Math 1 Moodle Quiz Solutions There is a one question Moodle quiz associated with most lectures. A quiz will open the day of the lecture and close at midnight on the day before the net lecture (e.g., a quiz will open on Monday and close on Tuesday at 11:9 pm). You will earn points for trying a quiz and points if you get the correct answer. To access a quiz, go to http://www.moodle.umn.edu and select Math 1. When you open a quiz, read it and write your solution on paper. Be careful when you enter your answer since Moodle is not very smart and will simply match your response to the eact characters I have entered in the answer section. Some questions are multiple choice so all you have to do is enter a or b or c or d or e (with no periods or spaces or anything else). Other questions will require you to do something to your answer and then enter a number. For eample, if the question asks you to find the center of a circle the answer might be (, -3). The question might then ask you to add the - and y-coordinates to get a single number, + -3 = -1, so you would enter -1. This makes things a bit more confusing for you but easier for Moodle to interpret. Never include units or a period (ecept for a decimal point) or spaces or your answer will be marked as incorrect. Solutions will be posted on my web site after each quiz closes. 1 Wed 7 Sep Thu 8 Sep Sec A. Geometry Answer: c How fast is the surface of the earth traveling West to East at Minneapolis? Minneapolis is eactly midway between the equator and the North Pole. Round your answer to the nearest hundred miles per hour. Hint: At the equator the earth is 4,000 miles in circumference and it takes 4 hours to make one revolution so the surface is traveling at 1,000 miles per hour. Use Pythagoras to find the circumference at Minneapolis. a. 00 b. 900 c. 700 d. 00 e. 0 Circumference is c r r r 3,90 r 1,60,00 r 7,801, 0 r 79, 3 c 3.14,793 c 17,4 0 miles
Math 1 Moodle Quiz Solutions, page Distance 17,40 miles v 731mph Time 4 hours Rounded to nearest 0 mph we have 700, whichischoi ce c. Fri 9 Sep Sun 11 Sep Sec A.3 Polynomials-Start Answer: 1 4 What is the remainder when you divide 3 by 1? 3 3 3 3 4 3 1 3 0 3 3 4 3 3 3 3 3 3 3 3 3 1 Remainder is 1. - - - -
Math 1 Moodle Quiz Solutions, page 3 3 Mon 1 Sep Tue 13 Sep Sec A.3 Factoring-Finish Answer: c Which of the following is a factor of 3 0 18 18 Your answer will be one of the following soenteraorborcordore(donot type a period after the letter). a. 9 b. 3 7 c. 3 d. 9 e. 9 Factor out GCF first: 3 0 18 18 9 9 Now, factor trinomial: a, b 9, c 9 so ac 9 90 Possible whole number pairs whose product is 90 are 190, 4, 3 30, 4 na, 18, 6 1, 7 na, 8 na, 9 6 and 1 add to give 9 so replace 9 with 6 1 9 9 6 1 9 3 3 3 3 3
Math 1 Moodle Quiz Solutions, page 4 4 Wed 14 Sep Thu 1 Sep Sec A. Rational Epressions Answer: e What is the numerator of the fraction you get when you simplify 3 6 9 Your answer will be one of the following soenteraorborcordore(donot type a period aftertheletter). a. 9 b. 3 1 c. 1 d. 4 3 9 e. 11 6 3 9 3 3 So LCD 3 3 3 3 3 6 9 3 3 3 3 3 9 33 33 11 So, answer is e
Math 1 Moodle Quiz Solutions, page Fri 16 Sep Sun 18 Sep Sec A.6 Equations Answer: -1 30 Solve 1 4 4 Add your two values for and write the sum. 1 4 4 0 4 41 0 3 0 or 30 3 or Add solutions to get 1 6 Mon 19 Sep Done in class Sec A. to A.6 3 1. Factor 1 0 Answer: 3 3 1 0 6 11 a 6 b 11 c ac 6 60 3 3 3 60 160 30 3 0 4 1 1 6 7 na 8 na 9 na Replace 11 with 4 1 6 4 1 Factor by grouping 3. Simplify Answer: 1 1 3 3 1 1 1 1 1 3 11 11 1 11 1 3 1 1 1 1 0 1 - - 1 1 1
