Question The curve C has equation , The point P on C has x-coordinate equal to 2. a. Show that the equation of the tangent to C at the point P is y = 1 – 2x. b. Find an equation of the normal to C at the point P. The tangent at P meets the […]
Question The line passes through the point A (2, 5) and has gradient . a. Find an equation of , giving your answer in the form y = mx + c. The point B has coordinates (–2, 7). b. Show that B lies on . c. Find the length of AB, giving your answer in the form […]
Question The first term of an arithmetic series is a and the common difference is d. The 18th term of the series is 25 and the 21st term of the series is . a. Use this information to write down two equations for a and d. b. Show that a = –17.5 and find the value […]
Question The point P (1, a) lies on the curve with equation y = (x + 1)2(2– x). a. Find the value of a. b. On the axes below sketch the curves with the following equations: i. y = (x + 1)2(2– x) ii. On your diagram show clearly the coordinates of any points at […]
Question The equation kx2 + 4x + (5 – k) = 0, where k is a constant, has 2 different real solutions for x. a. Show that k satisfies k2 – 5k + 4 > 0. b. Hence find the set of possible values of k. Solution a. We are given; We are given that given […]
Question Given that can be written in the form 2xp – xq, a. Write down the value of p and the value of q. Given that , b. find , simplifying the coefficient of each term. Solution a. We are given that; Hence, p=3/2 while q=1. b. We are given that; We […]
Question Figure 1 shows a sketch of the curve C with equation y=f(x). There is a maximum at (0, 0), a minimum at (2, –1) and C passes through (3, 0). On separate diagrams sketch the curve with equation a. y = f(x + 3), b. y = f(–x). On each diagram show clearly the coordinates of the […]
Question A curve has equation y=f(x) and passes through the point (4, 22). Given that use integration to find f(x), giving each term in its simplest form. Solution We are required to find f(x), when; We are also given that the curve passes through the point (4,1). Clearly it is the case of finding equation from its derivative. We […]
Question Expand and simplify . Solution We are given; We have algebraic formula;
Question Find , giving each term in its simplest form. Solution We are required to find; Rule for integration of is: Rule for integration of is: Rule for integration of is:
Question a. Write down the value of . b. Find the value . Solution a. b.