Concordia MATH 203 Readiness Checklist

Nablio · 8 minPublished September 11, 2026

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This independent checklist reviews algebra, functions and trigonometry that support the transition into Concordia MATH 203. It is not an official Concordia assessment, an admission test, or a prediction of your midterm.

Try the six questions without notes. Show your working even when the answer seems obvious. A correct result you cannot explain deserves another look. Use your current course outline to decide what else to review.

1. Simplification and the original domain

Limits often require simplifying an expression near an excluded input. The expression’s domain and its nearby behaviour are different questions. Practise stating the restriction before cancelling.

Worked example

$\frac{x^2-9}{x-3}$ simplifies to $x+3$ only when $x\ne3$ . You can investigate values near 3 without claiming the original expression has a value at 3.

Common mistake. Cancelling terms before factoring, or forgetting the excluded input.

Try it yourself

Simplify $\frac{x^2-4x}{x}$ and state its restriction.

Show answer and reasoning

Factor $x(x-4)$ , then cancel $x$ : the result is $x-4$ , with $x\ne0$ . The original denominator still excludes zero.

2. Complete quadratic solutions

A graph’s intercepts and an application’s feasible values often start with an equation. Find every solution first, then decide which ones fit the original context.

Worked example

$x^2-x-6=(x-3)(x+2)$ , so its zeros are 3 and $-2$ . Expanding and substituting provide independent checks.

Common mistake. Keeping just the positive root without a reason from the problem.

Try it yourself

Solve $x^2+2x-8=0$ .

Show answer and reasoning

4 and $-2$ multiply to $-8$ and add to 2. Thus $(x+4)(x-2)=0$ gives $x=-4$ or $x=2$ .

3. Algebraic inputs to a function

Difference quotients use inputs such as $x+h$ . Replace every occurrence of the input, preserve parentheses, then simplify. This skill prepares you for the derivative definition before any derivative rules are needed.

Worked example

For $g(x)=x^2$ , $\begin{aligned}g(2+h)-g(2)&=(2+h)^2-4\\&=4h+h^2\end{aligned}\text{.}$ Dividing by $h$ gives $4+h$ for $h\ne0$ .

Common mistake. Writing $(a+1)^2=a^2+1$ ; the middle term $2a$ is essential.

Try it yourself

If $f(x)=x^2-3x$ , find $f(a+1)$ .

Show answer and reasoning

$\begin{aligned}(a+1)^2-3(a+1)\;&=a^2+2a+1-3a-3\\&=a^2-a-2\end{aligned}\text{.}$

4. Radians and familiar angles

Review the unit circle, quadrant signs and exact trigonometric values. Radians are especially important for the standard calculus formulas involving sine and cosine.

Worked example

A half-turn is $\pi$ radians and a full turn is $2\pi$ . To convert degrees to radians, multiply by $\frac{\pi}{180}$ .

Common mistake. Using a calculator in degree mode when the input is in radians.

Try it yourself

Convert $150^\circ$ to radians and find its sine.

Show answer and reasoning

$\frac{150\pi}{180}=\frac{5\pi}{6}\text{.}$ The angle is in quadrant II with reference angle $\frac{\pi}{6}$ , so $\sin\!\left(\frac{5\pi}{6}\right)=\frac{1}{2}$ .

5. Logarithms as inverse operations

Exponential and logarithmic functions appear throughout calculus. First make the exponential the subject of an equation, then apply its inverse. Keep exact values when possible.

Worked example

$e^{2x}=5$ gives $2x=\ln 5$ and $x=\frac{\ln 5}{2}$ . A logarithm is an inverse function, not division by its base.

Common mistake. Splitting $\ln(a+b)$ into $\ln a+\ln b$ ; there is no logarithm sum rule.

Try it yourself

Solve $3e^x=12$ .

Show answer and reasoning

Divide by 3 to obtain $e^x=4$ . Apply $\ln$ to both sides: $x=\ln 4$ .

6. Average rate versus average output

A rate measures change in output per unit change in input. A derivative refines this idea locally, so interpret the quotient as well as calculating it.

Worked example

For position, an average rate has distance/time units. It does not state the velocity at every instant in the interval.

Common mistake. Using $\frac{p(5)+p(2)}{2}$ , which averages outputs rather than measuring their rate of change.

Try it yourself

For $p(t)=t^2+1$ , find the average rate from $t=2$ to $t=5$ .

Show answer and reasoning

$\begin{aligned}\frac{p(5)-p(2)}{5-2}&=\frac{26-5}{3}\\&=7\end{aligned}\text{.}$ We compare output differences, not the average of 26 and 5.

Your next revision session

Mark a topic comfortable only if you can explain every step without a hint.
Choose two uncertain topics. Study one worked example, solve three new variations, and retry a day later without notes.
For MATH 203 exam preparation, add derivative-rule selection, curve interpretation and application setup according to your section’s current outline. This checklist alone is not a complete course review.

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Concordia MATH 203 Readiness Checklist

1. Simplification and the original domain

Worked example

Try it yourself

2. Complete quadratic solutions

Worked example

Try it yourself

3. Algebraic inputs to a function

Worked example

Try it yourself

4. Radians and familiar angles

Worked example

Try it yourself

5. Logarithms as inverse operations

Worked example

Try it yourself

6. Average rate versus average output

Worked example

Try it yourself

Your next revision session

Connect these skills to your course

Work on the step you’re missing.

Free resources to work through

Cancelling Factors: Why the Missing Input Stays Missing

Before Calculus: 10 Algebra Skills You Should Know