Korean CSAT Mathematics case studies
Korean CSAT Mathematics · Put your knowledge to work in context.
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 case studies are 4 cases and about 675 words.
1A quadratic production model
A student models the height of a small display panel by h(x)=−x²+6x+1 for a horizontal coordinate x measured in meters. The model is intended only for 0≤x≤4. A classmate finds a stationary point but does not compare it with the endpoints, while another assumes that the constant term must be the maximum height. The teacher asks for a complete mathematical explanation using the stated interval rather than a sketch alone.
176 words, under 1 min2A savings sequence with explicit assumptions
For a school mathematics exercise, a student deposits 10 units at the end of the first week and increases the weekly deposit by 3 units each week. The exercise runs for eight weeks and assumes no interest, fees or missed deposits. A worksheet has separate boxes for the eighth deposit and the total deposited over all eight weeks. One student writes the same answer in both boxes because both questions mention eight weeks.
164 words, under 1 min3Sampling colored counters without replacement
A classroom bag contains five red counters and three blue counters, all identical except for color. Two counters will be drawn randomly without replacement. Before the experiment, students must calculate the probability that both counters are red and compare it with the result for an otherwise identical experiment with replacement. The bag is thoroughly mixed before the first draw, and every counter is equally likely to be selected at each permitted draw.
178 words, under 1 min4A coordinate model and a tangent
A graphing exercise uses the parabola y=x² and asks for its tangent at the point where x=2. Students have access to the derivative rule for powers, but the teacher requires both the slope and a complete line equation. A classmate writes y=4x because the derivative at the point is four, while another chooses a line through the origin because the parabola passes through the origin elsewhere. The axes use the same numerical coordinate scale.
157 words, under 1 min