Math & Nature  Fish feeding mechanisms ◦ Suction feeding  Goliath grouper Epinephelus itajara  Questions  What fluid velocity can the goliath grouper generate during suction feeding?  How does suction feeding by the goliath grouper compare to other fish?
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Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9  N/A b  153.6 Cone B Length (mm) Area (mm2) a  34.9 Time 0 c  54.3 N/A d  6.4 e   Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a   N/A b   Cone B Length (mm) Area (mm2) a   Time 1 c     d   e   Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3)   Volume (mm3)     Volume (mm3)   Volume (mm3)       0.132     
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Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9  N/A b  153.6 Cone B Length (mm) Area (mm2) a  34.9 Time 0 c  54.3 N/A d  6.4 e  12.2 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a   N/A b   Cone B Length (mm) Area (mm2) a   Time 1 c     d   e   Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3)  195916.8 Volume (mm3)  84289.7  180206.5 Volume (mm3)   Volume (mm3)       0.132     
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Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9  N/A b  153.6 Cone B Length (mm) Area (mm2) a  34.9 Time 0 c  54.3 N/A d  6.4 e 12.2 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a  39.5 N/A b  161.3 Cone B Length (mm) Area (mm2) a  39.5 Time 1 c  56.4   d  32.6 e   Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 195916.8  Volume (mm3) 84289.7   280206.5 Volume (mm3)   Volume (mm3)        0.132    
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Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9  N/A b  153.6 Cone B Length (mm) Area (mm2) a  34.9 Time 0 c  54.3 N/A d  6.4 e 12.2 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a  39.5 N/A b  161.3 Cone B Length (mm) Area (mm2) a  39.5 Time 1 c  56.4   d  32.6 e  266.5 Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 195916.8  Volume (mm3) 84289.7   280206.5 Volume (mm3)  263547.1 Volume (mm3)  230974.7  494521.7  214315.3  0.132    
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Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9  N/A b  153.6 Cone B Length (mm) Area (mm2) a  34.9 Time 0 c  54.3 N/A d  6.4 e 12.2 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a  39.5 N/A b  161.3 Cone B Length (mm) Area (mm2) a  39.5 Time 1 c  56.4  3338.8 d  32.6 e  266.5 Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 195916.8  Volume (mm3) 84289.7   280206.5 Volume (mm3)  263547.1 Volume (mm3)  230974.7  494521.7  214315.3  0.132 3338.8   
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Goliath Grouper Suction Feeding Cone A Length (mm) Area (mm2) a 34.9  N/A b  153.6 Cone B Length (mm) Area (mm2) a  34.9 Time 0 c  54.3 N/A d  6.4 e 12.2 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a  39.5 N/A b  161.3 Cone B Length (mm) Area (mm2) a  39.5 Time 1 c  56.4  3338.8 d  32.6 e  266.5 Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 195916.8  Volume (mm3) 84289.7   280206.5 Volume (mm3)  263547.1 Volume (mm3)  230974.7  494521.7  214315.3  0.132 3338.8   486
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Math & Nature  Suction feeding in the goliath grouper ◦ Given  Dimensions of cone B at maximum expansion (t1) 3) Find the area of the goliath grouper mouth at maximum expansion (t1).  A. Collins mouth
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Math & Nature   Suction feeding in the goliath grouper ◦ Given  Volume of the goliath grouper feeding mechanism at rest (t0) and at maximum expansion (t1)  Duration of the feeding event (t1 - t0)  Area of the mouth opening at maximum expansion (t1) 4) Find the velocity of water flow into the mouth of
