University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT A30 Final Exam
Examiners: Sophie Chrysostomou
Date: December 9, 2011
Duration: 170 minutes
Brian Pike
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Section 8. Calculus: Limits and Derivatives 65
8. Calculus: Limits and Derivatives
This section contains review material on:
0 Limits
0 Derivatives
Limits. We do not intend to go into theoretical considerations about limits and other concepts of
calculu
Section 6. Trigonometry
6. Trigonometry
This section contains review material on:
o Trigonometric ratios and trigonometric functions
0 Trigonometric identities and trigonometric equations
Angles. Recall that a positive angle is measured counterclockwise
Section 7. Exponential and Logarithmic Functions
7. Exponential and Logarithmic Functions
This section contains review material on:
o Exponential functions and the natural exponential function
0 Logarithmic functions and the natural logarithmic function
30
Mathematics Review Manual
5. Functions
This section contains review material on:
0 Denition of a function, domain, range
0 Graph of a function
0 Important graphs
0 Creating new functions from old
Function. A function f is a rule that assigns, to each
Section 4. Elements of Analytic Geometry
4. Elements of Analytic Geometry
This section contains review material on:
o Cartesian coordinate system and distance between points
0 Equations of a line
0 Graphs of second degree equations: circle, ellipse, par
Section 3. Equations and Inequalities
3. Equations and Inequalities
This section contains review material on:
0 Solving linear equations in one variable
0 Solving inequalities in one variable
0 Solving equations and inequalities involving absolute value
Section 1. Basic Algebra
1. Basic Algebra
This section contains review material on:
0 Real numbers, intervals and absolute value
0 Polynomials
o Radicals and rational expressions
0 Fractional expressions
Real Numbers and Its Famous Subsets. In Calculus,
Section 2. Basic Formulas from Geometry
2. Basic Formulas from Geometry
This section contains review material on:
0 Plain geometry
0 Geometry in threedimensional space.
Plane Geometry. Usually, we use lowercase letters a, b, c, . . to denote the sides (
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MATA30: Calculus I - Midterm Test
Examiner: Sophie Chrysostomou Date: Monday, October 26, 2009.
Duration: 110 minutes
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HLTB03 Summer 2012
General Paper Guidelines Version 3
OPTION 1:
Your task is to choose from one of three recent articles (posted on Blackboard) that make a claim about a
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