MATHCOUNTS 100 Classroom Lessons August 2000 Prepared by John Cocharo The Oakridge School 5900 W. Pioneer Parkway Arlington, TX 76013 (817) 451-4994 (school) jcocharo@esc11.net (school) cocharo@hotmail.com (home)
MATHCOUNTS - 100 Classroom Lessons Number Lesson AA 1 Square Two Digit Natural Number Ending in 5. AB 2 Square a Natural Number from 1 to 36. AC 3 Cube a Natural Number from 1 to 36. AD 4 Multiply Two Two-digit Natural Numbers Ending in 5. AE 5 Multiply Two Natural Numbers between 100 and 110. AF 6 Multiply Two Natural Numbers between 90 and 100. AG 7 Multiply a Natural Number between 100 and 110 by a Natural Number between 90 and 100. AH 8 Multiply by 11, 111, 101, 1001,. AI 9 Square a Natural Number between 50 and 60. AJ 10 Multiply Two Digit Natural Numbers with Same Decade, Sum of Units Digits = 10. AK 11 Multiply Two Digit Natural Numbers with Same Units, Sum of Tens Digits = 10. AL 12 Use FOIL to Multiply Two Two-Digit Natural Numbers. AM 13 Multiply Two Mixed Numbers with = Whole Numbers and Fractions = 1. AN 14 Use FOIL to Multiply Mixed Numbers. AO 15 Use Additive Inverses and Multiplicative Inverses. AP 16 Find the Product of Two Mixed Numbers with the Same Fractions. AQ 17 Find the Sum of Consecutive Natural Numbers 1 to n. AR 18 Find the Sum of Consecutive Natural Odd Numbers 1 to n. AS 19 Find the Sum of Consecutive Natural Even Numbers 1 to n. AT 20 Find the Sum of Reciprocals of Two Natural Numbers. AU 21 Generate Arithmetic Sequences. AV 22 Generate Geometric Sequences and Other Sequences. AW 23 Use PEMDAS. AX 24 Use the Weiwen Chen Method. AY 25 Multiply by 25, 12 1/2, 16 2/3, 33 1/3,. BA 26 Divide by 25, 12 1/2, 16 2/3, 33 1/3,. BB 27 Change from Some Base to Base 10. BC 28 Change from Base 10 to Another Base. BD 29 Change from Base 2 to Base 4, 8, 16,. BE 30 Convert Roman Numerals. BF 31 Use A Continued Fraction Algorithm. BG 32 Use Ratio and Proportion. BH 33 Use Subsets of Sets. BI 34 Use Percents. BJ 35 Find What Percent a Number is Greater than Another. BK 36 Convert Fahrenheit to/from Centigrade. BL 37 Find Simple Interest. BM 38 Find Rates of Change. BN 39 Find the Union and/or the Intersection of Sets. BO 40 Find the (Arithmetic) Mean of a Set of Data. BP 41 Find the Mode of a Set of Data. BQ 42 Find the Median of a Set of Data. BR 43 Find the Range of a Set of Data. BS 44 Find the Geometric Mean of a Set of Data. BT 45 Find the Harmonic Mean of Two Numbers. BU 46 Find Factorials. BV 47 Find Permutations. BW 48 Find Combinations. BX 49 Estimate in Addition or Subtraction. BY 50 Estimate in Multiplication or Division.
