Textbook Notes
(363,236)

Canada
(158,278)

University of Toronto Scarborough
(18,341)

Mathematics
(60)

MATA30H3
(0)

Chapter

# a0.pdf

Unlock Document

University of Toronto Scarborough

Mathematics

MATA30H3

Sophie Chrysostomou

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

More
Less
Related notes for MATA30H3