A: Super-Basic Algebra Skills. A1. True or false. If false, change what is underlined to make the statement true. a.

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1 A: Super-Basic Algebra Skills A1. True or false. If false, change what is underlined to make the statement true. 1 T F 1 b. T F c. ( + ) = + 9 T F 1 1 T F e. ( + 1) = 16( + ) T F f. 5 T F g. If ( + )( 10) =, then + = or 10 =. T F A. More basic algebr If 6 is a zero of f, then is a solution of f () = 0. b. Lucy has the equation ( + 6) 8 = 16. She multiplies both sides by ½. If she does this correctly, what is the resulting equation? c. Simplify 10 Rationalize the denominator of 1 1 e. If f () = + + 5, then f ( + h) f () = (Give your answer in simplest form.) 1 f. A cone s volume is given by V r h. If r = h, write V in terms of h. g. Write an epression for the area of an equilateral triangle with side length s. h. Suppose an isosceles right triangle has hypotenuse h. Write an epression for its perimeter in terms of h.

2 T: Trigonometry You should be able to answer these quickly, without referring to (or drawing) a unit circle. T1. Find the value of each epression, in eact form. sin b. cos 11 6 c. tan sec 5 csc f. cot e. T. Find the value(s) of in [0, ) which solve each equation. sin b. cos 1 c. tan sec e. csc is undefined f. cot 1 T. Solve the equation. Give all real solutions, if any. sin 1 b. cos( ) c. tan 0 sec 1 9 e. csc( ) 0 f. cot 6 0 T. Solve by factoring. Give all real solutions, if any. sin + sin + 1 = 0 b. cos cos = 0 c. sin cos sin = 0 tan + tan = + T5. Graph each function, identifying - and y-intercepts, if any, and asymptotes, if any. y = -sin () b. y = + cos c. y = tan 1 y = sec + 1 e. y = csc () f. y = cot

3 F1. Solve by factoring = 0 F: Higher-Level Factoring b. + 6 = 0 c. ( 6) + ( 6) 10 = = + 8 F. Solve by factoring. You should be able to solve each of these without multiplying the whole thing out. (In fact, for goodness sake, please don t multiply it all out!) ( + ) ( + 6) + ( + )( + 6) = 0 b. ( ) ( 9) + ( ) 5 ( 9) = 0 c. ( + 11) 5 ( + 5) ( 1) + ( + 11) ( + 5) ( 1) = ( 1) ( ) F. Solve. Each question can be solved by factoring, but there are other methods, too. 1 a ( a ) (a ) 0 b. 6 0 c. 6 1 ( 1) 1 1

4 L: Logarithms and Eponential Functions L1. Epand as much as possible. ln y b. ln y c. ln ln y L. Condense into the logarithm of a single epression. ln + 5ln y b. lna 5ln c. ln ln ln ln (contrast with part c) L. Solve. Give your answer in eact form and rounded to three decimal places. ln ( + ) = b. ln + ln = 1 c. ln + ln ( + ) = ln ln ( + 1) ln ( ) = ln L. Solve. Give your answer in eact form and rounded to three decimal places. e + 5 = 1 b. = 8 1 c. 100e ln = 50 = 1 (need rounded answer only on d) L5. Round final answers to decimal places. At t = 0 there were 10 million bacteria cells in a petri dish. After 6 hours, there were 0 million cells. If the population grew eponentially for t 0 how many cells were in the dish 11 hours after the eperiment began? after how many hours will there be 1 billion cells? b. The half-life of a substance is the time it takes for half of the substance to decay. The half-life of Carbon-1 is 5568 years. If the decay is eponential what percentage of a Carbon-1 specimen decays in 100 years? how many years does it take for 90% of a Carbon-1 specimen to decay?

5 R1. b. c. f ( ) Function 8 R: Rational Epressions and Equations Domain Hole(s): (, y) if any Horiz. Asym., if any ( ) 8 f ( ) 6 f ( ) skip skip 10 8 Vert. Asym.(s), if any R. Write the equation of a function that has asymptotes y = and = 1, and a hole at (, 5) b. holes at (-, 1) and (, -1), an asymptote = 0, and no horizontal asymptote R. Find the -coordinates where the function s output is zero and where it is undefine For what real value(s) of, if any, is the output of the function f ( ) e equal to zero? undefined? 6 1 b. For what real value(s) of, if any, is the output of g ( ) equal to zero? undefined? cos sin R. Simplify completely. (Don t worry about rationalizing) b. 1 (Your final answer should have just one numerator and one denominator) c. 5 1 ( ) 1 ( ) 5 (Don t worry about rationalizing)

6 G: Graphing G1. PART of the graph of f is given. Each gridline represents 1 unit. Complete the graph to make f an EVEN function. b. What are the domain and range of f even? c. What is f even (-)? Complete the graph to make f an ODD function. e. What are the domain and range of f odd? f. What is f odd (-)? G. The graphs of f and g are given. Answer each question, if possible. If impossible, eplain why. Each gridline represents 1 unit. f -1 (5) = b. f (g(5)) = c. (g f )() = Solve for : f (g ()) = 5 e. Solve for : f () = g () For parts f i, respond in interval notation. f. For what values of is f () increasing? g. For what values of is g () positive? h. Solve for : f () < i. Solve for : f () g() G. Given the graph of y = f () (dashed graph), sketch each transformed graph. b. c. y = f ( + ) y = f () y = f () y = f () + 1