MATHCOUNTS - 100 Classroom Lessons Number Lesson CA 51 Use Divisibility Rules for 2 n Power. CB 52 Use Divisibility Rule for 5. CC 53 Use Divisibility Rule for 3, 37,. CD 54 Use Divisibility Rule for 7, 11, 13,. CE 55 Find GCF. CF 56 Find LCM. CG 57 Find Product of the GCF and the LCM of Two Numbers. CH 58 Find the Number of Factors of a Natural Number. CI 59 Find the Sum of the Factors of a Natural Number > 1. CJ 60 Find the Sum of the Recipr+B2ocals of Factors of a Natural Number > 1. CK 61 Find Remainders. CL 62 Find Maximum Number not Covered by a Combination of Two Numbers. CM 63 Solve Path Problems. CN 64 Utilize Simple Radical Form. CO 65 Find the Probability of an Event. CP 66 Find the Odds of an Event. CQ 67 Find the Number of Diagonals in a Polygon. CR 68 Use Pythogorean Triples. CS 69 Utilize 30-60-90 Triangles. CT 70 Utilize Right Isosceles Triangles. CU 71 Find Perimeter of Triangles and Quadrilaterals. CV 72 Find Circumference of Circles. CW 73 Find Perimeter of Regular Polygons. CX 74 Find Area of Triangles. CY 75 Find Area of Quadrilaterals with Perpendicular Diagonals. DA 76 Find the Area of Squares and Rectangles. DB 77 Find the Area of Circles. DC 78 Find the Area of Equilateral Triangles. DD 79 Find the Area of Trapezoids. DE 80 Use Pick's Law. DF 81 Find the Surface Areas of Cubes. DG 82 Use Coordinate Formula for Area. DH 83 Use Hero(n)'s Formula DI 84 Find the Volumes of Cubes. DJ 85 Find the Surface Areas of Rectangular Prisms. DK 86 Find the Volumes of Rectangular Prisms. DL 87 Find the Surface Areas of Cylinders. DM 88 Find the Volumes of Cylinders. DN 89 Find the Surface Areas of Pyramids. DO 90 Find the Volumes of Pyramids. DP 91 Find the Surface Areas of Cones. DQ 92 Find the Volumes of Cones. DR 93 Find the Surface Areas of Spheres. DS 94 Find the Volumes of Spheres. DT 95 Find Supplements and/or Complements of Angles. DU 96 Find the Measures of Interior and/or Exterior Angles of Polygons. DV 97 Find the Slope of a Line. DW 98 Find the x-intercept, y-intercept, and Other Intercepts of a Line. DX 99 Find the Sum of Roots of Quadratic Equations. DY 100 Find the Product of Roots of Quadratic Equations.
