need coordinates of the two points on the line […]
Hits: 388 Question i. Given that Show that, for real values of ii. Hence solve the equation for . Solution i. We have the equation; We have the trigonometric identity; We can rewrite it as; Thus Now we have two options; NOT POSSIBLE So we are left with ONLY option; ii. To solve the equation […]
Hits: 1735 Question In the diagram, ABCD is a parallelogram with AB=BD=DC=10cm and angle ABD= 0.8 radians. APD and BQC are arcs of circles with centres B and D respectively. i. Find the area of the parallelogram ABCD. ii. Find the area of the complete figure ABQCDP. iii. Find the perimeter of the complete figure ABQCDP. Solution i. Expression for […]
Hits: 1249 Question The diagram shows a circle touching a circle at a point . Circle has centre A and radius 6cm, and circle has centre B and radius 10 cm. Points D and E lie on and respectively and DE is parallel to AB. Angle radians and angle radians. i. By considering the perpendicular distances of D […]
Hits: 553 Question i. Sketch, on a single diagram, the graphs of and for . ii. Write down the number of roots of the equation in the interval . iii. Deduce the number of roots of the equation in the interval . Solution i. ii. If two lines (or a line and a curve) intersect each other […]
Hits: 379 Question i. Prove the identity ii. Hence solve the equation , for . Solution i. We have the equation; We have the relation , therefore, We have the trigonometric identity; We can rewrite it as; Therefore; Using formula; ii. To solve the equation , for , as demonstrated in (i), we […]
Hits: 1499 Question In the diagram, AB is an arc of a circle, centre O and radius 6 cm, and angle radians. The line AX is a tangent to the circle at A, and OBX is a straight line. i. Show that the exact length of AX is cm. Find, in terms of and , ii. the area of the shaded […]