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Unit Assessment 1 – Set 1 Outcome 1 y 1. Find the gradient of the line shown in the diagram. 74º x 2. Find the equation of the line passing through the point (2,-1) and parallel to the line y – 2x – 4 = 0. 3. Find the equation of the line through the point (0,4) and perpendicular to the line x + y + 1 = 0 Outcome 2 4. If f(x) = 2 – 3x and g(x) = x – 1 find the values of a) f(g(x)) b) g(f(x)) Solve the equation f(g(x)) – g(f(x)) = 6x. 5. The diagram shows the graph of a function y = f(x). On separate diagrams sketch the graphs of a) 2 + f(x) b) -f(x) c) f(x-3) d) 4 - f(x) Outcome 3 6. If f(x) = (1 – 2x)2 , find f (-2) 7. Find y in each example a) y = 2x 1 5 x b) y = 3 x ( x 2) 8. Find the equation of the tangent to the curve y = (x-1)(x-2) at the point A(3,2). The tangent is shown in the diagram. 9. Find the stationary values of the function f(x) = 4x3 – 9x2 + 6x and determine their nature. Outcome 4 10. There are 40 tons of pollution in a loch. Each week the council remove 38% of the pollution in the loch and at the end of the week a local factory is allowed to deposit 9 tons of waste in the loch. a) Set up a recurrence relation. b) Find the amount of pollution in each of the first five weeks. c) Determine the long term state of the loch.