midterm_1_10C_solutions

# midterm_1_10C_solutions - Name Student ID TA/Section(circle...

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Unformatted text preview: Name Student ID TA/Section (circle): Craig Johanna Patrick C01-3pm C02-4pm C03-5pm C04-6pm C05-7pm C06-8pm Math 10C (Section C), Fall 2009, Midterm Exam 1 Solutions • Show all of your work to receive full credit. • Read each question carefully. • Answer each question completely. • Write your answers and work clearly and legibly; no credit will be given for illegible solutions. • You are allowed one notebook-sized sheet of handwritten notes (written on one side). • You are allowed to use a calculator. • 50 minutes. • Go back and check your answers if you finish early. # Points Score 1 4 2 5 3 3 4 4 5 6 6 4 7 4 Σ 30 1. (4 points) The table below contains some values of a linear function f ( x, y ). Fill in the six missing values. y 10 20 1 5 15 x 3 5 3 y 5 10 1 7 17 x 3 5 5 y 4 8 1 5 3 x 3 5 15 Solution: Since it is a linear function, the numbers going across a row should increase/decrease uniformly. For example, in the first table, the first row is 5, , 15; so the blank has to be 10. Likewise, down the first column we have 5, , 3; so the blank has to be 4. From this we know that going across each row the numbers must increase by 5, and going down each column the numbers must decrease by 1. (Similar for the other tables.) y 10 20 1 5 10 15 x 3 4 9 14 5 3 8 13 y 5 10 1 7 12 17 x 3 5 10 15 5 3 8 13 y 4 8 1 5 4 3 x 3 10 9 8 5 15 14 13 2. Let vectora = vector i − vector j + 4 vector k and vector b = − 2 vector i + vector k. (a) (3 points) Find 2 vectora + 3 vector b . (b) (2 points) Find bardbl vectora bardbl . Solution: 2 vectora + 3 vector b = 2( vector i − vector j + 4 vector k ) + 3( − 2 vector i + vector k ) = (2 vector i − 2 vector j + 8 vector k ) + ( − 6 vector i + 3 vector k ) = − 4 vector i − 2 vector j + 11 vector k and bardbl vectora bardbl = radicalbig (1) 2 + ( − 1) 2 + (4) 2 = √ 1 + 1 + 16 = √ 18...
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midterm_1_10C_solutions - Name Student ID TA/Section(circle...

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