Algebraic Expressions
Factoring & Inequalities
Evaluating Exponents
Logarithmic Properties
Solving eqns w/ Logs & Exponents
100
Combine the following two fractions over a common denominator: (a/b) - (1/a).
What is (a^2 - b) / (ab) ?
100
Find all solutions to: 2*x^2 - 3*x = 2.
What is x = -0.5 or 2 ?
100
Simplify the following: [ ((x^-5)(y^(2/5))) / ((x^3)(y)) ] ^2
What is (x^-16)(y^(-6/5)) ?
100
Evaluate: log5 (1/25).
What is -2 ?
100
Solve the following equation for x: e^(-4x) = 1.
What is 0 ?
200
Simplify the following: (1/a) / (a/2 - a/3).
What is 6 / (a^2) ?
200
Find all values of x that satisfy the inequality: 5*x + 3 > -2.
What is x > -1 ?
200
Evaluate: 4^(5/2).
What is 32 ?
200
Solve for x: log2 (x/8) = -6.
What is 1/8 ?
200
Solve the following equation for x: 2^(3*x) = 10.
What is: (ln 10) / (3*ln 2) (ln 10) / (ln 8) (log 10) / (3*log 2) log8 (10) log2 (10) / 3 ?
300
Suppose that: f(x) = x^2, x is negative f(x) = x^3, x is non-negative Evaluate f(-2) + f(0) + f(2).
What is 12 ?
300
Find all solutions to: 6*x^2 - x - 1 = 0.
What is x = 1/2 or -1/3 ?
300
Express the following as "3" to a single power: (3^(2x))(9^y) / (3^-1).
What is 3^(2*x + 2*y + 1) ?
300
Solve for x: logx (32) = 5.
What is 2 ?
300
Solve the following equation for x: ln(x + 4) = 3.
What is e^3 - 4 ?
400
Write the equation of the straight line that passes through the point (0,2) and is parallel to the line y = 3x.
What is y = 3x + 2 ?
400
Find all values of x that satisfy the inequality: x(x - 2) > 0.
What is x > 2 OR x < 0 ?
400
The number of bricks it took to finish Chase Hall.
What is 1 ?
400
Expand the following as a sum, difference, or multiple of logarithms. log [ (x^5)(y - 1) / (z^3) ].
What is 5*log x + log (y - 1) - 3*log z ?
400
Simplify: e^(-6*ln x) / (x^6).
What is x^(-12) ?
500
Expand the following: (y^2 + 2*y ^ -2) ^ 2.
What is y^4 + 4 + 4*y ^ -4 ?
500
Find all values of x that satisfy: | 2*x - 5 | < 7.
What is -1 < x < 6 ?
500
Express the following as "2" to a single power: [ (4^x)(2^y) / (2^2)(4^z) ].
What is 2^(2*x + y - 2*z - 2) ?
500
Write the following as the log of a single expression: 5*log(x^3) + log(x + 1) - 3*log(x - 1).
What is log[ (x^15)(x + 1) / ((x-1)^3) ] ?
500
Simplify: e^(x*ln 2) - 2^x.
What is 0 ?
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