UC MATH 1A - Sample Section 1: Answers and Explanations

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Sample Section 1 Answers and Explanations 1 A 2 C 3 D 4 5 6 7 8 C C A B B 9 D Use the Bowtie to find the value of each quantity Quantity A Quantity B Quantity A is greater than Quantity B When two lines intersect the big angles and the small angles are equal so s v r u and t w Therefore the quantities are equal To prove it Plug In Let u 50 v 100 and w 30 Because the angles are all small angles r 100 s 50 and t 30 So both r t v and s u w total 180 First find the value of x Multiply both sides by 3 to get 2x 21 Divide both sides by 2 to find that x 10 5 as well as being greater than 0 If x 2 then Quantity B is greater because 22 4 Eliminate A and C If x 10 then the two quantities are equal Eliminate B and select D because different numbers have given different answers Solve for k 9 3 3 4 9 27 4 243 4 247 So k 247 Use trial and error to find the prime factors of 247 They are 13 and 19 The average of 13 and 19 is 16 so the quantities are equal First divide 90 by 50 to find the bulk rate for a single pound of flour The amount saved per pound is 09 The quantities are equal Remember PEMDAS x 4 2 5 6 5 30 y 24 8 5 3 5 15 Quantity A 15 and Quantity B 15 The solutions to the equation 32 k are 32 and 32 Of those only 32 works in the equation 31 k 1 Quantity A has the value of 32 so Quantity B is greater Plug In First try a 100 and b 2 Alice weighs 100 kilograms Bob weighs 98 kilograms and the sum of their weights is 198 kilograms Quantity B is 2 100 or 200 Quantity B is greater so eliminate A and C Now try a second set of numbers If a 50 and b 10 then Quantity A is 90 and Quantity B is 100 Quantity B is again greater as it will be with any set of numbers that meets the restriction ab 0 Plug In for x and y Since xy must be positive either both variables are positive or both are negative First let x 5 and y 6 Quantity A is and Quantity B is 10 Quantity A is greater so eliminate B and C Now let x and y Quantity A is 23 and Quantity B is Quantity B is now greater so eliminate A and you re left with D because different numbers gave different answers The weird little symbol gives you a set of directions 2 2 2 4 4 4 8 Find the answer that also equals 8 2 2 2 4 4 4 8 10 A 11 B C and D Finding common denominators allows you to compare the values of fractions easily Because two answer choices are expressed in eighteenths and two in easily convertible ninths start there and Eliminate A and select B Choice D converts to so it s correct E though converts to and can be eliminated The answers are listed in ascending order and so C falling between correct answers B and D must be correct as well 12 C 13 C 14 24 15 D 16 A Plug In If the width of the smaller board is 3 then the width of the larger board must be 6 If the length of the smaller board is 2 then the length of the larger board must be 12 The area of the smaller board is 3 2 6 Therefore N 6 The area of the larger board is 12 6 72 The question asks for the difference between the areas 72 6 66 The last step is to check which answer choice equals 66 when N 6 Only C works Since the answer choices are far apart you can estimate If one manual weighs 400 grams then 48 manuals weigh 48 400 or about 20 000 grams To convert grams to kilograms divide by 1 000 20 000 1 000 20 Look for an answer a little less than 20 Only C is close Start by listing the factors of 12 in pairs 1 and 12 2 and 6 and 3 and 4 Because the question asks for the sum of the distinct positive even factors cross off 1 and 3 Now add up what s left 2 4 6 12 24 The store makes a profit of 300 for each computer sold Plug In the Answers starting with C 16 computers multiplied by 300 yields a profit of 4 800 not enough to cover costs You need to sell more computers so eliminate A B and C Try D 17 computers multiplied by 300 yields a profit of 5 100 just enough to cover costs Estimate If x is less than 50 of a fraction that is less than of a number that is less than 1 then x must be less than 1 Therefore A is correct 17 D 18 B 19 A 20 D 21 A 22 A 23 B Each number in the set occurs only once and the mode is the most frequently occurring number To create a mode x must be the same as one of the other numbers in the set Eliminate C and E Plug In the Answers For B the mode is 5 The median of 1 3 5 5 7 11 is 5 The median is equal to the mode You need a larger number for x For D the mode is 7 and the median of 1 3 5 7 7 11 is 6 The mode is now one less than the median Note that C is equal to the median and would be a trap answer if you didn t read the question carefully enough Redraw this figure by adding two descending lines from the upper corners of the figure perpendicular to the base below so that you have a rectangle and two right triangles Each triangle has a base of 1 and a hypotenuse of 2 Use the Pythagorean Theorem or the ratio for 30 60 90 triangles x x 2x to find the height is The area of each triangle is 1 The area of the rectangle is 2 The sum of the rectangle and two triangles is 2 2 2 3 If Mary s wage is 2 more than Mark s and Andy s wage is 6 more than Mark s then Andy s wage is 4 more than Mary s Anne s wage is 10 more than Mary s so Anne s wage is 6 more than Andy s Quantity A is greater than Quantity B Plug In and let t 5 M 5 7 9 21 the sum of the three consecutive odd integers of which t is the smallest For the second part of the problem t is the greatest integer …


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