AA0 1225 AF6 0.8556 AL7 936 AR1 49 AA1 2025 AF7 8736 AM0 20 8/81 AR2 100 AA2 3025 AG0 9870 AM1 2 2/9 AR3 256 AA3 4225 AG1 10593 AM2 72 6/25 AR4 64 AA4 5625 AG2 10290 AM3 30 10/49 AR5 2500 AA5 7225 AG3 9588 AM4 12 3/16 AS0 72 AA6 90.25 AG4 104.76 AM5 20 1/4 AS1 56 AA7 625 AG5 103.95 AM6 42 1/4 AS2 100 AA8 0.0225 AG6 0.9486 AM7 30 9/100 AS3 400 AA9 3035 AG7 8888 AN0 129 1/63 AS4 2550 AB0 841 AH0 473 AN1 27 1/12 AS5 900 AB1 784 AH1 5757 AN2 84 1/20 AT0 2 4/9 AB2 729 AH2 39039 AN3 26 26/35 AT1 13/40 AB3 676 AH3 4662 AN4 53 1/8 AT2 17/52 AB4 576 AH4 38295 AN5 30 1/4 AT3 19/24 AB5 529 AH5 2838 AN6 56 1/4 AT4 9/10 AB6 4.84 AH6 803 AO0 5/33 AT5 5/6 AB7 441 AH7 23634 AO1-5 1/3 AU0 22 AB8 0.0361 AI0 2601 AO2 1 1/3 AU1 63 AB9 324 AI1 2704 AO3-7 AU2 29 AC0 24389 AI2 2809 AO4 3 15/16 AU3 12 AC1 21952 AI3 2916 AO5 20 AU4-1 AC2 19683 AI4 3136 AO6 2 1/7 AU5 16 AC3 17576 AI5 3249 AO7 2 4/9 AU6 1683 AC4 13824 AI6 33.64 AO8 8/35 AU7 37 AC5 12167 AI7 3481 AO9 2 11/12 AV0 0.0625 AC6 10.648 AI8 0.2809 AO10-7.5 AV1 1 AC7 9261 AI9 2704 AO11 2 2/5 AV2 4951 AC8 0.006859 AJ0 9024 AO12 4/9 AV3 6399 AC9 5832 AJ1 7209 AO13 2 1/2 AV4 1575 AD0 2925 AJ2 5616 AO14 17 1/2 AV5 567 AD1 4875 AJ3 4209 AO15 3.7 AV6 15 AD2 1125 AJ4 30.21 AP0 17/4 AV7 38 AD3 3825 AJ5 12.16 AP1 65 1/64 AW0 31 AD4 26.25 AJ6 0.0621 AP2 38 1/16 AW1 0 AD5 24.75 AJ7 5621 AP3 39 1/25 AW2 34 AD6 0.4125 AK0 3381 AP4 59 1/25 AW3 34 AE0 10920 AK1 1764 AP5 29 1/36 AW4 0 AE1 11663 AK2 2349 AP6 61 1/9 AW5 2 AE2 11340 AK3 1536 AP7 35 1/16 AW6 2543 AE3 10608 AK4 26.25 AQ0 136 AW7 10 AE4 112.35 AK5 23.04 AQ1 21 AW8 6 AE5 114.45 AK6 0.2304 AQ2 15 AW9-5476 AE6 1.0506 AL0 3087 AQ3 6 AW10 6400 AF0 8930 AL1 1674 AQ4 190 AW11 729 AF1 9603 AL2 2001 AQ5 153 AW12-1 AF2 9310 AL3 1488 AQ6 1 AW13-8/3 AF3 8648 AL4 24.75 AQ7 1575 AW14 118 AF4 95.06 AL5 315 AQ8 15 AX0 4/33 AF5 94.05 AL6 0.2432 AR0 625 AX1 17/33
AX2 5/11 BE2 1401 BK4 25 BR1 3 AX3 3 31/198 BE3 MCXI BK5 55 BR2 6 AX4 421/666 BE4 29 BL0 5 BR3 9 AX5 713/1650 BE5 37 BL1 421.19 BR4 14 AY0 1600 BE6 LXXXII BL2 250 BR5 28 AY1 400 BE7 CXXXIV BL3 306.48 BS0 6 AY2 1200 BE8 MCIII BL4 51.94 BS1 4sqrt(5) AY3 1200 BE9 45 BL5 182.88 BS2 12.96 AY4 1300 BE10 CCXXII BM0 7 BS3 6 AY5 1200 BE11 MCMXCIX BM1 