Math 1. Midterm 1 (practice problems). Pre-calculus. Fall 2013. Disclaimer: The
following list of ... you should be familiar with for the exam on Monday (Oct. 28).
Math 1
Midterm 1 (practice problems) Pre-calculus
Fall 2013
Disclaimer: The following list of problems is provided to give you an idea of what topics you should be familiar with for the exam on Monday (Oct. 28). The problems found here might not be similar, in either form or content, from the ones you will find in the exam. However, being able to solve the majority of these problems will certainly give you a good indicator of what you can expect your performance to be on the Midterm. Questions. 1. Using the graph shown
i. ii. iii. iv. v.
Find g(1) Solve g(x) = 1 Find g −1 (1) Solve g −1 (x) = 1 Solve − g −1 (x))−1 = 1
2. Find the equation of the line that i. Passes through the points (1, −5) and (3, −2). ii. Passes through (1, −5) and it is perpendicular to the line that passes through (1, −5) and (3, −2). iii. Intersects the y-axis at 2 and it is parallel to the line that passes through (1, −5) and (3, −2). Where does this line intersect the x-axis? 3. Problem 34 on section 1.4 (page 59). 4. A rocket is launched in the air. Its height, in meters above sea level, as a function of time, in seconds, is given by h(t) = −4.9t2 + 229t + 234. i. From what height was the rocket launched? ii. How high above sea level does the rocket reach its peak? iii. Assuming the rocket will splash down in the ocean, at what time does the splashdown occur?
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Math 1
Midterm 1 (practice problems)
Fall 2013
5. For each of the following functions determine the x and y intercepts. If the function is quadratic, determine its vertex and explain if it corresponds to a maximum or minimum. i. R(x) = 3x2 − 6x − 9
ii. S(x) = x4 − x2
iii. T (x) = 16(x − 2)(2x − 9) 6. Problem 39 on section 3.2 (page 175). You should have solved this problem already (homework 5). Try changing the coefficients of the quadratic as well as changing the rate at which the land rises.1 7. Problem 28 on section 3.3 (page 185). 8. Problems 1, 19 and 27 on section 3.4 (pages 201 and 202).
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To obtain a meaningful answer make sure that the coefficient of the second order term is negative and the coefficient of the first order term is positive. What if the land starts dropping (instead of increasing), how does that change the way the problem is solved?
