TJC 2025 IP4 WA3 AM Revision Student - Practice 5

1 Practice 5 (31 Marks – 46 minute) Answer all questions in the spaces provided. Show all working clearly. [2024 AM WA3 Q1] 1 The diagram above (not drawn to scale) shows part of the curve 28 54y x= + intersecting the y-axis at A(0, 7). The tangent to the curve at the point P(2, 2) intersects the y-axis at B . The normal to the curve at P intersects the x-axis at C. (i) Show that the equation of the tangent to the curve at P is 5 24 77 xy=− + . [3] (ii) Find the exact area of shaded region BPCO. [7] A(0, 7) P(2, 2) B C O x y

2 [2022 AM WA1 Q4 ] 2 (i) Sketch the graph of ( )ln 5 5yx=+ , indicating all points of intersection with the axes and the equation(s) of any asymptotes. [3] (ii) On the same set of axes from (i), draw the graph of 3 2yx=+ , indicating all points of intersection with the axes. [2] (iii) Hence solve the equation ( )2 ln 5 5 2 3xx+ = + . [2] [2023 AM WA3 Q3] 3 A gardener uses 30 m of fencing with which to enclose 2 flower beds. One flower bed is to be a square of side x m. The other flower bed is to be a circle of radius r m. (i) Show that the total area, A m2, of the two flower beds is given by ( ) 2 2 15 2 π xAx −=+ . [3] (ii) Given that x can vary, find the exact value of x which gives a stationary value of A. [3] (iii) Explain clearly why the gardener might be happy or disappointed with the value of x from part (ii). [3] [2022 AM WA1 Q2] 4 (i) Sketch the graph of 2yx=− . [3] (ii) By sketching a suitable straight line on the same axes as in (i), state the number of solutions to the equation 121 5xx− = − . [2]

3 Answer Keys: 1 (i) 4 units2 2 (i) & (ii) (iii) 0.891 or 0.398 or 0.543x=− − . 3 (ii) 30 4x = + (iii) Disappointed having the small area for planting 4 (i) (ii) 2