## SDS Topics in Numerical Order

VISUAL PROBLEMS: 1000 – 1170 | |
---|---|

1000 | visual problems |

1007 | networks, tracing |

1008 | pattern completion (visual) |

1009 | counting shapes in shapes |

1010 | visual sequences, linear |

1015 | visual sequences, 2-dimen. |

1020 | geometry, informal |

1026 | tesselation |

1027 | partitions |

1030 | connecting dots |

1040 | trees in rows, planting |

1050 | pennies, arranging |

1060 | toothpicks |

1070 | grabbers, trick quest, cheap shots |

1079 | words, problems about |

1080 | optical illusions |

Three-Dimensional Problems: 1090 – 1095 | |

1090 | three-dimen. problems, elem. |

1093 | geoblocks |

1094 | two-dimen. versions of 3-d prob. |

1095 | missing faces of solids |

Problems With Numbers, non-computational: 1100 – 1170 | |

1100 | number patterns (cf. 2530, 2850) |

1110 | numbers in patterns, arranging |

1120 | cross-number puzzles |

1130 | magic squares |

1140 | pails and measuring |

1160 | crypt-arithmetic |

1170 | money/coins: change; value (cf. 1350, 2480) |

LOGICAL DEDUCTION: 1180 – 1290, 3750 (Formal) | |

1180 | logic, analysis (classic brainteasers) |

1190 | time, incl. calendars |

1192 | calendars |

1200 | rank ordering |

1210 | hats: who has which hat on |

1220 | sorting: Canadian owns the wombat |

1230 | sorting, misc.: which is which |

1232 | incomplete information charts |

1240 | river crossing |

1245 | Jeep problems |

1250 | false coins (2-pan scales) |

1255 | scales, two-pan |

1260 | handshake problem |

1270 | pigeonhole principle |

1280 | liars/truthtellers |

1290 | venn diagrams (cf. 2030) |

ARITHMETIC: 1300 – 2022 | |

Arithmetic with Whole Numbers: 1300 – 1342 | |

1300 | numerals, writing; digits (pl. value, cf. 1720) |

1305 | odd-even numbers |

1307 | consecutive integers |

1310 | adding and subtracting (cf. 1140) |

1320 | multiplying and dividing (incl +, -) (cf. 1140) |

1322 | remainders |

1330 | squares & square roots (cf.1670) |

1331 | squares (cf. 1670) |

1332 | square roots |

1333 | higher powers & roots |

1334 | powers, higher |

1335 | roots, higher |

1340 | counting (how many) |

1342 | counting: how many ways |

Arithmetic with Real Numbers: 1350 – 1450 | |

1350 | decimal arithmetic, incl. $ (cf. 1170, 2480) |

1360 | rational numbers |

1365 | fractions (numerical) |

1367 | fractions, equivalent |

1368 | rational number arithmetic |

1370 | percent, numerical (cf. 2410, 2290) |

1380 | integers |

1385 | integer operations |

1390 | irrationals |

1395 | radical manipulation |

1400 | rationalization |

1410 | exponents, arithmetic using (cf. 2100) |

1412 | exponents, laws of |

1420 | approximation |

1430 | arithmetic means, numerical (cf. 2452, 2860) |

1440 | geometric means, num. (cf. 2454, 2870, 3590) |

1450 | harmonic means, num. (cf. 2456, 2880) |

Calculator use: 1460 – 1480 | |

1460 | calculator, use of |

1465 | calculator, broken key |

1470 | calculator: heavy calculations |

1480 | calculator pattern discovery |

Pre-Algebra Word Problems: 1490 – 1550 | |

1490 | bargains (cf. linear programming 2220) |

1510 | living life (1/8 as boy , 1/4 as..) |

1520 | wages |

1530 | word problems, whole #'s (typical) |

1540 | word problems, hard but (typical) |

1550 | word problems: soft-core algebra |

1560 | pickanumba |

1600 | prime numbers |

1610 | factors |

1620 | prime factorization |

1630 | factor, greatest common |

1640 | divisibility |

1650 | multiples |

1660 | multiples, least common |

1680 | factorials |

1690 | diophantine equations |

1700 | number bases |

1710 | sums of integers |

1720 | place value, prob about (cf.1300) |

1730 | number theory proofs |

1740 | modular arithmetic |

1800 | measurement, elementary |

1810 | dimensional analysis |

1900 | flow charts |

2010 | real number system, structure |

Complex Numbers: 2020 – 2022 | |

2020 | i |

2021 | complex numbers |

2022 | complex number operations |

SYMBOL MANIPULATION: 2030 – 2390, 2745, 4100 | |

2030 | sets (cf. 1290) |

2040 | operations, prop. of ("new math") |

2050 | numerical expressions: order of op. |

2070 | formulas, inventing (alg. expr.) (cf. 2530, 2580) |

2080 | symbol manipulation (cf. 2110) |

