GRE Math Subject Preparation Seminar
ORGANIZER: SCOT ADAMS
(notes on practice test 1)
Problem 1:
- Topic tested: arc length of parametric curve
- calc(50%), alg(25%) or other(25%): CALC
- Accessible after 2nd year calc.
- NOTE: Could even be done with precalc, by a student who knows that
(cos t, sin t), 0≤t≤π, parametrizes a semicircle of radius 1.
- Arc length of parametric curves: Stewart 7E, Section 10.4
- Arc length of parametric curves video: click here
Problem 2:
- Topic tested: equation of tangent line
- calc(50%), alg(25%) or other(25%): CALC
- Accessible after 1st year calc
- Equation of tangent line: click here
- Equation of tangent line video: click here
Problem 3:
- Topic tested: possible intersection dimensions for subspaces
- calc(50%), alg(25%) or other(25%): ALG
- Postcalc
- Possible intersection dimensions for subspaces: couldn't find a good reference
- Possible intersection dimensions for subspaces video: couldn't find a good video
Problem 4:
- Topic tested: first derivative and monotonicity
- calc(50%), alg(25%) or other(25%): CALC
- Accessible after 1st year calc
- first derivative and monotonicity: click here
- first derivative and monotonicity video: click here
Problem 5:
- Topic tested: information from a graph
- calc(50%), alg(25%) or other(25%): CALC
- Accessible after 1st year calc
- NOTE: The alternate solution shows that this problem can be solved by precalculus techniques.
- couldn't find a good reference
- couldn't find a good video
Problem 6:
- Topic tested: graphing conic sections
- calc(50%), alg(25%) or other(25%): CALC
- Precalc
- graphing conic sections: click here
- graphing conic sections videos:
Problem 7:
- Topic tested: integrate piecewise polynomial
- calc(50%), alg(25%) or other(25%): CALC
- Accessible after 1st year calc
- integrate piecewise polynomial: click here
- integrate piecewise polynomial video: click here
Problem 8:
- Topic tested: optimization
- calc(50%), alg(25%) or other(25%): CALC
- Accessible after 1st year calc
- optimization: click here
- optimization video: click here
Problem 9:
- Topic tested: integration preserves inequalities
- calc(50%), alg(25%) or other(25%): CALC
- Accessible after 1st year calc
- integration preserves inequalities: point to click here, and then scroll down to "Inequalities"
- integration preserves inequalities video: couldn't find a good video
Problem 10:
- Topic tested: increasing/decreasing tests
- calc(50%), alg(25%) or other(25%): CALC
- Accessible after 1st year calc
- increasing/decreasing tests: click here
or click here
- increasing/decreasing tests video: couldn't find a good video
Problem 11:
- Topic tested: basic estimation
- calc(50%), alg(25%) or other(25%): CALC
- Precalc
- basic estimation: couldn't find a good reference
- basic estimation video: couldn't find a good video
Problem 12:
- Topic tested: eigenvectors and eigenvalues
- calc(50%), alg(25%) or other(25%): ALG
- Postcalc
- eigenvectors and eigenvalues: click here
- eigenvectors and eigenvalues video: click here
Problem 13:
- Topic tested: optimization
- calc(50%), alg(25%) or other(25%): CALC
- Accessible after 1st year calc
- optimization: click here
- optimization video: click here
Problem 14:
- Topic tested: mod 10 congruences
- calc(50%), alg(25%) or other(25%): ALG
- Precalc
- mod 10 congruences: click here
- mod 10 congruences video: click here
Problem 15:
- Topic tested: rigorous calculus
- calc(50%), alg(25%) or other(25%): OTHER
- Postcalc
- rigorous calculus: no suitable reference
- rigorous calculus video: no suitable video
Problem 16:
- Topic tested: volumes of solids of revolution
- calc(50%), alg(25%) or other(25%): CALC
- Accessible after 1st year calc
- volumes of solids of revolution: click here
- volumes of solids of revolution video (disk method only):
click here
Problem 17:
- Topic tested: counting real roots
- calc(50%), alg(25%) or other(25%): CALC
- Accessible after 1st year calc
- couldn't find a good reference
- couldn't find a good video
Problem 18:
- Topic tested: rank-nullity theorem
- calc(50%), alg(25%) or other(25%): ALG
- Postcalc
- rank-nullity theorem: click here
- rank-nullity theorem video: couldn't find a good video
Problem 19:
- Topic tested: integrating and differentiating inequalities
