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 […]
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. Use the […]
Question The parametric equations of a curve are , , i. Show that . ii. Find the equation of the normal to the curve at the point where t = 0. Solution i. We are given that; We are required to show that . If a curve is given parametrically […]
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 of is: […]
Question Solve the equation , giving answers correct to 2 decimal places where appropriate. Solution i. Let, . We can write it as; We have to consider two separate cases; When When We have the equation; We have to consider two separate cases; When ; When ; Taking logarithm of both sides. Power […]
Question The polynomial , where and are constants, is denoted by . It is given that is a factor of , and that when is divided by the remainder is 8. i. Find the values of a and b. ii. When a and b have these values, factorise p(x) completely. Solution […]
Question Solve the equation ln(3 − 2x) − 2 ln x = ln 5. Solution We are given; Power Rule; Division Rule; Taking anti-logarithm of both sides; for any Now we have two options. Since logarithm of a negative number is not possible, therefore is not possible because we have the term in the […]