2090 | linear expressions |

2100 | exponents, algebraic expr. with (cf. 1410) |

2110 | polynomial manipulation |

2120 | factoring, misc. |

2121 | factoring, quadratics |

2122 | factoring, cubics and higher |

2130 | absolute value (cf. 2285) |

2140 | ratio |

2150 | rational expressions |

2152 | rational expressions, evaluating |

2160 | fractions, complex |

2162 | fractions, continued |

2180 | radicals, roots |

2190 | reciprocals |

Equations and Inequalities, Linear and Quadratic: 2200 – 2288 | |

2200 | equations, linear & rational |

2210 | inequalities, linear, incl. abs. values |

2211 | inequalities w/ abs. value |

2220 | linear programming (cf. bargains 1490) |

2230 | equations, quadratic |

2232 | functions, quadratic |

2238 | equations, quadratic, non-routine |

2240 | factoring: quadratic equations |

2250 | inequalities, quadratic |

2250 | rational equations |

2260 | cubics & higher degrees (cf.2680) |

2270 | equations involving radicals |

2285 | equations with absolute value (cf. 2130) |

2286 | equations w/ radicals |

2288 | equations, misc. |

2290 | proportions (cf. 2560) |

2300 | equations, exponential |

2305 | exponential growth |

Systems of Equations: 2310 – 2340 | |

2310 | equations, systems of, linear |

2315 | equations, systems, 3 or more variables |

2320 | equations, systems of, non-linear |

2330 | equations, systems of, trig. |

2340 | equations, systems of, misc. |

2350 | inequalities, misc. |

2360 | matrices, determinants |

2361 | matrices |

2365 | determinants |

2370 | identities, algebraic |

2380 | binomial coefficients |

2385 | Pascal's triangle (cf. 2890) |

2390 | binomial expansion |

WORD PROBLEMS NEEDING ALGEBRA: 2400 – 2500 | |

2400 | problem solving, about |

Translating among Words, Equations, Diagrams: 2405 – 2408 | |

2405 | translating words to equations |

2407 | translating words to diagrams |

2408 | word prob. w/ diagrams |

Standard and Unusual Word Problems: 2410 – 2500 | |

2410 | percent, algebraic (cf. 1370) |

2412 | percent from Henle |

2420 | rates |

2430 | valves |

2440 | distance, rate, time |

2442 | distances upstream/downstream |

2445 | perimeter & area & volume |

2447 | area (cf. 3410-3450) |

2448 | volume (cf. 3650) |

2450 | means arith, geom, harm (cf. 2860-80) |

2452 | arithmetic means, algebraic |

2454 | geometric means, algebraic |

2456 | harmonic means, algebraic |

2460 | ages |

2465 | ages, complicated problems |

2470 | profit and loss |

2480 | money (cf. 1170, 1350) |

2485 | pre-calc text alg. probs. |

2490 | probs. w/ ans. a range of values |

2500 | probs. misc. (consecutive integers) |

FURTHER TOPICS IN ALGEBRA: 2510 – 2745, 2840 – 2990 | |

2510 | operations, made-up, e.g. 2*3 |

2520 | relations |

Functions: 2530 – 2630 | |

2530 | functions, informal (cf. 2580, 2630, 2070) |

2540 | domain, range |

2542 | domain |

2544 | range |

2560 | variation, direct (cf. 2290) |

2570 | variation, inverse |

2580 | f(x) notation |

2585 | functions, graphs of |

2590 | absolute value function (see 2130, 2285) |

2600 | greatest integer function |

2610 | composite functions |

2615 | functions, recursive |

2620 | inverse functions |

2630 | equations, functional |

2640 | equations, polynomial |

2650 | polynomials, real roots of |

2660 | polynomials, complex &/or real rts. |

2670 | remainder theorem |

2680 | cubics (cf. 2260) |

2700 | sequences & series (cf. 2860-80) |

2701 | sequences |

2702 | series |

2710 | functions, exponential |

2720 | optimization |

Logarithms: 2730 – 2745 | |

2730 | logarithms: manipulations |

2735 | log to exp. form & v.v. |

2740 | logarithms: change of base |

2745 | equations, logarithmic |

ANALYTIC GEOMETRY: 2750 – 2840, 3680 – 3723 | |

2750 | coordinate plane |

2760 | coord. geom: slope, dist, midpt. &c. |

2761 | slope of line |

2762 | distance formula |

2763 | midpoint formula |

2770 | lines on coordinate plane (cf. 3680) |

2780 | conic sections |

2782 | parabolas |

2784 | ellipses |

2786 | hyperbolas |

2788 | circles (equations) |

2790 | coordinate space: 3-d analyt. geom. |

2800 | spheres (analytical) |

2810 | graphing techniques symm, asymp. |

