MB Pre-Calculus 40S study guide
MB Pre-Calculus 40S · Work through your exam, one topic at a time.
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 study guide has 7 sections and about 2,006 words.
01Transformations of Functions
Transformations describe how a parent graph such as y=f(x) becomes y=a\,f(b(x-h))+k . Every symbol has a predictable geometric effect, and the exam tests whether you can read both directions: from equation to graph, and from graph to equation.
291 words, about 1 min02Radical and Rational Functions
This domain combines two function families that share a concern for restrictions : square-root graphs have limited domains, and rational graphs have excluded values that create asymptotes or holes. For y=ab(x-h)+k , the radicand must be non-negative, so the domain comes from solving b(x-h) 0 .
314 words, about 2 min03Trigonometry
Trigonometry in Pre-Calculus 40S spans the unit circle, radian measure, graphing sinusoidal functions, identities, and solving trigonometric equations. Know the unit circle exactly for multiples of 30^ and 45^ (equivalently /6 and /4 ), including signs by quadrant.
279 words, about 1 min04Exponential and Logarithmic Functions
Exponential and logarithmic functions are inverses, and nearly every question in this domain rests on that relationship plus the laws of logarithms. For f(x)=a b^x with b 0 , b 1 , the graph has a horizontal asymptote y=0 , a y -intercept at a , and shows growth if b 1 or decay if 0<b<1 .
275 words, about 1 min05Permutations, Combinations, and the Binomial Theorem
Counting problems hinge on one decision: does order matter? If yes, use permutations; if no, use combinations.
294 words, about 1 min06Conic Sections
Conic sections - circles, parabolas, ellipses, and hyperbolas - are best handled by converting general-form equations into standard form by completing the square. Standard forms to know.
275 words, about 1 min07Sequences and Series
A sequence is an ordered list; a series is the sum of its terms. This domain covers arithmetic and geometric patterns, notation, and infinite sums.
278 words, about 1 min