UIL Calculator Contest Solutions. Andy Zapata AMT Test Writing

Transcription

1 UIL Calculator Contest Solutions Andy Zapata AMT Test Writing

2 Azle ISD 1974 to 017 Andy Zapata 7 th grade math, high school math & Physics teacher ETS Physics reader 10 years Married 4 children & 3 grandchildren Co-founded Texas Math and Science Coaches Association (TMSCA) Coached all 4 UIL math & science events + slide rule Current UIL Elem/JH number sense, mathematics and calculator consultant adzapata74@gmail.com

3 Each year Dr. David Bourell writes at least nine UIL high school Calculator Application contests for competition. There are 1 stated problems and 14 geometry drawings. The stated and geometry problems range in difficulty from basic arithmetic to differential and integral calculus: from simple plane and 3D-geometry to fairly complex multi-step problems. I ve selected some of the problems that have appeared from the past year s competition to show how they are worked. My solutions might not be unique, and in fact they are the work of other coaches, but they are accurate solutions in that they yield answers that agree with the answers that Dr. Bourell gave. I will confess that my knowledge of the math topic, calculus, is rudimentary; and I will also admit that when I saw some of the solutions that eluded me, I had several aha moments. If you have not purchased a copy of the UIL Calculator Applications Contest Manual by Dr. Bourell; you need to do so. In any case, I hope these particular solutions will be of help to you so that you can pass them on to the students you coach since there really is no sense in keeping this information to yourself. z.

4 17A-7. What is the square of the average of 45, 8 and 39? = A-8. Solve for x if 6x equals 37/x = 37 6x x x x x x x 3 = 37 x 3 =

5 17B-8. Solve for x if y = 6x+5 and 14x = 9y = Substitution 14x = 9(6x + 5) x = 54x A-9 CIRCLE A = r R=? r Area = A-9 =

6 A b b 1 h A B-17. If a person travels Around the World in 80 Days, what is the average velocity, assuming traveling for 11 hr daily? = mph distance v distance = circumference = r earth radius = 3960 miles time h/ dy80 dys v 8.3

7 cos adjacent hypotenuse cos36.9? B-6. What is the percent error in assuming that 5/8 mi equals 1 km? = % 5 mi 8 (580 ft/mi)(1 in/ft)(.54 cm/in) (100,000 cm/km) = km A E % error 100% E %

8 17C-18. Ken buys himself and Katie a hamburger, but Ken added cheese to his. The total cost, including 8.5% tax was $6.80. If cheese cost is 10% of the hamburger cost, what is the menu price for a hamburger? =$ Let x = cost of a hamburger. (x +.1x)(1.085) = V h R R RR V

9 17C-36. A Makerbot 3D printer lays a 0.01 in diameter bead with a nozzle speed of 0 in/s. If parts have 0% porosity, how long does it take to build a part of volume 4.5 in 3? = min A 0% porosity means only 80% of the total volume is built. The part is not 100% solid material in 0.005in 1 sec 1 min in 60 sec 17E-37. A teenager eats 1380g of food daily. Over a -year period, their weight increases by 3.5 lb. What is the ratio of weight gain to food consumed? = %(SD) 3.5Lbs grams 1Lb = 10, g (3 SD) {3 SD} 100% 1380 {4 SD} (3SD)

10 TSA = ()(R ) + R(?) 963 = ()((9.4/) ) + (9.4)(?) = = 38.3/ = = 4 = = = 360 ()(141.7) = 76.6 R R = 76.6/ = Radius R = hypotenuse sin R

11 17E-46. A Chihuahua dog is 7 in tall and weighs.5 lbs. What does a 5 in tall Great Dane dog weigh? = lbs 7in 5in.5Lb x Lb 17E-47. A metal casting is smaller than the mold dimensions due to shrinkage on cooling. Part (x) and mold (y) dimensions measured on a part, in inches, are (0.97, 1), (1.4, 1.5), (1.85, 1.87), (1.91, ), (.6,.3). If the dimension of a part should be 5 in, what should the mold dimension be? = in List List Linear Regression y 1 y 1 (5) = 5.05

12 73 C 139 A x 73 = (139)(30)cosθ = x cos x = ( ) 183

13 A T h 3 A C = r h h 3 34 h = h + 34 = E-6. There are 56 professional football games in a season. What is the probability of correctly wild guessing the winner of every game for 10 seasons? = Probability (.5) 560 = 0, (On HP calculator) 560(Log 0.5) = = x

14 x = 1.05 x = x =? 0.55 x F-8. Worldwide, there are 1.06 males for every female. If in 016 there were 7.4 billion people, how many more males were there than females? = = ( )(0.06).16 x 10 9

