- W 1. (2 marks) Simplify the fraction Wty-I 2. (2 marks ) Find all values of a, b, and c so that a2 + b2 + c2 + 2(2b - a - 4c)= -21 3. (6 marks ) (a) Write the quadratic expression ax2 + bx + c in the form a (x+ h)2 + k for suitable values of h and k in terms of a, b, and c. (b) When does the equation a (x + h)2 + k = 0 have solutions ? What are they ? -b + Vb2 - 4ac (c) Use your answers to (a) and (b) to show why the quadratic formula x = _ is the solu - 2 a tion to the quadratic equation ax + bx+ c = 0. 4. (5 marks) The amount of electricity produced by a solar panel decreases by a fixed percentage every year. A new solar panel produces 330 KW of electicity, and the manufacturers guarantee that after 25 years the panel production will have decreased by 10 %. (a) Without using a formula , how much electricity should the panel produce when it is 25 years old ? (b) If the formula for the electricity produced , E, is written as E (t) = A x B' for constants A and B, determine the values of A and B. Note that t is measured in years. (c) By a process of guessing , checking and fixing , estimate the time taken for the solar panels to produce half of their original electricity. Give your answer correct to 3 significant figures. (d) Make a sketch of the function over a 500 year period. Show the halving time on your graph, and show that the halving time is constant. 5. (5 marks) We want to make our own 200 gram block of milk chocolate, containing 35% cocoa powder, 20% cocoa butter, 25% milk, and 20% sugar. Unfortunately our only source of cocoa powder and cocoa butter is some dark chocolate (which contains 60% cocoa powder, 25% cocoa butter, and 15% sugar) and some white chocolate (which contains 30% cocoa butter, 30% milk, and 40% sugar). We also have plenty of milk and sugar. How much of each ingredient (dark chocolate, white chocolate, milk, and sugar) do we need to make the milk chocolate we want ? Give your answer to the nearest gram, but remember to keep using the exact answers in your calculation to prevent errors