TEST 1 May Summer 2019, questions PDF

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Math 1505 Practice PASS Exam 1...

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PASS MATH 1505 MOCK TEST 1 SUMMER 2019 Weekly sessions held on Tuesdays, 4-5:30pm, Bethune College Room 202 Wednesdays, 4-5:30pm, Bethune College Room 202 PASS Leader: Francis Calingo

Please note: Do not substitute this mock test for studying. The questions included are only examples of what may appear on the midterm and are not necessarily representative of the degree of difficulty. This test is copyright of the PASS program at Bethune College.

For more information visit bethune.yorku.ca/pass and join the Facebook group PASS MATH 1505 SUMMER 2019

1) a) Solve each inequality. | i) ||x − sin( 2π 3 )| < 3 ii) l og3 (x) − log 3 (2) ≤ 2 b) Find ALL the six trigonometric ratios for θ = 5π6 c) Show that the triangle with vertices (3,3), (7,3), and (7,6) produce a right-angled triangle. 2) a) For each function, ● Identify what type of function it is ● Find its inverse. If it does not have an inverse, explain why. ● Identify the function’s domain. i) A(x) = x2 − 8x + 16 ii) B (x) = √4x + 5 iii) C (x) =

4x−1 2x+7

b) Find the following composite functions then state their domains. i) C ° B ii) A ° B iii) B ° A 3) Find the formula for each part, given that P (x) = x2 , Q (x) = x + 6 , R (x) = |x | , S(x) = ln(x), T (x) = sin(x)

a) Horizontally stretch P (x) by a factor of 2, then reflect about the y-axis. b) Translate Q (x) 2 units up then 2 units to the right. c) Reflect R(x) about the x-axis, then vertically stretch by a factor of 2. d) Translate S (x) 2 units to the left, then reflect about the x-axis and the y-axis. e) T ° Q , expanded. 4) If the limit exists, find it. If not, prove that the limit doesn’t exist. a) lim tan(x) π x→ 2

b) lim f (x) , where x→0

c) lim [ex sin( 3x ) − sin( 3x )] x→0

n

d) lim [ 4 8−1 n + n→∞

√

6x2 −3x+4 2x2 +1 x→∞ sin2 (x) lim xcos(x) x→0

e) lim f)

5n2 −1 n+3 ]

5) An unknown substance, labelled “Substance X”, has a half-life of 10 years. On January 1st, 2020, a scientist obtained a sample of Substance X weighing exactly 50 mg. a) Find an expression for the mass m(t) that remains after 3 years.

b) Find the mass remaining after 32 years. c) In what calendar year should the scientist expect the mass of the substance reach 3.125 mg? 6) Determine if each function is continuous on each given interval. a) b) t an(x), xε [− π2 , 2π ) c) l n(x), xε (0, ∞) d) 1 1 , xε (− ∞, ∞) 1+e x

7) A drug is administered to a patient at the same time every day. Suppose the concentration of the drug in the bloodstream is C n (measured in mg/mL) after the injection on the nth day. Before the injection the next day, only 25% of the drug present on the preceding day remains in the bloodstream. If the daily dose raises the concentration by 0.2 mg/mL, find the concentration after 5 days. (Since calculators are not permitted during tests, try using fractions instead of decimals)....