MATH 90

In Grade 10, sine and cosine were ratios of sides in a right triangle — useful, but trapped between 0° and 90°, because a right triangle cannot hold an angle any larger. This year those same words are given a bigger definition, built on a circle instead of a triangle, and suddenly sine and cosine accept *any* angle: 200°, −45°, ten full turns. That upgrade is what turns them from measurement tricks into genuine functions — and functions can model tides, sound waves, daylight hours, and anything else that repeats. The old right-triangle theorem you have carried since Grade 8, the Pythagorean Theorem, does not retire here; it becomes the engine inside the new machine.

MatchingMultiple choiceFill in the blankMultiple choice (misconception distractors)Problem solving

Watch only the height of a point traveling around the unit circle and you get a wave: rising, cresting, falling, bottoming out, and rising again — forever. Graphed, that wave is y = sin x, and it is the mathematical signature of everything that cycles: tides, heartbeats, alternating current, the hours of daylight across a year. This unit is about reading and writing that signature. By the end you will look at a Ferris wheel or a tide chart and see four numbers — midline, amplitude, period, starting point — waiting to be turned into a formula.

MatchingMultiple choiceFill in the blankMultiple choice (misconception distractors)Problem solving

You met exponential and logarithmic functions in MATH 88. This year they must reach KS-7: recognizing and wielding them in problems that never announce themselves — a car losing value, a bacterial culture doubling, an investment compounding, a medication level fading. The common thread is change by *multiplication* rather than addition, and the logarithm is the tool that answers the question multiplication-based growth always raises: *how long until…?*

Multiple choiceFill in the blankMultiple choice (misconception distractors)Problem solvingTransfer problem

Probability is the arithmetic of uncertainty: it assigns numbers to statements like "it will rain" or "this test result is a false alarm," and then holds those numbers to strict rules. The rules matter because human intuition about chance is famously bad — casinos, lotteries, and misleading headlines are all funded by that badness. This unit gives you the four tools college statistics will assume you own: counting probabilities correctly, multiplying them only when you have earned the right, reversing conditional questions without fooling yourself, and pricing an uncertain future with expected value.

Multiple choiceFill in the blankMultiple choice (misconception distractors)Problem solvingTransfer problem

Statistics asks the question underneath every poll, every medical study, and every 'research shows' headline: what can a limited sample honestly tell us about the whole world, and how sure are we allowed to be? Inference is not a bag of formulas — it is a discipline of reasoning about evidence, and it runs on three ideas: samples wobble by pure chance, so an interesting-looking result must first outcompete the boring explanation 'it's just chance'; our confidence should be stated as a range, not a single number; and a pattern in data, however strong, is not yet a cause. Master these and you can read the news like a scientist. This is the reasoning MATH 100 and every college lab course will assume you have.

MatchingMultiple choiceFill in the blankMultiple choice (misconception distractors)Short answer