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Snook Suction Feeding Cone A Length (mm) Area (mm2) a 2.1  N/A b  27.6 Cone B Length (mm) Area (mm2) a  2.1 Time 0 c  12.3 N/A d  1.8 e   Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a  7.0 N/A b  28.9 Cone B Length (mm) Area (mm2) a  7.0 Time 1 c  12.3   d  5.9 e   Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3)   Volume (mm3)     Volume (mm3)   Volume (mm3)        0.036    
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Snook Suction Feeding Cone A Length (mm) Area (mm2) a 2.1  N/A b  27.6 Cone B Length (mm) Area (mm2) a  2.1 Time 0 c  12.3 N/A d  1.8 e 73.8  Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a  7.0 N/A b  28.9 Cone B Length (mm) Area (mm2) a  7.0 Time 1 c  12.3  109.4 d  5.9 e  66.0 Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 127.5  Volume (mm3)  147.2  274.7 Volume (mm3) 1482.9  Volume (mm3)  1611.5 3094.4   2819.7  0.036  109.4  716
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Longjaw Butterfly Fish Suction Feeding Cone A Length (mm) Area (mm2) a 5.0 N/A b 14.9 Cone B Length (mm) Area (mm2) a 5.0 Time 0 c 31.2 N/A d 1.1 e   Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a 5.0 N/A b 14.9 Cone B Length (mm) Area (mm2) a 5.0 Time 1 c 31.6   d 1.1 e   Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3)   Volume (mm3)     Volume (mm3)   Volume (mm3)        0.022    
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Longjaw Butterfly Fish Suction Feeding Cone A Length (mm) Area (mm2) a 5.0 N/A b 14.9 Cone B Length (mm) Area (mm2) a 5.0 Time 0 c 31.2 N/A d 1.1 e  8.8 Volume of feeding mechanism before expansion (t0) Cone A Length (mm) Area (mm2) a 5.0 N/A b 14.9 Cone B Length (mm) Area (mm2) a 5.0 Time 1 c 31.6  3.8 d 1.1 e  8.9 Volume of feeding mechanism at maximum expansion (t1) Volume change during feeding event (mm3) Duration of feeding event (sec) Area of mouth at maximum expansion (t1) (mm2) Velocity of water flow into mouth (mm/sec) Volume (mm3) 390.1  Volume (mm3)  1036.0  1426.1 Volume (mm3)  390.1 Volume (mm3)  1049.3  1439.4  13.3  0.022  3.8  159
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Math & Nature  References ◦ Bishop, K.L., Wainwright, P.C., and Holzman, R. (2008). Anterior to posterior wave of buccal expansion in suction feeding fish is critical for optimizing fluid flow velocity profile. Journal of the Royal Society, Interface. 5:1309-1316. ◦ Ferry-Graham, L.A., Wainwright, P.C., and Bellwood, D.R. (2001).  Prey capture in long-jawed butterflyfishes (Chaetodontidae): the functional basis of novel feeding habits. Journal of Experimental Marine Biology and Ecology. 256:167-184. ◦ Galileo Galilei, The Assayer, as translated by Stillman Drake (1957), Discoveries and Opinions of Galileo pp. 237 - 238. New York: Doubleday & Company. ◦ Gibb, A.C. and Ferry-Graham, L.A. (2005). Cranial movements during suction feeding in teleost fishes: Are they modified to enhance suction production? Zoology. 108(2): 141-153. ◦ Grubich, J.R. (2001). Prey Capture in Actinopterygian Fishes: A Review of Suction Feeding Motor Patterns with New Evidence from an Elopomorph Fish, Megalops atlanticus. Integrative and Comparative Biology. 41(6): 1258-1265. ◦ Holzman, R., Day, S.W., and Wainwright, P.C. (2007). Timing is everything: coordination of strike kinematics affects the force exerted by suction feeding fish on attached prey. Journal of Experimental Biology. 210: 3328-3336. ◦ Holzman, R., Day, S.W., Mehta, R.S., and Wainwright, P.C. (2008). Jaw protrusion enhances forces exerted on prey by suction feeding fishes. Journal of the Royal Society, Interface. 5(29): 1445-1457.
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Math & Nature  Suction feeding in the goliath grouper ◦ Given  Dimensions of cones A and B at maximum expansion (t1) 2) Find the volume of the goliath grouper feeding mechanism at maximum expansion (t1).
