Precalculus Placement Test - The Putney School

8. Give three solutions to the equation: 4x 3 − 16x 2 + 12x= 09. If P (t) is an exponential function of the form P (t) = Aekt and it is known thatP (1) = 12, P (3) = 20, find P (4) .10. Solve the equation: √x 2 + 3 = x + 13π11. Convert radians to degrees.4π12. Given f (x) = 3sin( 2x + 2)− 5 provide the following information:a. What is the function’s amplitude?b. What is the function’s period (in radians)?c. What is the y coordinate of the function’s horizontal line of symmetry?13. Find the length of d in the following diagram:14. What is the sum of the infinite geometric series 27 + 9 + 3 + ...?15. If the third term of an arithmetic sequence is 5 and the common difference between terms is -4,find the 450 th term.∑ 9n=516. Evaluate (n 2 − 1 )

17. Solve the equation: 3sin 2 x + 18 + 3cos2 x = 39 − 6 x