Question Figure 2 shows a sketch of the curve C with equation , x ≠ 0 The curve crosses the x-axis at the point A. a. Find the coordinates of A. b. Show that the equation of the normal to C at A can be written as 2x+8y−1=0 The normal to C at A meets C again at the […]
Question A company offers two salary schemes for a 10-year period, Year 1 to Year 10 inclusive. Scheme 1: Salary in Year 1 is £P. Salary increases by £(2T) each year, forming an arithmetic sequence. Scheme 2: Salary in Year 1 is £(P+1800). Salary increases by £T each year, forming an arithmetic sequence. a. Show that the total earned under […]
Question The curve has equation a. Find . b. Sketch , showing the coordinates of the points where C1 meets the x-axis. c. Find the gradient of at each point where C1 meets the x-axis. The curve has equation where k is a constant and . d. Sketch , showing the coordinates of the points where meets the x […]
Question A curve with equation y = f (x) passes through the point (2,10). Given that f ′(x) = 3×2 − 3x + 5 find the value of f (1). Solution We are required to find f(1) but we are not given f(x) but f ′(x). f ′(x) = 3×2 − 3x + 5 Therefore, we need to […]
Question The line has equation 2x − 3y +12 = 0. a. Find the gradient of . The line crosses the x-axis at the point A and the y-axis at the point B, as shown in Figure. The line is perpendicular to and passes through B. b. Find an equation of . The line crosses the x-axis at the point […]
Question The curve C has equation y=x(5−x) and the line L has equation 2y=5x+4. a. Use algebra to show that C and L do not intersect. b. In the space on page 11, sketch C and L on the same diagram, showing the coordinates of the points at which C and L meet the axes. Solution […]
Question A sequence is defined by , Where is a positive integer. a) Write down an expression for in terms of a. b) Show that Given that c) Find the possible values of a. Solution a) We are given that sequence is defined by We are required to find . We can utilize the given expression […]
Question Find the set of values of x for which a. b. Solution a. We are given; b. We are required to solve the inequality; We solve the following equation to find critical values of ; Now we have two options; Hence the critical points on the curve for the given condition are 6 & -2. Standard form […]
Question a. Simplify giving your answer in the form , where is an integer. b. Simplify giving your answer in the form , where b and c are integers. Solution a. We are given; Since ; Since ; b. As demonstrated in (a) we can write the numerator as; If we need a rational number in the […]
Question Given that , , find, in their simplest form, a. b. . Solution a. We are given; We are required to find . Gradient (slope) of the curve is the derivative of equation of the curve. Hence gradient of curve with respect to is: Therefore; Rule for differentiation is of is: Rule for differentiation is of is: […]