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Math & Nature  Suction feeding in the goliath grouper ◦ Given  Dimensions of cones A and B at rest (t0) 1) Find the volume of the goliath grouper feeding mechanism at rest (t0). b c a a e d
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Math & Nature  Suction feeding in the goliath grouper ◦ Given  Dimensions of cones A and B at rest (t0) 1) Find the volume of the goliath grouper feeding mechanism at rest (t0). c b a a e d
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Math & Nature  References ◦ Liem, K., Bemis, W., Walker, W.F., and Grande, L. (2001). Functional Anatomy of the Vertebrates: An Evolutionary Perspective. New York. Cengage Learning. ◦ Merrill, M.D. (2002). First principles of instruction. Educational Technology Research and Development. 50 (3): 43 – 59. ◦ Motta, P.J., Hueter, R.E., Tricas, T.C., Summers, A.P., Huber, D.R., Lowry, D., Mara, K.R., Matott, M.P., Whitenack, L.B., and Wintzer, A.P. (2008). Functional morphology of the feeding apparatus, feeding constraints, and suction performance in the nurse shark Ginglymostoma cirratum. Journal of Morphology. 269(9): 1041-1055. ◦ Motta, P.J., Maslanka, M., Hueter, R.E., Davis, R.L., de la Parra, R., Mulvany, S.L., Habegger, M.L., Strother, J.A., Mara, K.R., Gardiner, J.M., Tyminski, J.P., and Zeigler, L.D. (2010). Feeding anatomy, filter-feeding rate, and diet of whale sharks Rhincodon typus during surface ram filter feeding off the Yucatan Peninsula, Mexico. Zoology. 113: 199-212. ◦ Sanford, C.P.J. and Wainwright, P.C. (2002). Use of sonomicrometry demonstrates the link between prey capture kinematics and suction pressure in largemouth bass. Journal of Experimental Biology. 205: 3445-3457. ◦ Svanback, R., Wainwright, P.C., and Ferry-Graham, L.A. (2002). Linking cranial kinematics, buccal pressure, and suction feeding performance in largemouth bass. Physiological and Biochemical Zoology. 75(6): 532-543.
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Math & Nature    Suction feeding in the snook Centropomus undecimalis ◦ Given  Dimensions of cones A and B at rest (t0) and at maximum expansion of the feeding mechanism (t1)  Duration of the feeding event (t1 - t0) 5) Find the velocity of water flow into the mouth of the snook during suction feeding.
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Math & Nature    Suction feeding in the longjaw butterfly fish Forcipiger longirostris ◦ Given  Dimensions of cones A and B at rest (t0) and at maximum expansion of the feeding mechanism (t1)  Duration of the feeding event (t1 - t0) 6) Find the velocity of water flow into the mouth of the longjaw butterfly fish during suction feeding.
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PLACEMENT HOW? Placement Placement Test Test Transfer Transfer Credits Credits SAT SAT or or ACT ACT Scores Scores High High School School AP AP Scores Scores (Mathematics) (Mathematics) WHAT TO DO? Take Take placement placement test test on on any any campus campus at at Testing Testing Center. Center. Accuplacer Accuplacer MATH MATH can can be be taken taken twice. twice. Students Students who who wish wish higher higher placement placement must must then then “appeal”. “appeal”. Appeal Appeal is is request to take a pencil-and-paper type test on material from the course they request to take a pencil-and-paper type test on material from the course they placed placed into. into. Bring Bring transcript transcript showing showing general general education education math math credits credits from from another another college college or or university university to to CCBC CCBC for for evaluation. evaluation. If If completed completed in in Maryland, Maryland, the the highest highest level level developmental math course, Intermediate Algebra can be used for placement. developmental math course, Intermediate Algebra can be used for placement. Placement Placement by by SAT SAT MATH MATH score score of of 500 500 or or higher higher (or (or by by ACT ACT MATH MATH score score 21 21 or or higher) places the student into an entry-level general education math course higher) places the student into an entry-level general education math course (MATH (MATH 111, 111, 125, 125, 131/2/3, 131/2/3, 135, 135, 163). 163). For For higher higher placement, placement, the the student student must must take take Accuplacer MATH. MATH. Accuplacer Students Students with with documentation documentation of of AP AP math math scores scores of of 3, 3, 4, 4, or or 5 5 from from high high school school can can be awarded college credit and placement according to this chart. be awarded college credit and placement according to this chart.