300 BS4 6 AY6 3100 BE12 LVII BM2 8 5/6 BS5 20 AY7 900 BF0 29/12 BM3 6.7*10 8 BT0 5 7/13 BA0 1.8 BF1 43/40 BM4 17280 BT1 6.46 BA1 4.48 BF2 103/24 BM5 18.2 BT2 1.8 BA2 3.84 BF3 10/33 BM6 13 BT3 54 5/9 BA3 1.5 BF4 12/29 BM7 11.5 BT4 524 BA4 0.96 BF5 266/115 BN0 2 BT5 35 BA5 9.84 BG0 9 BN1 2 BU0 720 BA6 2.56 BG1 9 BN2 0 BU1 3 BA7 2.94 BG2 5 1/3 BN3 {A,D} BU2 48 BB0 22 BG3 5.4 BN4 7 BU3 5 BB1 6 BG4 8498.06 BN5 {A,E,I,O,U,B,C,D} BU4 10080 BB2 12 BG5 90 BN6 {J,O,H,N,U,L,I,A} BU5 210 BB3 30 BG6 40 BN7 {J} BV0 4 BB4 36 BH0 16 BO0 88 BV1 222 BB5 194 BH1 15 BO1 1 BV2 240 BB6 985 BH2 16 BO2 1/3 BV3 1/2 BC0 53 BH3 1 BO3 1000 BV4 20 BC1 110 BH4 32 BO4 21 BV5 2/5 BC2 7 BH5 4 BO5 101 BV6 18 BC3 7 BH6 31 BO6 18 BV7 72 BC4 34 BI0 210 BO7 (-4,3) BV8 5040 BC5 2 BI1 3/10 BO8 20 BV9 65610 BC6 10100 BI2 0.1725 BO9 14 BW0 1 5/14 BC7 100 BI3 7/150 BO10 97 BW1 165 BC8 8 BI4 38 BO11 76.9 BW2 9 BD0 212 BI5 275 BP0 3 BW3 30 BD1 312 BI6 350 BP1 44 BW4 120 BD2 34F BI7 87.5 BP2 I BW5 180 BD3 1754 BI8 25 BP3-1 BW6 7000 BD4 1311 BI9 3 BP4 92 BX0 70000 BD5 724 BJ0 20 BP5 73 BX1 191916to212116 BD6 51 BJ1 37 BQ0 19 BX2 33246to36744 BD7 220 BJ2 303.75 BQ1 169 BX3 297786to329130 BD8 1700 BJ3 56.25 BQ2 82 BX4 7734to8548 BD9 15A BJ4 5.7 BQ3 23 BX5 224433to248057 BD10 1110010100 BJ5 44 BQ4 4.5 BY0 70000 BD11 1100110011 BK0-40 BQ5 23 BY1 7600 BD12 1101001011 BK1 122 BQ6 12.5 BY2 214 BE0 CCXXII BK2 167 BQ7 10.5 BY3 18000 BE1 29 BK3 77 BR0 70 BY4 4285714.3
BY5 1024 CH5 6 CO5 0 CT5 2sqrt(2) CA0 2 CH6 3 CO6 3/4 CU0 8 CA1 3 CH7 9 CO7 2 CU1 23 CA2 2 CH8 2 CO8 1/3 CU2 0 CA3 3 CI0 98 CO9 21 CU3 42 CA4 16 CI1 20 CO10 4/5 CU4 15 CA5 2 CI2 168 CO11 7/8 CU5 38 CA6 4 CI3 56 CO12 1/2 CU6 24 CB0 4 CI4 6 CO13 2/3 CU7 30 CB1 2 CI5 12 CO14 3/10 CU8 14 CB2 4 CI6 2 CO15 13/36 CV0 5π CB3 4 CJ0 49/25 CO16 2/3 CV1 12π CB4 2 CJ1 14/5 CO17 7808/19683 CV2 4 CB5 5 CJ2 2 CP0 2/19 CV3 16 CC0 8 CJ3 2 CP1 3/29 CV4 10π CC1 1 CJ4 7/3 CP2 8/117 CV5 80π CC2 0 CJ5 3/2 CP3 1:1 CW0 84 CC3 0 CK0 6 CP4 1:1 CW1 24 CC4 1 CK1 1 CP5 1/25 CW2 25 CC5 0 CK2 1 CP6 1/17 CW3 42 CD0 10 CK3 1 CQ0 10 CW4 56 CD1 5 CK4 1 CQ1 2 CW5 72 CD2 8 CK5 1 CQ2 7 CW6 100 CD3 1 CL0 607 CQ3 2 CX0 11.5 CD4 4 CL1 31 CQ4 5 CX1 16 CD5 11 CL2 3 CQ5 9 CX2 35/2 