MATH 102 • Tüm Sınavlar • Calculus
Koç Üniversitesi MATH 102 (Calculus) Midterm I sınavına hazırlık paketi.
İşlenen konular: Limits of Functions, Limits at Infinity and Infinite Limits, Asymptotes, Continuity, Discontinuity, The Derivative, Differentiation Rules, Tangent Line Equations, The Chain Rule, Implicit Differentiation, Marginal Analysis (Economics and Derivative), Elasticity of Demand, First Derivative and Graphs, Second Derivative And Graphs, Curve Sketching Techniques, Absolute Maxima and Minima, Optimization.
Ayda 1899 TL, peşin fiyatına 3 taksit
Eğitmenler
Dorukhan Özcan
Co-Founder & CEO
Unicourse şirketinin kurucu ortağıyım. 2016 senesinde Galatasaray Lisesinden mezun oldum. Geçtiğimiz dört sene içerisinde 2000 saatten fazla ders anlattım. Anlattığım dersler sırasıyla; Calculus, Çok değişkenli Calculus, Lineer Cebir, Differansiyel Denklemler, Uygulamalı İstatistik ve Stokastik Modelleme dersleridir. Doping Hafıza şirketinde 2017 - 2022 seneleri arasında CEO danışmanlığı yaptım. Koç Üniversitesi Endüstri Mühendisliği ve Ekonomi çift anadal programını tam burslu olarak, 3.96/4.00 not ortalamasıyla bitirdim. Kadıköy Modalıyım.
Tolga Temiz
Eğitmen
2016 senesinde başladığım Koç Üniversitesi Matematik bölümünden 2020 senesinde fakülte üçüncüsü olarak mezun oldum. Lisans ve yüksek lisans eğitimlerim boyunca çeşitli derslerde asistanlık yaptım. 2021'de Koç Üniversitesi'nde Matematik yüksek lisansına başladım ve 2023 yılında mezun oldum. Şimdi Michigan State Üniversitesi'nde doktora yapıyorum. Topoloji alanıyla ilgilenmekteyim.
Kerem Başol
Eğitmen
2019 senesinde Koç Üniversitesi Matematik bölümüne başladım. Geçtiğimiz senelerde Calculus ve Linear Algebra derslerinde Tutor ve Teaching Assistant pozisyonlarında görev aldım. Halen Koç Üniversitesi Matematik ve Bilgisayar Mühendisliği çift anadal programını 4.00/4.00 ortalamayla fakülte birincisi olarak sürdürüyorum. Trigonometrik fonksiyonların elips üzerinde nasıl tanımlanabileceğini merak etmemle başlayan Matematik tutkumu aktarmak için Unicourse Matematik Zümresine katıldım.
Konular
Chapter 8.1: Limits of Functions
3 konu anlatımı · 8 soru
Limits of Functions
Limits with Absolute Value
Limits Rules
Exam-like Questions 1
Exam-like Questions 2
Exam-like Questions 3
Exam-like Questions 4
Exam-like Questions 5
Exam like Question 6
Exam-like Questions 7
Exam-like Questions 8
Ch.8.2: Limits at Infinity and Infinite Limits
3 konu anlatımı · 8 soru
Limits at Infinity I
Limits at Infinity II
Infinite Limits
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Exam like Question 6
Exam like Question 7
Exam like Question 8
Ch. 8.2: Asymptotes
1 konu anlatımı · 2 soru
Vertical and Horizontal Asymptotes
Exam like Question 1
Exam like Question 2
Ch.8.3: Continuity
1 konu anlatımı · 6 soru
Continuity
Exam like Question 1
Exam like Question 2
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Ch.8.3: Discontinuity
1 konu anlatımı · 3 soru
Discontinuity and Continuous Extension
Exam like Question 1
Exam like Question 2
Exam like Question 3
Ch.8.4: The Derivative
3 konu anlatımı · 4 soru
Rate of Change: Derivative at a Point
Derivative as a Function
Differentiable or not ?
