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 i. […]
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 12. i. Find the values of a and b. ii. When a and b have these values, factorise p(x) completely. Solution i. […]
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 i. […]
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 2 significant […]
Question Find the exact value of the positive constant k for which Solution We are given that; Rule for integration of , or ; Therefore; Let ; Therefore; Taking logarithm of both sides; Power Rule; Since ;
Question The diagram shows the curve y= x − 2 ln x and its minimum point M. i. Find the x-coordinates of M. ii. Use the trapezium rule with three intervals to estimate the value of giving your answer correct to 2 decimal places. iii. State, with a reason, whether […]
Question Use logarithms to solve the equation 4x+1 = 52x-3, giving your answer correct to 3 significant figures. Solution We are given; Taking natural logarithm of both sides; Power Rule; Power Rule; Division Rule; Multiplication Rule;
Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following with their corresponding inequality; When When When If then above four intervals translate to following with […]