Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
MAT 111 Practice Test for Test 1 ( Chapter 1 and 2.1 – 2.2 ) 1. (1.1 and 2.2) Calculate the following. Answers must be exact. Simplify any radicals completely. a. The distance between the points (1,11) and (17, 5) b. The midpoint between the points (4.5, 9) and (3.2, 50) c. The slope of the line that contains the points (2,1) and (5,11) 2. (1.2 and 2.1) Find the intercepts of the graph of the functions: a. y x 2 9x 14 (algebraically) b. y 7 x 2 4 x 5 (use graphing calculator as needed, rounding correctly to 3 decimal places) 3. (1.2) Solve: 4 x 2 3x 5 2 x 6 4. (1.2) Solve: a. x 2x 4 3 2 x 4 x 4 x2 b. 2 x 1 2 x3 x x 2 3 x x 2 5. (1.3 and 1.4) Solve the following equations. Find all real and complex solutions. a. 3 x 2 8 x 3 b. 3x 2 7 x 6 c. 3x 3 2 x 2 5 x 0 d. 5 x 2 2 x 1 0 6. (1.4) Perform the indicated operations by hand, showing your work. Write answers in standard a + bi form. 7i a. (6 4i) (1 2i) b. (5 4i)( 2 3i) c. d. 5i (4 - i 22 ) - 7 + 3i 3 e. i 278 1 4i 7. (1.5) Solve. If solved algebraically, answer must be exact. If solved by graphing, you must sketch your graph answer must be rounded correctly to 2 decimal places. a. 3x 1 6 2 x 0 b. x 4 7 x 2 10 0 c. 5 2 4 3x 11 8. (1.6) Jacob purchased some bonds yielding 10% annually and some certificates of deposit yielding 14% annually. If Jacob’s investment amounts to $24,000 and the annual income is $3000, how much money is invested in bonds and how much is invested in certificates of deposit? 9. (1.6) A chemistry experiment calls for 2.4 liters of a 2% acid solution. On hand, the lab has containers of 1% acid solution and 5% acid solution. How much of each must be mixed in order to have what is needed for the experiment? (You must solve this algebraically to receive credit; no credit for guess and check.) 10. (1.6) A plane flies from city A to city B in 5 hours with a tailwind of 2 mph. It takes the same plane 9 hours to travel back to city A against the wind. What is the plane’s speed in still air? 11. (1.6) How many cc of pure acid should be added to 30cc of a 40% acid solution to get a 50% acid solution? 12. (1.6) A health food retailer sells a mixture of dried cherries, blueberries, and pecans for $15.00 per pound and dried banana chips for $2.25 per pound. The retailer decides to create a new mix by adding banana chips to the original mix. How many pounds of banana chips must be mixed with 40 pounds of the original mix to obtain a new mixture that sells for $10.25 per pound with no loss in revenue? (round to two decimal places.) 13. (1.7) Solve the following inequalities. Write your answers in interval notation. a. 4x 9 11 b. 3x 5 2( x 1) 4 5(3 x) c. 2 x 7 1 6 d. 3 2 4 x 1 11 14. (2.1) Determine what kind of symmetry, if any, the graph of each of the following has: a. x 2 y 2 16 b. y x 2 3 c. y x2 2x 3 d. y x3 15. (2.1) Sketch the graph of the following functions by plotting points, finding any intercepts, and checking for symmetry. a. y x2 b. y x3 c. y x d. y x 16. (2.2) Find the equation in y mx b form of the following lines. a. Passing through the points (4,7) and (3, -5) b. Contains the point (-2, 3) and parallel to the line whose equation is 3x – 4y = -1 c. Passing through the point (5, -2) and perpendicular to 2x – 6y = 1 e. y 1 x