2820 | polar coordinates |

2840 | DeMoivre's theorem |

2850 | sequences (progressions) |

2860 | sequences, arithmetic (cf. 1430) |

2870 | sequences, geometric (cf. 1440, 3590) |

2880 | sequences, harmonic (cf. 1450) |

2890 | Fibonacci numbers (cf. 2385) |

2900 | series |

2950 | induction |

2970 | vectors |

2980 | limits |

2990 | probs. w/ (seemingly) insuff. info |

INFORMAL GEOMETRY: 3000 – 3080 | |

3000 | geometry, informal (for geom. class) (cf. 1020) |

3004 | four-color problem |

3050 | geometry: early (segments, angles) |

3060 | points in plane |

3065 | points in space |

3070 | suppl., compl. angles |

3071 | complementary angles |

3072 | supplementary angles |

3080 | separation (regions, counting) |

EUCLIDEAN GEOMETRY: 3100 – 3650, 3750 – 3850 | |

Triangles: 3100 – 3250 | |

3100 | triangles and congruence |

3140 | three-dimen. prob. w/ cong. triang. |

3150 | triangles, elementary: general |

3155 | triangles, advanced, general |

3160 | triangles, isosceles |

3170 | triangles, equilateral |

3180 | triangles, right |

3190 | triangles, right, 30-60 |

3200 | triangles, right isosceles |

3210 | inequalities, geometric |

3220 | optimization, geometric |

3230 | median, alt, angle bis, &c. |

3231 | medians of triangles |

3232 | altitudes of triangles |

3233 | angle bisection of triangles |

3234 | perpendicular bisection of sides of triangles |

3235 | midline of triangles |

3240 | Menelaus's theorem |

3250 | Ceva's theorem |

3260 | parallel and perpendicular lines |

3261 | parallel lines |

3262 | perpendicular lines |

3270 | parallel &perp. lines & planes |

Polygons: 3300 – 3390 | |

3300 | polygons |

3305 | polygons, regular |

3310 | polygons, angles of |

3320 | inscribed & circumscr. polyg. (cf.3570) |

3321 | inscribed polygons |

3322 | circumscribed polygons |

3330 | convexity |

3340 | trapezoids |

3350 | parallelograms |

3360 | rectangles |

3370 | rhombi |

3380 | squares |

3390 | other polygons |

3400 | perimeter |

3405 | area and perimeter |

3410 | area (cf. 3420-3460) |

3420 | polygons, area of |

3440 | circles, area of |

3450 | area, surface |

3460 | area in coordinate plane |

3470 | Pythagorean theorem |

3475 | Pythagoras in 3 dimensions |

Circles: 3500 – 3572 | |

3500 | circles |

3510 | arcs and angles |

3520 | chords and angles |

3530 | tangents |

3540 | secants |

3550 | circumference |

3560 | power of a point |

3570 | inscribed & circumscribed circles |

3571 | inscribed circles |

3572 | circumscribed circles |

3580 | similarity (proportion) |

3590 | means, geometric, in geometry (cf. 1440, 2870) |

Solid Geometry: 3600 – 3650 | |

3600 | solids |

3601 | patterns of solids |

3602 | sections of solids |

3610 | cubes |

3615 | rectangular prisms |

3618 | cylinders |

3620 | pyramids |

3625 | cones |

3630 | tetrahedrons |

3640 | spheres |

3650 | volume |

3680 | analytic geometry: lines (cf. 2770) |

3685 | analytic triangles |

3687 | lattice points |

3690 | analytic geometry: circles (cf.2780) |

3695 | analytic problems in 3-dimensions |

3700 | analytic geometry: spheres (cf. 2800) |

3720 | reflections, rotations, translations |

3721 | reflections |

3722 | rotations |

3723 | translations |

3750 | logic, formal |

Proof: 3752 – 3755 | |

3752 | proofs, geometric |

3754 | proofs, algebraic |

3755 | proofs, phony |

3800 | constructions |

Locus: 3850 | |

3850 | locus |

TRIGONOMETRY: 4000 – 4340 | |

4000 | trigonometry, basics |

4040 | trigonometry functions, graphs of |

4050 | trigonometry on triangles |

4060 | sin(x + y) |

4080 | cos(x+ y) |

4100 | identities, trigonometric |

4120 | functions, inverse trigonometric |

4140 | law of sines |

4160 | law of cosines |

4180 | radians |

4200 | trigonometry probs, juicy numerical |

4220 | trigonometry, spherical / 3-d probs |

4300 | combinatorics |

4340 | trigonometry on polyhedra, numer. |

PROBABILITY: 4400 – 4420 | |

4400 | probability (cf. 1340) |

4410 | combinations |

4420 | permutations |

EVERYTHING ELSE: 5000 – | |

5000 | SAT for algebra 1 |

5200 | SAT for geometry |

5300 | SAT for algebra/trig and beyond |

5400 | achievement level 1 |

5500 | achievement level 2 |