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Ch.8.5-9.2-9.3: Differentiation Rules
4 konu anlatımı · 12 soru
Power Rule
Derivatives of Exponential and Logarithms
Product Rule
Quotient Rule
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Exam like Question 6
Exam like Question 7
Exam like Question 8
Exam like Question 9
Exam like Question 10
Exam like Question 11
Exam like Question 12
Ch.8.5: Tangent Line Equations
2 konu anlatımı · 7 soru
Equation of a Tangent Line
Horizontal and Vertical Tangent
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Exam like Question 6
Exam like Question 7
Ch.9.4: The Chain Rule
2 konu anlatımı · 6 soru
Chain Rule I
Chain Rule II
Exam like Question 1
Exam-like Question 2
Exam-like Question 3
Exam like Question 4
Exam like Question 5
Exam like Question 6
Ch.9.5: Implicit Differentiation
3 konu anlatımı · 5 soru
Implicit Differentiation I
Implicit Differentiation II
Tangent Line of Implicit Functions
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Ch.8.7: Marginal Analysis (Economics and Derivative)
2 konu anlatımı · 2 soru
Revenue, Cost, Profit and Price Demand Function
Marginal Analysis in Economics
Exam like Question 1
Exam like Question 2
Ch.9.7: Elasticity of Demand
1 konu anlatımı · 1 soru
Elasticity of Demand
Spring 2025 Exam Problem
Ch.10.1: First Derivative and Graphs
1 konu anlatımı · 2 soru
Local Extremas & First Derivative Test
Exam like Question 1
Exam like Question 2
Ch.10.2: Second Derivative And Graphs
1 konu anlatımı · 3 soru
Second Derivative, Concavity and Inflections
Exam like Question 1
Exam like Question 2
Exam like Question 3
Ch.10.4: Curve Sketching Techniques
3 konu anlatımı
Curve Sketching 1
Curve Sketching 2
Curve Sketching 3
Ch.10.5: Absolute Maxima and Minima
1 konu anlatımı · 4 soru
Absolute Extrema on a Closed Interval
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Ch. 10.6: Optimization
3 konu anlatımı
Optimization 1
Optimization 2
Optimization 3
Past Exam Problems (Konus Sırasıyla)
22 soru
Spring 2022 Exam: Limit with Absolute Value
Spring 2024 Exam: Limit with Absolute Value
Fall 2022 Exam: Limit without L'Hopital's Rule
Spring 2024 Exam: Limit without L'Hopital's Rule
Fall 2024 Exam: Limit without L'Hopital's Rule
Fall 2023 Exam: Limit (Infinity, Absolute Value)
Spring 2022 Exam: Limits at Infinity
Spring 2024 Exam: Limit at Infinity
Spring 2022 Exam: Infinite Limits
Fall 2024 Exam: Limits at Infinity
Fall 2022 Exam: Infinite Limits
Fall 2022 Exam: Continuity
Fall 2021 Exam: Continuity
Spring 2024 Exam: Continuity
Fall 2022 Exam: Asymptotes
Spring 2022 Exam: Discontinuity & Asymptotes
Fall 2023 Exam: Discontinuity and Asymptotes
Spring 2024 Exam: Differentiation Rules
Spring 2024 Exam: Differentiation Rules
Fall 2024 Exam: Differentiation Rules
Spring 2024 Exam: Limit Definition of Derivative
Fall 2024 Exam: Limit Definition of Derivative
Past Exam Problems (Konus Sırasıyla)
21 soru
Absolute Maximum and Minimum
Absolute Maximum and Minimum
Absolute Maximum and Minimum
First Derivative, Local Extremas
Relative (Local) Extremas
Relative and Absolute Extremas
Second Derivative and Concavity
Second Derivative and Concavity
Curve Sketching Techniques
Curve Sketching Techniques
Curve Sketching Techniques
Curve Sketching Techniques
Curve Sketching Techniques
Optimization Problem
Optimization Problems
Optimization Problems
Optimization Problems
Optimization Problems
Optimization: Economics Applications
Optimization: Economics Applications
Bonus: Absolute Maxima - Economics Applications
Sınav Provası: Spring 2025 Exam
4 soru
Limits without L'Hopital's Rule (Infinity, Absolute Value)
Asymptotes (Vertical, Horizontal)
Equation of a Tangent Line & Differentiation Rules
Derivative & Economics (Marginal Cost, Revenue)
Sınav Provası: Fall 2025 Exam
8 soru
Limit Rules
Continuity
Differentiation Rules
Elasticity of Demand
Implicit Differentiation
Tangent Line of Implicit Function
Differentiable or not
8
Bonus Part: Her şeyi çözdüm, ek soru yok mu?
