FLC Math 370 Precalculus Basic Skills Handout Use A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set.

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1 FLC Math 370 Precalculus Basic Skills Handout Use A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set. 1) (A B) C Determine which value(s), if any, must be excluded from the domain of the variable in the expression. 2) x 3 + 4x4 x ) x 2 + 5x - 2 x3-25x Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0. -6x2y-6-2 4) 7z2 Solve. 5) What is the value of (6666) 5 (3333)5? Solve. If necessary, round to the nearest tenth. 6) A flagpole casts a shadow of 38 feet. Nearby, a 6-foot tree casts a shadow of 4 feet. What is the height of the flagpole? Factor completely. If the polynomial cannot be factored, say it is prime. 7) 20x3 + 9x2-20x Use synthetic division to determine whether x - c is a factor of the given polynomial. 8) 6x5-5x4 + x - 4; x Perform the indicated operations and simplify the result. Leave the answer in factored form. 9) 7 - x x - 5-2x x 10) x - 9 x x - 9 x ) The focal length f of a lens with index of refraction n is 1 f = (n - 1) 1 R1 + 1 R2 where R1and R2 are the radii of curvature of the front and back surfaces of the lens. Express f as a rational expression. Solve the equation. 5 12) x + 8 = 2 x (x + 8)(x + 16) Page 1 of 5

2 13) 9x + 1 = x + 5 Solve the equation by the Square Root Method. 14) (x + 4)2 = 15 Solve the equation by completing the square. 15) x2 + 2x = 0 Write the expression in the standard form a + bi. 16) 8 + 6i 7-2i 17) i10 + i8 + i6 + 1 Perform the indicated operations and express your answer in the form a + bi. 18) (3 + 4i)(4i - 3) Solve the equation in the complex number system. 19) x4-4x2-5 = 0 Without solving, determine the character of the solutions of the equation in the complex number system. 20) x2-8x + 16 = 0 A) two complex solutions that are conjugates of each other B) two unequal real solutions C) a repeated real solution 21) x2 + 3x + 6 = 0 A) two unequal real solutions B) a repeated real solution C) two complex solutions that are conjugates of each other 22) x2 + 8x + 7 = 0 A) two complex solutions that are conjugates of each other B) a repeated real solution C) two unequal real solutions 23) An airplane flies 450 miles with the wind and 330 against the wind in the same length of time. If the speed of the wind is 30, what is the speed of the airplane in still air? Solve the inequality. Express your answer using interval notation. 24) x(9x - 3) (3x + 2)2 Page 2 of 5

3 25) 0 3x + 4 < ) 6x ) 5-7x > 9 Find the real solutions of the equation. 28) x = -2 Simplify the expression. 29) -2431/5 An expression that occurs in calculus is given. Write the expression as a single quotient in which only positive exponents and/or radicals appear. 30) (49 - x 2) 1/2 + 3x2(49 - x2) -1/ x2 In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. 31) ( 4 7, 33 ) Find sin t. 7 Find the exact value. Do not use a calculator. 32) sin 2 33) cos 0 34) tan 0 35) cot 0 36) sin (22 ) 37) sin 4 38) cos 45 Find the exact value of the expression if = 45. Do not use a calculator. 39) g( ) = sin Find 6g( ). Page 3 of 5

4 Find the exact value. Do not use a calculator. 40) sec 30 41) tan 6 42) sin 3 - cos 6 Find the exact value of the expression if = 60. Do not use a calculator. 43) g( ) = cos Find [g( )]2. Find the exact value. Do not use a calculator. 44) cos ) sec ) sin ) cot 570 Find the exact value of the expression. Do not use a calculator. 48) tan tan ) sin sin ) cos 3 + tan 5 3 Answer the question. 51) Which one of the equations below matches the graph? A) y = 3 sin 1 4 x B) y = 3 cos 4x C) y = 3 cos 1 x D) y = -3 sin 4x 4 Page 4 of 5

5 52) Which one of the equations below matches the graph? A) y = -2 cos 3x B) y = -2 sin 3x C) y = 2 sin 1 3 x D) y = -2 sin 1 3 x Write the equation of a sine function that has the given characteristics. 53) Amplitude: 3 Period: 5 Graph the function. Show at least one period. 54) y = 3 sin(4 x + 2) Find the exact solution of the equation. 55) cos-1 x = 0 56) sin-1 x = 6 57) 3 tan-1(2x) = 58) 7 cos-1 x - = 5 cos-1 x Page 5 of 5

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