- calc(50%), alg(25%) or other(25%): CALC
- Accessible after 1st year calc
- integrating and differentiating inequalities: §11.2 of click here
- couldn't find a good video
Problem 20:
- Topic tested: density of the rationals and irrationals
- calc(50%), alg(25%) or other(25%): OTHER
- Postcalc
- density of the rationals and irrationals:
click here
- density of the rationals and irrationals video: couldn't find a good video
Problem 21:
- Topic tested: prime factorization
- calc(50%), alg(25%) or other(25%): OTHER
- Precalc
- prime factorization: click here
- prime factorization video: click here
Problem 22:
- Topic tested: vector subspace (a.k.a. linear subspace)
- calc(50%), alg(25%) or other(25%): ALG
- Postcalc
- vector subspace: click here
- vector subspace video: couldn't find a good video
Problem 23:
- Topic tested: tangent line
- calc(50%), alg(25%) or other(25%): CALC
- Accessible after 1st year calc
- tangent line: click here
- tangent line video: click here
Problem 24:
- Topic tested: integration and differentiation techniques
- calc(50%), alg(25%) or other(25%): CALC
- Accessible after 1st year calc
- integration and differentation techniques: click here
- integration and differentiation techniques video: click here
Problem 25:
- Topic tested: recursion
- calc(50%), alg(25%) or other(25%): OTHER
- Precalc
- recursion: couldn't find a good reference
- recursion video: couldn't find a good video
Problem 26:
- Topic tested: multivariable max/min
- calc(50%), alg(25%) or other(25%): CALC
- Accessible after 2nd year calc
- multivariable max/min: click here
- multivariable max/min video: couldn't find a good video
Problem 27:
- Topic tested: intersecting subspaces
- calc(50%), alg(25%) or other(25%): ALG
- Postcalc
- intersecting subspaces: click here
- intersecting subspaces video: couldn't find a good video
Problem 28:
- Topic tested: spanning trees
- calc(50%), alg(25%) or other(25%): OTHER
- Precalc
Postcalc
- spanning trees: click here
- spanning trees video: couldn't find a good video
Problem 29:
- Topic tested: asymptotics
- calc(50%), alg(25%) or other(25%): CALC
- Accessible after 1st year calc
- asymptotics: couldn't find a good reference
- asymptotics video: couldn't find a good video
Problem 30:
- Topic tested: properties of functions
- calc(50%), alg(25%) or other(25%): OTHER
- Precalc
- properties of functions: click here
- properties of functions video: click here
Problem 31:
- Topic tested: ODEs (via line fields a.k.a.~slope fields)
- calc(50%), alg(25%) or other(25%): CALC
- Postcalc
- ODEs (via line fields a.k.a.~slope fields): click here
- ODEs (via line fields a.k.a.~slope fields) video: click here
Problem 32:
- Topic tested: algebraic operations
- calc(50%), alg(25%) or other(25%): ALG
- Postcalc
- algebraic operations: couldn't find a good reference
- algebraic operations video: couldn't find a good video
Problem 33:
- Topic tested: Euclidean algorithm
- calc(50%), alg(25%) or other(25%): OTHER
- Precalc
- Euclidean algorithm: click here
- Euclidean algorithm video: click here
Problem 34:
- Topic tested: symmetry and minimizing distance
- calc(50%), alg(25%) or other(25%): OTHER
- Precalc
- symmetry and minimizing distance: couldn't find a good reference
- symmetry and minimizing distance video: couldn't find a good video
Problem 42:
- Topic tested: discrete random variables
- calc(50%), alg(25%) or other(25%): OTHER
- Postcalc
- discrete random variables: click here
- discrete random variables video: couldn't find a good video
Problem 46:
- Topic tested: endomorphisms of cylic groups
- calc(50%), alg(25%) or other(25%): ALG
- Postcalc
- endomorphisms of cylic groups: click here
- endomorphisms of cylic groups video: couldn't find a good video
Problem 49:
- Topic tested: structure of finite Abelian groups
- calc(50%), alg(25%) or other(25%): ALG
- Postcalc
- structure of finite Abelian groups: click here
- structure of finite Abelian groups video: couldn't find a good video
Problem 59:
- Topic tested: Cauchy-Riemann equations
- calc(50%), alg(25%) or other(25%): other
- Postcalc
- Cauchy-Riemann equations: click here
- Cauchy-Riemann equations video: click here,
and watch, esp., the application starting at 07:20.