Math 1 Moodle Quiz Solutions, page 6 7 Wed 1 Sep Thu Sep Sec A.8 Word Probs Finish Answer:. Almonds cost $ per pound and cashews cost $9 per pound. How many pounds of almonds should be mied with the cashews to make pounds of a mi that sells for $8 per pound? Enter a number only (NO units). Let a pounds of almonds Then a pounds of cashews Value of almonds Value of cashews Value of mi a a 9 8 4a a. 8 Fri 3 Sep Sun Sep Sec A.9 Inequalities Answer: d Solve 40 8 4 1 Your answer will be one of the following so enter a or b or c or d or e (do NOT type a period after the letter). a. 6,8 b. 4, c.,0 4, d., 11 13, e., 4, 40 8 4 1 48 4 1 1 1 1 1 11 or 1 1 13 or 11 So d is correct -1 - - 1 - - -1-0 - -30-3 -40-4 -0
Math 1 Moodle Quiz Solutions, page 7 9 Mon 6 Sep Tue 7 Sep Sec A.7 Comple Num HW08 & Answer: -4 6 8 Write in abi form. 9 i 1 What is the real part (the a in a bi)? 6 8 6 8 6 i 8 i 1 6i 8i 8 9 i 1 3i i 1 3i i i 1 i 1 3i i i i 1 8i 8 8 i 1 i i i 4i 1 i 4i 4 4i The real part is 4 :(and the imaginary part is ) Wed 8 Sep Thu 9 Sep Review Apendi for Eam 1 Answer: - Solve 3 1 4 1 0 3 To remove the fractions, multiply each term by the LCD, which is 6 1 6 63164 6 0 3 318 1 4 0 318184 40 16 40 17 34
Math 1 Moodle Quiz Solutions, page 8 11 Mon 3 Oct Tue 4 Oct Sec 1.1 Dist & Midpt HW11 & Answer: 7 Find the center of the circle that has a diameter whose end points are,6 and 4,. What number do you get when you add the - and y-coordinates? The center is the midpoint of the diameter: 1 4 y1 y 6 midpoint 3 y midpoint 4 Adding these gives 3 4 7 1 Wed Oct Thu 6 Oct Sec 1.3 Lines Answer: -4 Find the y-intercept of the line that passes through 4,6 and which is perpendicular to the line y. Write your answer as a single number and NOT as an ordered pair. First, find the slope of the: given line: y y y The slope is so the slope: of the perpendicular line is. Thelinewewantis y b. Use the given: point to find b : 6 4b b 4 So, the y-intercept is (0, 4) : andtheansweris4
Math 1 Moodle Quiz Solutions, page 9 13 Fri 7 Oct Sun 9 Oct Sec 1.4 Circles Answer: 3 Find the radius of this circle: y 4 16y 16 0 Before completing the squares we must divide by to make the coefficients of the squared terms 1. 4 16 16 0 8 8 0 y y y y 1 To complete square for add and subtract 1 1 To complete square for y add and subtract 8 16 y y 1 1 8 16 16 8 0 y 1 1 4 16 8 0 y 1 4 9 So r 3 - - - 14 Mon Oct Tue 11 Oct Sec.1 Functions HW1 & Answer: 1 Find the difference quotient of f 3. Simplify the epression you get. Then, put in -1for and 0 for h. When you simplify, what number do you get? f h f h 3 h 3 h h hh 33h 3 h h h 3h hh3 h3 h h For 1 and h 0 we have 1 0 3 1 1 Wed 1 Oct Thu 13 Oct Sec.3 Prop of Functions Answer: 3 3 Find the Average Rate of Change of f 1 from 0 t o. ARC is the slope of the line that connects two points on the curve. b a b Rise f f f a f ARC Run b a a b 1 1 f ARC 3 0 3 f 0 0 3 0
Math 1 Moodle Quiz Solutions, page 16 Fri 14 Oct Sun 16 Oct Sec.4 Function Library Answer: 4, 4 3,6 What is the range of f 3 3 1 3 4 6 6 Write your answer without spaces and with the proper use of ( ) [ and ]. Use uppercase U for the union symbol. Plot points within eachinterval for each part: y The single point 6, 4 has a -value of 4. We write this in interval notation as 4, 4. The y-values for the parabola go from 3 up to 6. The 3 is included and the 6 is not so the interval is 3,6. The y-values for the line go from 3 to. This interval is taken care of by the parabola. Putting these together we have the range 4, 4 3,6.
