THE PUTNEY SCHOOL
ALGEBRA II PLACEMENT TEST
1. What is the factored form of the algebraic expression x2 − x − 6? a. (x − 1)(x + 6) b. (x − 3)(x − 2) c. (x + 3)(x − 2) d. (x − 3)(x + 2) 2. What are the roots of f (x) = x2 − x − 6 ? 3. What are the roots of g(x) = x2 − 25 ? 4. Solve with the quadratic formula. Give answers rounded to the nearest hundredth: 4k 2 + 3k − 2 = 0 5.
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A square pool measuring 4 meters on each side is completely surrounded by a walkway x meters wide. The total area of the walkway is equal to that of the pool. How wide is the walkway? Solve the following system of equations: y = 2x + 4 3x − y = 3 Solve the following system of equations: 3x + 2y = 12 6x − 7y = 21 Find the inverse of f (x) = 7x − 12 a. g(x) = 2x − 7 b. g(x) = 17x + 12 c. g(x) = 121 x + 7 d. g(x) = x+12
7 9. Solve 3(2x + 6) = 2(6x + 2) 10. Given f (x) = 3x − 3 , g(x) = (1/2) x + 3 , f ind f(g(3)) . 11. Given f (x) = 3x − 3 , g(x) = (1/2) x + 3 , find g(f(0)) . 12. Two planes leave an airport at the same time, one flying at 400 km/hr, one at 320 km/hr. The angle between their flight paths is 40 ° . How far apart are they after 1 ½ hours? Give answer rounded to the nearest kilometer. 13. The straight line distance from Boston to Putney is 140 km; it is 306 km from Boston to New York; and 280 km from New York to Putney. What is the measure of the angle formed between New York and Boston, with Putney as the vertex? 14. Two people stand 65m apart on the beach, and look out at an island in the bay. According to one person, the island makes an angle of 41 ° from the other person. The second person sees the island as making a 79 ° angle from the first person. What is the shortest distance between the island and the beach? 15. In the image below, the radius shown makes an angle of measure 1.3 radians with the positive x­axis. What are the coordinates of the point at the end of the indicated radius if the circle has radius one (rounded to two decimal places)? 16. What is 78° into radians? Round to two decimal places. 17. What is π/3 radians in degrees? Round to two decimal places. 18. Given a wheel of radius 50 cm, what distance will it roll if it rotates π/4 radians? Round to two decimal places. 19. In order to move through one season (i.e. ¼ of a revolution around the Sun) the Earth moves 2.36 x 1011 m. If the Earth is 1.5 x 1011 m from the Sun, and Mars is 2.3 x 1011 m from the Sun, how far does Mars travel in one Martian season? Assume that the orbits are circular. Round to two decimal places. 20. Solve. Round to two decimal places: x 7 = 1478 3
21. Solve. Round to two decimal places: x 7 = 8 22. Solve. Round to two decimal places: log 3 x = 4 23. Solve. Round to two decimal places: log 5 196 = x 24. A dose of 100 micrograms of medication is given to a horse. Each day, the horse metabolises (i.e. processes and removes) 8% of the medication in its body. a. How much of the dose (in micrograms) is in the horse after 10 days? b. In how many days does the amount in the horse’s body reach 50 micrograms? 25. What is the numerical value of 7P4 ? 26. In a chemistry class of twelve students, two students need to be selected to set up a bench for an experiment. How many ways are there for two students to be chosen if the order in which they are selected does not matter? 27. In a chemistry class of twelve students, two students need to be selected so one of them can set up a bench and the other can discuss the instructions. How many ways are there for two students to be chosen? 28. If you roll two dice, find the probability that the first die is a 4. Give answer as a decimal rounded to the nearest hundredth. 29. If you roll two dice, find the probability that both dice are 4s. Give answer as a decimal rounded to the nearest hundredth. 30. If you roll two dice, find the probability that you roll one 2 and one 6. Give answer as a decimal rounded to the nearest hundredth.