Hits: 145
Hits: 145 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: 132 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: 127 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: 110 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: 95 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: 72 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: 75 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: 57 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: 68 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: 56 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: 130 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: 69 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: 81 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: 98 Question The parametric equations of a curve are for . At the point P on the curve, the gradient of the curve is 2. i. Show that the value of the parameter at P satisfies the equation . ii. By first expressing in the form , where R > 0 and […]
Hits: 73 Question a. Show that b. Find Solution a. We are required to show; Rule for integration of is: Rule for integration of is: Division Rule; Power Rule; Multiplication Rule; b. We are required to find; provided that provided that Rule for integration of is: Rule for integration of is: […]
Hits: 105 Question i. Show the equation For . Show all necessary working. Solution We are given that; Let , then; Now we have two options. Since ; Using calculator Now we find all solutions in the interval . Properties of Domain Range Periodicity Odd/Even Translation/ Symmetry We utilize the periodicity/symmetry property of […]
Hits: 70 Question i. Use the factor theorem to show that (2x+3) is a factor of ii. Show that the equation can be expressed as iii. Solve the equation For . Solution i. We are given that; We are also given that is a factor of . When a polynomial, […]
Hits: 66 Question The diagram shows the curve with equation for values of x such that . Find the x-coordinate of the stationary point M, giving your answer correct to 3 significant figures. Solution We are required to find the x-coordinate of stationary point M. A stationary point on the curve is the point […]
Hits: 102 Question The diagram shows the curve with equation for . At the points P and Q on the curve, the gradient of the curve is 3. i. Find an expression for . ii. By first expressing in the form , where R > 0 and , find the […]
Hits: 69 Question The diagram shows the curve for . The region R is bounded by the curve, the axes and the line . i. Use the trapezium rule with two intervals to find an approximation to the area of R, giving your answer correct to 3 significant figures. ii. The […]