Korean CSAT Mathematics study guide
Korean CSAT Mathematics · Work through your exam, one topic at a time.
This independent study page provides practice for Korean CSAT Mathematics. Its editorial learning areas include Functions, algebra and sequences; Limits, derivatives and integration; Coordinate geometry, trigonometry and vectors; Counting, probability and statistical summaries. The questions develop subject knowledge and application through worked reasoning, distinctions between competing answers, and practical scenarios. Study the relevant guide before attempting a mixed set, then explain the evidence or calculation that supports each answer. Topics on this exam: Functions, algebra and sequences, Limits, derivatives and integration, Coordinate geometry, trigonometry and vectors, and Counting, probability and statistical summaries. The Korean CSAT Mathematics study guide has 4 sections and about 783 words.
01Functions, algebra and sequences
Start with the domain before manipulating an expression. A denominator cannot be zero, a real square root requires a nonnegative argument, and a real logarithm requires a positive argument. Squaring or multiplying by an expression can introduce solutions or reverse an inequality, so substitute proposed answers into the original conditions. Composition means applying the inner function first; an inverse reverses an allowed one-to-one input-output relationship.
195 words, under 1 min02Limits, derivatives and integration
A limit describes nearby function values and may exist even when the function is undefined at the point. Factoring can reveal a removable discontinuity, but cancel a factor only away from the excluded input. Continuity requires the function value and the limit to agree. A derivative describes instantaneous rate and tangent slope.
196 words, under 1 min03Coordinate geometry, trigonometry and vectors
Draw the relationships and label the given conditions before selecting a formula. A circle equation identifies both its center and squared radius; changing a sign inside a coordinate shift changes the center. The distance formula follows from the Pythagorean theorem. A line’s slope is rise divided by run, while a vertical line needs separate treatment because the usual slope is undefined.
196 words, under 1 min04Counting, probability and statistical summaries
First identify the sample space and whether order matters. Selecting a committee differs from assigning distinct offices to its members. Sampling without replacement changes the composition for later draws; replacement can restore the same probabilities when draws are independent. For a conditional probability, restrict the denominator to the event already known to have occurred.
196 words, under 1 min