Ovs-mhf4u-t1-test-1 (1)
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School
City Colleges of Chicago, Harold Washington College**We aren't endorsed by this school
Course
MATH 99
Subject
Mathematics
Date
Dec 29, 2024
Pages
7
Uploaded by ChiefFire14748
OVS MHF4U T1 - test 1Advanced Functions (Ontario Virtual School)Scan to open on StudocuStudocu is not sponsored or endorsed by any college or universityOVS MHF4U T1 - test 1Advanced Functions (Ontario Virtual School)Scan to open on StudocuStudocu is not sponsored or endorsed by any college or universityDownloaded by Crinson (mu729337@gmail.com)lOMoARcPSD|24201497
Page 1 of 6 MHF4U Test #1: Chapters 1-3 Name: Part A –Multiple Choice [K/U –20 marks] Date: 1.If the leading coefficient of an even-degree polynomial function is negative, then the function extends from the third quadrant to the fourth quadrant; that is, as a., and as , b., and as , c., and as , d., and as , 2.Which polynomial function would have the end behaviour of as, ?→∞,?→∞and ?→ -∞,?→∞?? a. b. ?(?) = −6?3+ 3?2+ ?−11c. d. ?(?) = −?2−23. The degree of the polynomial function y = x (x + 4)3(x - 5)2is a. 2 b. 3 c. 5 d. 6 4.Given the function y = 2x3–3x2–5x + 1, which finite differences will be equal (or constant)? a. first differences b. second differences c. third differences d. none 5.Given a function of the form y = a [k (x –d)] n+ c, where k > 0, the transformation that occurs by changing the value of k is a.a horizontal stretch or compression b. a vertical stretch or compression c.a horizontal translation d. a reflection in the x-axis 6.If 4x3+ 9x2–1 is divided by 2x + 1, then the restriction on x is a. b. c. d. 7.If P(x) = 4x3–11x2–6x + 9 is divided by x –3, what is the remainder?? a.P(3) b. 0 c. P(-3)d. a) and b) 8.For what interval(s) is the graph of the rational function negative? a. b. c. d. Downloaded by Crinson (mu729337@gmail.com)lOMoARcPSD|24201497
Page 2 of 6 19.The graph of which of the following rational functions has a hole? a. y b. c. y d. 10.Over what interval does the graph of the rational function have positive, decreasing slope? a. b. c. d. x > 2 Show all work from this point forward for full marks. 11.Solve the following. ✓✓✓& ✓✓✓ 1a) ?4+2?2= 24 b)?−3?−1+ ?2 −9?> ?+312.Determine the average rate of change of the function ?(?) = −2x?2 +3?over the interval [−1,]?✓✓✓✓ 2Downloaded by Crinson (mu729337@gmail.com)lOMoARcPSD|24201497
Page 3 of 6 Part B –Thinking and Investigation [TI –20 marks] 1.Determine an equation in the form for a function with a vertical asymptote at ? = 2and a y-intercept of 18✓✓2.Determine the instantaneous rate of change at x = 2 for the curve?(?) =−2(?−1)3?, to 1 decimal place. ✓✓✓3.Prove that ?2+ 5? + 6is a factor of ✓✓✓✓✓✓4.The polynomial ?(?) = 6?3+ ??2+ ?? − 5 has a factor of x + 1. When divided by x –1, the remainder is –4. W What are the values of m and n? ✓✓✓✓✓✓ Downloaded by Crinson (mu729337@gmail.com)lOMoARcPSD|24201497
Page 4 of 6 4.Solve the following inequalities using an algebraic method. ✓✓✓✓✓?+42?−1> 3Part C –Communication [COMM –20 marks] ***Fully label your graphs for full marks!*** 1.Determine an equation for the graph of the polynomial function shown. ✓✓ 2.Determine whether the function ?= −2?3+ 4 ?is even, odd, or neither. Justify your answer. ✓✓✓ 3.Write a quadratic inequality with the solution: −3 < ? < −52✓✓✓ Downloaded by Crinson (mu729337@gmail.com)lOMoARcPSD|24201497
Page 5 of 6 4.Consider the function. ?(?) = −1?2−?−12a)Determine the key features of the function: i)domain and range✓✓ ii)intercepts✓✓ iii)equations of any asymptotes ✓✓ iv)intervals where the function is increasing and intervals where the function is decreasing✓✓ b)Sketch a graph of the function. ✓✓✓✓ Downloaded by Crinson (mu729337@gmail.com)lOMoARcPSD|24201497
Page 6 of 6 Part D –Application [APP –12 marks] 1.The population of a small town is modelled by the function , where P(t) is the population, in thousands, and tis time, in years, since the start of 1990. a)Is the population currently increasing or decreasing? Justify your answer. ✓✓b) The town will need its own transit system if the population exceeds 50 000. Will the town’s populationexceed 50 000? Explain. ✓✓2.a) Use long division to divide ?6+ 3?2− 7by x+ 2. Express the result in quotient form. ✓✓✓b) Write the corresponding statement that can be used to check the division. ✓ 2. The height of a square-based box is 4 cm more than the side length of its square base. If the volume of the box is 225 cm3, what are its dimensions? ✓✓✓✓ Test Summary Knowledge ThinkingCommunicationApplication/20 /20 /20 /12 Downloaded by Crinson (mu729337@gmail.com)lOMoARcPSD|24201497