CE0 7 CL3 27 CQ6 14 CX3 24 CE1 11 CL4 65 CQ7 20 CX4 54 CE2 79 CL5 5 CQ8 27 CX5 5 5/8 CE3 6 CM0 20 CQ9 35 CY0 72 CE4 4 CM1 38 CR0 405 CY1 98 CE5 8 CM2 15 CR1 17 CY2 60 CF0 301 CM3 14 CR2 48 CY3 35 CF1 360 CM4 6 CR3 10 CY4 50 CF2 2310 CM5 29 CR4 33 CY5 1/2 CF3 144 CN0 7sqrt(2) CR5 34 CY6 14sqrt(2) CF4 2520 CN1 sqrt(2) CR6 234 CY7 40 CF5 42 CN2 -sqrt(17) CR7 8 CY8 2 CF6 120 CN3 2sqrt(5) CR8 15.59 DA0 165 CF7 63 CN4 sqrt(21) CS0 28 DA1 128 CG0 3692 CN5 10sqrt(3) CS1 3 DA2 12 CG1 1056 CN6 sqrt(5),-sqrt(5) CS2 3sqrt(3) DA3 3200 CG2 104 CN7 3sqrt(3) CS3 30sqrt(3) DA4 43 CG3 350 CN8 sqrt(2) CS4 60 DA5 9.1 CG4 48 CN9 14sqrt(2) CS5 18 DA6 7 CG5 56 CN10 7sqrt(2) CS6 9 DA7 5/9 CH0 20 CO0 2/21 CT0 27 DA8 225 CH1 72 CO1 3/32 CT1 12sqrt(2) DA9 108 CH2 20 CO2 8/125 CT2 15sqrt(2) DB0 30π CH3 6 CO3 3/5 CT3 24 DB1 256/625 CH4 6 CO4 1/10 CT4 16 DB2 1/3
DB3 12 DJ1 2645 DQ5 846.66 DX4 4 DB4 796 DJ2 94 DR0 16π DX5 3 DB5 44.2 DJ3 1174 DR1 15 DY0 24 DB6 9 DJ4 52 DR2 16π DY1-6 DB7 16π DJ5 37.64 DR3 100π DY2 56 DB8 42π DK0 237.5 DR4 64π DY3-12 DB9 72π DK1 18 DR5 25 DY4 7/3 DB10 6.25π DK2 96 DS0 299 DY5-15 DC0 25 sqrt(3) DK3 60 DS1 40 DC1 26.3 DK4 2730 DS2 8 DC2 24 DK5 24 DS3 36π DC3 0.32 DK6 10.39 DS4 288π DC4 36sqrt(3) DK7 63.87 DS5 523.60 DC5 216sqrt(3) DL0 20π DT0 1/4 DD0 517 DL1 15π DT1 17 DD1 2 DL2 70π DT2 168 DD2 30 DL3 5.5π DT3 240 DD3 48 DL4 487.38 DT4 116 DD4 18sqrt(3) DL5 329.9 DT5 89 DD5 77/2 DM0 16/3 DT6 42.5 DE0 8 DM1 686π DT7 28 DE1 7 DM2 523-577 DT8 99 DE2 10 DM3 20π DU0 18 DE3 10 DM4 11.25π DU1 119 DE4 12 DM5 50π DU2 45 DE5 10 DM6 1.25π DU3 54 DF0 486 DM7 783.56 DU4 36 DF1 96 DM8 432.0 DU5 72 DF2 54 DN0 260 DU6 45 DF3 288 DN1 800 DU7 40 DF4 18 DN2 36sqrt(3) DV0 1/2 DF5 72 DN3 1040 DV1-2 DG0 4 DN4 96 DV2-1 2/3 DG1 24 DN5 75 DV3 12/5 DG2 30 DO0 400 DV4 5 DG3 5 DO1 1280 DV5 0 DG4 3/8 DO2 18sqrt(2) DV6 1 DG5 4 DO3 3200 DV7 2 DH0 2.90 DO4 48 DV8 2 DH1 72.31 DO5 129.90 DV9 2/3 DH2 14.70 DP0 65π DV10-2/3 DH3 180 DP1 136π DW0 (-2,-3) DH4 120 DP2 36π DW1 5/2 DH5 261.82 DP3 24π DW2-5/3 DI0 1.26 DP4 285.86 DW3 7 DI1 729 DP5 195.3 DW4-7/5 DI2 512 DQ0 100π DW5-4 DI3 6/7 DQ1 287-316 DX0 5 DI4 750sqrt(6) DQ2 332-368 DX1-1 DI5 64 DQ3 150π DX2 15 DJ0 1 1/2 DQ4 320π DX3 13/2