UW MATH 112 Business Calculus: Study Guide and Practice
A study guide for University of Washington MATH 112 (Application of Calculus to Business and Economics): derivatives, optimization and integrals.
University of Washington Updated 3 min read
At a glance
- Course code
- MATH 112
- Credits
- 5 (one quarter)
- Offered
- Winter and spring
- Prerequisites
- Minimum grade of 2.0 in MATH 111 or MATH 120, or a score of 2 on the AP Calculus AB exam
- Covers
- Rates of change, tangents, the derivative, accumulation, area and integrals in economic contexts, differentiation and integration techniques, optimization
- Restrictions
- Does not count toward a mathematics major; overlaps with MATH 124
- Practice here
- Calculus 1
On this page
UW MATH 112, Application of Calculus to Business and Economics, is the University of Washington's one-quarter calculus course for business and economics. It carries 5 credits and covers both derivatives and integrals in economic settings. This guide maps every MATH 112 topic to practice with instant feedback.
What UW MATH 112 covers
The UW course catalog lists rates of change, tangents, the derivative, accumulation, area and integrals, all in specific contexts, particularly economics. It also covers techniques of differentiation and integration, their application to problem solving, and optimization. MATH 112 does not count toward a mathematics major, and it overlaps with MATH 124.
Compared with a standard Calculus 1 course, MATH 112 keeps the two central ideas, the derivative as a rate and the integral as accumulation, and applies them to cost, revenue and profit. It covers both in a single quarter, while the main sequence spreads them across MATH 124 and MATH 125.
MATH 112 topic map
| MATH 112 topic | Practice | Read |
|---|---|---|
| Rates of change | Average rate of change | Linear functions |
| Tangent lines | Tangent lines | Linear approximation |
| The derivative | Notation and meaning | Limit definition of the derivative |
| Differentiation techniques | The power rule | Power rule, product and quotient rules |
| Chain rule and exponentials | Chain rule: e and ln | Chain rule, exponential functions |
| Marginal analysis and optimization | Optimization | Optimization problems |
| Increasing, decreasing and concavity | Increasing and decreasing | Curve sketching |
| Accumulation and area | Area with rectangles | Riemann sums |
| Integrals and the FTC | Evaluating definite integrals | Fundamental Theorem of Calculus |
| Integration techniques | The reverse power rule | Antiderivatives, u-substitution |
| Total change from a rate | Net change and displacement | Definite integral properties |
MATH 112 vs MATH 124
| MATH 112 | MATH 124 | |
|---|---|---|
| Title | Application of Calculus to Business and Economics | Calculus with Analytic Geometry I |
| Credits | 5 | 5 |
| Offered | Winter, spring | Autumn, winter, spring, summer |
| Content | Derivatives and integrals in economic contexts | Differential calculus |
If you think you may need more calculus later, read the MATH 124 guide before choosing.
Example problems at the MATH 112 level
1. Average vs instantaneous rate. For revenue R(x) = 100x - x^2, the average rate from x = 10 to x = 20 is \frac{1600 - 900}{10} = 70 dollars per unit, while the marginal revenue at x = 10 is R'(10) = 100 - 20 = 80 dollars per unit.
2. Maximizing revenue. Set R'(x) = 100 - 2x = 0, so x = 50. Since R''(x) = -2 < 0, revenue is largest at 50 units, with R(50) = 2500 dollars.
3. Accumulated cost. If marginal cost is C'(x) = 4 + 0.2x dollars per unit, the added cost of increasing production from 10 to 20 units is
How to do well in UW MATH 112
- Read every derivative as a rate. Marginal cost, marginal revenue and marginal profit are derivatives. Write their units to keep the meaning straight.
- Treat integrals as totals. Integrating a marginal function gives total change. The net change lesson shows the idea.
- Check every optimum. Use the second derivative or endpoints, as in the critical points lesson.
- Use the formula sheet and timed practice exams, and review common calculus mistakes before exams.
Tip: the quarter is short and covers both derivatives and integrals, so do a few problems every day rather than catching up on weekends.
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Average rate of change
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