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Core Math MATH 95 MATH 96 MATH 126 MATH 176 MATH 96 MATH 126 MATH 176 MATH 126E MATH 176 Recommendation: If you start in Math 95 or Math 96 take summer classes to stay on track! MATH 126 MATH 176 MATH 181 or Math 182 will meet the College of Business math requirement. MATH 176 Pg. 12 of your Advising Manual
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Rounding Methods Examples Math.ceil(2.1) returns 3.0 Math.ceil(2.0) returns 2.0 Math.ceil(-2.0) returns –2.0 Math.ceil(-2.1) returns -2.0 Math.floor(2.1) returns 2.0 Math.floor(2.0) returns 2.0 Math.floor(-2.0) returns –2.0 Math.floor(-2.1) returns -3.0 Math.rint(2.1) returns 2.0 Math.rint(2.0) returns 2.0 Math.rint(-2.0) returns –2.0 Math.rint(-2.1) returns -2.0 Math.rint(2.5) returns 2.0 Math.rint(-2.5) returns -2.0 Math.round(2.6f) returns 3 Math.round(2.0) returns 2 Math.round(-2.0f) returns -2 Math.round(-2.6) returns -3 8
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Using the Decorator Pattern • Take the IceCream object • Let’s create the Cone object. • IceCream cone = new Cone(); • Decorate it with the Fudge topping. • Create a Fudge object and wrap it around Cone. • cone = new Fudge(cone); • Decorate it with the Nuts topping. • Create a Nuts object and wrap it around Cone. • cone = new Nuts(cone); • Call the cost method and rely on delegation to add the cost of all toppings. • Call cost on the outmost decorator. • System.out.println(cone.cost());
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Introduction to the new mainframe Storage areas in an address space z/OS V1R13 BAR Problem (user) programs Run here LINE CVT (offset 16 (hex10) within PSA) All storage above 2 GB This area is called high virtual storage and is addressable only by programs running in 64-bit mode. It is divided by the high virtual shared area, which is an area of installation-defined size that can be used to establish cross-address space viewable connections to obtained areas within this area. Extended areas above 16 MB This range of areas, which lies above the line (16 MB) but below the bar (2 GB), is a kind of “mirror image” of the common area below 16 MB. They have the same attributes as their equivalent areas below the line, but because of the additional storage above the line, their sizes are much larger. Nucleus This is a key 0, read-only area of common storage that contains operating system control programs. System queue area (SQA) (2048 MBs)This area contains system level (key 0) data accessed by multiple address spaces. The SQA area is not pageable (fixed), which means that it resides in central storage until it is freed by the requesting program. The size of the SQA area is predefined by the installation and cannot change while the operating system is active. Yet it has the unique ability to “overflow” into the CSA area as long as there is unused CSA storage that can be converted to SQA. Pageable link pack area (PLPA), fixed link pack area (FLPA), and modified link pack area (MLPA) This area contains the link pack areas (the pageable link pack area, fixed link pack area, and modified link pack area), which contain system level programs that are often run by multiple address spaces. For this reason, the link pack areas reside in the common area that is addressable by every address space, therefore eliminating the need for each address space to have its own copy of the program. This storage area is below the line and is therefore addressable by programs running in 24-bit mode. CSA This portion of common area storage (addressable by all address spaces) is available to all applications. The CSA is often used to contain data frequently accessed by multiple address spaces. The size of the CSA area is established at system initialization time (IPL) and cannot change while the operating system is active. LSQA/SWA/subpool 228/subpool 230 This assortment of subpools, each with specific attributes, is used primarily by system functions when the functions require address space level storage isolation. Being below the line, these areas are addressable by programs running in 24-bit mode. User Region This area is obtainable by any program running in the user’s address space, including user