20 soru
Limit of Functions
Limit (Mixed) Problems
Limit (Mixed) Problems
Limits at Infinity and Infinite Limits
Asymptotes
Asymptotes
Continuity and Discontinuity
Continuity and Discontinuity
Continuity and Discontinuity
Differentiation Rules
Differentiation Rules
Equation of a Tangent Line
Equation of Tangent Line
Equation of a Tangent Line
Chain Rule
Chain Rule
Chain Rule & Tangent Line
Implicit Differentiation
Implicit Differentiation & Tangent Line
Implicit Differentiation
Ch 10.3: L’Hôpital’s Rule
1 konu anlatımı
L'Hopital's Rule: (0/0) and (∞/∞)
Ch. 11.1: Anti-Derivative & Integration
3 konu anlatımı · 6 soru
Anti-Derivative: Integration Rules I
Anti-Derivative: Integration Rules II
Integral of Exponential Functions
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Exam like Question 6
Ch. 11.2: Integration with Substitution
3 konu anlatımı
Integration with Substitution I
Integration with Substitution II
Integration with Substitution III
Ch. 11.4: Riemann Sum
2 konu anlatımı
Riemann Sum 1
Riemann Sum 2
Ch. 11.4: The Definite Integral & Properties
3 konu anlatımı
Definite Integral & Properties I
Definite Integral & Properties II
Definite Integral & Properties III
Ch. 11.5: Fundamental Theorem of Calculus
2 konu anlatımı
Fundamental Theorem of Calculus
FTC and L'Hospital's Rule
Ch. 11.5: Average Value of a Function
1 konu anlatımı · 1 soru
Average Value of a Function
Exam like Question
Ch. 12.1: Integration by Parts
4 konu anlatımı
Integration By Part I
Integration By Part II
Integration By Part III
Faster Method for Integration By Part
(NEW) Ch.12.3: Applications in Business and Economics
3 konu anlatımı · 2 soru
Marginal Cost to Cost Function
Exam-like Question 1
Consumer's Surplus
Producer's Surplus
Exam-like Question 2
(NEW) Ch.13.1: Functions of Several Variables
1 konu anlatımı · 3 soru
Functions of Several Variables
Exam like Question 1
Exam like Question 2
Exam like Question 3
(NEW) Ch.13.2: Partial Derivatives
2 konu anlatımı · 7 soru
Partial Derivative
Second Order Partial Derivative
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Exam like Question 6
Exam like Question 7
Sample Exam Problems Part I
8 soru
L'Hopital's Rule
L'Hopital's Rule
L'Hopital's Rule
L'Hopital's Rule
L'Hopital's Rule
L'Hopital's Rule
L'Hopital's Rule
Optimization: Economics Applications
Sample Exam Problems Part II
25 soru
Substitution Method 1-2
Substitution Method 3-4
Substitution Method 5
Substitution Method 6-7
Substitution Method 8
The Definite Integral 1
The Definite Integral 2
The Definite Integral 3
The Definite Integral 4
Properties of Integration 1
Properties of Integration 2
Average Value of a Function
Average Value of a Function
Average Value of a Function
Fundamental Theorem of Calculus
Fundamental Theorem of Calculus
Fundamental Theorem of Calculus
Fundamental Theorem of Calculus
Integration by Part 1
Integration by Part 2-3
Integration by Part 4-5
Integration by Part 6
Integration by Part 7
Integration by Part 8-9
Integration by Part 10
(NEW) Sample Exam Problems Part III
4 soru
Partial Derivative
Second Order Partial Derivative
Second Order Partial Derivative
Partial Derivative and Marginal Costs
Sınav Provası I: Fall 2023 Exam
9 soru
Absolute Maxima and Minima
First Derivative, Local Extremas
Second Derivative, Concavity
Curve Sketching
L'Hopital's Rule
L'Hopital's Rule
Optimization Problems
Fall 2023 Final: Fundamental Theorem of Calculus
