Math 10150 Exam 1 Practice Fall 2024 PDF

Exam 1 Practice: Fall 2024 MATH 10150 Name: Exam 1 consists of 14 multiple choice questions worth 5 points each (13 out of 14 count towards your grade, meaning you get one “free miss”), and three multi-part short answer questions that total 35 points. You will be given par...

Exam 1 Practice: Fall 2024 MATH 10150 Name: Exam 1 consists of 14 multiple choice questions worth 5 points each (13 out of 14 count towards your grade, meaning you get one “free miss”), and three multi-part short answer questions that total 35 points. You will be given partial credit on incorrect responses for the short answer if appropriate work is shown in the exam. What you see below is exactly what page 1 of the actual exam will look like. Multiple choice (5 pts each): Fill in the box for your answer selection. 1 A B C D E 8 A B C D E 2 A B C D E 9 A B C D E 3 A B C D E 10 A B C D E 4 A B C D E 11 A B C D E 5 A B C D E 12 A B C D E 6 A B C D E 13 A B C D E 7 A B C D E 14 A B C D E Multiple choice earned: / 65 Short answer (points as marked): Do not write here. Show all work in the exam. 15 / 13 16 / 14 17 /8 Short answer earned: / 35 Total score earned: / 100 1 Multiple Choice: the following questions would appear at multiple choice questions on the exam. (1) Simplify completely: 1 1 − x y 3 xy f (x + h) − f (x) (2) Find and simplify the difference quotient for f (x) = 2x − 3. h (3) Solve for x: 3 2 1 − = x 3x x+1 (4) Find all solutions: 2|x + 1| − 6 = 0 √ √ (5) Simplify g ( x) when g(x) = x4 − x2 + 2. (6) Simplify completely:
3 2 x2 y 3 (4xy 2 )2 (7) Solve for x: 4(3 − 2x) = −2(−x) − 7(x + 3) (8) Solve for x: x(x − 4) = 10  The graph of h(x) is shown. Use it to answer questions (9) and (10). 2 1 −2 −1 1 2 −1 −2 (9) Find the average rate of change of h(x) from x = −2 to x = 0. (10) Find the equation of the line segment from (−7, 1) to the point on the graph (1, h(1)). (11) What is the center the circle x2 + 8x + (y − 1)2 = 10? (12) Solve and write your answer in interval notation: 2|x| < 10 (13) Find the equation of the line with x-intercept 1 and y-intercept −5. (14) Find any point(s) √ of intersection of the line x − y + 2 = 0 and the circle centered at (0, 2) with radius 8 Short answer: Consider the following three questions short answer questions. You would show all work in the exam. (1) Coach Marcus Freeman is constantly adding to his music collection to keep the mu- sic at Notre Dame football practices modern and fresh. On September 1, 2023, he had 200 songs in his collection. The first of every month he adds 5 new songs to the collection. (a) Write a formula for the number of songs, N , in his collection as a function of time, t, the number of months since September 1, 2023. (b) If you were to substitute N = 1000 into your answer from (a) and solve, you would get a single numeric value for t. Clearly explain what this number represents rel- ative to Marcus Freeman and his collection of songs (rather than a mathematical explanation). Note: you do NOT need to actually solve any equations for this part. ( 3x + 1, if 0 ≤ x < 1 (2) Consider the piecewise function P (x) =. −2, if x > 1 (a) Find 3P (2 + P (0)). (b) Find the domain of P (x), writing your answer S in interval notation. If the domain involves multiple intervals, use the union symbol. (3) Consider the two points P = (3, 1) and Q = (0, −2). (a) Find an equation of the horizontal line through P. (b) There is a single line through the point (−7, 4) that is parallel to the line through P and Q (that is, parallel to the line segment connecting P and Q). Find an equation of it, writing your answer in the form y = mx + b.