Math 1 Moodle Quiz Solutions, page 11 17 Mon 17 Oct Tue 18 Oct Sec. Transformations Answer: e Starting with the graph of f which of the following would be the function that is reflected about the -ais, shifted 3 units left, andshifted 4 units up? Your answer will be one of the following so enter aorborcordore(do NOT type a period after the letter). a. g 3 4 b. g 3 3 c. g 4 3 d. g 4 3 e. g 4 3 - - - f g reflects about -ais h j 3 shifts 3 units left (left because the signs of and 3 are the same) 3 4 shifts 4 units up So the answer is e. - 18 Mon 4 Oct Tue Oct Sec.6 Math Models Answer: e A rectangle has a length that ismorethan 3 times the width. Epress the area as a function of the width only. Your answer will be one of the following so enter a or b or c ordore(donottype a period after the letter). a. Aw w b. 3 Aw w c. Aw w d. Aw 6w 3 e. 3 Aw w w, lw 3w 3 A l w l w A w l w w A w w w 3 w w So the answer is e. width w length 3w length 3w width w
Math 1 Moodle Quiz Solutions, page 1 19 Wed 6 Oct Thu 7 Oct Sec 3.1 Linear Funct HW3 & Answer: 0 Find the verte of f 8 Then, add the - and y - coordinates to get a single number. What is that number? verte 8 b a y f f 8 18 verte verte 180 0 Fri 8 Oct Sun 30 Oct Sec 3.4 Quadratic Models Answer: 0 The price, p, of a product is related to the quantity demanded, Q, by p 0 Q. What price, p, will maimize revenue, R? Revenue Price Quantity Since p0 Q, Q0 p 0 R p p p p 0p This is a downward opening parabola. The p-component of the verte is p verte b 0 0 a 1 1-3000 00 000 0 00 00-0 0 40 60 80 0
Math 1 Moodle Quiz Solutions, page 13 1 Mon 31 Oct Tue 1 Nov Sec 4.1 Polynomial Functions Answer: 18 3 Given f 1 3 Find the behavior of this function near where its graph touches the -ais. That is, what function does f look like when its graph touches the -ais? When you get your function enter the coefficient of its dominant term (the term with the highest eponent of ). This is when 1. So, replace with 1in the 3 factor. Graph touches -ais at zeros with even multiplicity like f. 1 3 3 1 1 11 3 3 1 13 18 1 f f g 3 0 18 618 This is an upward opening parabolawithverte 1,0 Coefficient of dominant term is 18. - 0 0
Math 1 Moodle Quiz Solutions, page 14 Wed Nov Thu 3 Nov Sec 4. Rational Functions Answer: 9 8 Given f 1 Find the equation of its oblique asymptote (OA). Your equation will be in the form y mb. To answer this question, enter the value of b, the y-intercept of the OA. Divide to find the oblique asymptote. 9 1 8 9 9 9 11 8 11 So, we can write f 9-30 1 1 As, the last term goes to 0 and f looks like y 9. The y-intercept of this is 9. 40 3 30 0 1-0 -1 - - - 1 0 - -1-0 -
Math 1 Moodle Quiz Solutions, page 1 3 Fri 4 Nov Sun 6 Nov Sec 4.3 Rational Graphs-Start Answer: 3 3 7 0 Given f 6 What is the value of the y-intercept of its asymptote? Enter your answer as a single number (not an ordered pair). 3 y 3 f 3 3 7 0 3 4 6 The vertical asymptotes are and 3. Since these are vertical lines, they have no y-intercepts. The degree of the numerator is and the degree of the denominator is also. Since the degrees are the same, there is a horizontal asymptote whose y-intercept is the ratio of the coefficients of the 3 dominant terms. That is y 3. The HA is the horizontal line y 3, which has 3 as its y-intercept.
