MB Pre-Calculus 40S case studies
MB Pre-Calculus 40S · Put your knowledge to work in context.
Pre-Calculus 40S is the senior pre-calculus course in Manitoba's Grade 12 mathematics pathway, and the associated provincial exam is the assessment that many students write at the end of it. It is intended for students who plan to enter university programs in science, engineering, commerce, or mathematics, where a calculus-ready background is expected. The MB Pre-Calculus 40S case studies are 6 cases and about 3,208 words.
1Stretching a Parabolic Arch to Fit a Bridge Deck
A landscape architect models a decorative concrete arch with the base function y = x^2. The arch must span a walkway 12 m wide and rise exactly 4 m at its centre.
669 words, about 3 min2Mixing a Brine Tank: Rational Function With a Hole
A chemistry class models the concentration C(t), in grams per litre, of salt in a 200 L tank as brine is added and drained. Their model is C(t) = (5t + 20)/(t^2 - 16) for t ≥ 0, where t is minutes after the experiment begins.
587 words, about 3 min3Two Triangles From One Sine Value: The Ambiguous Case in a Survey
A surveyor measures a triangular plot ABC. Side a (opposite angle A) is 7.0 m, side b (opposite angle B) is 9.5 m, and angle A is 38°.
489 words, about 2 min4Doubling Time and Half-Life in a Cooling and Growth Model
A biology lab tracks two populations in separate containers. Population P grows according to P(t) = 250 · 2^(t/6), where t is in hours.
442 words, about 2 min5Committee and Seating Counts With Restrictions
A student council has 9 members: 5 seniors and 4 juniors. They must form a 4-person fundraising committee and, separately, arrange all 9 members in a row for a photograph.
458 words, about 2 min6Classifying a Conic From Its General Equation
An engineering student is given the equation 4x^2 - 9y^2 + 16x + 54y - 101 = 0 and told it models the cross-section of a cooling tower's support. She must identify the conic, find its centre and key features, and decide whether a circular reinforcing ring of radius 5 centred at the conic's centre would intersect the curve.
563 words, about 3 min