MHF4U 1-11Culminating Activity MHF4U Advanced Functions 12Adult REMOTE NIGHT SCHOOLSemester XXXXXXXXXXCULMINATING ACTIVITYCOURSE: MHF4U1-11WEIGHT: 20% # of PAGES: 9 # of Questions:...

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MHF4U 1-11Culminating Activity MHF4U Advanced Functions 12 Adult REMOTE NIGHT SCHOOL Semester 1 2022-2023 CULMINATING ACTIVITY COURSE: MHF4U1-11 WEIGHT: 20% # of PAGES: 9 # of Questions: 10 STUDENT NAME: __________________________________________________ INSTRUCTIONS: 1. Read each question carefully. 2. Scientific calculators are permitted. 3. Answer all questions in the space provided. 4. Round answers to one decimal place if necessary. 5. All questions must be answered in proper form, showing all necessary steps to receive full marks. 6. All submissions must be one single PDF, correct orientation; failure to submit proper format may result in a mark of zero. 7. Any sharing of materials constitutes cheating. 8. The penalty for cheating or plagiarism is a grade of zero on this culminating activity in accordance with the TDSB’s anti-plagiarism policies. Start Date: January 26th, 2023 @ 6:30 pm Due date & Ultimate Due Date: January 31th, 2023 @ 9:30 pm Total Marks: _____ /54 1 MHF4U Advanced Functions 12 1. Corners are cut from a 30 cm by 20 cm piece of cardboard. The volume is ?(?) = ?(30 – 2?)(20 – 2?) with height . [___/2x4 = 8]? a) Calculate the volume when the height is 2 cm. b) Calculate the dimensions of a box with a volume of 1000 cm3. c) Solve V(x) > 0 and discuss the meaning in the context of the question. d) State the restrictions in the context of the question. 2 MHF4U Advanced Functions 12 2. a) Determine an equation for the family of cubic functions with zeros – 3, 1 and 2. [___/2x4 = 8] b) Determine the equation of the cubic function of the family with y-intercept 5. c) Determine the equation of the cubic function of the family that passes through the point (3, –24). d) Sketch the graphs of parts b) and c). Clearly indicate all graphs. 3 MHF4U Advanced Functions 12 3. Sketch the function Using intercept(s), hole(s), asymptote(s), end behaviours, and? ?( ) = ? 2 − 4 ?2 − 6? + 8 . behaviours approaching asymptotes. Show all of your supporting work algebraically and label the graph clearly. [__/8] Function ? ?( ) = ? 2 − 4 ?2 − 6? + 8 x–intercept(s) y–intercept Hole(s) Vertical Asymptote(s) Horizontal Asymptote(s) End Behaviours Behaviours approaching vertical asymptotes 4 MHF4U Advanced Functions 12 4. Solve the following inequalities algebraically. State your answers using interval notation. [___/4] ≥? + 4? − 3 ? − 5 ? + 2 5 MHF4U Advanced Functions 12 5. A cosine function has maximum value of 185 at x = 8?, a minimum value of –15 at x = 40 ?. [___/6] a) Find the equation of the function. b) Sketch and label the graph of the function for one period. 6. Solve the equation , for . Express answer as an exact value.6cos2? + 7 cos ? − 5 = 0 − 2π ≤ ?≤ 2π [__/3] 7. Solve the equation [__/3]log(? + 2) + log(? − 1) = 2 6 MHF4U Advanced Functions 12 8. Armin bought a rare Wayne Gretzky rookie card for $18 in 2020. The function ?(?) = 18(9) 5 ?+1 represents the increase of the value of the card in dollars over the years, where x is the number of years. When the card reaches a value of $1125, he wants to sell it. What year will Armin sell the card? Only algebraic solutions will be accepted. [___/4] 9. The pH of a solution is calculated by using the formula pH , where is the concentration of the hydronium ions. [___/4] a) If the pH of a solution is 4.2, what is the concentration of the hydronium ions? b) A strong acid has a pH less than 3. If the concentration of the hydronium ions is in a particular solution, is the solution a strong acid? Explain. 7 MHF4U Advanced Functions 12 10. a) Given the functions f(x) = x + 2 and g(x) = 3x, determine an equation for (f ∘ g)(x) and (g ∘ f)(x). [__/6] b) Determine f(g(3)) and g(f(3)). c) Determine all values of x for which f(g(x)) = g(f(x)) algebraically. 8 MHF4U Advanced Functions 12 MHF4U Formula Sheet Cofunction Identities Logarithmic Scale Formulas 9