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Practice Problems for Final

Practice Problems for Final - If GA” 45 PRACTICE PROBLEMS...

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Unformatted text preview: If GA”- 45!:- PRACTICE PROBLEMS FOR THE FINAL, MATH 3 PRECALU ULUS, 1. Use your calculator to evaluate the following expressions. Rounci to the nearest hundredth1 if necessary. (a) ten 35 (b) cot 35" (6) sec 5% (cl) tan 45° —— tan(—%) (B) 62 (f) 1031001! 2)) (s) logz 5 (M10315 3 2. Use the reference angle principle to get the exact value of the following expressions: (3.) sec 135° (1)) cot 120” (c) sin(—§) 3. Graph the following functions. (a) fix) = tan“($) (b) f(3) = arctanm *1 (1)) HI) = 31660603 -1) 4. Graph the function f(a:). = -— sin(1r2 + 7r) after finding the amplitude, period, phase shift and main cycle._Do the same for 9(2) = 7cos(27r:r: -- 4) 5- Graph K1?) = %c5c(2:a + %) 6. Give the exact value of sin(arccos £4) by using an appropriate triangle. Do the same for tan(a.rcsin "T1) and sec(arcta.n 3:). 7. Determine whether the equation for the given graph has the form :1; z Asin Be or y = Acos Hz: (with B > 0) and then find the values for A and B. '7. 8. Find the equation and graph at least 2 cycles of the sine curve 3; 2 Asin(Bs - C) + D with amplitude 2, phase shift 3'45, period 2 and a vertical shift up by 1. Assume that A > 0. 9. (a) Show that tange- — 1 = tam2 :r:si.u2 :I: ~— cos2 x (b) Show that 1%“ch — Jel— '“ 1-«su16I 10. Solve the triangle with sides a = 8,6 = 6 and c = 10. 11. Let 6 be an angle such that sinfi = fi and g < 0 < it. Find tan 9, cos 0, sec 3, csc 3, cot 0, sin 20, cos 26, sin(%), sin(%) and H. 12. Use the appropriate formulas to solve the following. (a) Find the exact value of sin 105° using the sum/difference formulas. (b) Verify the identity cos(:r + 2n) = cos n 13. Give all real solutions (if there are any) to the following equations. (a)lnzz=2 (b)log3m=2logs(z+2)—2 (c)sin:c==—% (d)sinz=3csc:c-—2 (e) e2”~5e“—6=D (f) tanzwzi (g)'cosga:-—cosz—2=0 f) 14. A 10ft vertical antenna is on the roof of a building. From a point on the ground, the angles of elevation to the top and the bottom of the antenna are 25° and 21° respectively. Find the height of the building. 15. A bank offers the following retirement deal: 8% interest, compounded quarterly, invested money cannot be withdrawn for 30 years. What is the eifective yield of this deal ? How much do you ham to invest today if you want to have $ 1 million after the 30 years ? 16. Consider the quadratic function defined by f(::) = iii—$2 + a: —- 1, dom(f) = [0, 6] (3.) Find the vertex form of f(a:). (13) Find the :1:— and y- intercepts of f(:r). (0) Graph the function flit). ((1) Determine the maximum and minimum value for f(a:) on its domain. 1?. Graph the following functions. (a) 112) = e (b) it») = 1 + r” (c) ft») = 411(3) + 1 (d) 111) = Int: + 1) ~ 1 (9) Km) = (3 +1)(z - 1) (1') fix) = (x + 1)($ _ 1)(z + 2) (E) flat) = (2 + 1X3 - 1)(== + 2X3 - 3) {11) ii!) = (I + 1)(='5 — 1)(m + 2)2 18. Give the domains of the following functions: (3)1192): 13(3 + 1) (13) 9(3) =10ga($2 -" 1) 19. Find the equation and the graph of the inverse of f(2) = 2:3 + 1. 20 For the rational function f(m) : 3,—— find ail intercepts, the equation of all asymptotes _z—2 and the graph. Does the graph intersect its horizontal asymptote ? 21 Find the equation of the quadratic functions with the following graphs: VENOEC '1’...” Uflilql ("4) l) 7'“th “—1 - 9. 22. Give a. reason Why each of the following two graphs cannot represent a. p ynornial function with highest degree term 2.1:“. . (on 3’ Cb) . >6 7“ 23. 100 grams of a substance with a half-life of 12 years are released. How much is left after 100 years ? When will only 1 gram be left ? 24. What' is the largest area possible of among all rectangles with a fixed perimeter P. What are the dimensions and the shape of this largest rectangle? ...
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