ANDSS 4E5N2025AMATH_WA2 (Qn)

WA2 4E/5N Add Maths 2025 2 1 Differentiate each of the following with respect to x. (a) 621 33 xx −−+ [1] (b) 31ln 52 x x + − [2] (c) 2 3sin 2 53 x x − [3]

WA2 4E/5N Add Maths 2025 3 2 The equation of a curve is 2(2 3) 4 1yx x= −+ . (a) Show that 2 2 d 16 12 2 d 41 yx x x x −+= + . [2] (b) Find the range of values of x for which 2(2 3) 4 1yx x= −+ is an increasing function. [4]

WA2 4E/5N Add Maths 2025 4 3 It is given that 43eexxyP Q −= + , and that 2 43 2 dd 2 12e 3edd xxyy xx −+= + . Find the value of each of the constants P and Q. [4]

WA2 4E/5N Add Maths 2025 5 4 The equation of a curve is 31 2 xyx x −= + − , where 0x> . (a) Find d d y x . [2] (b) Find the equation of the tangent to the curve at 1x= . [1] (c) Find the equation of the normal to the curve at 1x= . [2]

WA2 4E/5N Add Maths 2025 6 5 The table shows experimental values of two variables, x and y, which are connected by the equation e2 x kyA= + , where A and k are constants. x 2 4 6 8 y 2.135 2.368 3 4.718 (a) On the grid provided on the next page, draw a graph of ( )ln 2y− plotted against x. [3] (b) Use your graph to estimate the value of A and of k. [4] (c) On the same diagram, draw the straight line representing the equation 52e x y − −= . Hence find the value of x for which ln 5 xx Ak += − . [2]

WA2 4E/5N Add Maths 2025 7 END OF PAPER x 1 2 2 4 6 8 0 −1 −2 −3