Student resource
Calculus readiness skills
Calculus becomes much easier when the algebra underneath it is automatic. Use this guide to find the exact skill you want to strengthen, learn it with a free explanation, and practice it before it slows you down in class.
How to use this page
- Notice. Identify the step where you get stuck or make an error.
- Practice. Open the linked Khan Academy unit and begin with its explanation, then complete a few practice problems.
- Return. Try a similar calculus problem the next day without notes to see if the skill now holds.
Find a skill to strengthen
Each Khan Academy link includes free instruction and interactive practice. This resource guide is not graded and does not collect student data.
| Skill | A common roadblock | Free explanation & practice |
|---|---|---|
| Algebra foundations | ||
| Signed numbers & order of operations | Applying operations left-to-right or losing a negative sign. | Khan Academy: Algebra foundations |
| Expressions, distribution & like terms | Combining unlike terms or distributing incorrectly across a product or power. | Khan Academy: Algebraic expressions |
| Solving linear equations | “Moving” a term without tracking the operation, or doing different operations to each side. | Khan Academy: Basic equations & inequalities |
| Inequalities & interval notation | Forgetting to reverse an inequality after multiplying or dividing by a negative; omitting an endpoint. | Khan Academy: Basic equations & inequalities |
| Exponent laws | Adding exponents when powers should multiply, or distributing a power over a sum. | Khan Academy: Expressions with exponents |
| Radicals & rational exponents | Confusing a reciprocal with a root, or using a negative exponent when none is needed. | Khan Academy: Radical equations & functions |
| Factoring polynomials | Missing the greatest common factor, making sign errors, or expecting every expression to factor. | Khan Academy: Factoring polynomials |
| Quadratics, roots & the zero-product property | Setting factors equal to zero before one side of the equation is zero, or dropping a solution. | Khan Academy: Quadratic equations & functions |
| Rational expressions | Canceling terms instead of factors, adding denominators directly, or losing excluded values. | Khan Academy: Simplifying rational expressions |
| Radical equations & extraneous solutions | Squaring both sides and not checking whether the answer works in the original equation. | Khan Academy: Radical equations & functions |
| Functions & precalculus | ||
| Function notation & evaluation | Reading f(x) as multiplication, or substituting an expression without parentheses. | Khan Academy: Functions |
| Domain, range & restrictions | Allowing a zero denominator, or overlooking restrictions from even roots and logarithms. | Khan Academy: Functions |
| Function transformations | Reversing the direction of a horizontal shift or missing a reflection or stretch. | Khan Academy: Functions |
| Polynomial & rational graphs | Confusing zeros with vertical asymptotes, or mistaking a hole for an intercept. | Khan Academy: Rational expressions, equations & functions |
| Composition & inverse functions | Reversing composition order, treating a reciprocal as an inverse, or skipping domain restrictions. | Khan Academy: Composite & inverse functions |
| Trigonometry | ||
| Degrees, radians & the unit circle | Using degree-mode values in a radian-based calculus problem, or mixing up signs by quadrant. | Khan Academy: Unit circle |
| Right-triangle trig ratios | Choosing the wrong ratio, confusing sin−1 with 1/sin, or using the wrong calculator mode. | Khan Academy: Right triangles & trigonometry |
| Special angles & exact trig values | Using a decimal when an exact value is needed, or mixing up values for π/6, π/4, and π/3. | Khan Academy: Trigonometry |
| Trig identities | Treating sin(a + b) as sin a + sin b, or misusing the Pythagorean identity. | Khan Academy: Trigonometric functions |
| Graphs of sine & cosine | Confusing amplitude with period, shifting in the wrong direction, or graphing in degrees. | Khan Academy: Trigonometric functions |
| Exponentials & logarithms | ||
| Exponential growth, decay & graphs | Treating exponential change as a constant additive change, or mishandling negative exponents. | Khan Academy: Exponential & logarithmic functions |
| e, natural log & inverse relationships | Treating ln(x) as x·ln, or allowing ln(0) or ln(negative). | Khan Academy: Exponential & logarithmic functions |
| Log laws & change of base | Using log(a + b) = log a + log b, or moving a coefficient incorrectly. | Khan Academy: Log practice |
| Solving exponential & logarithmic equations | Applying logs to a sum incorrectly or failing to check a log-domain restriction. | Khan Academy: Exponential & logarithmic practice |
What comes next
A future short self-check will help you identify the most useful starting points from this list. Until then, start with the skill that shows up most often in your homework, quizzes, or feedback—small, focused practice is more useful than trying to review all of precalculus at once.
This guide was informed by Thomas L. Scofield’s Top Algebra Errors Made by Calculus Students and adapted for practical self-directed review.