1. Learning from past mistakes – mat 271
Amanda Whitt
Asheville-Buncombe Technical Community College

2. Struggles ALGEBRA SKILLS! 𝑥+2 𝑥+1 =2
Application Problems (word problems)
Understanding and applying definitions.
Struggle to memorize “shortcuts”
Confidence

3. Why Make or Use the Project?
Review exams, labs, and graded assignments that have feedback.
Helps students realize they need to continuously review material!

4. Project Overview Project 1 Project 2 Topics: Limits Derivatives
Take previously asked questions (or similar questions). Answer every question with the most common, incorrect answer given by the students.
Project 1
Project 2
Topics:
Limits
Derivatives
Product Rule, Quotient Rule, Chain Rule
Logarithmic Differentiation
Implicit Differentiation
Related Rates
Topics:
Analyzing graph of functions
Increasing, decreasing, concavity, minimums, maximums, etc…
l’Hospital’s Rule
Rolle's Theorem, Mean Value Theorem
Optimization
Riemann Sums
Definite, Indefinite Integrals
Fundamental Theorem of Calculus
Integration by substitution

5. The Project
True or False: If lim 𝑥→6 [𝑓 𝑥 𝑔 𝑥 ] exists, then the limit must be 𝑓 6 𝑔 6 .
True. Since we know the limit exists, then we use direct substitution to evaluate the limit.
Use the definition of the derivative to find 𝑓′(4), where 𝑓 𝑥 = 𝑥 2 −3𝑥+4.
𝑓 ′ 𝑥 =2𝑥−3
𝑓 ′ 4 =2 4 −3= 5

6. Problem 1
True or False:
𝑓 𝑥 = 𝑥 2 −3𝑥+40 𝑥−8 and 𝑔 𝑥 =𝑥+5 are equivalent functions.
Explain your answer.
Forget about domain
Get lost in notation
lim 𝑥→8 𝑥 2 −3𝑥+40 𝑥−8 = lim 𝑥→8 𝑥+5

7. Problem 2 True or False: If 𝑦= 𝑒 2 , then 𝑦 ′ =2𝑒.
Explain your answer.
Students don’t think about the problem, just go through the motions.
Still not sure about the number 𝑒

8. Problem 3 True or False: If 𝑓 𝑥 = 𝑥 6 − 𝑥 4 5 , then 𝑓 (31) =0.
Explain your answer.
Lack of algebra skills
Lost in notation

9. Problem 4 Find 𝑓′ in terms of 𝑔′. 𝑓 𝑥 = 𝑥 2 𝑔 𝑥
Not sure about what is being asked
Not comfortable with derivative rules

10. Problem 5
Find the local and absolute extreme values of the function on the given interval.
𝑓 𝑥 = 𝑥 3 −6 𝑥 2 +9𝑥+2, [2,4]
Understand interval notation
Forget to check the endpoints for extreme values

11. Problem 6 Differentiate with respect to x. ℎ 𝑥 = sin x x
Students rely on Power Rule too much!
Applying definitions.

12. Problem 7
Find the general indefinite integral. (Use C for the constant of integration.)
3 𝑥 2 +𝑥+ 4 𝑥 𝑑𝑥
Forget about the constant “c”
Do not recognize trigonometric integrals

13. Results Realize common mistakes and how to correct them
Learn from past mistakes
Build confidence
Review material
Helps the instructor enforce critical thinking questions for the students

14. Contact Me!