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Suggested number of
"50 minute" lectures
(MWF schedule)
Alg review
Ch 4
6
7 or 8
Test 2 review
1
Ch 5
Ch 6
Test 3 rev
7
3
1
Ch 7
Ch 8
Test 4 Review
3
6
1
Vectors
Polar
2
2
Final Review
1
PreCalculus Topics (Work)
Algebra Review:
Composition and inverse (are on Test 1!)
New: definition of even and odd functions, finding difference quotient.
Rational Functions (especially lim as x infinity, asymptotes)
Exp and log functions (recognizing graphs and asymptotes and end behavior, properties,
equations)
Day 1: Introduction, Composition of functions, inverse fn, finding difference quotient, odd/even
functions.
Day 2: Rational Functions (finding domain, asymptotes and holes; does it intersect HA?)
Limit as xinfinity (rational and polynomial fn examples)
NOTE: if x increases/decreases without bound, we will say limit does not exist. Mention 3 cases of
“dne”; f increases without bound, decreases without bound, or none (like sin(x) ). Better to show with
graphs. For us, limit is a finite number (as in 1431).
Day 3: Exponential functions (identifying graphs, limits as x +-infinity), solving exponential equations
by converting; may start log functions. Emphasize finding HA after transformations. Add an example of
quadratic type exponential:
Solve: 10^(x^2+x)=100^x.
Solve: 9^x -7* 3^x + 10= 0 (change to y^2 – 7y+10=0).
Day 4: Logarithmic functions (basic graphs, properties, limit, solving equations by converting);
emphasize finding asymptotes after transformations (especially if there is reflection).
Find limit of a*log(mx+n) + d as x infinity (some of a,m,n,d will be 0)
Find limit of log_a(x) + d as x infinity (with a>1, a<1).
Ex: 3ln(x) +5; 2log_{1/5}(x) , -2log(x), log(3x) +1
Find limit of m*a^(bx) + d as x infinity and as x negative infinity (with a>1, a<1).
Ex: 2*e^(5x)+1; f(x)= (1/5)^(4x) -3
For exponential and log functions, please use the terms “increasing/decreasing” to describe their behavior.
Even though we may not ask them to graph a log function, they should be able to sketch an exp or a log
function quickly (just a sketch showing the behavior).
May Add examples about composing exponential and log functions. Also, finding the inverse:
F(x)= ln(mx)+b, find f^(-1)(c) =? (also with different bases). (this is on the quiz)
Spend 2 weeks on Algebra review. Emphasize that they need to recall many things from algebra (graphs
of exponential and log, solving equations). We are not teaching these subjects, we are only reviewing
what they already know with some additions.
Trigonometry
Chapters 4,5,6,7 from text book. We can follow the order in the textbook. We need to edit our notes to
improve student learning.
Conic Sections (Chapter 8; emphasize identifying, don’t spend too much time on graphing hyperbolas,
completing the square is important)
Recognize conic sections and their geometric properties.
(a) Differentiate between four conic sections circle, ellipse, hyperbola, parabola using the standard and
the general form of the equations.
(b) Describe the terms center, foci, vertices, and directrix.
(c) Graph the conic sections.
Solve non-linear systems with two unknowns (using algebra and/or graphing)
Vectors (new) – need to create notes considering what they need to know in Physics.
Draw the components of a vector.
Construct a visual representation of scalar multiplication, vector addition, and vector subtraction.
Find the dot product of two vectors; find the angle between two vectors.
Use the dot product to determine if two vectors are orthogonal, parallel, or neither.
Polar Coordinates and Polar curves (from 10.1 in Calculus)
Recognize polar coordinates and use them to draw graphs and plot points.
Define polar coordinates and be able to convert between Cartesian and polar coordinates.
Understand the basic curves in polar coordinates (lines, circles)
Graph in polar coordinates and use graphs to recognize parametric representations of polar equations
Convert equations