Worked examples
Every question, solved in full.
Free worked GRE and GMAT questions: the correct answer, the reasoning that gets there, and why each other option is wrong. No account needed to read them.
Worked questions by exam
GRE Physics Subject Test
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Net Force and Acceleration
A public mechanics question that shows how to combine opposing horizontal forces before applying Newton's second law.
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Energy Conservation on a Frictionless Track
A public energy-conservation question showing why mass cancels when gravitational potential energy converts into speed on a frictionless track.
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Perfectly Inelastic Collision
A public momentum question showing how to find the shared final speed after two carts couple in a perfectly inelastic collision.
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Mass-Spring Oscillation Period
A public oscillation question showing how mass and spring constant set the period of simple harmonic motion independent of amplitude.
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Gauss's Law and Sphere Radius
A public Gauss's law question contrasting how the enclosed-charge flux and the surface electric field respond when a Gaussian sphere is enlarged.
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Series-Parallel Branch Current
A public DC-circuit question showing how to reduce a series-parallel network before tracing the current through a single branch.
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Infinite Square Well Transitions
A public quantum question showing how infinite-square-well energies scale with the square of the quantum number and set photon transition energies.
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Photoelectric Effect
A public photoelectric-effect question showing how a photon's energy splits between the work function and the electron's maximum kinetic energy.
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Carnot Engine Work Output
A public heat-engine question showing how absolute reservoir temperatures set a Carnot engine's efficiency and per-cycle work output.
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Time Dilation
A public special-relativity question showing how to identify the proper time and apply the Lorentz factor to a moving clock.
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Double-Slit Bright Fringes
A public interference question showing how wavelength, slit separation, and screen distance set the position of a double-slit bright fringe.
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GRE General Test
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Part-to-Whole Ratios
A public ratio question that shows how to convert a part-to-part ratio into a part-to-whole share before scaling to a real quantity.
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Exponent Rules
A public exponents question that combines the power-of-a-product rule with the quotient rule to simplify an algebraic fraction.
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Addition Rule of Probability
A public probability question that shows why the probability of an overlap must be subtracted when combining two non-mutually-exclusive events.
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Combinations
A public counting question that shows when to use a combination rather than a permutation for an unordered selection.
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Median of a Data Set
A public descriptive-statistics question that shows how to find the median of an even-sized data set and how it differs from the mean.
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Z-Scores on a Normal Distribution
A public statistics question that shows how to standardize a raw score into a z-score using the mean and standard deviation.
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GRE Mathematics Subject Test
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Limits of Rational Functions
A public limits question that resolves a $0/0$ indeterminate form by factoring and canceling a common factor before substituting.
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Geometric Series Convergence
A public series question that checks the common-ratio convergence condition and applies the closed-form sum of an infinite geometric series.
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GMAT Focus Edition
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Combined Work Rates
A public work-rate question that shows why individual completion times must be converted to rates before combining two workers.
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Dilution Mixtures
A public mixture question that shows how to track the unchanged amount of solute with a proportion when a solution is diluted.
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