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MATA30H3 (0)
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School
University of Toronto Scarborough
Department
Mathematics
Course
MATA30H3
Professor
Sophie Chrysostomou
Semester
Winter

Description
University of Toronto at Scarborough Department of Computer & Mathematical Sciences MAT A30F Fall 2013 Assignment #0 To prepare for the diagnostic test you could • Complete this assignment, the ”Review” and the More High School Material Review exercises on WebAssign. You do not need to hand in these assignments and they are not worth any marks. Their sole purpose is to help you review and prepare for the diagnostic test. • Read notes posted on http://ctl.utsc.utoronto.ca/mslc/reviewmodules and on http://www.math.mcmaster.ca/lovric/rm.html . Try all the exercises and practice tests posted there. • From the textbook, read the insert on ”Review of Algebra”, the ﬁrst chapter and appendix D. Attempt questions from these sections. It is also worth while to try the diagnostic tests in the text book in pages xxiv-xxviii. (A) Worked Example: Find all x satisfying the inequality |x + 2| + x < 0 SOLUTION: x + 2 if x ≥ −2 |x + 2| = −(x + 2) if x < −2 Case 1.If x ≥ −2, then |x + 2| + x = 2x + 2 < 0 =⇒ x + 1 < 0 =⇒ x < −1. For this case x ≥ −2 and x < −1 =⇒ x ∈ [−2,−1). Case 2. If x < −2, then |x + 2| + x = −(x + 2) + x = −2 < 0 for all x < −2; that is x ∈ (−∞,−2). Thus |x + 2| + x < 0 if x ∈ [−2,−1) or x ∈ (−∞,−2) ⇐⇒ x ∈ (−∞,−1). 1 (B) Problems Algebraic Manipulations and Equations Solve for x: 4 3 5 17 1. + = . x = 7 x + 2 3 23 √ 2. x − 27 +√x = 9. (x = 36) √3 3. x − 5 − 2 = 2. (x = 69) r ! 1 22 4. 2x + 7 = 3x . ± 3 9 5. 2x + |x| = −6. ({x = −6}) 6. Solve by completing the square: 4 −x + 3x = 4. x = , −1 3 2 Simplify: √ 1. 3 ab (ab ) b . a b515 r r √ ! 7 3 √ −73 21 2. 2 − − 2 84. 3 7 21 p 3 p4 3 7 5 3. x y xy . x 4y4 a (y2−x)2 −5x 2+3x 4. . a 2 y 2 a y −2x x−3y−1 + y−5 xy + x 4 5. −4 5 . 10 x y y 1 2 + 3a 6. 4x . 4ax + 4b + 6ab a+3 + 2b 3 Graphs and Analytic Geometry 1. Find the equation of the line that passes through (1,0) and (0,1). (y = −x + 1) 2. Find the equation of the line that passes through (3,−2) and is perpendicular to the 1 line 2y + 6x = 5 (y = x3− 3) 3. Sketch the graph of each function: 2 1 a) y = x b) y = 2 x 4. Write the equation of each graph: a) b) √ 5. Find the distance between the point (3,5) and line y = x − 10 (6 2) 2 2 6. The equation x +y
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