Mathematics Higher Level Robert Joinson

©Sumbooks2002Higher Level13. SubstitutionExercise 1Evaluate each of the following, given that a = 6, b = 4 and c = –5.1) 3a + 5b 2) 4a – 6b 3) 2a – 7b 4) 4c + 2a5) 5a – 4c 6) 3a 2 + 2b 7) 4b 2 – 2a 8) 5a + 3c 29) ( 4b – 6c) 10) ( 2a) + 3b 11) 4c – 5b 2 12) 6a – ( 5c) Exercise 21) If y = 3x + 4 a) Calculate the value of y when x = 6 b) What value of x is needed if y = 19?2) If a = 3b – 6 a) Calculate the value of a when b = –7 b) What value of b is needed if a = 54?3) If y = 7x + 3 a) Calculate the value of y when x = –6 b) What value of x is needed if y = –81?4) Carol works for a garden centre and plants rose bushes in her nursery. She works out thelength of each row of bushes using the formula L = 50R+200, where L represents the lengthof the row in centimetres and R is the number of bushes she plants. Use the formula to calculatea) the length of a row containing 10 bushesb) the number of bushes in a row 15 metres long.15) The volume of a cone is given by the formula V = --πr 2 h .3a) Calculate the volume of a cone when π = 3.142 , r = 3cm and h = 2.5cm.b) A cone has a volume of 183cm 3 . Calculate the value of its height h, if r = 5cm andπ = 3.142 . Give your answer correct to the nearest millimetre.PTR6) Simple interest can be calculated from the formula I = ---------- .100a) If the principal (P) = £250, the time (T) = 3 years and the rate (R) = 9.5%, calculate theinterest.b) If the interest required is £200, what principal needs to be invested for 6 years at 7%?7) The temperature F (degrees fahrenheit) is connected to the temperature C (degrees celsius)5by the formula C = -- ( F – 32).9a) Calculate C if F = –20°F .b) Convert – 10°C into °F8) A bus company uses the formula T =D S 1----- + ----- + -- to calculate the time needed for their bus20 60 4journeys. D is the distance in miles and S the number of stops on the journey. If T is measuredin hours, calculatea) the time needed for a bus journey of 10 miles with 10 stops.b) the time needed for a bus journey of 20 miles with 4 stops.c) During the rush hour, more people get on the bus and the extra traffic slows the bus down.What would you do to the formula to take this into account?