15 17F-46. A company s brand of kitchen pans all have constant thickness. If a -qt capacity pan weighs 3.75 lbs. what is the weight of a gallon capacity pan? = lbs 0.5 gal 1gal 3.75 Lbs /3 / x 17F-36. Sam runs 3 mi in 4 min and walks 3 mi in an hour. What fraction of the time was spent running if he covered the 3 mi in 4 min? = % Let t be the time spent running the 3 miles. 3mi 4 min t 3mi 4 t 3mi 60 min t = 1 min 1 min 4 min 100% 8.6

16 17F-63. A trampoline specialist bounces off a trampoline and lights onto a platform 10 ft above the trampoline. Her angle leaving the trampoline is 75 relative to horizontal. What must her minimum initial velocity be = ft/s d vmax v sin g Where v is the initial speed; is the angle relative to the horizontal; g is the acceleration due to gravity, ft/s and d v(max) is the maximum vertical distance. 10ft v sin ft / sec 6.3

17 17G-7. A shot put competition involves throwing a ~ 16 lb ball as far as possible. Randy threw the ball 50 ft 6.8 in, and Ron tossed it 48 ft 11.3 in. What was the percent difference in their tosses? = %(SD) When working with inexact measurements with differing units of measurements, convert the measurements to the smallest units given. 50 ft 6.8 in = in {4 SD}; 48 ft 11.3 in = in {4 SD} nd Value Mentioned %difference 1 st 100% 1 Value Mentioned 587.3{4SD} %difference 1 100% 606.8{4SD} [ {4SD} 1] (100%) [= {3SD}] (100%) -3.1 {3 SD}

18 Since the two scalene triangles have a common side: Use the Law of Cosines and set each equation equal to each other ()(19.0)(33.7)cos118.3 =.3 +? ()(.3)(?)cos SA SPHERE = 4R

19 17H-8. Stones 8 in in diameter are ground down to particulate that is 0.1-in in diameter. What is the percent increase in total surface area on a unit mass basis? = % V Sphere = (4/3)R 3 ; SA Sphere = 4R (4/3)(4) 3 = {store in A}; (4/3)(0.05) 3 = {store in B} Ratio of volumes, (A/B), yields = 51,000 (bigger stone is larger than small stone) (4)(4) = {store in C}; (4)(0.05) (51000) = {store in D} Larger Value % increase 1 100% Smaller Value % increase 1 100%

20 x 1 x 9.8 w = w m = x 1 w cos30 = x = 9.8cos30 = Inscribed radius Leg1Leg hypotenuse radius 3.86

21 17I-61. Josh rides an elevator up 5 stories. A story is 13 ft. The elevator accelerates at 1g to 0 mph and decelerates at the same rate as it approaches the final floor. How long was the elevator ride? = s (0 mph)(/15) = ft/sec { Store in A} v v ay = 0 (-3.174)(y) y = ft {Store B} f i 5(13) y = ft {Store C} distance traveled at constant speed t 1 = [(v f 0)/g] = [ ]/3.174 t 1 = sec {Store D} time during acceleration t = d/v f = 98.56/9.333 = sec time during constant speed t Total = t 1 + t 1.0

22 R r R r? sin? R = r (? sin?) sin R r R = rsin (rsin) = r (? sin?)? = r sin = r ( sin) sin = ( sin) Solver = ? =.03

23 17I-57. A water tank is a cylinder on end with D = ft and h = 8 ft. It is filled and then drained from the bottom using a tap. The volume release rate is proportional to the height (or head ) of water. If the tank drains 0% in 30 min, how much more time is needed to drain it by 90%? = hr h(t) = 8e kt h = height of cylinder; t = time (hours); k = constant 30 minutes = 0.5 hours; 80% of 8 feet = 6.4 feet h(0.5) = 6.4 ft ln ft = 8e k(0.5) 8 k k = % of 8 feet = 7. feet; difference = 7. ft 6.4 ft = 0.8 ft h(t) = 8e kt ln ft = 8e ( )(t) t 8 t = time difference =

24 I-58. What is K 1 if K is the product of and? 58= Integer Using a calculator: = Using your math knowledge: (4)(13) + (7)(-1) = -95

25 From Page 65 of UIL Calculator Applications Contest Manual: Rotating Parallel to the x-axis (y = b, Disc Method) x 1 x 0 V f x b g x b dx V x 4 1 x 1 dx

26 r r Letting? = (r /)(θ sinθ)(3.5) = (r /)[(π θ) (sin(π θ))] (θ sinθ)(3.5) = [(π θ) (sin(π θ))] Since: sin(π θ) = sin (θ sinθ)(3.5) = π θ + sin θ Using Solver, with > 0:.0

27 Many Thanks to: Cliff McCurdy Shayna Reasoner Genny Zapata Without the efforts of these people, much of the work presented today would not have been possible. z.