What’s fair game for the final



What’s fair game for the final?

In a nutshell, everything we’ve covered.

Chapter P – Yes, it’s fair game. Am I going to give a problem out of chapter P? Sure. We spent time on it. Am I going to give more than one? It’s possible – but unlikely. Obviously, you’ll need to know everything from P to do the other problems in the book.

Chapter 1 – We didn’t spend a lot of time on most of this, since we knew most of it from 120. Is there going to be a problem on the stuff we already knew? If we spent time on it, it’s fair game.

1. Equations in one variable

2. Constructing models to solve problems

3. Equations and graphs in two variables – completing the square to get the formula for circles

4. Linear equations in two variables

6. Quadratic equations

7. Linear and absolute value inequalities

2.1 Functions – domain, range, vertical line test, average rate of change, difference quotient (ahem)

2.2 Graphs of relations and functions – piecewise functions, greatest integer function, increasing/decreasing/constant…

2.3 Families of functions, transformations & symmetry – shifting up/down, right/left, flip/stretch/shrink… it’s all good – and showed up in many places later in the book. Know the graphs on p. 223 (and others from later sections)

2.4 Operations with functions – adding/subtracting/multiplying/dividing functions to get new functions, the composition function

2.5 Inverse functions – one-to-one, inverse of a function (and its symmetry to the original function), horizontal line test

2.6 Constructing functions with variation – varies inversely/directly/jointly

1. Quadratic functions and inequalities – More on completing the square (as it applies to parabolas), the beginning of sign graphs, applied problems (max/min)

2. Zeros of polynomial functions – the remainder theorem, synthetic division, the beginning of factoring higher order polynomials, rational zero theorem (the p/q thing)

3. Theory of equations – multiplicity of zeros, finding all roots of a polynomial, conjugate pairs, Descartes’ rule of signs, bounds on roots

4. Miscellaneous equations – factoring higher order polynomials, squaring both sides to get rid of radicals, u-substitution, absolute values, etc

5. Graphs of polynomial functions – more on symmetry, leading coefficient test, graphing ugly polynomials without a calculator…

6. Rational functions and inequalities – graphing rational functions: vertical/horizontal/oblique asymptotes, graphs with holes, rational inequalities

1. Exponential functions and their applications – Graphing exponential functions (b0), exponential applications (compound interest, bacteria, etc)

2. Logarithmic functions and their applications – Logs. Lots of logs. Graphing logs. Changing between exponential notation & logarithmic notation. Memorize the graphs on p. 376.

3. Rules of logarithms – There are tons of log rules in this section. Know them.

4. More equations and applications – Solving equations with exponents & logs. Tricks: taking the log of both sides, combining many logs into one – and then rewriting, etc…see p. 399. Half-life.

1. Angles and their measurements – angles 101, arc length

2. The sine and cosine functions – sin x, cos x for multiples of 30 and 45 degrees, reference angles, sin2x + cos2x = 1… Of course, you’ve memorized the unit circle.

3. The graphs of the sine and cosine functions – The basic shape of the sin/cos functions – and what happens when we change A, B, C & D. Labeling the fundamental five points… You know how to graph for any values of A, B, C & D, right?

4. The other trig functions and their graphs – Rewriting tan, cot, sec & csc in terms of sin & cos, the graphs & periods of these trig functions Memorize the graphs on p. 473

5. The inverse trig functions – sin-1x (or arcsin x) & all the other inverse trig functions. You won’t have to memorize the graphs on p. 481.

6. Right angle trigonometry – SOH-CAH-TOA & solving right triangles. Applications of right triangles

1. Basic identities – Basic identities & whether a trig function is even or odd. Here we go...you should know all these…

2. Verifying identities – No new identities here – only strategies for verifying identities p. 523

3. Sum and difference identities – cos(a + b), sin(a + b), tan(a + b) know these identities. The sin(pi/2 – u) formula (and the other 5) will be on the formula sheet – know how to use them.

4. Double-angle and half- angle identities – These will not be on the formula sheet

5. Product and sum identites & the reduction formula – These will be on the formula sheet. Know how to use them.

1. The law of sines – law of sines, ASA, SSA, area of triangles Know these formulas

2. The law of cosines – law of cosines, SSS, SAS, area of triangles Know the law of cosines. Good review of 7.1/7.2 on p. 592.

1. The parabola – Focus, directrix, vertex, etc…graphing parabolas

2. The ellipse and the circle – Foci, center, etc…graphing ellipses & circles

3. The hyperbola – Foci, asymptotes, etc…graphing hyperbolas

Okay, how should you study? Begin now. Start by re-doing all exams and quizzes. They’ll highlight major areas you might have forgotten. Go over this sheet & look for concepts that don’t seem familiar to you. Work on those problems. Review your notes & look for problems I emphasized. Do the chapter tests in the book – or better yet on MyMathLab. After you take the chapter tests in MML, look at the study plan it produces to see what concepts you need more work on (the computer will give you more problems like the ones you missed!) Visit Maryem’s review sessions, the tutoring center or my office hours.

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