Fall 2023 Final: Substitution - Integration by Part
Sınav Provası II: Spring 2024 Exam
6 soru
Absolute Maxima and Minima
Curve Sketching
L'Hopital's Rule
Optimization Problem
Integration with Substitution
Integration by Part
(NEW) Spring 2025 Exam
4 soru
Absolute and Local Extremas
L'Hopital's Rule
Integration with Substitution
Elasticities of Demand
(NEW) Fall 2025 Exam
7 soru
Limit of Functions and L'Hopital's Rule
Derivatives of Graph of Function
Extremum Values of Graph of Function
Absolute Extremum Values
Maximum Profit
Extremum Values of Graph of Function
Integration Rules
Economics Applications (Cost & Productivity & Profit)
2 konu anlatımı · 2 soru
Partial Derivative & Marginal Cost 1
Partial Derivative & Marginal Cost 2
Partial Derivative & Marginal Productivity 1
Partial Derivative & Marginal Productivity 2
Chapter 13.3: Maxima and Minima
1 konu anlatımı · 5 soru
Maxima & Minima & Saddle Points
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Maxima and Minima in Economics
1 konu anlatımı · 2 soru
Maxima and Minima on Economics
Exam like Question 1
Exam like Question 2
Chapter 13.4: Lagrange Multipliers
2 konu anlatımı · 3 soru
Lagrange Multiplier
Exam like Question 1
Exam like Question 2
Optimization Problems with Lagrange Multipliers
Costs, Production and Lagrange Multipliers
Spring 2026: Sample Final Part I
12 soru
Partial Derivative
Second Order Partial Derivative
Second Order Partial Derivative
Partial Derivative and Marginal Costs
Maxima-Minima and Saddle Points
Maxima-Minima and Saddle Points
Maxima-Minima and Saddle Points
Maxima-Minima and Saddle Points
Lagrange Multipliers
Lagrange Multipliers
Lagrange Multiplier
Lagrange Multiplier
Spring 2026: Sample Final Part II
10 soru
Maxima/Minima
Maxima/Minima
Lagrange multipliers
Lagrange multipliers
Minimum Cost & Lagrange multipliers
Maximum Production & Lagrange multipliers
Cobb Douglas, Maximum Production & Lagrange multipliers
Maximum Area & Lagrange multipliers
Maximum Surface & Lagrange multipliers
Maximum Volume & Lagrange multipliers
Spring 2026: Sample Final Part III
10 soru
Marginal Revenue to Revenue Function
Marginal Cost to Cost Function
Integration with Substitution
Integration by Part 1
Integration by Part 2-3
Integration by Part 4-5
Integration by Part 6
Integration by Part 7
Integration by Part 8-9
Integration by Part 10
Spring 2024 Final - Fall 2023 Final Exams
8 soru
Spring 2024 Final: Absolute Maximum and Minimum
Fall 2023 Final: Absolute Maximum - Minimum
Spring 2024 Final: Implicit Differentiation & Tangent Line
Spring 2024 Final: Derivative of Logarithm
Fall 2023 Final Exam: L'Hopital's Rule
Fall 2023 Final: Fundamental Theorem of Calculus
Fall 2023 Final: Substitution - Integration by Part
Spring 2024 Final: Integration by Part
Bonus Part: Midterm Subjects
20 soru
Marginal Cost, Average Costs and Marginal Profit
Marginal Cost and Marginal Profit
Marginal Cost and Marginal Profit
Equation of a Tangent Line
Equation of a Tangent Line
Horizontal Tangent
Implicit Differentiation
Implicit Differentiation
Implicit Dif. & Tangent Lines
Implicit Dif. & Tangent Lines
Implicit Dif. & Tangent Lines
Absolute Maximum and Minimum I
Absolute Maximum and Minimum II
Absolute Maximum and Minimum III
Extreme Values and Concavity
Extreme Values and Concavity
Extreme Values and Concavity
Curve Sketching
Curve Sketching
Curve Sketching