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1510_t2a_sol - York University Faculty of Science and...

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Unformatted text preview: York University Faculty of Science and Engineering Math 1510 Class Test 2 Version A NAME (print): (Family) > (Given) SIGNATURE: STUDENT NUMBER: ‘d Instructions: 1. Time allowed: 90 minutes. 2. NO CALCULATORS OR OTHER AIDS PERMITTED 3. Show your work. Your work must justify any answers you give. Use page backs for any scrap work. 4. Use pen to fill in cover. If you use pencil for your solutions, you may not submit your paper for regrading. Question Points _[.1V_Iarks_fl 1 15 2 7 3 7 4 7 5 T 7 6 7 7 20 as: 8 20 9 10 Total 100 5. There are 9 questions on 8 pages. Page 1 MATH 1510 Test 2 Version A November 24, 2010 1. Solve each of the following. 1 6-316 1 ' — > > —. (a) (8 pomts) 2 _ 8 _ 4 MU’Wf/aLLOi 8: fit >/ éw—Bf 51/ (Z; EBX 7/” 7£ EEVQFSQ \ l - é .___A€7( \/ 3 j Page 2 MATH 1510 Test 2 Version A November 24, 2010 2 ’3 1. 70—2.) x - 5 2' ><+ ( 4 O >(r2‘ \ 293:4 XVZ‘O 2. (7 points) Find the point on the I—axis that is equidistant from the points (4, —4) and (2,1). Lgt (CZ/o) be, ULfiaJC' fdiw' Z ’27 Q" “2'75 (/ZESM/fi ("5 (5:730 Page 3 MATH 1510 Test 2 Version A November 24, 2010 3. (7 points) Find the equation of the circle for which the points (— —2 ,5) and (6,17) are endpoints of a diameter. Mfogwmf I; éi [7:/F— :(‘2/ H) 2” / 5%Uad‘ldwx. if L [x Z) Lfi—(OLLEHL 2r USQ Fol/Vt C?— /é> + 36 cr‘ jfi 'F‘~-:-§_L 4. (7 pints) Find an equation of the line with intercepts (0, 5) and (3,0 . I (0/?) if Page 4 MATH 1510 Test 2 Version A November 24, 2010 5. (7 points) Find an equation of the line through (-—1, 3) perpendicular to the line through (5, 2) and (2, 6). - r“ j 2 Zugfi; AQI J‘fcerL 6. (7 points) Find the domain of the function with formula f(;L‘) = interval notation. Page 6 MATH 1510 Test 2 Version A November 24, 2010 8. (a) (6 points) Write —3$2 — 6x — 1 in the form a(I — h)2 +_ k for suitable a, h, k. (b) (6 points) Indicate (in order) the geometric transformations which can be performed to the graph of y = 9:2 to obtain the graph of y = —3:c2 — 62: ~ 1. Page 5 MATH 1510 Test 2 Version A November 24, 2010 :c—L—l2 if—-2OS:C<—3 7. Let f be the piecewise defined function with f(x) = x2 if —3 S :c g 1 4 if 2 < CL“ S 4 (a) (10 points) Sketch the graph of y = f(:c). (b) (3 points) What is the domain of f? Write your answer in interval notation. 1:1—20/ r l a (2/51 (c) (3 points) Use your sketch to determine the range of f. X?- % ‘G (d) (4 points) What are the maximum and minimum values of f. Moe-F f/ (1 {Minimum 51 "‘ 8 Page 8 MATH 1510 Test 2 Version A November 24, 2010 9. A wire 10 cm long is cut into two pieces7 one of length m and the other of length 10 — m. Each piece is bent into the shape of a square. (a) (5 points) Find a function that models the total area enclosed by the two squares. P2 Note: The area of a square with perimeter P is 1—6' X _ (70 #9?— (b) (5 points) Find the value of :L' that minimizes the total area of the two squares. Show your work. 24C X) :: K>7L “)0 “’2‘” 0+ 02’ The end Page 7 MATH 1510 Test 2 Version A November 24, 2010 (c) (5 points) Sketch the graph of y = ~3x2 -— 6w — 1. Your sketch should include labels for the vertex and the y—mtercept. g F I MTG/”CW (7 . K o ~I> / (d) (3 points) What is the range of f(.r) = —33:2 — 61' — 1? was} ...
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