Bagrut Mathematics (3/4/5 Units) case studies
Bagrut Mathematics (3/4/5 Units) · Put your knowledge to work in context.
The Bagrut in Mathematics is the Israeli matriculation examination in mathematics, taken at one of three study levels: 3, 4, or 5 units (yehidot limud). The level determines how much material you study and how the Bagrut score is weighted in the matriculation certificate and in university admission, with 5 units being the demanding track that opens science, engineering, and advanced mathematics programs. The Bagrut Mathematics (3/4/5 Units) case studies are 5 cases and about 2,984 words.
1Rational Equation with a Parameter and a Hidden Domain Restriction
A tutoring group is analyzing the rational equation (x^2 − (a + 2)x + 2a)/(x − 1) = 0, where a is a real parameter. A student substituted a = 4, canceled the denominator immediately, and reported the solutions x = 1 and x = 2.
705 words, about 4 min2Parabolic Tunnel Cross-Section and Clearance for a Light Strip
A pedestrian tunnel has a cross-section modeled by a parabola. The floor is horizontal, the tunnel is 12 m wide at floor level, and the highest point is 8 m above the floor at the center.
602 words, about 3 min3Two Exponential Bacteria Models and a Misleading Linear Approximation
A laboratory starts with 500 bacteria in a controlled culture. After 3 hours the count is 2000, and the growth is modeled as exponential, N(t) = 500·4^(t/3), where t is in hours.
486 words, about 2 min4Ambiguous Triangle from Survey Data and a Fencing Budget
A land surveyor measures triangle ABC and records AB = 8 m, BC = 6 m, and angle BAC = 30°. The surveyor needs the length AC to order fencing.
616 words, about 3 min5Screening Test: One Positive, Two Positives, and the Base Rate
A clinic uses a screening test for a condition that affects 6% of the population being screened. The test is positive in 92% of people who have the condition and negative in 85% of people who do not.
575 words, about 3 min