Math 1 Moodle Quiz Solutions, page 16 4 Mon 7 Nov Tue 8 Nov Sec 4.3 Rational Graphs-Finish Answer: -1 3 1 16 Given f What is the value of where the graph of f crosses its oblique asumptote? First, find the oblique asymptote: 1 0 1 16 3 3 3 3 3 0 16 1 1 So, oblique asymptote is y 1. Function crosses OA when f y 3 1 16 1 1 16 1 1 16 6 1 1 1 0 1-0 -1 - - 1 0 - - -1-0 -
Math 1 Moodle Quiz Solutions, page 17 Wed 9 Nov Thu Nov Sec 4.4 Rational Inequalities Answer: a 1 Solve Your answer will be one of the following so enter a or b or c or d or e (do NOT enter aperiodafter the letter). 0 1,1 a.,0 1,1 b., c.,0 1,1 d.,0 1,1 e.,0 1,1 - - - 1 1. Write inequality with 0 on one side. 0. Combine terms and find the real zeros of the numerator and denominator. - 1 0 1 0 1 0 11 0 Real zeros are 0 and 1. 3. Use the real zeros to break up the number line into intervals. Interval: - 0 1 4. Use a test point in each interval to see if the function is positive or negative. Interval: - 0 1 Try -1 1/ Signs of 1 1 NN N Sign of f N P P f 0? yes no no NN P Since we want f 0, the solution is,0 1,1. Note that = 0 is not in the solution since = 0 is not in the domain of the original function since it causes division by 0. Also note that the interval 1,1 is a single point and is part of the solution since the inequality is not strict (that is f 0 says f can be 0). PP P
Math 1 Moodle Quiz Solutions, page 18 6 Wed 16 Nov Thu 17 Nov Sec.1 Composites HW3 & Answer: b 1 1 Given f 1 and g find g f and its domain. Which of the following is NOT in the domain of g f? Your answer will be one ofthefollowing so enter a or b or c or d or e (do NOT - - enter a period after the letter). a. b. 3 - c. 0 d. e. 1 1 1 1 g fgf g 1 1 1 1 1 1 3 Since the denominator cannot be 0, 3. So, the answer is b 7 Fri 18 Nov Sun 0 Nov Sec.3 Eponential Funct Answer: 1 3 e Solve e 1 e 3 e ee 1 3 1 e ee 3 1 1 e e e e 3 e e 3 3 3 1
Math 1 Moodle Quiz Solutions, page 19 8 Mon 1 Nov Tue Nov Sec.4 Log Functions Answer: 3 Solve 3 log 4 log 0 3log 4 log 3log 4 log 4 1 log 4 1 1 4 3 9 Wed 3 Nov Thu 4 Nov Sec. Properties of Logs Answer: 4 Find the value of log 3 90 Round your answer to the nearest whole number. Use the change of base formula and your calculator: ln 90 4.49980967 Using natural logs we have: log3 90 4.0990374 4 ln 3 1.0986189 log 90 1.94409 Using common logs we have: log3 90 4.099038 4 log 3 0.477114 30 Mon 8 Nov Tue 9 Nov Sec.6 Log and Ep Equ Answer: 3 1 Solve: log 1 log3 9 log log 1 1 log3 log 1 3 log1 log log11 log log1 1 1 1 log 1 log 1 1 0 4 3 0 4or 3 - - The -4 is not in the domain of the equation because it would cause us to take the log of a negative number, which is not possible. So, 3 is the only answer. - -
Math 1 Moodle Quiz Solutions, page 0 31 Mon Dec Tue 6 Dec Sec.7 Models Answer: 6 If I and I denote the intensity of light 0 before and after going through a material and is the distance (in feet) the light travels in the material, then according to the Beer-Lambert Law 1 I ln k I0 Solve this equation for I. Acertainlake has a value of k 0.04 and the light intenstiy at the top of the lake is 14 lumens. Find the light intensity in the lake at a depth of 1 feet. Round your answer to the nearest whole lumen (do NOT include the units). 1 I ln k I0 I k ln I0 k I e I Ie 0 k I 0 The given values are k 0.04, I 14, and 1. So, the light intensity at a depth of 1feet is I 14e 6.04 6 0.041 0 1-1 0 30