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HL1 Midterm Exam Review Given that f(x) = 2e3x, find the inverse function f –1(x). 1 x f ( x) ln 3 2 1 When the function f (x) = 6x4 + 11x3 – 22x2 + ax + 6 is divided by (x + 1) the remainder is –20. Find the value of a. a=-1 Twelve people travel in three cars with four people in each car. Each car is driven by its owner. Find the number of ways in which the remaining nine people may be allocated to the cars. (The arrangement of people within a particular car is not relevant.) When they arrive at their destination, the 12 people must divide into 3 equal groups to go through the corn maze. How many ways can they be assigned to groups? 1680 ways 5775 ways The function f is given by ln( x 2) Find the domain of the function. (No calculator!) x3 a) Give the value of 1 tan (1). 2 b) Give the value of tan arccos . 3 a) 4 b) 5 2 Determine the constant term in the expansion of 2 x 2 x 9 -672 (z + 2i) is a factor of 2z3–3z2 + 8z – 12. Find the other two factors. (z-2i)(2z-3) Solve the inequality. 3 x 4 x 2 –2.30 < x < 0 or l < x < 1.30 Exact: 1 ( 13 1) x 0 or 2 1 1 x ( 13 1) 2 The depth, y metres, of sea water in a bay t hours after midnight may be represented by a sinusoidal model. The water is at a maximum depth of 14.3 m at midnight and noon, and is at a minimum depth of 10.3 m at 06:00 and at 18:00. Write a function to model the depth and use it to find the first time after noon when the water is below 12 m. EQ : y 2 cos t 12.3 6 t 15.3 (3 :18 pm)