key programs. It resides below the line and is therefore addressable by programs running in 24-bit mode. System Region This small area (usually only four pages) is reserved for use by the region control task of each address space. Prefixed Save Area (PSA) This area is often referred to as “Low Core.” The PSA is a common area of virtual storage from address zero through 8191 in every address space. There is one unique PSA for every processor installed in a system. The PSA maps architecturally fixed hardware and software storage locations for the processor. Because there is a unique PSA for each processor, from the view of a program running on z/OS, the contents of the PSA can change any time the program is dispatched on a different processor. This feature is unique to the PSA area and is accomplished through a unique DAT manipulation technique called prefixing. © Copyright IBM Corp., 2010. All rights reserved. Page 42 of 85
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Math questions • Evaluate the following expressions: – – – – – – – Math.abs(-1.23) Math.pow(3, 2) Math.pow(10, -2) Math.sqrt(121.0) - Math.sqrt(256.0) Math.round(Math.PI) + Math.round(Math.E) Math.ceil(6.022) + Math.floor(15.9994) Math.abs(Math.min(-3, -5)) • Math.max and Math.min can be used to bound numbers. Consider an int variable named age. – What statement would replace negative ages with 0? – What statement would cap the maximum age to 40? 27
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                  ACT SCORES PLACEMENT English 18 - 27 Engl 1010 Math 19 - 27 Math 1020/1810/1100 (check major) Math 28 + Credit given for Math 1020 SAT SCORES PLACEMENT Verbal 450 – 620 Engl 1010 Verbal 630 - 710 Credit given for Engl 1010 Verbal 720 + Credit given for Engl 1010 & 1020  Math 460 - 620 Math 1020/1810/1100 (check major)  Math 630 + Credit given for Math 1020 COMPASS SCORES PLACEMENT Writing 68 + Engl 1010  Pre-Algebra 56 - 94 Math 1020 Algebra 36 – 88 Math 1020 College Algebra 30 - 66 Math 1020  Pre-Algebra 95+ Credit for Math 1020 Algebra 89+ Credit for Math 1020 College Algebra 67+ Credit for Math 1020
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Topological Sort A topological sort of an acyclic directed graph orders the vertices so that if there is a path from vertex u to vertex v, then vertex v appears after vertex u MATH 120 One topological sort in the ordering. of the course prerequisite graph at left: MATH 150 MATH 224 ECE 282 CS 111 CS 150 ECE 381 CS 111, MATH MATH 152 120, CS 140, MATH 423 MATH 125, CS ECE 482 MATH 250 150, MATH 224, CS 234 CS 240 STAT 380 CS 234, CS 240, ECE 483 MATH 321 ECE 282, CS 312, CS 312 CS 321 CS 325, MATH CS 325 150, MATH 152, CS 482 STAT 380, CS 321, CS 340 MATH 250, MATH CS 382 CS 434 321, CS 314, CS 314 MATH 423, CS CS 330 340, CS 425, ECE CS 425 381, CS 434, ECE CS 447 482, CS 330, CS CS 423 382, CS 423, CS CS 499 CS 438 CS 456 438, CS 454, CS 447, CS 499, CS CS 454 482, CS 456, ECE MATH 125 CS 340 CS 140 Page 5
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Math Study Skills Inventory Rate your achievement of the following statements by placing a 3 for almost always, 2 for sometimes, and 1 for almost never. If you have never even thought about doing what the statement says, put a 0. Selecting a math class _______ 1. I schedule my math class at a time when I am mentally sharp. _______ 2. When I register for a math class, I choose the best instructor for me. _______ 3. If I have a choice, I select a math class that meets three or four days a week instead of one or two. _______ 4. I schedule the next math class as soon as possible after I have completed the current course. _______ 5. I am sure that I have signed up for the correct level math course.  Time and place for studying math _______ 6. I study math every day. _______ 7. I try to get my math homework immediately after math class. _______ 8. I have a specific time to study math. _______ 9. I have a specific place with few distractions to study math. ______ 10. I seek help with my math homework in the lab/tutoring center. ______ 11. I am careful to keep up to date with math homework. ______ 12. I study math at least 8 to 10 hours a week. 
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