practicefsm

# practicefsm - p y 2-p 2 y 5 =-1 33 x 2 6 1 4 = x Absolute...

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Practice Fundamental Skills Module MAT 1330 Robert Smith? University of Ottawa Polynomial simplification Simplify the following polynomials: 1. p x 5 y 7 x 3 y 1 / 4 2. 3 + 5 x 6 x - 1 3. k +1 k + 1 k k k +1 - k k +2 4. x - 1 - y - 1 ( x - y ) - 2 Factoring Factor the following: 5. 6 x 2 - 5 x - 4 6. x 3 + 1000 Rationalising Rationalise the denominator: 7. p x 3 y · xy p x 3 y 3 1

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8. 1 8 - 5 9. 1 2 + 3 10. 1 13 + 6 Graphs of functions 11. Sketch y = | x + 3 | - 2 12. Sketch y = - ( x - 2) 2 + 1 Trigonometric graphs 13. Sketch y = 1 + 3 cos ( 2 π 3 ( t - 2) ) 14. Sketch y = - 2 + 0 . 5 cos ( 2 π 5 ( t - 3) ) Transforming functions 15. If f ( x ) = 3 x - 6, find f (3 x - 6). 16. Can a function be even and odd at the same time? (If yes, give an example.) Equation of a line 17. Find the equation of the line through ( - 2 , 1) and ( - 3 , 4). Domain and range Find the domain and range of the following functions: 18. y = x 2 - 1 19. y = x + 2 - 3 20. y = 1 x - 6 2
21. y = 1 x - 2 22. y = 1 e x +1 23. y = p ln( x + 2) Exponents and logs 24. Solve 3 x - 2 = 27 x +5 25. Simplify log 4 ( x - 3) - log 4 x + 2 log 4 3 26. Solve 4 3 x +2 = 5 2 x - 7 27. Solve log 7 ( x + 5) - log 7 ( x - 1) = log 7 ( x + 1) 28. Solve 2 ln x - ln( x + 4) = ln 2 Quadratics Solve the following: 29. x = x + 6 30. x =

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Unformatted text preview: p y + 2-p 2 y + 5 =-1 33. ( x 2 + 6) 1 / 4 = x Absolute value Solve the following: 34. | x 2-9 | = 7 3 35. | x 2 + 9 | = 7 Absolute value inequalities Solve the following: 36. | 2 x-1 | < 5 37. | 2 x-1 | > 5 38. | 5 x-3 | -7 > 4 39. 6- | 2 x + 1 | >-5 40. | 7-8 x | ≥ -9 41. | 6 x-9 | <-8 42. | 7 x + 21 | = 0 Function inequalities 43. 3 x-2 4 x + 1 > 5 44. x + 1 x-2 ≤ 7 Trigonometric functions 45. In the range (0 ,π ), when is sin x < cos x ? 46. When does cos(4 x ) = 1 2 in the range (0 ,π )? Trig deﬁnitions 47. If tan θ = 12 5 and θ is in the third quadrant, ﬁnd sin θ and cos θ . 4 48. If sin x = y , ﬁnd cos x and tan x . 49. Convert 210 ◦ to radians and 3 π 4 to degrees. 50. Find a polynomial of degree 3 that satisﬁes f (2) = 4 and has roots at x =-2 , 1 , 3. 5...
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