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ENM1500Assignment 1When answering, link your mathematical working with short explanations, use good English and write in grammatically correct sentences.Question 1.For the following expressions, arrange and simplify A+B-C, [12 marks]A = a3 – b, B = -2c + b – 2a3 , C = -4c + 2b + 2.Question 2.Simplify the expression [12 marks]px – 3{p2 – 1 – [1 + (p – x)2 + px]}.Question 3.Open brackets in the expression [12 marks](x – 3)2(x + 1 – x2).Question 4.Simplify [12 marks].Question 5.By hand, without using a calculator, roughly sketch the linear functions [12 marks] represented by the following equations. High accuracy is not required. On your graphs, indicate only values of x-intercepts and y-intercepts (if they exist).1. y = -4,2.y = 3x + 2.Question 6.By hand, without using a calculator, roughly sketch the functions [30 marks]1.,2.,3. y = -x2 – 3,4. y = 2×2 + 1,5.y = x2 + x – 2.High accuracy is not required. On your graphs, indicate the values of xintercepts and y-intercepts (if they exist) and any other special values which, in your opinion, deserve being shown.Question 7.Express y in terms of x:1. lne + lnx – lny = 0,2.5x – 3y+1 = 0,3. log2 1 – log4 x + log4 y = 2,4.x = 2(1 + ey) ,In your answers do not replace logarithms or exponentials by their decimal approximations.Question 8. [20 marks]Solve the equations(a) AxB1+x = Cx+5(express x through A, B and C). [20 marks](b) ln((if your answer includes number e, do not replace it by a decimal approximation but keep as a symbol).Question 9.The time t required to chemically change certain amount of substance into another is given by [20 marks],where x is the mass that have been changed by the time t. Sketch the graph x versus t (with axis x going vertically and axis t going horizontally).[Total:150 marks]

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