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high school mathematics (Topic)

The aim of this meta entry is to index entries suitable for high school students.

Basics

  1. set, union, intersection
  2. natural numbers, rational numbers, real numbers
  3. associativity of multiplication
  4. product of negative numbers
  5. equation, inequality
  6. proportion equation
  7. per cent
  8. mathematical induction
  9. proof by contradiction
  10. converse
  11. contrapositive

Algebra

  1. opposite number, difference
  2. inverse number, division
  3. multiple, product
  4. rational numbers, irrational numbers
  5. factorization of integers
  6. linear equation
  7. square of sum
  8. difference of squares
  9. grouping method for factoring polynomials
  10. factoring a sum or difference of two cubes
  11. zero rule of product
  12. conjugation
  13. even-even-odd rule
  14. completing the square
  15. quadratic formula
  16. quadratic inequality
  17. strange root
  18. inequality with absolute values
  19. absolute value inequalities
  20. long division of polynomials

Geometry

  1. basic geometric figures:
  2. basic geometric properties:
  3. acute angles, convex angles, radian
  4. complementary angles, supplementary angles, explementary angles
  5. angle between two lines, angle of view
  6. projection of point
  7. locus
  8. normal line, angle bisector, angle bisector as locus
  9. measurements (lengths, areas, and volumes) of basic geometric figures
  10. compass and straightedge constructions:
  11. trisection of angle
  12. axiomatic proofs in geometry:

Analytic geometry

  1. analytic geometry
  2. Cartesian coordinates
  3. coordinates of midpoint
  4. slope
  5. tangent line
  6. condition of orthogonality
  7. angle between two lines
  8. conics (ellipse, hyperbola, parabola)
  9. polar coordinates

Vectors and Matrices

  1. sum of vectors (i.e. parallelogram principle), difference of vectors
  2. Euclidean vectors
  3. mutual positions of vectors
  4. scalar product
  5. matrices, addition and multiplication of matrices

Trigonometry

  1. right triangle
  2. regular triangle
  3. isosceles triangle
  4. altitudes
  5. bisectors
  6. ASA, SSS, SAS, SSA (triangle solving)
  7. exact trigonometry tables
  8. sohcahtoa
  9. determining signs of trigonometric functions
  10. addition formulas for sine and cosine
  11. addition formula for tangent
  12. goniometric formulae
  13. trigonometric equation

Functions

  1. definitions and operations of functions
  2. argument
  3. polynomial functions (including linear functions)
  4. rational functions
  5. functions involving radicals
  6. exponential functions
  7. Briggsian logarithms
  8. trigonometric functions
  9. sequences and series

Differential calculus

  1. concept of a limit
  2. limit rules of functions, improper limit
  3. continuous
  4. limit of sine divided by angle at 0
  5. intermediate value theorem
  6. derivative
  7. derivatives of sine and cosine
  8. derivative of inverse function
  9. related rates
  10. minimum and maximum of functions (extrema)
  11. least and greatest value of function
  12. mean value theorem
  13. Rolle's theorem

Integral calculus

  1. Riemann sum
  2. integral
  3. left hand rule
  4. right hand rule
  5. midpoint rule
  6. trapezoid rule
  7. fundamental theorem of calculus
  8. integration techniques

Complex numbers

  1. complex numbers
  2. complex function

Applications (word problems)

  1. graphing of equations and inequalities
  2. counting and basic probability
  3. length, area, volume
  4. distance, rate, speed, velocity
  5. money, simple interest, compound interest



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See Also: index of entries on compass and straightedge constructions


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least and greatest value of function (Theorem) by pahio
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Cross-references: compound interest, distance, complex function, complex numbers, integration techniques, fundamental theorem of calculus, midpoint rule, right hand rule, left hand rule, integral, Riemann sum, Rolle's theorem, theorem, mean, least and greatest value of function, extrema, related rates, derivative of inverse function, derivatives of sine and cosine, derivative, intermediate value theorem, continuous, improper limit, limit rules of functions, limit, series, sequences, trigonometric functions, Briggsian logarithms, exponential functions, rational functions, polynomial functions, argument, functions, operations, definitions, trigonometric equation, goniometric formulae, addition formula for tangent, addition formulas for sine and cosine, determining signs of trigonometric functions, sohcahtoa, exact trigonometry tables, triangle solving, SSA, SAS, SSS, ASA, bisectors, altitudes, isosceles triangle, regular triangle, right triangle, multiplication, addition, matrices, scalar product, mutual positions of vectors, Euclidean vectors, difference of vectors, parallelogram principle, sum of vectors, polar coordinates, parabola, hyperbola, ellipse, conics, condition of orthogonality, tangent line, slope, coordinates of midpoint, Cartesian coordinates, analytic geometry, mid-segment theorem, opposing angles in a cyclic quadrilateral are supplementary, Thales theorem, construct the center of a given circle, Pythagorean theorem, regular polygon and circles, parallelogram theorems, converse of isosceles triangle theorem, isosceles triangle theorem, determining from angles that a triangle is isosceles, angles of an isosceles triangle, geometry, trisection of angle, circle with given center and given radius, construction of tangent, erecting the perpendicular, dropping the perpendicular, perpendicular bisector, compass and straightedge constructions, volumes, areas, lengths, angle bisector as locus, angle bisector, normal line, locus, projection of point, angle of view, angle between two lines, explementary angles, supplementary angles, complementary angles, radian, convex angles, acute angles, tangent of circle, similar triangles, similarity, perpendicularity, parallelism, endpoints, properties, circles, regular polygons, polygons, trapezoids, rectangles, parallelograms, triangles, angles, rays, line segments, planes, lines, points, polynomials, long division, absolute value inequalities, inequality with absolute values, strange root, quadratic inequality, quadratic formula, completing the square, even-even-odd rule, zero rule of product, factoring a sum or difference of two cubes, grouping method for factoring polynomials, difference of squares, square of sum, linear equation, integers, irrational numbers, product, multiple, division, inverse number, difference, opposite number, contrapositive, converse, proof by contradiction, induction, per cent, proportion equation, inequality, equation, product of negative numbers, associativity of multiplication, real numbers, rational numbers, natural numbers, intersection, union
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This is version 84 of high school mathematics, born on 2005-05-15, modified 2008-03-20.
Object id is 7056, canonical name is HighschoolMathematics.
Accessed 15595 times total.

Classification:
AMS MSC00A20 (General :: General and miscellaneous specific topics :: Dictionaries and other general reference works)

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divisibility by 11 by PARASHAR on 2007-12-10 21:41:45
I am just confused with the ways to find divisibility by 11.
1) If sum of alternate digits is same then number is divisible by 11 -> this is sufficient but not necessary
2) If sum of digits is 11, then number is divisible by 11. This does not seem true always. For eg: 605 is divisible by 11 but 434 is not.

Can anyone please prove how to find divisibility by 11?
[ reply | up ]
Units digit by PARASHAR on 2007-03-29 00:30:23
Whats the units digit in the expansion of

(15+sqrt220)^19 + (15+sqrt220)^82
[ reply | up ]

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