Course drills
Four courses · original retrieval prompts. Attempt on paper before revealing the approach.
Foundational Quiz 2 · Maths I, CT, Python, Stats I
Original drills. No live paper.
Analogous retrieval prompts — attempt on paper first. Pair with pattern atlas or exam-eve sprint.
BSMA1001
Mathematics I
Name the object, the allowed domain, then transform. Check every candidate in the original statement.
Week notes
One-screen recall
- A set is a collection of distinct objects. ∈ is membership; ⊆ is every element of A also in B.
- Union is “in A or B”; intersection is “in both”; complement is “not in A” relative to a stated universe.
- A function assigns each allowed input exactly one output. Domain first, then the rule.
- Algebra is a sequence of permitted rewrites. Squaring, cancelling, and dividing can add or drop solutions.
- Average rate of change is Δy/Δx on an interval. Instantaneous rate is the limiting idea as the interval shrinks.
Common traps
- — Treating “for all” as “I found one example that works”.
- — Cancelling a factor that might be zero without a separate case.
- — Calling a relation a function when one input maps to two outputs.
- — Confusing average slope on [a, b] with the derivative at a point.
Treating “for all” as “I found one example that works”.
Cover the screen. Explain why a rushed student would fall for this, and what check stops it.
Drill 1
Let A = {1, 2, 3} and B = {3, 4}. Write A ∪ B, A ∩ B, and a statement that is false for every x in A. Then give one counterexample that kills a careless “all even numbers in A” claim.
Translate each symbol into a sentence before you write braces.
Drill 2
f(x) = 1/(x − 2). Give one valid input, one invalid input, and say what the domain is in words.
The expression is undefined exactly where a denominator is zero.
Drill 3
Solve (x − 1)(x + 4) = 0, then invent a nearby equation where dividing both sides by (x − 1) would be illegal for some x. Explain the permission you lost.
Zero-product is safe. Division by an expression is not, unless that expression cannot be zero.
Drill 4
A quantity goes from 4 to 10 between t = 1 and t = 3. What is the average rate? What question does that number not answer?
Keep the interval visible in the units.